scatamp-dir.cpp File Reference

#include <map>
#include <string>
#include <vector>
#include "hex-interpolate.h"
#include "hex-chebyshev.h"
#include "hex-special.h"
#include "hex-version.h"
#include "../quantities.h"
#include "../utils.h"

Include dependency graph for scatamp-dir.cpp:

Functions
	createNewScatteringQuantity (ScatteringAmplitudeDir, "scatamp-dir") std
void	hex_scattering_amplitude_dir (int ni, int li, int mi, int nf, int lf, int mf, int S, double E, int N, double alpha, double beta, double gamma, double *angles, double *result)
	Scattering anplitude for non-aligned impact direction (C). More...
void	hex_scattering_amplitude_dir_ (int *ni, int *li, int *mi, int *nf, int *lf, int *mf, int *S, double *E, int *N, double *alpha, double *beta, double *gamma, double *angles, double *result)
	Scattering anplitude for non-aligned impact direction (Fortran). More...

Function Documentation

createNewScatteringQuantity()

createNewScatteringQuantity	(	ScatteringAmplitudeDir	,
		"scatamp-dir"
	)

hex_scattering_amplitude_dir()

void hex_scattering_amplitude_dir	(	int	ni,
		int	li,
		int	mi,
		int	nf,
		int	lf,
		int	mf,
		int	S,
		double	E,
		int	N,
		double	alpha,
		double	beta,
		double	gamma,
		double *	angles,
		double *	result
	)

C prototype.

See hex_scattering_amplitude_dir_ for theory.

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
E	Impact energy in Rydbergs.
N	Sample count.
alpha	Impact angle (first of Euler angles).
beta	Impact angle (second of Euler angles).
gamma	Impact angle (third of Euler angles).
angles	Real array of length N containing scattering angles.
result	Complex array of length N (or real array of length 2N) to contain the amplitudes.

hex_scattering_amplitude_dir_()

void hex_scattering_amplitude_dir_	(	int *	ni,
		int *	li,
		int *	mi,
		int *	nf,
		int *	lf,
		int *	mf,
		int *	S,
		double *	E,
		int *	N,
		double *	alpha,
		double *	beta,
		double *	gamma,
		double *	angles,
		double *	result
	)

This function will evaluate the scattering amplitude when the projectile is coming in a direction different from the quantization axis, i.e. when

\[ \mathbf{k}_i \neq (0, 0, k_i) \,. \]

In that case the of the scattering amplitude can be computed using Wigner d-function and all possible amplitudes from scattering between various magnetic levels. The reason for this is that such situation is equivalent to a change of the quantization axis by the same amount. To be precise, it is

\[ T_{n_f l_f m_f \leftarrow n_i l_i m_i} = \sum_{m_i' m_f'} D_{m_i' m_i}^{l_i} D_{m_f' m_f}^{l_f \ast} T_{n_f l_f m_f' \leftarrow n_i l_i m_i'} \,. \]

Fortran prototype equivalent to

subroutine scattering_amplitude (ni,li,mi,nf,lf,mf,S,E,N,angles,result)
  integer, intent(in) :: ni,li,mi
  integer, intent(in) :: nf,lf,mf
  integer, intent(int) :: s,n
  double precision, intent(in)     :: e
  double precision, dimension(N)   :: angles
  double precision, dimension(2*N) :: result

Parameters

ni	Initial atomic principal quantum number.
li	Initial atomic orbital quantum number.
mi	Initial atomic magnetic quantum number.
nf	Final atomic principal quantum number.
lf	Final atomic orbital quantum number.
mf	Final atomic magnetic quantum number.
S	Total spin (0 = singlet, 1 = triplet).
E	Impact energy in Rydbergs.
N	Sample count.
alpha	Impact angle (first of Euler angles).
beta	Impact angle (second of Euler angles).
gamma	Impact angle (third of Euler angles).
angles	Real array of length N containing scattering angles.
result	Complex array of length N (or real array of length 2N) to contain the amplitudes.