added Klein-Nishina distribution

demo/xrayphysics_example.py

@@ -8,7 +8,7 @@
 # The next line prints out the version number and some other information about this package
 #physics.about()
 
-whichPlot = 10
+whichPlot = 9
 
 
 #########################################################################################
@@ -166,10 +166,11 @@
 if whichPlot == 9:
     plt.figure(figsize=(10,5))
     plt.subplot(1, 2, 1)
-    plt.plot(thetas, dsigma_incoh)
+    plt.plot(thetas, dsigma_incoh, thetas, physics.KleinNishinaScatterDistribution(60.0, thetas, True))
     plt.title('Incoherent (Compton) Scatter Distributions')
     plt.xlabel('angle (degrees)')
     plt.ylabel('normalized differential cross section')
+    plt.legend(['true distribution','Klein-Nishina approximation'])
     plt.xlim((0.0,180.0))
 
     plt.subplot(1, 2, 2)

docs/source/index.rst

@@ -3,10 +3,10 @@
    You can adapt this file completely to your liking, but it should at least
    contain the root `toctree` directive.
 
-Welcome to XrayPhysics's documentation!
-=======================================
+XrayPhysics Library Documentation
+=================================
 
-This is a C/C++ library with Python bindings with the following capabilities:
+This is a C/C++ library (Linux, Windows, Mac) with Python bindings with the following capabilities:
 
 1. x-ray cross sections (energies from 1 keV to 20 MeV and elements 1-100) specified by chemical formula or element/compound mass fractions
 2. incoherent and coherent x-ray scattering angle distributions specified by chemical formula or element/compound mass fractions

src/xrayphysics.py

@@ -750,6 +750,25 @@ def coherentScatterDistribution_normalizationFactor(self, Z, gamma):
             self.libxrayphysics.coherentScatterDistribution_normalizationFactor.restype = ctypes.c_float
             self.libxrayphysics.coherentScatterDistribution_normalizationFactor.argtypes = [ctypes.c_float, ctypes.c_float]
             return self.libxrayphysics.coherentScatterDistribution_normalizationFactor(float(Z), gamma) * self.cross_section_scalar()
+
+    def KleinNishinaScatterDistribution(self, gamma, theta, doNormalize=False):
+        ELECTRON_REST_MASS_ENERGY = 510.975
+        CLASSICAL_ELECTRON_RADIUS = 2.8179403267e-13
+        AVOGANDROS_NUMBER = 6.0221414107e23
+        KNconstant = CLASSICAL_ELECTRON_RADIUS*CLASSICAL_ELECTRON_RADIUS*AVOGANDROS_NUMBER
+        cos_theta = np.cos(theta*np.pi/180.0)
+        P = 1.0 / (1.0 + (gamma / ELECTRON_REST_MASS_ENERGY) * (1.0 - cos_theta))
+        retVal = 0.5 * P * P * (P + 1.0 / P - 1.0 + cos_theta * cos_theta) / (self.ComptonBasis(gamma) / KNconstant)
+        if doNormalize:
+            return retVal / self.KleinNishinaScatterDistribution_normalizationFactor(gamma)
+        else:
+            return retVal
+
+    def KleinNishinaScatterDistribution_normalizationFactor(self, gamma):
+        thetas = np.linspace(0.0, 180.0, 1800)
+        KN = self.KleinNishinaScatterDistribution(gamma, thetas, False)
+        return np.sum(KN*np.sin(thetas*np.pi/180.0)*2.0*np.pi*np.pi/180.0*0.1)
+
     ###
 
     def simulateSpectra(self, kV, takeOffAngle=11.0, Z=74, gammas=None):
@@ -1271,7 +1290,10 @@ def ComptonBasis(self, gammas):
         KNconstant = CLASSICAL_ELECTRON_RADIUS*CLASSICAL_ELECTRON_RADIUS*AVOGANDROS_NUMBER
         two_PI_KNconstant = 2.0*np.pi*KNconstant
 
-        alpha = gammas.copy() / ELECTRON_REST_MASS_ENERGY
+        if type(gammas) is np.ndarray:
+            alpha = gammas.copy() / ELECTRON_REST_MASS_ENERGY
+        else:
+            alpha = gammas / ELECTRON_REST_MASS_ENERGY
         one_plus_two_alpha = 1.0+2.0*alpha
         log_term = np.log(one_plus_two_alpha)
         basisFcn = (1.0+one_plus_two_alpha)/(2.0*one_plus_two_alpha*one_plus_two_alpha) + ((alpha*alpha-1.0-one_plus_two_alpha)*log_term + 4.0*alpha)/(2.0*alpha*alpha*alpha) * two_PI_KNconstant