diff --git a/TrackRecon.C b/TrackRecon.C index 88cda54..510b804 100644 --- a/TrackRecon.C +++ b/TrackRecon.C @@ -24,6 +24,8 @@ Int_t colors[40] = { #include #include #include // gSystem->mkdir for the pc_calib_raw/ output directory +#include // p/alpha graphical cuts (classifySiPc) +#include #include // std::floor/fabs/lround for vertexZSliceTag() #include @@ -102,29 +104,39 @@ inline bool siPcCoincident(double t_si, double t_pc) return dt > kSiPcDtMin && dt < kSiPcDtMax; } -// PC anode dE gate, gas-region proton/alpha separation for the p(a,a)p elastic -// branches (protonAlphaElastic_core, formerly protonMiscHistograms / -// protonMiscHistograms_sx3). Rough, -// energy-independent threshold read off Calib_dE_AnodeE_vs_QQQE (calibrated -// anode dE, MeV, vs QQQ/SX3 E): proton and alpha loci are well separated below -// ~5-6 MeV Si energy but converge at high Si energy/high dE (the bright -// corner near the top of the plot) -- events there are NOT reliably -// classified by a flat cut. Revisit with a TCutG/polygon if that corner -// matters. anodeE_MeV < 0 means no valid per-wire calibration was available -// for this hit, not "low dE" -- kUnknown must be handled as its own case, -// never silently folded into kProton. constexpr double kProtonAlphaAnodeDeGate_MeV = 0.045; +// |Ex| window that counts a p + 4He hit as elastic, for the _exgate vertex-z / theta_cm histograms. +constexpr double kElasticExGate_MeV = 1.0; enum class SiPcPid { kUnknown = -1, kProton = 0, - kAlpha = 1 + kAlpha = 1, + kMaybeProton = 2 // graphical cuts only: the proton band below E_Si 5 MeV }; -inline SiPcPid classifyByAnodeDe(double anodeE_MeV) +struct PidCuts +{ + TCutG *alpha = nullptr; + TCutG *proton = nullptr; + TCutG *maybep = nullptr; +}; +PidCuts pidCutsQQQ, pidCutsSX3; +bool pidUseCuts = false; // true once Begin() has found all six pid_* cuts in CUTLIST + +inline SiPcPid classifySiPc(double siE_MeV, double anodeE_MeV, bool isQQQ) { if (anodeE_MeV < 0.0) return SiPcPid::kUnknown; - return (anodeE_MeV < kProtonAlphaAnodeDeGate_MeV) ? SiPcPid::kProton : SiPcPid::kAlpha; + if (!pidUseCuts) + return (anodeE_MeV < kProtonAlphaAnodeDeGate_MeV) ? SiPcPid::kProton : SiPcPid::kAlpha; + const PidCuts &cuts = isQQQ ? pidCutsQQQ : pidCutsSX3; + if (cuts.alpha->IsInside(siE_MeV, anodeE_MeV)) + return SiPcPid::kAlpha; + if (cuts.proton->IsInside(siE_MeV, anodeE_MeV)) + return SiPcPid::kProton; + if (cuts.maybep->IsInside(siE_MeV, anodeE_MeV)) + return SiPcPid::kMaybeProton; + return SiPcPid::kUnknown; } inline TVector3 beamAxisOrigin() @@ -588,7 +600,39 @@ void TrackRecon::Begin(TTree * /*tree*/) std::cerr << "CUTLIST=" << getenv("CUTLIST") << " set but no cut named 'simcprfgate2' found in it -- Gate2 Si-MCP/RF gating disabled" << std::endl; } + + const char *pidNames[6] = {"pid_alpha_qqq", "pid_proton_qqq", "pid_maybep_qqq", + "pid_alpha_sx3", "pid_proton_sx3", "pid_maybep_sx3"}; + TCutG *pidFound[6] = {}; + int pidListed = 0; + for (int i = 0; i < 6; ++i) + { + try + { + pidFound[i] = plotter->FindCut(pidNames[i]); + ++pidListed; + } + catch (const std::out_of_range &) + { + } + } + if (pidListed > 0) + { + if (pidListed < 6 || std::find(pidFound, pidFound + 6, nullptr) != pidFound + 6) + { + std::cerr << "CUTLIST=" << getenv("CUTLIST") << ": needs all six pid_{alpha,proton,maybep}_{qqq,sx3}, each a " + << "file with a TCutG named CUTG -- stopping" << std::endl; + gSystem->Exit(1); + } + pidCutsQQQ = {pidFound[0], pidFound[1], pidFound[2]}; + pidCutsSX3 = {pidFound[3], pidFound[4], pidFound[5]}; + pidUseCuts = true; + } } + if (pidUseCuts) + std::cout << "p/alpha PID: graphical cuts pid_{alpha,proton,maybep}_{qqq,sx3} from CUTLIST=" << getenv("CUTLIST") << std::endl; + else + std::cout << "p/alpha PID: flat anode gate " << kProtonAlphaAnodeDeGate_MeV << " MeV (no pid_* cuts in CUTLIST)" << std::endl; if (getenv("reactiondata")) { @@ -1084,9 +1128,8 @@ inline void pcEnergyCalibrationAccumulateProton(const std::vector &PC_Eve if (!(pcevent.multi1 >= 1 && pcevent.multi2 >= 1)) return; if (!(pcevent.Energy2 > 1400)) // cathode-tagged alpha; intentionally NOT anode-dE - return; // PID (classifyByAnodeDe) -- this function derives the - // anode calibration those thresholds depend on, so it - // needs a selection that doesn't presuppose it. + return; + if (TMath::Abs(sievent.pos.DeltaPhi(pcevent.pos)) > phi_win) return; @@ -4158,7 +4201,9 @@ void protonAlphaElastic_core(HistPlotter *plotter, const std::vector &Si_ { // const std::string ejtag = (alphaHyp && sievent.Energy1 < 5) ? "_a" : "_p"; std::string ejtag; - if (alphaHyp && sievent.Energy1 < 5) + if (pidUseCuts) + ejtag = alphaHyp ? "_a" : (pid == SiPcPid::kMaybeProton ? "_maybep" : "_p"); + else if (alphaHyp && sievent.Energy1 < 5) ejtag = "_a"; else if (sievent.Energy1 >= 5.0 && sievent.Energy1 < 7.0) ejtag = "_p"; @@ -4185,6 +4230,25 @@ void protonAlphaElastic_core(HistPlotter *plotter, const std::vector &Si_ plotter->Fill2D(rx + "_Ex_vs_X" + ejtag + sfx, 100, -100, 120, 800, -6, 15, sievent.pos.X(), Ex, pmlabel); plotter->Fill2D(rx + "_Ex_vs_Y" + ejtag + sfx, 100, -100, 120, 800, -6, 15, sievent.pos.Y(), Ex, pmlabel); + { + const double thetaCM = alphaHyp ? 180.0 - 2.0 * theta * 180 / M_PI + : (theta + TMath::ASin(TMath::Sin(theta) * mass_1H / mass_4He)) * 180 / M_PI; + const bool exGate = TMath::Abs(Ex) < kElasticExGate_MeV; + auto fillZTheta = [&](const std::string &variant) + { + plotter->Fill2D(rx + "_VertexZ_vs_ThetaCM" + variant + ejtag + sfx, 800, -400, 400, 180, 0, 180, vertex_z, thetaCM, pmlabel); + }; + fillZTheta(""); + if (exGate) + fillZTheta("_exgate"); + if (hasCathode) + { + fillZTheta("_cath"); + if (exGate) + fillZTheta("_cath_exgate"); + } + } + if (isQQQ) { const std::string qtag = "_q" + std::to_string(sievent.ch1 / 16); @@ -4276,10 +4340,23 @@ void protonAlphaElastic_core(HistPlotter *plotter, const std::vector &Si_ } }; - if (pid != SiPcPid::kAlpha) - fillHypothesis(false); // proton, or PID unavailable (legacy default) - if (pid == SiPcPid::kAlpha && sievent.Energy1 < 6.2) - fillHypothesis(true); + if (pidUseCuts) + { + // Graphical cuts: each hit as what the cuts call it (p and maybe-p both with proton kinematics, filed apart); + // kUnknown (in no gate, or no anode calibration) is filled as nothing -- counted in elastic_pidUnknown. + if (pid == SiPcPid::kProton || pid == SiPcPid::kMaybeProton) + fillHypothesis(false); + else if (pid == SiPcPid::kAlpha) + fillHypothesis(true); + } + else + { + // Old flat gate, kept as it was: kUnknown is filled as a proton (legacy default). + if (pid != SiPcPid::kAlpha) + fillHypothesis(false); + if (pid == SiPcPid::kAlpha && sievent.Energy1 < 6.2) + fillHypothesis(true); + } }; // --- a1c1/a1c2 (multi1==1) and a2c1/a2c2 (multi1==2), from PC_Events. The @@ -4306,7 +4383,7 @@ void protonAlphaElastic_core(HistPlotter *plotter, const std::vector &Si_ plotter->Fill1D(rx + "_dt_Cathode" + sfx, 600, -2000, 2000, pcevent.Time2 - sievent.Time1, misclabel); double anodeE_MeV = (pcevent.Anodech >= 0 && pcevent.Anodech < 24) ? pcevent.Energy1MeV : -1.0; - SiPcPid pid = classifyByAnodeDe(anodeE_MeV); + SiPcPid pid = classifySiPc(sievent.Energy1, anodeE_MeV, isQQQ); if (pid == SiPcPid::kUnknown) plotter->Fill1D(rx + "_pidUnknown" + sfx, 2, 0, 2, 1.0, misclabel); @@ -4448,7 +4525,7 @@ void protonAlphaElastic_core(HistPlotter *plotter, const std::vector &Si_ if (!anyValidWire) anodeE_MeV_a0 = -1.0; - SiPcPid pid = classifyByAnodeDe(anodeE_MeV_a0); + SiPcPid pid = classifySiPc(sievent.Energy1, anodeE_MeV_a0, isQQQ); if (pid == SiPcPid::kUnknown) plotter->Fill1D(rx + "_pidUnknown" + sfx, 2, 0, 2, 1.0, misclabel); diff --git a/cross_section/README.md b/cross_section/README.md new file mode 100755 index 0000000..51d3a0a --- /dev/null +++ b/cross_section/README.md @@ -0,0 +1,197 @@ +# Cross-section pipeline (ANASEN active target) + +This folder turns data into a cross section for any reaction in the ANASEN active target. There are three steps, +one script each, and one config file per study shared by all three: + +``` +root -l -b -q 'extract_yields.C+("examples/27Al_ap_runA.toml")' # 1. ROOT -> yields_.csv +~/myenv/bin/python -B geometric_efficiency.py examples/27Al_ap_runA.toml # 2. detectors.py -> eps_.csv ~10 s +~/myenv/bin/python -B cross_section.py examples/27Al_ap_runA.toml # 3. -> xs_.csv, xs.png ~3 s +``` + +Run them in WSL from this folder (`~/ANASEN_analysis/cross_section`). Step 1 needs ROOT; steps 2 and 3 need +`~/myenv/bin/python`, not ROOT. + +| file | what it does | +|---|---| +| `extract_yields.C` | **Step 1, the only step that reads the data.** It reads a TH1/TH2, or fills a histogram from a TTree with a cut, and writes a plain CSV histogram. | +| `geometric_efficiency.py` | Step 2: geometric efficiency per bin, a toy Monte Carlo of the reaction, with every hit rule taken from `detectors.py`. | +| `detectors.py` | **The detectors as they are now** (Run A): QQQ3, the four analysed SX3s, the counter, the beam tube and the PCB hole, plus the hit rules. To change the geometry, edit this file. | +| `cross_section.py` | Step 3: reads only CSVs (the yields and an efficiency) and computes σ(E_cm) or dσ/dΩ(θ_cm). | +| `common.py` | What the three scripts share: the config, the beam track E(z), the bins. | +| `examples/` | One commented config per study: `27Al_ap_runA.toml` and `paap_ta_runs_hist.toml`. | +| `examples/reference/` | Barnard 1964 (EXFOR A1113) for p + ⁴He. | +| `inputs/` | The beam track (`beam_tracks.csv`) and the TALYS states (`talys_27Al_ap.csv`). The p + ⁴He track is read from `../eloss_calculations/`. | +| `out//` | Each study's outputs: `yields_.csv`, `eps_.csv`, `xs_.csv`, `xs.png`. | + +## Starting a new study + +1. Copy the closest example in `examples/` (excitation function: `27Al_ap_runA.toml`; angular distribution: + `paap_ta_runs_hist.toml`) and give it its own `out_dir`. +2. Fill in `[extract]` for your histogram or tree, then run step 1 and look at `yields_.csv`. +3. Fill in `[reaction]`, `[beam]` and `[bins]`, then run step 2. Check that `eps_.csv` is non-zero where you + expect events. +4. Fill in `[target]`, `[acceptance]` and any `[[reference]]`, then run step 3. + +If the detectors have changed, edit `detectors.py`, not the configs. + +![27Al(a,p)](out/27Al_ap/xs.png) + +## The formula + +| mode | result | formula | +|---|---|---| +| `excitation` | σ(E_cm), mb | Y / (N_b · n · dz · ε) | +| `angular` | dσ/dΩ(θ_cm) in one E_cm (or z) window, mb/sr | Y / (N_b · n · dz · ε · ΔΩ) | + +- **Y:** the yield in the bin. +- **N_b:** the number of beam particles. +- **n:** target atoms per cm² per mm of path. +- **dz:** the length of beam path over which the beam's E_cm lies in the bin, read off the beam track E(z). +- **ε:** the efficiency of the bin. + +## Step 1: `extract_yields.C`, data to CSV + +`[extract] source` says where the events are: +- `"hist"`: a TH1 or TH2 in a ROOT file. A TH2 is projected on the axis that holds `variable`, or kept 2D with + `angle_axis` for the angular mode. +- `"tree"`: a ROOT TTree (`file` may be a glob or a list of runs), filled into `bins` after `cut`. + +Cuts use `and` / `or` (the macro turns them into `&&` / `||`) and ROOT's TTree::Draw syntax. + +**Histogram paths** are `"folder/name"`. +- **They are case-sensitive.** Production files of different vintages spell the detector differently: the 27Al + outputs use `_m27Alax+misc_qqq/...`, the proton runs' `Output_p/Al_protons.root` uses `elastic+misc_QQQ_a/...`. + Put the spelling in `[det_vars]`: + ```toml + dets = ["qqq", "sx3"] # the names detectors.py knows + [det_vars.qqq] + DET = "QQQ" + [det_vars.sx3] + DET = "SX3" + [extract] + hist = "elastic+misc_{DET}_a/elastic_VertexReconZ_a_{DET}" + ``` +- **A name that itself contains `/`** (e.g. `dE3_E_AnodeQQQR_A1C2_(vertex_fix_z/100)=0.000000`) is found too. +- **If the path doesn't exist,** the macro stops and names the closest histogram paths in the file. + +The CSV it writes, `/yields_.csv`, is the hand-off between the steps. `cross_section.py` reads nothing +else, so a yield made any other way works too as long as it is in this format: + +``` +1D: _lo, _hi, counts, variance +2D: _lo, _hi, theta_cm_lo, theta_cm_hi, counts, variance (angular mode) +``` + +`` is `z` (vertex z, mm), `e_beam` (MeV) or `ecm` (MeV). The bins may be finer than the analysis bins and need +not line up with them. Step 3 shares each one out by overlap. + +It is run like this: + +``` +root -l -b -q 'extract_yields.C+("examples/27Al_ap_runA.toml")' +root -l -b -q 'extract_yields.C+("examples/27Al_ap_runA.toml", "out/elsewhere")' # optional output folder +``` + +- **Trees:** it fills the histogram with `TTree::Draw` on a `TChain`, so `file` may be a glob or a list of runs. +- **Cuts:** write them with `and` / `or` (e.g. `"det == 1 and e_si > 0.5"`). The macro turns them into `&&` / `||`. +- **TOML:** the macro has a small reader that handles only what these configs use: strings, numbers, one-line lists + and `{start, stop, step}` tables. It stops with an error on anything else. +- **Errors:** a missing file or tree, or a tree with no entries, stops it with exit code 1 rather than writing zeros. +- **One edge case:** an entry exactly on a tree histogram's last upper edge goes to ROOT's overflow. + +## Step 2: `geometric_efficiency.py`, ε from the detector geometry + +The toy runs once per bin: +- vertices uniform over the bin's path (angular mode: over the window); +- beam energy at each vertex from the nominal track; +- the residual state drawn from fixed weights, or from TALYS state cross sections at the bin's E_cm; +- isotropic CM emission (angular mode: inside the θ_cm bin); +- relativistic two-body kinematics and straight tracks. + +The particle the silicon sees can be the ejectile or the recoil (`detect`). θ_cm is always the ejectile's, so with +`detect = "recoil"` the bins are still in the ejectile's CM angle. For p + ⁴He that is the proton's angle, Barnard's +convention, which TrackRecon's `elastic_VertexZ_vs_ThetaCM` histograms also use. The output has one column per +condition, each times the azimuthal coverage: + +| column | the particle... | +|---|---| +| `eps_si` | reaches the analysed silicon (solid angle) | +| `eps_si_thr` | ...and has a vertex energy above the Si threshold. This is the ch5 "solid angle" convention: a kinematic cut, not geometry. | +| `eps_counter` | `eps_si`, and it crosses the guard, anode and cathode radii inside the counter | +| **`eps_geometric`** | `eps_counter`, and it clears the beam tube and the PCB hole. **This is the geometric efficiency.** | + +Each column has a Monte Carlo error, `_rel_err`. Gas energy loss, Si thresholds after the gas and the counter's +deposit threshold are **not** included, because they are not geometry. That is why the adopted `eps_tube` of +`../scratch/xs_27Al_lowE_2026-10-15` is lower than `eps_geometric`; to use it instead, see the commented +`[acceptance]` block in the example. The angular distribution is isotropic. + +## Step 3: `cross_section.py` + +`[acceptance] source` picks ε: +- `"geometric"`: step 2's file; `column` chooses which efficiency. +- `"csv"`: any file, matched on a bin edge or interpolated. +- `"value"`: one number for every bin. +- `"none"`: ε = 1, which gives σ_app. + +`[[acceptance.extra]]` multiplies in further factors, such as an intrinsic efficiency. The output `xs_.csv` keeps +every intermediate number: the bins, z ranges, dz, counts, σ_app, ε, σ and its errors (stat, ε, total), and the +references. The header lines record every input. The N_b and n uncertainties are a common scale, so the header gives +them as a percentage and they stay out of the error columns. + +## The config (TOML) + +Paths are relative to the config file, and `~` is the home folder. `{det}` is replaced by each entry of `dets`, and +so is every key of `[det_vars.]`. Commented templates in `examples/`: +- `27Al_ap_runA.toml`: a TH2 from the merged Run A production file, all three steps. +- `paap_ta_runs_hist.toml`: p + ⁴He elastic **straight from a TrackRecon.C production file**, as for 27Al. It reads + the TH2 `elastic_VertexZ_vs_ThetaCM_cath_exgate_a_` (vertex z × proton θ_cm). `protonAlphaElastic_core` fills + that histogram since 2026-10-16 in every species folder, in four variants: all, `_cath`, `_exgate`, `_cath_exgate`. + - Input: `~/ANASEN_analysis/Output_p/results_run022.root` (run 22 alone, run_tr.sh block 5 with CUTLIST), + N_b = 1.35 pA × 672.65 s = 5.67 × 10⁹, vertex window z = −170 to −53 mm. + - On 2026-10-16 the merged runs 18–22 agreed with a per-hit route to 2–4% in QQQ3 counts and about 3% in dσ/dΩ. + +| section | used by | keys | +|---|---|---| +| top | all | `title`, `mode` (`excitation` / `angular`), `dets` (names in `detectors.py`: `qqq`, `sx3`), `out_dir` | +| `[extract]` histogram | 1 | `source = "hist"`, `file`, `hist`, `variable`, `axis` (the axis holding `variable`), `angle_axis` (keep it 2D), `other_range` | +| `[extract]` tree | 1 | `source = "tree"`, `file` (glob or list), `tree`, `variable`, `branch`, `bins`, `cut`, `weight_branch`, `angle_branch` + `angle_bins` | +| `[reaction]` | 2, 3 | `beam_mass_u`, `target_mass_u`; for step 2 also `ejectile_mass_u`, `recoil_mass_u`, `detect`, and `states` *or* `states_csv`; optional `ecm_per_ebeam` | +| `[beam]` | 2, 3 | track: `track_csv` + `track_e_col` (+ `nominal_e_col`, `track_z_col`), *or* `eloss_table` + `e_entrance_mev` + `z_entrance_mm`. N_b: `n_beam` *or* `charge_c` *or* `current_a` + `time_s`; `charge_state`, `n_beam_rel_err`. For Run A runs, `../runlog/beam_exposure.py` gives `n_beam` for any set of runs from the elog's cup readings | +| `[bins]` | 2, 3 | `ecm_edges` (a list or `{start, stop, step}`); angular: `theta_edges_deg` and `window_ecm` *or* `window_z_mm` | +| `[efficiency]` | 2 | `n_per_bin` (default 400 000), `seed` | +| `[target]` | 3 | `pressure_torr`, `temperature_k`, `mole_fraction`, `atoms_per_molecule`, `rel_err`; *or* `n_per_cm2_per_mm` | +| `[yield]` | 3 | `csv`: only to read yields from somewhere other than step 1's output | +| `[acceptance]` | 3 | `source` and its keys (see above), `[[acceptance.extra]]` | +| `[[reference]]` | 3 | `csv`, `x_col`, `y_col`, `label`, `scale`, `dets` | +| `[plot]` | 3 | `yscale`, `xlim`, `ylim`, `xlabel`, `ylabel` | + +## Example: p + ⁴He elastic scattering, Ta run 22 (`examples/paap_ta_runs_hist.toml`) + +``` +root -l -b -q 'extract_yields.C+("examples/paap_ta_runs_hist.toml")' +~/myenv/bin/python -B geometric_efficiency.py examples/paap_ta_runs_hist.toml +~/myenv/bin/python -B cross_section.py examples/paap_ta_runs_hist.toml +``` + +dσ/dΩ(θ_cm) from the α recoils (`detect = "recoil"`, bins in the proton's θ_cm, Barnard's convention), against +Barnard, Jones & Weil (1964). Histogram: `elastic_VertexZ_vs_ThetaCM_cath_exgate_a_` (cathode topologies, +graphical α cut, |E_x| < 1 MeV). The merged runs 18–22 gave QQQ3 0.44–0.54 × Barnard at 132–156°; SX3 is at 1–3%. +Not in `detectors.py`: the Ta holder rod (~28% of the azimuth downstream of each foil) and Si thresholds after the gas. + +## Checks (run in the Windows repo, `/mnt/c/Users/sengi/ANASEN_analysis/cross_section`; the scripts are not in this copy) + +- 27Al(α,p), Run A: yields, dz and nominal E_cm equal the earlier study's in every bin; ε_si_thr agrees with its + independent toy within the MC errors. +- Synthetic events with a known σ, ε and dσ/dΩ are returned with unit-Gaussian pulls. +- `extract_yields.C` and the Python version gave byte-identical yields on every example. + +**Not verified:** the physics inputs are whatever the config and `detectors.py` say. The checks show the arithmetic and +the bookkeeping are right, and that `detectors.py` reproduces the geometry of `anasen_detectability.py`. They cannot +show that the geometry, a track or an N_b is right. In particular: +- The dE/dx scale of a `.dat` table is not written in the file. The live 250 Torr / 3% tables were regenerated on + 2026-10-16 and match the 0.962 track to 3 keV. +- `detectors.py` gives QQQ3 0.967 of the azimuth, but TrackRecon drops QQQ pixels without a calibration, which leaves + about 0.675. QQQ3 ε is therefore about 1.4× too high, and its cross sections about 1.4× too low. +- Where only a sliver of solid angle is open, ε is tiny and σ explodes. Example: QQQ3 at E_cm 5.4 MeV, ε = 1.5 × 10⁻⁵, + behind the beam tube. The error bar shows it; no ε cut is applied. \ No newline at end of file diff --git a/cross_section/common.py b/cross_section/common.py new file mode 100755 index 0000000..e897cb5 --- /dev/null +++ b/cross_section/common.py @@ -0,0 +1,183 @@ +"""Shared by extract_yields.py, geometric_efficiency.py and cross_section.py: the config, the beam track, the bins. + +The cross section in this active target: + sigma(E_cm) = Y / (N_b * n * dz * eps) mode = "excitation" + dsigma/dOmega(th) = Y / (N_b * n * dz * eps * dOmega) mode = "angular" +The beam loses energy along z, so a vertex at z means the reaction happened at the beam energy E(z) there. +An E_cm bin is the stretch of beam path dz over which the beam's E_cm lies in the bin. +""" +import os +import tomllib +from pathlib import Path + +import numpy as np +import pandas as pd + + +# ============================================================ config + +def read_config(config_file): + """Read the TOML config. Returns the config and a function that turns paths in it into absolute paths + (relative paths are relative to the config file's folder).""" + config_file = Path(config_file).resolve() + with open(config_file, "rb") as f: + config = tomllib.load(f) + + def full_path(p): + p = os.path.expanduser(str(p)) # "~/..." is the home folder, as in a shell + if p.startswith("/") or Path(p).is_absolute(): + return p + return str((config_file.parent / p).resolve()) + + return config, full_path + + +def config_for_detector(config, det): + """Copy of the config with "{det}" (and any key of [det_vars.]) replaced in every string. + This lets one config serve several detectors, e.g. hist = "..._{det}".""" + replacements = {"det": det} + replacements.update(config.get("det_vars", {}).get(det, {})) + + def replace(value): + if isinstance(value, str): + for key, new in replacements.items(): + value = value.replace("{" + key + "}", str(new)) + return value + if isinstance(value, dict): + return {k: replace(v) for k, v in value.items()} + if isinstance(value, list): + return [replace(v) for v in value] + return value + + return replace(config) + + +def output_file(config, full_path, kind, det): + """Where each step writes for one detector: /_.csv, kind = yields, eps or xs.""" + out_dir = Path(full_path(config.get("out_dir", "out"))) + out_dir.mkdir(parents=True, exist_ok=True) + return out_dir / (f"{kind}_{det}.csv" if det else f"{kind}.csv") + + +def make_edges(spec): + """Bin edges from a list [e0, e1, ...] or from {start = .., stop = .., step = ..} (stop included).""" + if isinstance(spec, dict): + n_bins = int(round((spec["stop"] - spec["start"]) / spec["step"])) + return spec["start"] + spec["step"] * np.arange(n_bins + 1) + return np.array(spec, dtype=float) + + +def write_csv(table, header_lines, out_file): + with open(out_file, "w", newline="\n") as f: + for line in header_lines: + f.write(f"# {line}\n") + table.to_csv(f, index=False, float_format="%.6g") + + +# ============================================================ beam track + +class BeamTrack: + """Beam energy (MeV, lab) along z (mm). The energy falls with z and is 0 past the stopping point. + + `energy` is the track used to define the bins (the one the data were reconstructed with). `nominal` is an + optional second track (e.g. another stopping-power scale): it gives each bin's nominal E_cm and the beam + energy in the efficiency toy. It defaults to the same track.""" + + def __init__(self, z, energy, nominal=None, description=""): + self.z = np.asarray(z, dtype=float) + self.energy = np.asarray(energy, dtype=float) + self.nominal = self.energy if nominal is None else np.asarray(nominal, dtype=float) + self.description = description + + def energy_at(self, z, nominal=False): + return np.interp(z, self.z, self.nominal if nominal else self.energy) + + def z_where_energy_is(self, e): + """The z where the beam has energy e. + e <= 0 gives the stopping point; e above the entrance energy gives the entrance z.""" + if e <= 0: + stopped = np.flatnonzero(self.energy <= 0) + return float(self.z[stopped[0]]) if len(stopped) else float(self.z[-1]) + # np.interp needs increasing x: energy decreases along z, so interpolate in -energy + return float(np.interp(-e, -self.energy, self.z)) + + +def load_beam_track(beam, full_path): + """Either a CSV with columns z and E (e.g. beam_tracks.csv), or an energy-loss table from + eloss_calculations/ plus the beam energy at the entrance.""" + if "track_csv" in beam: + table = pd.read_csv(full_path(beam["track_csv"]), comment="#") + z = table[beam.get("track_z_col", "z_mm")] + energy = table[beam["track_e_col"]] + nominal = table[beam["nominal_e_col"]] if "nominal_e_col" in beam else None + text = f"{beam['track_csv']}, column {beam['track_e_col']}" + if nominal is not None: + text += f" (nominal E_cm from {beam['nominal_e_col']})" + return BeamTrack(z, energy, nominal, text) + + if "eloss_table" in beam: + # Table columns: energy (MeV), thickness (mg/cm2), distance along the path (cm) + table = np.loadtxt(full_path(beam["eloss_table"]), comments="#") + table_energy, table_cm = table[:, 0], table[:, 2] + e_entrance, z_entrance = float(beam["e_entrance_mev"]), float(beam["z_entrance_mm"]) + if e_entrance > table_energy[0]: + raise ValueError(f"e_entrance_mev = {e_entrance} is above the table's start energy {table_energy[0]}") + # Where in the table the beam starts, then walk along it in 0.1 mm steps + start_cm = np.interp(-e_entrance, -table_energy, table_cm) + z = np.arange(z_entrance, beam.get("z_max_mm", 400.0) + 0.05, 0.1) + path_cm = start_cm + (z - z_entrance) / 10.0 + energy = np.interp(path_cm, table_cm, table_energy, right=0.0) + return BeamTrack(z, energy, None, f"{beam['eloss_table']}, {e_entrance} MeV at z = {z_entrance} mm") + + raise KeyError("[beam] needs either track_csv or eloss_table") + + +def ecm_per_beam_energy(reaction): + """E_cm = E_beam x m_target / (m_beam + m_target) (non-relativistic; or give ecm_per_ebeam directly).""" + if "ecm_per_ebeam" in reaction: + return float(reaction["ecm_per_ebeam"]) + return reaction["target_mass_u"] / (reaction["beam_mass_u"] + reaction["target_mass_u"]) + + +# ============================================================ bins + +def energy_bins(bins, track, k): + """E_cm bins and, for each, the stretch of beam path [z_up, z_down] where the beam's E_cm is inside it. + The higher energy is upstream, so z_up belongs to the bin's top edge.""" + ecm_edges = make_edges(bins["ecm_edges"]) + t = pd.DataFrame({"ecm_lo_mev": ecm_edges[:-1], "ecm_hi_mev": ecm_edges[1:]}) + t["ecm_c_mev"] = 0.5 * (t["ecm_lo_mev"] + t["ecm_hi_mev"]) + t["z_up_mm"] = [track.z_where_energy_is(e / k) for e in t["ecm_hi_mev"]] + t["z_c_mm"] = [track.z_where_energy_is(e / k) for e in t["ecm_c_mev"]] + t["z_down_mm"] = [track.z_where_energy_is(e / k) for e in t["ecm_lo_mev"]] + t["dz_mm"] = t["z_down_mm"] - t["z_up_mm"] + t["ecm_nominal_mev"] = k * track.energy_at(t["z_c_mm"], nominal=True) + # True if the beam enters the chamber already inside this bin (dz then starts at the entrance) + t["partial_top"] = t["ecm_hi_mev"] / k > track.energy[0] + t["d_omega_sr"] = 1.0 # not used in excitation mode + return t + + +def angle_bins(bins, track, k): + """theta_cm bins inside one window, given in E_cm (window_ecm) or in vertex z (window_z_mm). + Returns the bins and the window as (ecm_lo, ecm_hi, z_up, z_down).""" + if "window_ecm" in bins: + ecm_lo, ecm_hi = bins["window_ecm"] + z_up, z_down = track.z_where_energy_is(ecm_hi / k), track.z_where_energy_is(ecm_lo / k) + else: + z_up, z_down = bins["window_z_mm"] + ecm_lo, ecm_hi = k * track.energy_at(z_down), k * track.energy_at(z_up) + theta_edges = make_edges(bins["theta_edges_deg"]) + t = pd.DataFrame({"theta_lo_deg": theta_edges[:-1], "theta_hi_deg": theta_edges[1:]}) + t["theta_c_deg"] = 0.5 * (t["theta_lo_deg"] + t["theta_hi_deg"]) + t["d_omega_sr"] = 2 * np.pi * (np.cos(np.radians(t["theta_lo_deg"])) - np.cos(np.radians(t["theta_hi_deg"]))) + t["z_up_mm"], t["z_down_mm"] = z_up, z_down + t["dz_mm"] = z_down - z_up + return t, (ecm_lo, ecm_hi, z_up, z_down) + + +def make_bins(config, track, k): + """The bins of the config's mode. Returns (table, window or None).""" + if config.get("mode", "excitation") == "excitation": + return energy_bins(config["bins"], track, k), None + return angle_bins(config["bins"], track, k) diff --git a/cross_section/cross_section.py b/cross_section/cross_section.py new file mode 100755 index 0000000..15f4287 --- /dev/null +++ b/cross_section/cross_section.py @@ -0,0 +1,332 @@ +"""Step 3: the cross section, from the yields CSV (step 1) and an efficiency (step 2, or any other). + + ~/myenv/bin/python -B cross_section.py examples/27Al_ap_runA.toml # no ROOT needed; any python with pandas + + sigma(E_cm) = Y / (N_b * n * dz * eps) mode = "excitation" + dsigma/dOmega(th) = Y / (N_b * n * dz * eps * dOmega) mode = "angular" + + Y yield in the bin, from /yields_.csv (or [yield] csv); see extract_yields.py for the format + N_b number of beam particles [beam] + n target atoms per cm^2 per mm of beam path [target] + dz length of beam path (mm) over which the beam's E_cm lies in the bin, from the beam track E(z) + eps efficiency of the bin [acceptance] + dOmega solid angle of the theta_cm bin (angular mode) + +Writes /xs_.csv (every intermediate number; the header records every input) and /xs.png. + +WHAT IT DOES, STEP BY STEP (see analyse_detector()) + 1. beam track: beam energy E at every z + 2. normalisation: N_b and n + 3. bins: E_cm bins -> their z ranges and dz (or theta_cm bins inside one energy window) + 4. yields: share the yield histogram's bins into those bins + 5. efficiency: eps for each bin + 6. cross section: the formula, with statistical and efficiency errors +""" +import argparse +import datetime +import re +from pathlib import Path + +import numpy as np +import pandas as pd + +import common + +BOLTZMANN = 1.380649e-23 # J/K +PASCAL_PER_TORR = 133.322368 +ELEMENTARY_CHARGE = 1.602176634e-19 # C +CM2_PER_MB = 1e-27 +YIELD_VARIABLES = ("z", "e_beam", "ecm") + + +# ============================================================ normalisation + +def number_of_beam_particles(beam): + """N_b from: n_beam directly, or integrated charge, or current x time. Returns (N_b, relative error, text).""" + charge_state = beam.get("charge_state", 1) + if "n_beam" in beam: + n_b, text = beam["n_beam"], "given" + elif "charge_c" in beam: + n_b = beam["charge_c"] / (charge_state * ELEMENTARY_CHARGE) + text = f"{beam['charge_c']} C / ({charge_state} e)" + elif "current_a" in beam: + n_b = beam["current_a"] * beam["time_s"] / (charge_state * ELEMENTARY_CHARGE) + text = f"{beam['current_a']} A x {beam['time_s']} s / ({charge_state} e)" + else: + raise KeyError("[beam] needs n_beam, charge_c, or current_a and time_s") + return float(n_b), float(beam.get("n_beam_rel_err", 0.0)), text + + +def target_atoms_per_cm2_per_mm(target): + """n = (gas molecules per cm^3) x (mole fraction of the target molecule) x (target atoms per molecule) x 0.1 cm/mm. + E.g. He in 250 Torr He + 3% CO2 at 293.15 K: mole_fraction 0.97, atoms_per_molecule 1 -> 7.988e17. + Returns (n, relative error, text).""" + if "n_per_cm2_per_mm" in target: + return float(target["n_per_cm2_per_mm"]), float(target.get("rel_err", 0.0)), "given" + pressure_pa = target["pressure_torr"] * PASCAL_PER_TORR + molecules_per_cm3 = pressure_pa / (BOLTZMANN * target["temperature_k"]) * 1e-6 + fraction = target.get("mole_fraction", 1.0) + atoms = target.get("atoms_per_molecule", 1) + n = molecules_per_cm3 * fraction * atoms * 0.1 + text = f"{target['pressure_torr']} Torr, {target['temperature_k']} K, mole fraction {fraction}, {atoms} atom(s)/molecule" + return n, float(target.get("rel_err", 0.0)), text + + +# ============================================================ yields + +def read_yields(file): + """The yields CSV of extract_yields.py. Returns (table, variable), variable = z, e_beam or ecm.""" + table = pd.read_csv(file, comment="#") + for variable in YIELD_VARIABLES: + if f"{variable}_lo" in table.columns: + return table, variable + raise ValueError(f"{file}: no column z_lo, e_beam_lo or ecm_lo (see extract_yields.py for the format)") + + +def in_yield_units(variable, k, ecm_range, z_range): + """Convert a bin, given both as an E_cm range and a z range, into the units of the yield's variable.""" + if variable == "ecm": + return ecm_range + if variable == "e_beam": + return ecm_range[0] / k, ecm_range[1] / k + return z_range + + +def fraction_inside(src_lo, src_hi, lo, hi): + """Fraction of each yield bin [src_lo, src_hi) that lies inside [lo, hi). Used to share the yield's bins + between the analysis bins when their edges do not line up.""" + return np.clip(np.minimum(src_hi, hi) - np.maximum(src_lo, lo), 0, None) / (src_hi - src_lo) + + +def yields_excitation(table, variable, t, k): + """Yield and its error in each E_cm bin.""" + if "theta_cm_lo" in table.columns: # a 2D yield: add up the theta bins first + table = table.groupby([f"{variable}_lo", f"{variable}_hi"], as_index=False)[["counts", "variance"]].sum() + src_lo, src_hi = table[f"{variable}_lo"].to_numpy(), table[f"{variable}_hi"].to_numpy() + lo, hi = in_yield_units(variable, k, (t["ecm_lo_mev"], t["ecm_hi_mev"]), (t["z_up_mm"], t["z_down_mm"])) + counts, errors = [], [] + for a, b in zip(lo, hi): + f = fraction_inside(src_lo, src_hi, a, b) + counts.append(np.sum(f * table["counts"])) + errors.append(np.sqrt(np.sum(f ** 2 * table["variance"]))) + return np.array(counts), np.array(errors) + + +def yields_angular(table, variable, t, window, k): + """Yield and its error in each theta_cm bin, for the part of the yield inside the energy (or z) window.""" + if "theta_cm_lo" not in table.columns: + raise ValueError("angular mode needs a 2D yield (theta_cm_lo/hi columns): set angle_axis or angle_branch in [extract]") + ecm_lo, ecm_hi, z_up, z_down = window + w_lo, w_hi = in_yield_units(variable, k, (ecm_lo, ecm_hi), (z_up, z_down)) + in_window = fraction_inside(table[f"{variable}_lo"].to_numpy(), table[f"{variable}_hi"].to_numpy(), w_lo, w_hi) + th_lo, th_hi = table["theta_cm_lo"].to_numpy(), table["theta_cm_hi"].to_numpy() + counts, errors = [], [] + for a, b in zip(t["theta_lo_deg"], t["theta_hi_deg"]): + f = in_window * fraction_inside(th_lo, th_hi, a, b) + counts.append(np.sum(f * table["counts"])) + errors.append(np.sqrt(np.sum(f ** 2 * table["variance"]))) + return np.array(counts), np.array(errors) + + +# ============================================================ efficiency + +def efficiency(config, det, t, full_path): + """eps and its relative error for every bin. [acceptance] source = + "geometric": /eps_.csv from geometric_efficiency.py; `column` picks the efficiency + (default eps_geometric), its Monte Carlo error comes with it + "csv": any file: csv, x_col, eps_col, match = "bin" (same bin edge: our column `key` = their x_col) + or "interp" (interpolate at our column `key`; NaN outside the file's range), rel_err_col or rel_err + "value": one number for every bin (value, rel_err) + "none": eps = 1, the apparent cross section (the default) + [[acceptance.extra]] name, value, rel_err: further factors, multiplied in (e.g. an intrinsic efficiency).""" + eff = config.get("acceptance", {}) + mode = config.get("mode", "excitation") + source = eff.get("source", "none") + n_bins = len(t) + eps, rel_err = np.ones(n_bins), np.zeros(n_bins) + text = "none (eps = 1: apparent cross section)" + + if source == "geometric": + column = eff.get("column", "eps_geometric") + file = common.output_file(config, full_path, "eps", det) + eff = {"csv": str(file), "match": "bin", "eps_col": column, "rel_err_col": f"{column}_rel_err", + "x_col": "ecm_lo_mev" if mode == "excitation" else "theta_lo_deg", "extra": eff.get("extra", [])} + source = "csv" + if source == "csv": + table = pd.read_csv(full_path(eff["csv"]), comment="#") + match = eff.get("match", "interp") + default_key = {("excitation", "bin"): "ecm_lo_mev", ("excitation", "interp"): "ecm_nominal_mev", + ("angular", "bin"): "theta_lo_deg", ("angular", "interp"): "theta_c_deg"}[(mode, match)] + key = eff.get("key", default_key) + their_x = table[eff["x_col"]].to_numpy(float) + their_eps = table[eff["eps_col"]].to_numpy(float) + if "rel_err_col" in eff: + their_err = table[eff["rel_err_col"]].to_numpy(float) + else: + their_err = np.full(len(table), eff.get("rel_err", 0.0)) + + ours = t[key].to_numpy(float) + if match == "bin": + for i, x in enumerate(ours): + same = np.flatnonzero(np.isclose(their_x, x, rtol=1e-6, atol=1e-9)) + eps[i] = their_eps[same[0]] if len(same) else np.nan + rel_err[i] = their_err[same[0]] if len(same) else np.nan + else: + order = np.argsort(their_x) + eps = np.interp(ours, their_x[order], their_eps[order], left=np.nan, right=np.nan) + rel_err = np.interp(ours, their_x[order], their_err[order], left=np.nan, right=np.nan) + text = f"{eff['csv']}, column {eff['eps_col']} ({match} on {eff['x_col']} = our {key})" + elif source == "value": + eps = np.full(n_bins, float(eff["value"])) + rel_err = np.full(n_bins, float(eff.get("rel_err", 0.0))) + text = f"constant {eff['value']}" + elif source != "none": + raise ValueError(f"[acceptance] source must be geometric, csv, value or none, not {source!r}") + + for extra in eff.get("extra", []): + eps = eps * extra["value"] + rel_err = np.hypot(rel_err, extra.get("rel_err", 0.0)) + text += f" x {extra.get('name', 'extra factor')} {extra['value']}" + return eps, rel_err, text + + +# ============================================================ cross section + +def cross_section(t, n_b, n, eps, eps_rel_err, name): + """The formula. `name` is "sigma_mb" (excitation) or "dsdo_mb_sr" (angular). Adds columns to t: + _app, _app_err apparent cross section (eps = 1), statistical error + , _err_stat divided by eps + _err_eps, _err error from eps; total (stat and eps in quadrature) + The N_b and n uncertainties are a common scale for all bins and are NOT in these columns.""" + exposure = n_b * n * t["dz_mm"] * t["d_omega_sr"] * CM2_PER_MB # events per mb (per mb/sr) + exposure = exposure.where(exposure > 0) # dz = 0 (past the stopping point) -> NaN + eps = pd.Series(eps, index=t.index).where(lambda e: e > 0) # eps = 0 -> NaN + t[f"{name}_app"] = t["counts"] / exposure + t[f"{name}_app_err"] = t["stat_err"] / exposure + t["eps"] = eps + t["eps_rel_err"] = eps_rel_err + t[name] = t[f"{name}_app"] / eps + t[f"{name}_err_stat"] = t[f"{name}_app_err"] / eps + t[f"{name}_err_eps"] = t[name] * t["eps_rel_err"] + t[f"{name}_err"] = np.hypot(t[f"{name}_err_stat"], t[f"{name}_err_eps"]) + return t + + +def add_references(t, references, det, x_col, full_path): + """Reference curves ([[reference]]: csv, x_col, y_col, label, optional scale and dets) interpolated at our x + (NaN outside their range). Returns the curves for the plot.""" + curves = [] + for ref in references or []: + if "dets" in ref and det not in ref["dets"]: + continue + table = pd.read_csv(full_path(ref["csv"]), comment="#").sort_values(ref["x_col"]) + x = table[ref["x_col"]].to_numpy(float) + y = ref.get("scale", 1.0) * table[ref["y_col"]].to_numpy(float) + label = ref.get("label", Path(ref["csv"]).stem) + column = "ref_" + re.sub(r"\W+", "_", label).strip("_").lower() + t[column] = np.interp(t[x_col], x, y, left=np.nan, right=np.nan) + curves.append((label, x, y)) + return curves + + +def analyse_detector(config, det, full_path): + """Steps 1-6 for one detector. Returns the result table, its header lines, the x column, the cross-section + column name and the reference curves.""" + mode = config.get("mode", "excitation") + k = common.ecm_per_beam_energy(config["reaction"]) + + # 1. beam track + track = common.load_beam_track(config["beam"], full_path) + + # 2. normalisation + n_b, n_b_rel_err, n_b_text = number_of_beam_particles(config["beam"]) + n, n_rel_err, n_text = target_atoms_per_cm2_per_mm(config["target"]) + + # 3. bins and 4. yields + yield_file = full_path(config["yield"]["csv"]) if "csv" in config.get("yield", {}) \ + else common.output_file(config, full_path, "yields", det) + yields, variable = read_yields(yield_file) + t, window = common.make_bins(config, track, k) + if mode == "excitation": + t["counts"], t["stat_err"] = yields_excitation(yields, variable, t, k) + name, x_col, window_text = "sigma_mb", "ecm_nominal_mev", "" + else: + t["counts"], t["stat_err"] = yields_angular(yields, variable, t, window, k) + name, x_col = "dsdo_mb_sr", "theta_c_deg" + ecm_lo, ecm_hi, z_up, z_down = window + window_text = f"; window E_cm {ecm_lo:.4g} to {ecm_hi:.4g} MeV, z {z_up:.2f} to {z_down:.2f} mm" + + # 5. efficiency and 6. cross section + eps, eps_rel_err, eps_text = efficiency(config, det, t, full_path) + t = cross_section(t, n_b, n, eps, eps_rel_err, name) + curves = add_references(t, config.get("reference"), det, x_col, full_path) + + header = [ + f"{config.get('title', '')} {det.upper()}: {mode} mode{window_text}", + f"yield: {yield_file} (binned in {variable})", + f"beam track: {track.description}; E_cm = {k:.6g} x E_beam", + f"N_b = {n_b:.6g} ({n_b_text}); n = {n:.6g} target atoms per cm2 per mm ({n_text})", + f"eps: {eps_text}", + f"common scale uncertainty from N_b and n: {100 * np.hypot(n_b_rel_err, n_rel_err):.3g} % (not in the error columns)", + f"written by cross_section.py on {datetime.date.today().isoformat()}", + ] + return t, header, x_col, name, curves + + +def make_plot(results, config, out_file): + import matplotlib + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + opts = config.get("plot", {}) + excitation = config.get("mode", "excitation") == "excitation" + fig, ax = plt.subplots(figsize=opts.get("figsize", (9, 6))) + plotted_refs = set() + for det, (t, x_col, name, curves) in results.items(): + ok = np.isfinite(t[name]) & (t[name] > 0) + ax.errorbar(t.loc[ok, x_col], t.loc[ok, name], yerr=t.loc[ok, f"{name}_err"], + fmt="o", ms=4, capsize=2, label=det.upper() or "data") + for label, x, y in curves: + if label not in plotted_refs: + ax.plot(x, y, "-", lw=1.2, label=label) + plotted_refs.add(label) + ax.set_xlabel(opts.get("xlabel", "E$_\\mathrm{cm}$ (MeV)" if excitation else "$\\theta_\\mathrm{cm}$ (deg)")) + ax.set_ylabel(opts.get("ylabel", "$\\sigma$ (mb)" if excitation else "d$\\sigma$/d$\\Omega$ (mb/sr)")) + ax.set_yscale(opts.get("yscale", "log")) + if "xlim" in opts: + ax.set_xlim(*opts["xlim"]) + if "ylim" in opts: + ax.set_ylim(*opts["ylim"]) + ax.set_title(config.get("title", "")) + ax.legend(fontsize=8) + fig.tight_layout() + fig.savefig(out_file, dpi=110) + plt.close(fig) + + +def main(argv=None): + parser = argparse.ArgumentParser(description="Step 3: cross section from the yields CSV and an efficiency.") + parser.add_argument("config", help="TOML config file") + args = parser.parse_args(argv) + config, full_path = common.read_config(args.config) + + results = {} + for det in config.get("dets", [""]): + print(f"--- {det or 'data'}") + det_config = common.config_for_detector(config, det) + t, header, x_col, name, curves = analyse_detector(det_config, det, full_path) + common.write_csv(t, header, common.output_file(config, full_path, "xs", det)) + results[det] = (t, x_col, name, curves) + print("\n".join(header[:-1])) + show = [x_col, "dz_mm" if name == "sigma_mb" else "d_omega_sr", "counts", f"{name}_app", "eps", name, + f"{name}_err"] + [c for c in t.columns if c.startswith("ref_")] + print(t[show].to_string(index=False, float_format=lambda v: f"{v:.4g}"), "\n") + + out_png = common.output_file(config, full_path, "xs", "").with_suffix(".png") + make_plot(results, config, out_png) + print(f"written to {out_png.parent}") + return results + + +if __name__ == "__main__": + main() diff --git a/cross_section/detectors.py b/cross_section/detectors.py new file mode 100755 index 0000000..a421257 --- /dev/null +++ b/cross_section/detectors.py @@ -0,0 +1,80 @@ +"""The ANASEN detectors as they are now (Run A, 27Al campaign), for the geometric efficiency. + +geometric_efficiency.py reads everything about the detectors from here. Change a number here and every efficiency +computed afterwards follows it. + +Sources: + - Si and counter: anasen_detectability.py of ~/TALYS/al027_a_scripts_stoichgas_dedx0962_2026-10-08 + ("detector geometry as used by TrackRecon.C"; counter radii from ClassPW.h) + - beam tube and PCB hole: the author, 2026-10-15 (../scratch/reaction_efficiency_tube_2026-10-15) +Geometry only: straight tracks from the vertex, no energy loss. +""" +import numpy as np + +# ---------------------------------------------------------------- silicon +# QQQ3: the downstream annular detector +QQQ_Z_MM = 105.0 # TrackRecon.C qqq_z +QQQ_R_MM = (50.0, 100.0) # inner and outer active radius (16 rings: rho = 50 + 50/16 (ring + 0.5)) +QQQ_PHI_FRACTION = 4 * 87.0 / 360.0 # 4 quadrants x 87 deg of wedges + +# SX3: the barrel; only the four detectors TrackRecon.C builds events for, downstream half only +SX3_R_MM = 88.0 +SX3_Z_MM = (-3.0, 72.0) # z_local + 75/2 - 3 +SX3_IDS = (1, 3, 7, 9) +SX3_HALF_ANGLE = np.arctan(4 * 40.30 / (8.0 * 88.0 * np.cos(np.radians(15.0)))) # outer strip edge, each side +SX3_PHI_FRACTION = len(SX3_IDS) * 2 * SX3_HALF_ANGLE / (2 * np.pi) + +PHI_FRACTION = {"qqq": QQQ_PHI_FRACTION, "sx3": SX3_PHI_FRACTION} + +# Si energy thresholds (MeV), TrackRecon.C reaction_ax_core si_ecut. Used only for the eps_si_thr column. +SI_THRESHOLD_MEV = {"qqq": 0.45, "sx3": 0.6} + +# ---------------------------------------------------------------- proportional counter +COUNTER_HALF_LENGTH_MM = 174.3 +COUNTER_RADII_MM = (32.0, 37.0, 42.0) # guard, anode, cathode (ClassPW.h) + +# ---------------------------------------------------------------- upstream apertures +# (name, radius mm, z mm of the face that binds). A track from an on-axis vertex only moves away from the axis, +# so an opening binds at its downstream end. +APERTURES = (("beam tube", 16.0, -189.0), + ("PCB hole", 18.0, -174.3)) + + +# ---------------------------------------------------------------- hit rules +# z_vertex in mm, theta = lab polar angle of the particle (radians). All return one True/False per track. + +def hits_silicon(det, z_vertex, theta): + """Does the straight track from z_vertex at angle theta reach the active silicon of `det` ("qqq" or "sx3")? + Polar angle only: multiply by PHI_FRACTION[det] for the azimuthal coverage. + A track that reaches the SX3 barrel's z range is counted as SX3, not QQQ.""" + s, c = np.sin(theta), np.cos(theta) + with np.errstate(divide="ignore", invalid="ignore"): + z_at_sx3 = z_vertex + SX3_R_MM * c / s # z where the track reaches the barrel radius + on_sx3 = (z_at_sx3 >= SX3_Z_MM[0]) & (z_at_sx3 <= SX3_Z_MM[1]) + if det == "sx3": + return on_sx3 + r_at_qqq = np.where(c > 0, (QQQ_Z_MM - z_vertex) * s / c, -1.0) # radius where it reaches the QQQ plane + if det == "qqq": + return (QQQ_Z_MM > z_vertex) & (r_at_qqq >= QQQ_R_MM[0]) & (r_at_qqq <= QQQ_R_MM[1]) & ~on_sx3 + raise ValueError(f"unknown detector {det!r}: detectors.py defines 'qqq' and 'sx3'") + + +def crosses_counter(z_vertex, theta): + """Does the track cross the guard, anode and cathode radii inside the counter's length?""" + with np.errstate(divide="ignore", invalid="ignore"): + cot = np.cos(theta) / np.sin(theta) + ok = np.ones(np.shape(z_vertex), bool) + for r in COUNTER_RADII_MM: + ok &= np.abs(z_vertex + r * cot) <= COUNTER_HALF_LENGTH_MM + return ok + + +def clears_apertures(z_vertex, theta): + """Does the track pass the beam tube and the PCB hole? Only vertices upstream of an aperture can be blocked + by it: blocked when the track is farther from the axis than the opening's radius at the opening's z.""" + s, c = np.sin(theta), np.cos(theta) + tan_theta = s / np.where(c > 0, c, 1e-9) # backward tracks from upstream never reach the detectors + ok = np.ones(np.shape(z_vertex), bool) + for _name, radius, z_face in APERTURES: + ok &= ~((z_vertex < z_face) & ((z_face - z_vertex) * tan_theta > radius)) + return ok diff --git a/cross_section/examples/27Al_ap_runA.toml b/cross_section/examples/27Al_ap_runA.toml new file mode 100755 index 0000000..ac619ae --- /dev/null +++ b/cross_section/examples/27Al_ap_runA.toml @@ -0,0 +1,88 @@ +# 27Al(a,p)30Si excitation function, Run A, QQQ3 and SX3. Same inputs as ../../scratch/xs_27Al_lowE_2026-10-15. +# +# ~/myenv/bin/python -B extract_yields.py examples/27Al_ap_runA.toml # 1. ROOT -> out/27Al_ap_runA/yields_.csv +# ~/myenv/bin/python -B geometric_efficiency.py examples/27Al_ap_runA.toml # 2. detectors.py -> eps_.csv +# ~/myenv/bin/python -B cross_section.py examples/27Al_ap_runA.toml # 3. -> xs_.csv, xs.png +# +# Each script reads the sections it needs. Paths are relative to this file's folder. +# "{det}" is replaced by each entry of `dets`. + +title = "27Al(a,p)30Si, Run A" +mode = "excitation" # "excitation": sigma(E_cm); "angular": dsigma/dOmega(theta_cm) +dets = ["sx3", "qqq"] # names known to detectors.py +out_dir = "../out/27Al_ap" + +# ------------------------------------------------------------- step 1: extract_yields.py +[extract] +# One fill per candidate: x = vertex z, y = tracked beam energy. Projected on y (all z, including overflow). +source = "hist" +file = "~/ANASEN_analysis/Output_27Al_X0_Y0/Output_27Al.root" +hist = "_m27Alax+misc_{det}/m27Alax_BeamEnergy_vs_VertexZ_{det}" +axis = "y" +variable = "e_beam" + +# ------------------------------------------------------------- the reaction (steps 2 and 3) +[reaction] +beam_mass_u = 26.981538 # 27Al (atomic masses, as TrackRecon.C) +target_mass_u = 4.002603254 # 4He +ejectile_mass_u = 1.007825032 # p -> Q = 2.372 MeV for the ground state +recoil_mass_u = 29.973770 # 30Si +detect = "ejectile" +ecm_per_ebeam = 0.12918 # the rounded factor of the established analysis (the masses give 0.129182) +# 30Si states weighted by the TALYS (a,p) state cross sections at each bin's E_cm +states_csv = "../inputs/talys_27Al_ap.csv" +# or fixed weights: states = [{ex_mev = 0.0, weight = 1.0}, {ex_mev = 2.235, weight = 0.5}] + +[beam] +# Beam energy along z; +# the nominal E_cm of each bin and the beam energy in the efficiency toy come from the 0.962 track. +track_csv = "../inputs/beam_tracks.csv" +track_z_col = "z_mm" +track_e_col = "e_beam_mev_0962" +# Alternative: build the track from an energy-loss table (check which dE/dx scale the table was made with): +# eloss_table = "../../eloss_calculations/aluminum_lookup_80MeV_250torr_3pc.dat" +# e_entrance_mev = 56.16 +# z_entrance_mm = -454.0 +n_beam = 1.4405e12 # Faraday cup, ch5 ssec:beam_exposure: the 45 runs (2.2096e12) +# For another set of runs: ../../runlog/beam_exposure.py "" --data-dir ../../Output_27Al_fb +n_beam_rel_err = 0.5 + +[bins] +ecm_edges = { start = 0.0, stop = 7.25, step = 0.25 } + +# ------------------------------------------------------------- step 2: geometric_efficiency.py +[efficiency] +n_per_bin = 400000 +seed = 20261016 + +# ------------------------------------------------------------- step 3: cross_section.py +[target] +# 4He in 250 Torr He + 3% CO2 at 20 C -> 7.988e17 He atoms per cm2 per mm +pressure_torr = 250.0 +temperature_k = 293.15 +mole_fraction = 0.97 +atoms_per_molecule = 1 + +# [yield] csv = "..." # only to read yields from somewhere other than /yields_.csv + +[acceptance] +source = "geometric" # /eps_.csv from step 2 +column = "eps_geometric" # or eps_si, eps_si_thr, eps_counter +# To use the adopted efficiency of ../../scratch/xs_27Al_lowE_2026-10-15 instead (includes gas loss and thresholds): +# source = "csv" +# csv = "../../scratch/xs_27Al_lowE_2026-10-15/out/xs_{det}.csv" +# match = "bin" +# x_col = "ecm_lo_mev" +# eps_col = "eps_tube_adopted" +# rel_err_col = "eps_tube_rel_err" + +[[reference]] +csv = "../inputs/talys_27Al_ap.csv" +x_col = "ecm_mev" +y_col = "sigma_total_mb" +label = "TALYS (a,p), discrete states" + +[plot] +yscale = "log" +xlim = [0, 7.4] +ylim = [1e-3, 3e4] diff --git a/cross_section/examples/paap_ta_runs_hist.toml b/cross_section/examples/paap_ta_runs_hist.toml new file mode 100755 index 0000000..c56b489 --- /dev/null +++ b/cross_section/examples/paap_ta_runs_hist.toml @@ -0,0 +1,87 @@ +# p + 4He elastic scattering, dsigma/dOmega(theta_cm), from the alpha recoils of the Run A Ta-foil runs 18-22, straight +# from a TrackRecon.C production file -- the same route as 27Al_ap_runA.toml. The histogram is +# elastic_VertexZ_vs_ThetaCM__a_, filled by protonAlphaElastic_core since 2026-10-16. +# paap_ta_runs.toml is the same measurement from the p-alpha study's per-hit list. +# +# (once) process runs 18-22 with CUTLIST=pid_cuts/pid_cutlist.txt and merge them, e.g. +# bash scratch/paap_hist_2026-10-16/reprocess.sh (or run_tr.sh block 5, then hadd runs 18-22 only) +# ~/myenv/bin/python -B extract_yields.py examples/paap_ta_runs_hist.toml # or, the same in ROOT: +# root -l -b -q 'extract_yields.C+("examples/paap_ta_runs_hist.toml")' +# ~/myenv/bin/python -B geometric_efficiency.py examples/paap_ta_runs_hist.toml +# ~/myenv/bin/python -B cross_section.py examples/paap_ta_runs_hist.toml +# +# Paths are relative to this file's folder. + +title = "p + 4He elastic, alpha recoils, Ta runs 18-22 (TrackRecon histograms)" +mode = "angular" +dets = ["qqq", "sx3"] +out_dir = "../out/paap_ta_run22" + +[det_vars.qqq] # TrackRecon.C spells the detector in upper case in these folders +DET = "QQQ" +[det_vars.sx3] +DET = "SX3" + +# ------------------------------------------------------------- step 1: extract_yields.py / extract_yields.C +[extract] +# The merged output of runs 18-22 (not 17: its foil, at z = -135.7 mm, sits inside the vertex window below). +# Point this at your own merged file to use your own processing. +source = "hist" +file = "~/ANASEN_analysis/Output_p/results_run022.root" +# Folder _a: hits the p/alpha cut (pid_alpha_, CUTLIST) calls alpha. Variant _cath_exgate: cathode topologies +# (a1c1, a1c2, a2c1, a2c2) and |Ex| < 1 MeV under the alpha hypothesis, i.e. elastic. Others: "" (all topologies, +# no Ex gate), "_cath", "_exgate". +hist = "elastic+misc_{DET}_a/elastic_VertexZ_vs_ThetaCM_cath_exgate_a_{DET}" +axis = "x" # x = vertex z (mm) +angle_axis = "y" # y = proton theta_cm (deg) +variable = "z" + +# ------------------------------------------------------------- the reaction (steps 2 and 3) +[reaction] +beam_mass_u = 1.007825032 # p +target_mass_u = 4.002603254 # 4He +ejectile_mass_u = 1.007825032 # p +recoil_mass_u = 4.002603254 # 4He +detect = "recoil" # the silicon sees the alpha; theta_cm is the proton's +states = [{ ex_mev = 0.0, weight = 1.0 }] + +[beam] +# As paap_ta_runs.toml: 6.89 MeV protons into the gas; N_b = run 17's Ta-foil Rutherford current (1.35 pA) times +# the wall time of runs 18-22. The run log's 13 pA would give 2.6378e11 (../../runlog/beam_exposure.py "18-22"). +eloss_table = "../../eloss_calculations/proton_lookup_30MeV_250torr_3pc.dat" +e_entrance_mev = 6.89 +z_entrance_mm = -454.0 +current_a = 1.35e-12 +time_s = 672.65 +charge_state = 1 + +[bins] +window_z_mm = [-170.0, -53.0] # upstream of every run's foil by 25 mm for runs 18-22, inside the counter +theta_edges_deg = { start = 88.0, stop = 168.0, step = 8.0 } + +# ------------------------------------------------------------- step 2: geometric_efficiency.py +[efficiency] +n_per_bin = 400000 +seed = 20261016 + +# ------------------------------------------------------------- step 3: cross_section.py +[target] +pressure_torr = 250.0 +temperature_k = 293.15 +mole_fraction = 0.97 +atoms_per_molecule = 1 + +[acceptance] +source = "geometric" +column = "eps_geometric" + +[[reference]] +csv = "reference/barnard1964_A1113003.csv" +x_col = "theta_cm_deg" +y_col = "dsdo_window_mb_sr" +label = "Barnard 1964, at the window's E_p" + +[plot] +yscale = "linear" +xlim = [80, 175] +ylim = [0, 130] diff --git a/cross_section/examples/reference/barnard1964_A1113003.csv b/cross_section/examples/reference/barnard1964_A1113003.csv new file mode 100755 index 0000000..64028c7 --- /dev/null +++ b/cross_section/examples/reference/barnard1964_A1113003.csv @@ -0,0 +1,144 @@ +# Barnard, Jones & Weil, NP 50, 604 (1964), EXFOR A1113003: p + 4He elastic, dsigma/dOmega_cm (mb/sr) +# Legendre order 6 fits of the 6.016 and 6.977 MeV distributions; dsdo_window: log-linear in E_p at 6.7437 MeV, +# the beam energy at the centre of the vertex window -170.0 to -53.0 mm of paap_ta_runs.toml +# written by make_barnard_reference.py +theta_cm_deg,dsdo_6p016_mb_sr,dsdo_6p977_mb_sr,dsdo_window_mb_sr +26,514.406,470.065,480.465 +27,504.693,461.948,471.98 +28,494.922,453.754,463.423 +29,485.115,445.501,454.81 +30,475.295,437.203,446.161 +31,465.481,428.878,437.491 +32,455.692,420.54,428.816 +33,445.946,412.203,420.153 +34,436.261,403.88,411.513 +35,426.651,395.584,402.912 +36,417.132,387.326,394.36 +37,407.715,379.117,385.87 +38,398.413,370.966,377.45 +39,389.235,362.882,369.111 +40,380.191,354.874,360.861 +41,371.288,346.947,352.705 +42,362.532,339.108,344.652 +43,353.928,331.362,336.705 +44,345.481,323.714,328.869 +45,337.192,316.166,321.147 +46,329.064,308.722,313.542 +47,321.097,301.384,306.056 +48,313.29,294.152,298.688 +49,305.642,287.028,291.44 +50,298.152,280.012,284.312 +51,290.816,273.103,277.302 +52,283.631,266.301,270.408 +53,276.592,259.604,263.63 +54,269.697,253.011,256.964 +55,262.94,246.52,250.409 +56,256.315,240.129,243.962 +57,249.819,233.836,237.62 +58,243.445,227.639,231.379 +59,237.189,221.535,225.238 +60,231.045,215.523,219.192 +61,225.008,209.599,213.24 +62,219.074,203.763,207.379 +63,213.237,198.013,201.606 +64,207.495,192.345,195.918 +65,201.842,186.761,190.315 +66,196.276,181.257,184.794 +67,190.793,175.833,179.353 +68,185.391,170.488,173.993 +69,180.069,165.223,168.711 +70,174.824,160.037,163.508 +71,169.656,154.931,158.384 +72,164.564,149.905,153.339 +73,159.549,144.961,148.375 +74,154.61,140.099,143.492 +75,149.75,135.322,138.691 +76,144.969,130.63,133.975 +77,140.27,126.028,129.346 +78,135.655,121.516,124.807 +79,131.127,117.097,120.359 +80,126.688,112.775,116.005 +81,122.342,108.552,111.75 +82,118.093,104.431,107.595 +83,113.945,100.416,103.545 +84,109.9,96.5094,99.6024 +85,105.964,92.7147,95.7706 +86,102.14,89.0351,92.0532 +87,98.4316,85.4736,88.4535 +88,94.8431,82.0333,84.9746 +89,91.378,78.7172,81.6197 +90,88.0401,75.528,78.3918 +91,84.8326,72.4683,75.2935 +92,81.7586,69.5403,72.3274 +93,78.8209,66.7463,69.4959 +94,76.0221,64.0881,66.8009 +95,73.3644,61.5673,64.2442 +96,70.8494,59.1852,61.8272 +97,68.4787,56.9427,59.5509 +98,66.2533,54.8405,57.4162 +99,64.1738,52.8789,55.4235 +100,62.2404,51.058,53.5729 +101,60.4529,49.3774,51.864 +102,58.8107,47.8365,50.2963 +103,57.3127,46.4343,48.8688 +104,55.9576,45.1696,47.5803 +105,54.7435,44.0406,46.4292 +106,53.6684,43.0456,45.4134 +107,52.7296,42.1824,44.5309 +108,51.9245,41.4485,43.7792 +109,51.25,40.8414,43.1556 +110,50.7026,40.3582,42.657 +111,50.279,39.9957,42.2804 +112,49.9752,39.7509,42.0224 +113,49.7873,39.6202,41.8794 +114,49.7114,39.6002,41.8479 +115,49.7433,39.6873,41.9241 +116,49.8787,39.8777,42.1041 +117,50.1134,40.1678,42.3841 +118,50.4431,40.5537,42.7601 +119,50.8637,41.0316,43.2282 +120,51.3709,41.5977,43.7844 +121,51.9605,42.2482,44.4248 +122,52.6287,42.9794,45.1456 +123,53.3713,43.7876,45.9431 +124,54.1848,44.6692,46.8133 +125,55.0653,45.6205,47.7529 +126,56.0094,46.6381,48.7581 +127,57.0138,47.7186,49.8256 +128,58.0753,48.8588,50.9522 +129,59.1907,50.0552,52.1344 +130,60.3572,51.305,53.3694 +131,61.5722,52.6049,54.654 +132,62.8329,53.9521,55.9855 +133,64.137,55.3437,57.3609 +134,65.4821,56.7769,58.7776 +135,66.8659,58.2489,60.2329 +136,68.2862,59.757,61.7243 +137,69.741,61.2987,63.2493 +138,71.2282,62.8712,64.8053 +139,72.7458,64.472,66.3899 +140,74.2917,66.0985,68.0005 +141,75.864,67.7481,69.6349 +142,77.4604,69.4181,71.2903 +143,79.079,71.1058,72.9644 +144,80.7174,72.8086,74.6544 +145,82.3734,74.5237,76.3578 +146,84.0445,76.2483,78.0719 +147,85.7282,77.9794,79.7937 +148,87.4218,79.7141,81.5205 +149,89.1225,81.4492,83.2491 +150,90.8273,83.1817,84.9765 +151,92.533,84.9082,86.6995 +152,94.2363,86.6253,88.4146 +153,95.9337,88.3298,90.1185 +154,97.6217,90.0179,91.8076 +155,99.2963,91.686,93.4782 +156,100.954,93.3306,95.1267 +157,102.59,94.9478,96.7491 +158,104.2,96.5338,98.3415 +159,105.781,98.0847,99.9001 +160,107.328,99.5967,101.421 +161,108.836,101.066,102.9 +162,110.3,102.488,104.333 +163,111.718,103.86,105.716 +164,113.083,105.178,107.045 diff --git a/cross_section/extract_yields.C b/cross_section/extract_yields.C new file mode 100755 index 0000000..444afe1 --- /dev/null +++ b/cross_section/extract_yields.C @@ -0,0 +1,378 @@ +// Step 1 in ROOT: yields out of ROOT, into a plain CSV histogram. The ROOT twin of extract_yields.py: +// same config, same output (/yields_.csv), same format. Use whichever is handier. +// +// root -l -b -q 'extract_yields.C+("examples/27Al_ap_runA.toml")' +// root -l -b -q 'extract_yields.C+("examples/27Al_ap_runA.toml", "out/elsewhere")' // another output folder +// // (relative to where root runs) +// THE CSV FORMAT (cross_section.py reads only this) +// 1D: _lo, _hi, counts, variance +// 2D: _lo, _hi, theta_cm_lo, theta_cm_hi, counts, variance (angular mode) +// is z (mm), e_beam (MeV) or ecm (MeV). One row per bin; under/overflow are not written. +// +// CONFIG: the [extract] section, `dets`, `out_dir`, `title` and [det_vars.] of the study's TOML, exactly as for +// extract_yields.py (keys listed there). Two differences: +// - `cut` is handed to TTree::Draw. Write it with and / or (e.g. "det == 1 and e_si > 0.5"): they become && / || +// here and stay valid pandas syntax for the Python version. +// - A tree histogram puts an entry exactly on the last upper edge in the overflow (numpy puts it in the last bin). +// The TOML reader below handles only what these configs use: "strings", numbers, one-line [lists] and +// { start = .., stop = .., step = .. } tables. Anything else stops with an error. + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include +#include + +namespace xs { + +using Section = std::map; // key -> raw value text +using Config = std::map; // section name ("" = top level) -> keys + +// ============================================================ minimal TOML reading + +std::string Trim(const std::string& s) +{ + const auto a = s.find_first_not_of(" \t\r\n"); + if (a == std::string::npos) return ""; + const auto b = s.find_last_not_of(" \t\r\n"); + return s.substr(a, b - a + 1); +} + +std::string StripComment(const std::string& line) +{ + bool inString = false; + for (size_t i = 0; i < line.size(); ++i) { + if (line[i] == '"') inString = !inString; + if (line[i] == '#' && !inString) return line.substr(0, i); + } + return line; +} + +Config ReadToml(const std::string& file) +{ + std::ifstream in(file); + if (!in) throw std::runtime_error("cannot open config " + file); + Config config; + std::string section, line; + while (std::getline(in, line)) { + line = Trim(StripComment(line)); + if (line.empty()) continue; + if (line.rfind("[[", 0) == 0) { section = line; continue; } // array tables (e.g. [[reference]]): not used here + if (line[0] == '[') { section = Trim(line.substr(1, line.size() - 2)); continue; } + const auto eq = line.find('='); + if (eq == std::string::npos) throw std::runtime_error("cannot read config line: " + line); + const std::string value = Trim(line.substr(eq + 1)); + if ((value[0] == '[' && value.back() != ']') || (value[0] == '{' && value.back() != '}')) + throw std::runtime_error("lists and tables must be on one line: " + line); + config[section][Trim(line.substr(0, eq))] = value; + } + return config; +} + +std::string Unquote(const std::string& v) +{ + if (v.size() >= 2 && v.front() == '"' && v.back() == '"') return v.substr(1, v.size() - 2); + return v; +} + +// "[a, b]" or "{ k = v, ... }" -> its items, split on commas outside quotes +std::vector SplitItems(const std::string& v) +{ + std::vector items; + std::string inner = Trim(v.substr(1, v.size() - 2)), item; + bool inString = false; + for (char c : inner) { + if (c == '"') inString = !inString; + if (c == ',' && !inString) { items.push_back(Trim(item)); item.clear(); } + else item += c; + } + if (!Trim(item).empty()) items.push_back(Trim(item)); + return items; +} + +// Bin edges from [e0, e1, ...] or { start = .., stop = .., step = .. } (stop included), computed as numpy does +std::vector Edges(const std::string& v) +{ + std::vector edges; + if (v.front() == '[') { + for (const auto& item : SplitItems(v)) edges.push_back(std::stod(item)); + return edges; + } + std::map table; + for (const auto& item : SplitItems(v)) { + const auto eq = item.find('='); + table[Trim(item.substr(0, eq))] = std::stod(Trim(item.substr(eq + 1))); + } + const double start = table.at("start"), stop = table.at("stop"), step = table.at("step"); + const long nBins = std::lround((stop - start) / step); + for (long i = 0; i <= nBins; ++i) edges.push_back(start + step * i); + return edges; +} + +// The [extract] section of one detector: every string with {det} and the [det_vars.] keys replaced +Section ExtractSection(const Config& config, const std::string& det) +{ + std::map replacements = {{"det", det}}; + const auto vars = config.find("det_vars." + det); + if (vars != config.end()) + for (const auto& kv : vars->second) replacements[kv.first] = Unquote(kv.second); + const auto ex = config.find("extract"); + if (ex == config.end()) throw std::runtime_error("the config has no [extract] section"); + Section out; + for (const auto& kv : ex->second) { + TString value = kv.second.c_str(); + for (const auto& r : replacements) value.ReplaceAll(("{" + r.first + "}").c_str(), r.second.c_str()); + out[kv.first] = value.Data(); + } + return out; +} + +std::string Get(const Section& s, const std::string& key, const std::string& fallback = "\x01") +{ + const auto it = s.find(key); + if (it != s.end()) return Unquote(it->second); + if (fallback == "\x01") throw std::runtime_error("[extract] needs the key " + key); + return fallback; +} + +// ============================================================ the yields table + +struct Row { + double lo, hi, thetaLo, thetaHi, counts, variance; +}; + +// Sum of weights squared of a bin (global index); a histogram without Sumw2 counts each entry once +double Variance(const TH1* h, int bin) +{ + return h->GetSumw2N() > 0 ? h->GetSumw2()->At(bin) : h->GetBinContent(bin); +} + +// The histogram at "folder/name". A name that itself contains '/' (e.g. "dE_(z/100)=1") is not reachable with Get(), +// so each split into an existing folder + a key of that folder is also tried. Not found: the error names the +// histograms whose path matches when case is ignored (e.g. "elastic+misc_qqq_a" for "elastic+misc_QQQ_a"). +TH1* FindHistogram(TFile* file, const std::string& path) +{ + if (auto* h = dynamic_cast(file->Get(path.c_str()))) return h; + // every split into folder + name: at each '/', from the last one back, and finally no folder at all + std::vector> splits; + for (size_t i = path.size(); i-- > 0;) + if (path[i] == '/') splits.emplace_back(path.substr(0, i), path.substr(i + 1)); + splits.emplace_back("", path); + for (const auto& [folder, name] : splits) { + TDirectory* dir = folder.empty() ? static_cast(file) : file->GetDirectory(folder.c_str()); + if (!dir) continue; + if (TKey* key = dir->GetKey(name.c_str())) + if (auto* h = dynamic_cast(key->ReadObj())) return h; + } + std::string close; + TString lower = path.c_str(); + lower.ToLower(); + std::function walk = [&](TDirectory* dir, const std::string& prefix) { + for (auto* obj : *dir->GetListOfKeys()) { + auto* key = static_cast(obj); + const std::string full = prefix + key->GetName(); + if (TString(key->GetClassName()).BeginsWith("TDirectory")) + walk(dir->GetDirectory(key->GetName()), full + "/"); + else if (TString(full.c_str()).EqualTo(lower, TString::kIgnoreCase)) + close += " '" + full + "'"; + } + }; + walk(file, ""); + throw std::runtime_error("no histogram " + path + " in " + file->GetName() + (close.empty() ? "" : "; same path ignoring case:" + close) + + ". Paths are case-sensitive; for upper-case names per detector use [det_vars], e.g. DET = \"QQQ\""); +} + +std::vector FromHistogram(const Section& ex, const std::string& path, bool& twoD) +{ + TFile* file = TFile::Open(path.c_str()); + if (!file || file->IsZombie()) throw std::runtime_error("cannot open " + path); + const std::string name = Get(ex, "hist"); + TH1* h = FindHistogram(file, name); + + std::vector rows; + twoD = false; + if (h->GetDimension() == 1) { + for (int i = 1; i <= h->GetNbinsX(); ++i) + rows.push_back({h->GetXaxis()->GetBinLowEdge(i), h->GetXaxis()->GetBinUpEdge(i), 0, 0, + h->GetBinContent(i), Variance(h, i)}); + file->Close(); + return rows; + } + + // TH2: `axis` holds the variable; the other axis is theta_cm (angle_axis given) or is summed + const bool varOnX = Get(ex, "axis", "x") == "x"; + TH2* h2 = static_cast(h); + TAxis* varAxis = varOnX ? h2->GetXaxis() : h2->GetYaxis(); + TAxis* otherAxis = varOnX ? h2->GetYaxis() : h2->GetXaxis(); + const int nVar = varAxis->GetNbins(), nOther = otherAxis->GetNbins(); + auto global = [&](int iVar, int iOther) { return varOnX ? h2->GetBin(iVar, iOther) : h2->GetBin(iOther, iVar); }; + + if (ex.count("angle_axis")) { // keep it 2D: one row per (variable bin, theta bin) + twoD = true; + for (int i = 1; i <= nVar; ++i) + for (int j = 1; j <= nOther; ++j) + rows.push_back({varAxis->GetBinLowEdge(i), varAxis->GetBinUpEdge(i), otherAxis->GetBinLowEdge(j), + otherAxis->GetBinUpEdge(j), h2->GetBinContent(global(i, j)), Variance(h2, global(i, j))}); + file->Close(); + return rows; + } + + // project on the variable: the other axis summed whole (with under/overflow), or the fraction inside other_range + std::vector weight(nOther + 2, 1.0); + if (ex.count("other_range")) { + const auto range = Edges(ex.at("other_range")); + weight.front() = weight.back() = 0.0; + for (int j = 1; j <= nOther; ++j) { + const double lo = otherAxis->GetBinLowEdge(j), hi = otherAxis->GetBinUpEdge(j); + weight[j] = std::max(0.0, std::min(hi, range[1]) - std::max(lo, range[0])) / (hi - lo); + } + } + for (int i = 1; i <= nVar; ++i) { + double counts = 0, variance = 0; + for (int j = 0; j <= nOther + 1; ++j) { + counts += weight[j] * h2->GetBinContent(global(i, j)); + variance += weight[j] * weight[j] * Variance(h2, global(i, j)); + } + rows.push_back({varAxis->GetBinLowEdge(i), varAxis->GetBinUpEdge(i), 0, 0, counts, variance}); + } + file->Close(); + return rows; +} + +std::vector FromTree(const Section& ex, const std::vector& files, bool& twoD) +{ + TChain chain(Get(ex, "tree").c_str()); + for (const auto& f : files) chain.Add(f.c_str()); // TChain::Add takes wildcards in the file name + if (chain.GetEntries() <= 0) // a missing tree or file must not become a table of zeros + throw std::runtime_error("no entries in tree " + Get(ex, "tree") + " of " + files.front() + (files.size() > 1 ? " ..." : "")); + + // The cut, with and / or as && / ||; a weight branch multiplies it + TString cut = Get(ex, "cut", "").c_str(); + cut.ReplaceAll(" and ", " && ").ReplaceAll(" or ", " || "); + if (cut.IsNull()) cut = "1"; + TString selection = ex.count("weight_branch") ? TString::Format("(%s)*(%s)", Get(ex, "weight_branch").c_str(), cut.Data()) + : cut; + + const auto edges = Edges(ex.at("bins")); + const TString branch = Get(ex, "branch").c_str(); + gROOT->cd(); + std::vector rows; + twoD = ex.count("angle_branch") > 0; + if (!twoD) { + TH1D h("h_extract_yields", "", edges.size() - 1, edges.data()); + h.Sumw2(); + const Long64_t n = chain.Draw(branch + ">>h_extract_yields", selection, "goff"); + printf(" %d file(s); %lld entries after the cut\n", chain.GetListOfFiles()->GetEntries(), n); + for (int i = 1; i <= h.GetNbinsX(); ++i) + rows.push_back({edges[i - 1], edges[i], 0, 0, h.GetBinContent(i), Variance(&h, i)}); + return rows; + } + const auto angleEdges = Edges(ex.at("angle_bins")); + TH2D h("h_extract_yields2", "", edges.size() - 1, edges.data(), angleEdges.size() - 1, angleEdges.data()); + h.Sumw2(); + const Long64_t n = chain.Draw(TString(Get(ex, "angle_branch").c_str()) + ":" + branch + ">>h_extract_yields2", + selection, "goff"); // "y:x" in TTree::Draw + printf(" %d file(s); %lld entries after the cut\n", chain.GetListOfFiles()->GetEntries(), n); + for (size_t i = 1; i < edges.size(); ++i) + for (size_t j = 1; j < angleEdges.size(); ++j) + rows.push_back({edges[i - 1], edges[i], angleEdges[j - 1], angleEdges[j], h.GetBinContent(h.GetBin(i, j)), + Variance(&h, h.GetBin(i, j))}); + return rows; +} + +void WriteCsv(const std::vector& rows, bool twoD, const std::string& var, const std::vector& header, + const std::string& outFile) +{ + FILE* f = fopen(outFile.c_str(), "w"); + if (!f) throw std::runtime_error("cannot write " + outFile); + for (const auto& line : header) fprintf(f, "# %s\n", line.c_str()); + fprintf(f, twoD ? "%s_lo,%s_hi,theta_cm_lo,theta_cm_hi,counts,variance\n" : "%s_lo,%s_hi,counts,variance\n", + var.c_str(), var.c_str()); + for (const auto& r : rows) { + if (twoD) fprintf(f, "%.6g,%.6g,%.6g,%.6g,%.6g,%.6g\n", r.lo, r.hi, r.thetaLo, r.thetaHi, r.counts, r.variance); + else fprintf(f, "%.6g,%.6g,%.6g,%.6g\n", r.lo, r.hi, r.counts, r.variance); + } + fclose(f); +} + +} // namespace xs + +void extract_yields(const char* configFile, const char* outDirOverride = "") +{ + using namespace xs; + try { + const Config config = ReadToml(configFile); + const std::string configDir = gSystem->GetDirName(configFile).Data(); + auto fullPath = [&](const std::string& p) -> std::string { + if (p.rfind("~/", 0) == 0 && getenv("HOME")) return std::string(getenv("HOME")) + p.substr(1); // "~/..." = home + return p.empty() || p[0] == '/' ? p : configDir + "/" + p; + }; + + const Section& top = config.count("") ? config.at("") : Section(); + std::vector dets = {""}; + if (top.count("dets")) { + dets.clear(); + for (const auto& d : SplitItems(top.at("dets"))) dets.push_back(Unquote(d)); + } + const std::string outDir = *outDirOverride ? std::string(outDirOverride) + : fullPath(top.count("out_dir") ? Unquote(top.at("out_dir")) : "out"); + gSystem->mkdir(outDir.c_str(), kTRUE); + const std::string title = top.count("title") ? Unquote(top.at("title")) : ""; + + for (const auto& det : dets) { + const Section ex = ExtractSection(config, det); + const std::string source = Get(ex, "source"), var = Get(ex, "variable"); + if (source != "hist" && source != "tree") + throw std::runtime_error("[extract] source must be \"hist\" or \"tree\", not " + source + + (source == "csv" ? " (event-list CSVs: use extract_yields.py)" : "")); + std::vector files; // `file` may be one path or a list + if (ex.at("file").front() == '[') for (const auto& f : SplitItems(ex.at("file"))) files.push_back(fullPath(Unquote(f))); + else files.push_back(fullPath(Get(ex, "file"))); + const std::string fileText = ex.at("file").front() == '[' ? ex.at("file") : Get(ex, "file"); + printf("--- %s: %s : %s\n", det.empty() ? "data" : det.c_str(), fileText.c_str(), + Get(ex, source == "hist" ? "hist" : "tree").c_str()); + + bool twoD = false; + std::vector rows; + std::string from; + if (source == "hist") { + rows = FromHistogram(ex, files.front(), twoD); + from = "histogram " + Get(ex, "hist"); + } else if (source == "tree") { + rows = FromTree(ex, files, twoD); + from = "tree " + Get(ex, "tree") + ", branch " + Get(ex, "branch"); + if (!Get(ex, "cut", "").empty()) from += ", cut: " + Get(ex, "cut"); + } else { + throw std::runtime_error("[extract] source must be \"hist\" or \"tree\", not " + source + + (source == "csv" ? " (event-list CSVs: use extract_yields.py)" : "")); + } + + TString detUpper = det.c_str(); + detUpper.ToUpper(); + const std::string outFile = outDir + "/" + (det.empty() ? "yields.csv" : "yields_" + det + ".csv"); + WriteCsv(rows, twoD, var, + {title + " " + detUpper.Data() + ": yields, binned in " + var, "from " + fileText + " : " + from, + "written by extract_yields.C"}, + outFile); + double total = 0; + for (const auto& r : rows) total += r.counts; + printf(" %.0f counts in %zu bins -> %s\n", total, rows.size(), outFile.c_str()); + } + } catch (const std::exception& e) { + fprintf(stderr, "extract_yields.C: %s\n", e.what()); + gSystem->Exit(1); // a failed extraction must not look like a finished one + } +} diff --git a/cross_section/geometric_efficiency.py b/cross_section/geometric_efficiency.py new file mode 100755 index 0000000..df77057 --- /dev/null +++ b/cross_section/geometric_efficiency.py @@ -0,0 +1,164 @@ +"""Step 2: geometric efficiency of every bin, for the detectors as they are now (detectors.py). + + ~/myenv/bin/python -B geometric_efficiency.py examples/27Al_ap_runA.toml # ~1 min; numpy and pandas only + +A toy Monte Carlo per bin (same bins as the cross section): + - vertices uniform over the bin's stretch of beam path (angular mode: over the window); + - beam energy at each vertex from the nominal beam track; + - the residual nucleus' state drawn from [reaction] states: fixed weights, or state cross sections + from a table (e.g. TALYS) at the bin's nominal E_cm; + - emission isotropic in the CM (angular mode: cos theta_cm uniform inside the theta bin, theta_cm of the ejectile); + - relativistic two-body kinematics, straight tracks from the vertex. + +Writes /eps_.csv, one row per bin, with these efficiencies (each times the azimuthal coverage): + eps_si the particle reaches the analysed silicon (solid angle) + eps_si_thr eps_si, and its energy at the vertex is above the Si threshold (the ch5 "solid angle" convention; + a kinematic cut, not geometry) + eps_counter eps_si, and it crosses the guard, anode and cathode radii inside the counter + eps_geometric eps_counter, and it clears the beam tube and the PCB hole <- THE GEOMETRIC EFFICIENCY +and the Monte Carlo relative error of each (_rel_err). +Not included, because they are not geometry: energy loss in the gas, the Si threshold after the gas, the counter's +deposit threshold, intrinsic efficiencies. They are why the adopted eps_tube of ../scratch/xs_27Al_lowE_2026-10-15 is lower. + +CONFIG + [reaction] beam_mass_u, target_mass_u, ejectile_mass_u, recoil_mass_u (atomic masses; Q from these) + detect = "ejectile" (default) or "recoil": the particle the silicon sees + states = [{ex_mev = 0.0, weight = 1.0}, ...] fixed state weights, or + states_csv = file with ecm_mev and one column ex_ per state (state cross sections) + [efficiency] n_per_bin (default 400000), seed + [beam], [bins], mode, dets as for the cross section. +""" +import argparse + +import numpy as np +import pandas as pd + +import common +import detectors + +U = 931.49410242 # MeV per u +EFFICIENCIES = ("eps_si", "eps_si_thr", "eps_counter", "eps_geometric") + + +def two_body(t_beam, reaction, ex, cos_cm): + """Relativistic two-body kinematics, beam on target at rest -> ejectile (at cos_cm in the CM) + recoil (state ex). + Returns the lab kinetic energy (MeV) and polar angle (rad) of the detected particle, and whether the channel is + open at this beam energy.""" + m1, m2 = reaction["beam_mass_u"] * U, reaction["target_mass_u"] * U + m3, m4 = reaction["ejectile_mass_u"] * U, reaction["recoil_mass_u"] * U + ex + s = (m1 + m2) ** 2 + 2 * m2 * t_beam # invariant mass squared + sqrt_s = np.sqrt(s) + is_open = sqrt_s > m3 + m4 + e_total = t_beam + m1 + m2 + beta = np.sqrt(t_beam ** 2 + 2 * t_beam * m1) / e_total # of the CM in the lab + gamma = e_total / sqrt_s + p_cm = np.sqrt(np.clip((s - (m3 + m4) ** 2) * (s - (m3 - m4) ** 2), 0, None)) / (2 * sqrt_s) + sin_cm = np.sqrt(1 - cos_cm ** 2) + + # the recoil goes the opposite way in the CM + mass, sign = (m3, 1.0) if reaction.get("detect", "ejectile") == "ejectile" else (m4, -1.0) + e_cm = np.sqrt(p_cm ** 2 + mass ** 2) + p_z = gamma * (sign * p_cm * cos_cm + beta * e_cm) + energy = gamma * (e_cm + beta * sign * p_cm * cos_cm) + theta = np.arctan2(p_cm * sin_cm, p_z) + return np.where(is_open, energy - mass, 0.0), theta, is_open + + +def q_value_mev(reaction): + return (reaction["beam_mass_u"] + reaction["target_mass_u"] + - reaction["ejectile_mass_u"] - reaction["recoil_mass_u"]) * U + + +def state_weights(reaction, ecm, states_table): + """Excitation energies of the residual nucleus and their probabilities at this E_cm. States that are closed + (Ex >= Q + E_cm) get weight 0; if none is open, the ground state alone.""" + if states_table is None: + states = reaction.get("states", [{"ex_mev": 0.0, "weight": 1.0}]) + ex = np.array([s["ex_mev"] for s in states], float) + w = np.array([s["weight"] for s in states], float) + else: + columns = [c for c in states_table.columns if c.startswith("ex_")] + ex = np.array([float(c[3:]) for c in columns]) + # the table row nearest this E_cm, among rows with any cross section (below the first such row, its weights) + rows = states_table[states_table[columns].sum(axis=1) > 0] + row = rows.iloc[np.argmin(np.abs(rows["ecm_mev"].to_numpy() - max(ecm, rows["ecm_mev"].min())))] + w = row[columns].to_numpy(float) + w = np.where(ex < q_value_mev(reaction) + ecm, w, 0.0) + if w.sum() <= 0: + w = (ex == 0).astype(float) + return ex, w / w.sum() + + +def efficiency_of_bin(det, reaction, track, z_range, cos_range, ecm, states_table, n, rng): + """Toy for one bin: n reactions with vertices uniform in z_range and cos(theta_cm) uniform in cos_range.""" + z = rng.uniform(z_range[0], z_range[1], n) + t_beam = track.energy_at(z, nominal=True) + ex_states, weights = state_weights(reaction, ecm, states_table) + ex = rng.choice(ex_states, size=n, p=weights) + cos_cm = rng.uniform(cos_range[0], cos_range[1], n) + energy, theta, is_open = two_body(t_beam, reaction, ex, cos_cm) + is_open &= t_beam > 0 + + on_si = is_open & detectors.hits_silicon(det, z, theta) + passed = {"eps_si": on_si, + "eps_si_thr": on_si & (energy > detectors.SI_THRESHOLD_MEV[det]), + "eps_counter": on_si & detectors.crosses_counter(z, theta)} + passed["eps_geometric"] = passed["eps_counter"] & detectors.clears_apertures(z, theta) + + phi = detectors.PHI_FRACTION[det] + row = {"ground_state_weight": float(weights[ex_states == 0].sum()), "frac_open": float(is_open.mean())} + for name, ok in passed.items(): + p = ok.mean() + row[name] = phi * p + row[f"{name}_rel_err"] = np.sqrt(p * (1 - p) / n) / p if p > 0 else np.nan # binomial + return row + + +def main(argv=None): + parser = argparse.ArgumentParser(description="Step 2: geometric efficiency per bin (detectors.py).") + parser.add_argument("config", help="TOML config file") + args = parser.parse_args(argv) + config, full_path = common.read_config(args.config) + + for det in config.get("dets", [""]): + c = common.config_for_detector(config, det) + reaction, settings = c["reaction"], c.get("efficiency", {}) + mode = c.get("mode", "excitation") + k = common.ecm_per_beam_energy(reaction) + track = common.load_beam_track(c["beam"], full_path) + bins, window = common.make_bins(c, track, k) + states_table = pd.read_csv(full_path(reaction["states_csv"]), comment="#") if "states_csv" in reaction else None + rng = np.random.default_rng(settings.get("seed", 20261016)) + n = int(settings.get("n_per_bin", 400_000)) + + rows = [] + for _, b in bins.iterrows(): + if b["dz_mm"] <= 0: # past the beam's stopping point + rows.append({name: np.nan for name in EFFICIENCIES}) + continue + if mode == "excitation": + ecm = b["ecm_nominal_mev"] + cos_range = (-1.0, 1.0) + else: + ecm = k * track.energy_at(0.5 * (b["z_up_mm"] + b["z_down_mm"]), nominal=True) + cos_range = (np.cos(np.radians(b["theta_hi_deg"])), np.cos(np.radians(b["theta_lo_deg"]))) + rows.append(efficiency_of_bin(det, reaction, track, (b["z_up_mm"], b["z_down_mm"]), cos_range, + ecm, states_table, n, rng)) + table = pd.concat([bins.reset_index(drop=True), pd.DataFrame(rows)], axis=1) + + states_text = reaction.get("states_csv", reaction.get("states", "ground state only")) + header = [f"{c.get('title', '')} {det.upper()}: geometric efficiency per bin ({mode} mode), detectors.py", + f"beam track: {track.description}; Q = {q_value_mev(reaction):.4f} MeV; detected: " + f"{reaction.get('detect', 'ejectile')}; states: {states_text}", + f"isotropic CM, straight tracks, {n} reactions per bin; azimuthal coverage {detectors.PHI_FRACTION[det]:.4f}", + "eps_geometric = silicon + counter + apertures; eps_si_thr adds the Si threshold at the vertex energy", + "written by geometric_efficiency.py"] + out = common.output_file(config, full_path, "eps", det) + common.write_csv(table, header, out) + x_col = "ecm_nominal_mev" if mode == "excitation" else "theta_c_deg" + print(f"--- {det}: -> {out}") + print(table[[x_col, *EFFICIENCIES]].to_string(index=False, float_format=lambda v: f"{v:.4g}")) + + +if __name__ == "__main__": + main() diff --git a/cross_section/inputs/beam_tracks.csv b/cross_section/inputs/beam_tracks.csv new file mode 100755 index 0000000..b7ac79f --- /dev/null +++ b/cross_section/inputs/beam_tracks.csv @@ -0,0 +1,7146 @@ +# 27Al beam energy (MeV) along z; pycatima midpoint steps of 0.025 mm, sampled every 0.1 mm; 0 beyond the stopping point +# 0922/0962/1002: stoichiometric fill x scale; old089: mass-fraction fill x 0.89 (xs_series.py); +# table089: the production table (data binning), aluminum_lookup_80MeV_250torr_3pc_prod089.dat; 80mev: 80 MeV entering at the same z +# written by tools/xs/03_beam_tracks.py +z_mm,e_beam_mev_0922,e_beam_mev_0962,e_beam_mev_1002,e_beam_mev_old089,e_beam_80mev_0962,e_beam_80mev_old089,e_beam_mev_table089 +-454.00000,56.16000,56.16000,56.16000,56.16000,80.00000,80.00000,56.16000 +-453.90000,56.14924,56.14877,56.14830,56.14859,79.99028,79.99016,56.14859 +-453.80000,56.13847,56.13754,56.13660,56.13718,79.98056,79.98031,56.13718 +-453.70000,56.12770,56.12630,56.12490,56.12576,79.97084,79.97047,56.12577 +-453.60000,56.11694,56.11507,56.11320,56.11435,79.96112,79.96062,56.11435 +-453.50000,56.10617,56.10383,56.10150,56.10293,79.95140,79.95078,56.10294 +-453.40000,56.09540,56.09260,56.08979,56.09152,79.94168,79.94093,56.09152 +-453.30000,56.08463,56.08136,56.07809,56.08010,79.93196,79.93108,56.08011 +-453.20000,56.07386,56.07012,56.06639,56.06869,79.92223,79.92124,56.06869 +-453.10000,56.06309,56.05889,56.05468,56.05727,79.91251,79.91139,56.05727 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the discrete-state columns ex_ (fig2 'all levels (sum)') +# group_