DWBA1 Namespace Reference

Functions
Complex	computeDirect1e (DistortingPotential const &U, int l, double k)
Complex	computeExchange1e (DistortingPotential const &U, int Ni, int Li, double ki, int Nf, int Lf, double kf)
Complex	computeDirect2e (const DistortingPotential &U, int lambda, int Nf, int Lf, double kf, int lf, int Ni, int Li, double ki, int li)
Complex	computeExchange2e (const DistortingPotential &U, int lambda, int Nf, int Lf, double kf, int lf, int Ni, int Li, double ki, int li)

Detailed Description

Namespace members compute contributions to the first order of the distorted wave Born approximation.

Function Documentation

Complex DWBA1::computeDirect1e	(	DistortingPotential const &	U,
		int	l,
		double	k
	)

Computes the one-electron part of direct T-matrix,

\[ D_\ell^{(1)} = \frac{1}{k^2} \sqrt{\frac{2\ell+1}{4\pi}} \int \chi_\ell(k,r) U(r) (\hat{j}_\ell(kr) - \chi_\ell(k,r)) \mathrm{d}r \]

Parameters

U	DistortingPotential class containing information of the distorting potential.
l	Partial wave (outgoing angular momentum).
k	Initial (= final) wavenumber.

Complex DWBA1::computeDirect2e	(	const DistortingPotential &	U,
		int	lambda,
		int	Nf,
		int	Lf,
		double	kf,
		int	lf,
		int	Ni,
		int	Li,
		double	ki,
		int	li
	)

Computes the two-electron part of the direct T-matrix,

\[ D_{l_f}^{(2)} = \frac{1}{k_i k_f} \sum_{l_i \lambda} \mathrm{i}^{l_i - l_f} \frac{\sqrt{4\pi(2l_i+1)}}{2\lambda + 1} G_{L_i M_i \lambda M_f-M_i}^{L_f M_f} G_{l_f M_i-M_f \lambda M_f-M_i}^{l_i 0} I_{\mathrm{dir}} \ , \]

\[ I_{\mathrm{dir}} = \int\int \chi_{l_f}(k_f,r_2) \psi_{L_f}(E_f,r_1) \left(\frac{r_<^\lambda}{r_>^{\lambda+1}}-\frac{\delta_\lambda^0}{r_2}\right) \psi_{L_i}(E_i,r_1) \chi_{l_i}(k_i,r_2) \mathrm{d}r_1 \mathrm{d}r_2 \ . \]

Parameters

U	DistortingPotential class containing information of the distorting potential.
lambda	Multipole moment.
Nf	Principal quantum number of the final state.
Lf	Orbital quantum number of the final state.
kf	Final projectile wave number.
lf	Final projectile partial wave.
Ni	Principal quantum number of the initial state.
Li	Orbital quantum number of the initial state.
ki	Initial projectile wave number.
li	Initial projectile partial wave.

Complex DWBA1::computeExchange1e	(	DistortingPotential const &	U,
		int	Ni,
		int	Li,
		double	ki,
		int	Nf,
		int	Lf,
		double	kf
	)

Computes the one-electron part of exchange T-matrix,

\[ E^{(1)} = -\frac{1}{k_i k_f} \mathrm{i}^{L_f-L_i} \sqrt{\frac{2L_f+1}{4\pi}} \int \chi_{L_i}(k_f,r) U_f(r) \psi_{L_i}(E_i,r) \mathrm{d}r \int \psi_{L_f}(E_f,r) \chi_{L_f}(k_i,r) \mathrm{d}r \]

Parameters

U	DistortingPotential class containing information of the distorting potential.
Ni	Initial atomic principal quantum number.
Li	Initial atomic orbital quantum number.
ki	Initial projectile wavenumber.
Nf	Final atomic principal quantum number.
Lf	Final atomic orbital quantum number.
kf	Final projectile wavenumber.

Complex DWBA1::computeExchange2e	(	const DistortingPotential &	U,
		int	lambda,
		int	Nf,
		int	Lf,
		double	kf,
		int	lf,
		int	Ni,
		int	Li,
		double	ki,
		int	li
	)

Computes the two-electron part of the exchange T-matrix,

\[ E_{l_f}^{(2)} = \frac{1}{k_i k_f} \sum_{l_i \lambda} \mathrm{i}^{l_i - l_f} \frac{\sqrt{4\pi(2l_i+1)}}{2\lambda + 1} G_{l_i 0 \lambda M_f}^{L_f M_f} G_{l_f M_i-M_f \lambda M_f}^{L_i M_i} I_{\mathrm{exc}} \ , \]

\[ I_{\mathrm{dir}} = \int\int \chi_{l_f}(k_f,r_2) \psi_{L_f}(E_f,r_1) \left(\frac{r_<^\lambda}{r_>^{\lambda+1}}-\frac{\delta_\lambda^0}{r_2}\right) \psi_{L_i}(E_i,r_2) \chi_{l_i}(k_i,r_1) \mathrm{d}r_1 \mathrm{d}r_2 \ . \]

Parameters

U	DistortingPotential class containing information of the distorting potential.
lambda	Multipole moment.
Nf	Principal quantum number of the final state.
Lf	Orbital quantum number of the final state.
kf	Final projectile wave number.
lf	Final projectile partial wave.
Ni	Principal quantum number of the initial state.
Li	Orbital quantum number of the initial state.
ki	Initial projectile wave number.
li	Initial projectile partial wave.