ultrarelativistic corrections

calculations.cpp

@@ -412,6 +412,31 @@ double bethek_lindhard_X(const Projectile &p){
     //return sum;
 }
 
+double pair_production(const Projectile &p, const Target &t){
+    double s=0.0;
+    double gamma=1.0 + p.T/atomic_mass_unit;
+    double d = 1.0/sqrt(gamma);
+    double logd2 = log(d*d);
+    double l0 = log(2.0*gamma);
+    double Zt13 = 183.0*power(t.Z,-1.0/3.0);
+    double L0screen = (19.0/9.0)*log(Zt13/(1.0 + 25.018803808*Zt13/gamma));
+    double L1 = (4178.0/(81.0*M_PI*M_PI))
+                - (21.0/27.0)
+                - (248.0*l0/(27.0*M_PI*M_PI))
+                + ( ((28.0*l0/(9.0)) - 446.0/27.0)*logd2/(M_PI*M_PI))
+                + (14.0*logd2*logd2/(9.0*M_PI*M_PI));
+    L1 *= d;
+    s = 0.25*dedx_constant*fine_structure*fine_structure*p.Z*p.Z*t.Z*t.Z*gamma*(1.0+(1.0/t.Z))*(L0screen + L1)/t.A;
+    return (s<0.0)?0.0:s;
+};
+
+double bremsstrahlung(const Projectile &p, const Target &t){
+    double gamma=1.0 + p.T/atomic_mass_unit;
+    double R = 1.18*(catima::power(p.A, 1.0/3.0) + catima::power(t.A, 1.0/3.0));
+    double Lbs = log(1.0 + 2.0*gamma*0.1*hbar*c_light/atomic_mass_unit/R/p.A);
+    double C = dedx_constant*fine_structure*(electron_mass/atomic_mass_unit);
+    return 16.0*C*gamma*p.Z*p.Z*p.Z*p.Z*t.Z*t.Z*Lbs/(t.A*p.A*3.0*4.0*M_PI);
+};
 
 
 double sezi_p_se(double energy,const Target &t){

calculations.h

@@ -59,6 +59,16 @@ namespace catima{
       */
     double bethek_lindhard_X(const Projectile &p);
 
+    /**
+      * calculates pair production stopping power
+      */
+    double pair_production(const Projectile &p, const Target &t);
+
+    /**
+      * calculates bremsstrahlung stopping power
+      */
+    double bremsstrahlung(const Projectile &p, const Target &t);
+
     /**
       * returns linhard correction (L) calulated from tabulated precalculated data
       * if energy is less than minimal calculated energy the LS coefficient of at  minimal 

constants.h

@@ -36,6 +36,7 @@ constexpr double fine_structure = 1/137.035999139;
 constexpr double fine_structure_inverted = 1/fine_structure;
 constexpr double c_light = 299.792458; //Mm/s
 constexpr double bohr_velocity = 2.19 / c_light; // in c unit
+constexpr double hbar = 6.582119514; // in eV*s * 10^-16
 
 constexpr double dedx_constant = 0.3070749187;  //4*pi*Na*me*c^2*r_e^2  //MeV cm^2
 constexpr double domega2dx_constant = dedx_constant*electron_mass;  //4*pi*Na*me*c^2*r_e^2  //MeV^2 cm^2

tests/test_calculations.cpp

@@ -119,6 +119,17 @@ const lest::test specification[] =
         p.T = 2794.4822;
         EXPECT( f()== approx(1.768018).R(0.01) );
     },
+    CASE("ultrarelativistic corrections"){
+        catima::Projectile p{238,92};
+        catima::Target t{27,13};
+        EXPECT(catima::pair_production(p(1e3),t) == approx(0.0,1e-3));
+        EXPECT(catima::bremsstrahlung(p(1e3),t) == approx(0.0,1e-3));
+
+        EXPECT(catima::pair_production(p(1e6),t) == approx(1900,300));
+        EXPECT(catima::bremsstrahlung(p(1e6),t) == approx(170,20));
+        EXPECT(catima::pair_production(p(7e6),t) == approx(21000,3000));
+        EXPECT(catima::bremsstrahlung(p(7e6),t) == approx(6000,500));
+    },
     CASE("dEdx for compounds"){
         catima::Projectile p{1,1,1,1000};
         catima::Material water({
@@ -385,6 +396,11 @@ const lest::test specification[] =
       EXPECT(res3[0] == approx(catima::dedx_from_range(p,energies[0],graphite),0.1));
       EXPECT(res3[1] == approx(catima::dedx_from_range(p,energies[1],graphite),0.1));
       EXPECT(res3[2] == approx(catima::dedx_from_range(p,energies[2],graphite),0.1));
+    },
+    CASE("constants"){
+        using namespace catima;
+        EXPECT(0.1*hbar*c_light/atomic_mass_unit == approx(0.21183,0.0001));
+        EXPECT(16.0*dedx_constant*electron_mass*fine_structure/(atomic_mass_unit*3.0*4.0*M_PI) == approx(5.21721169334564e-7).R(1e-3));
         }
     
 };