FGRP Namespace Reference

Flambaum-Ginges Radiative potential. More...

Namespaces
namespace	Fit
	Fitting factors from Ginges Berengut, Phys. Rev. A 93, 052509 (2016).

Enumerations
enum class	IntType { Linear , Log }

Functions
double	V_Uehling (double Z, double r, double rN=0.0)
	Uehling potential (r, rN in atomic units)
double	H_Magnetic (double Z, double r, double rN=0.0)
	Magnetic form-factor (r, rN in atomic units)
double	V_SEl (double Z, double r, double rN=0.0)
	Low-freq electric SE (NOT including Bl) (r, rN in atomic units)
double	V_SEh (double Z, double r, double rN=0.0)
	High-freq electric SE (NOT including Al) (r, rN in atomic units)
double	V_WK (double Z, double r, double)
	Effective Wickman-Kroll; not including FNS corrections.
double	t_integral (double(*f)(double, void *), std::vector< double > params, double eps=1.0e-6)
	Function that performs the t integral over [1,infinity)
double	Q_MLVP (double r, double rN=0.0)
	Magnetic-loop vacuum polarisation, includes finite-nuclear size.
template<IntType IT = IntType::Linear>
double	r_integral (std::function< double(double)> f, double a, double b, long unsigned n_pts=1000)
	Function that performs the r integral over [a,b] using mixed-quadrature.

Variables
constexpr double	alpha = 1.0 / 137.035999084
constexpr double	lam_c = alpha

Detailed Description

Flambaum-Ginges Radiative potential.

First introduced in: V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005).

With finite-nuclear-size corrections, and updated fitting factors, from; J. S. M. Ginges and J. C. Berengut, Phys. Rev. A 93, 052509 (2016). J. S. M. Ginges and J. C. Berengut, J. Phys. B 49, 095001 (2016).

Note: High- and low- frequency V(r) do NOT include A or B fitting coeficients. All radii (r and rN) are given in atomic units Sign convention: H -> H - V_rad V_rad = V_Uehling + V_SEh + V_SEl + V_WK + i(g.n())H_Magnetic

Function Documentation

V_Uehling()

double FGRP::V_Uehling	(	double	Z,
		double	r,
		double	rN
	)

Uehling potential (r, rN in atomic units)

H_Magnetic()

double FGRP::H_Magnetic	(	double	Z,
		double	r,
		double	rN
	)

Magnetic form-factor (r, rN in atomic units)

V_SEl()

double FGRP::V_SEl	(	double	Z,
		double	r,
		double	rN
	)

Low-freq electric SE (NOT including Bl) (r, rN in atomic units)

V_SEh()

double FGRP::V_SEh	(	double	Z,
		double	r,
		double	rN
	)

High-freq electric SE (NOT including Al) (r, rN in atomic units)

V_WK()

double FGRP::V_WK	(	double	Z,
		double	r,
		double
	)

Effective Wickman-Kroll; not including FNS corrections.

t_integral()

double FGRP::t_integral	(	double(*)(double, void *)	f,
		std::vector< double >	params,
		double	eps
	)

Function that performs the t integral over [1,infinity)

Q_MLVP()

double FGRP::Q_MLVP	(	double	r,
		double	rN
	)

Magnetic-loop vacuum polarisation, includes finite-nuclear size.

r_integral()

template<IntType IT = IntType::Linear>

double FGRP::r_integral	(	std::function< double(double)>	f,
		double	a,
		double	b,
		long unsigned	n_pts = 1000
	)

Function that performs the r integral over [a,b] using mixed-quadrature.