amplitudes.h File Reference

#include <vector>
#include "arrays.h"
#include "bspline.h"

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Functions
cArray	computeLambda (Bspline const &bspline, rArray const &kf, rArray const &ki, int maxell, int L, int Spin, int Pi, int ni, int li, int mi, rArray const &Ei, int lf, cArray const &Pf_overlaps, std::vector< std::pair< int, int >> const &coupled_states)
	Extract radial part of scattering amplitude. More...
cArrays	computeXi (Bspline const &bspline, int maxell, int L, int Spin, int Pi, int ni, int li, int mi, rArray const &Ei, rArray &ics, std::vector< std::pair< int, int >> const &coupled_states)
	Extract radial part of ionization amplitude. More...

Function Documentation

cArray computeLambda	(	Bspline const &	bspline,
		rArray const &	kf,
		rArray const &	ki,
		int	maxell,
		int	L,
		int	Spin,
		int	Pi,
		int	ni,
		int	li,
		int	mi,
		rArray const &	Ei,
		int	lf,
		cArray const &	Pf_overlaps,
		std::vector< std::pair< int, int >> const &	coupled_states
	)

Compute radial integrals for evaluation of the discrete T-matrices,

\[ \Lambda_l^{(1)LMS} = \int_0^{R_0} P_{n_f l_f}(r_1) \mathcal{W}\left[ \psi_{\ell_1 \ell_2}^{LMS}(r_1,\bullet), \hat{j}_l(k_f\bullet) \right]_{R_0} \mathrm{d}r_1 \ . \]

Parameters

bspline	The B-spline environment to use when evaluating the solutions.
kf	Outgoing projectile momenta.
ki	incoming projectile momenta.
maxell	Maximal angular momentum of the projectile.
L	Total angular momentum (partial wave).
Spin	Conserved total spin (partial wave).
Pi	Total parity (partial wave).
ni	Initial atomic state - principal quantum number.
li	Initial atomic state - orbital quantum number.
mi	Initial atomic state - magnetic quantum number.
Ei	Initial projectile energies.
lf	Final atomic orbital momentum.
Pf_overlaps	Hydrogenic function B-spline overlap integrals.
coupled_states	List of all coupled-state angular momenta pairs.

Returns

Vector of radial integrals.

cArrays computeXi	(	Bspline const &	bspline,
		int	maxell,
		int	L,
		int	Spin,
		int	Pi,
		int	ni,
		int	li,
		int	mi,
		rArray const &	Ei,
		rArray &	ics,
		std::vector< std::pair< int, int >> const &	coupled_states
	)

Compute hyperangular integrals for evaluation of the ionization T-matrices,

\[ \Xi_{\ell_1 \ell_2}^{LS}(k_1,k_2) = \int_0^{\pi/2} \left( F_{\ell_1}(k_1,r_1) F_{\ell_2}(k_2,r_2) \frac{\partial}{\partial\rho} \psi^{LS}_{\ell_1\ell_2}(r_1,r_2) - \psi^{LS}_{\ell_1\ell_2}(r_1,r_2) \frac{\partial}{\partial\rho} F_{\ell_1}(k_1,r_1) F_{\ell_2}(k_2,r_2) \right) \rho\mathrm{d}\alpha \ , \]

where \( r_1 = \rho \cos\alpha \) and \( r_2 = \rho \sin\alpha \).

Parameters

bspline	The B-spline environment to use when evaluating the solutions.
maxell	Maximal angular momentum of the free electrons.
L	Total angular momentum (partial wave).
Spin	Conserved total spin (partial wave).
Pi	Total parity (partial wave).
ni	Initial atomic state - principal quantum number.
li	Initial atomic state - orbital quantum number.
mi	Initial atomic state - magnetic quantum number.
Ei	Initial projectile energies.
ics	Ionization cross section (on return).
coupled_states	List of all coupled-state angular momenta pairs.

Returns

Vector of radial integrals.