grpp_nuclear_models.c File Reference

#include "grpp_nuclear_models.h"
#include "grpp_specfunc.h"
#include <math.h>

Go to the source code of this file.

Macros
#define	M_PI   3.14159265358979323846

Functions
double	libgrpp_fermi_model_Sk (int k, double x)
double	libgrpp_fermi_model_norm_factor (double c, double a)
double	libgrpp_fermi_bubble_model_norm_factor (double c, double a, double k)
double	libgrpp_estimate_nuclear_rms_radius_johnson_1985 (int A)
double	libgrpp_estimate_nuclear_rms_radius_golovko_2008 (int A)
int	libgrpp_estimate_fermi_model_parameters (double R_rms, double *c, double *a)
double	libgrpp_coulomb_potential_point (double r, double Z)
double	libgrpp_charge_density_ball (double r, double Z, double R_rms)
double	libgrpp_coulomb_potential_ball (double r, double Z, double R_rms)
double	libgrpp_charge_density_gaussian (double r, double Z, double R_rms)
double	libgrpp_coulomb_potential_gaussian (double r, double Z, double R_rms)
double	libgrpp_charge_density_fermi (double r, double Z, double c, double a)
double	libgrpp_rms_radius_fermi (int Z, double c, double a)
double	libgrpp_coulomb_potential_fermi (double r, double Z, double c, double a)
double	libgrpp_charge_density_fermi_bubble (double r, double Z, double c, double a, double k)
double	libgrpp_rms_radius_fermi_bubble (int Z, double c, double a, double k)
double	libgrpp_coulomb_potential_fermi_bubble (double r, double Z, double c, double a, double k)

Macro Definition Documentation

M_PI

#define M_PI   3.14159265358979323846

Definition at line 20 of file grpp_nuclear_models.c.

Function Documentation

libgrpp_fermi_model_Sk()

double libgrpp_fermi_model_Sk ( int k, double x )

extern

libgrpp_fermi_model_norm_factor()

double libgrpp_fermi_model_norm_factor ( double c, double a )

extern

normalization factor for the Fermi nuclear charge distribution

Definition at line 208 of file grpp_nuclear_models.c.

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libgrpp_fermi_bubble_model_norm_factor()

double libgrpp_fermi_bubble_model_norm_factor ( double c, double a, double k )

extern

normalization factor for the "Fermi bubble" nuclear charge distribution

Definition at line 323 of file grpp_nuclear_models.c.

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libgrpp_estimate_nuclear_rms_radius_johnson_1985()

double libgrpp_estimate_nuclear_rms_radius_johnson_1985

(

int

A

)

estimate for R(rms) from: W. R. Johnson, G. Soff. The Lamb shift in hydrogen-like atoms, 1 <= Z <=>

1. At. Data Nucl. Data Tables, 33(3), 405 (1985).

A = mass number returns R(rms) in [fm] units

Definition at line 42 of file grpp_nuclear_models.c.

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libgrpp_estimate_nuclear_rms_radius_golovko_2008()

double libgrpp_estimate_nuclear_rms_radius_golovko_2008

(

int

A

)

estimate for R(rms) from: O. A. Golovko, I. A. Goidenko, I. I. Tupitsyn. Quantum electrodynamic corrections for valence electrons in Eka-Hg. Opt. Spectrosc. 104(5), 662 (2008).

A = mass number returns R(rms) in [fm] units

Definition at line 55 of file grpp_nuclear_models.c.

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libgrpp_estimate_fermi_model_parameters()

int libgrpp_estimate_fermi_model_parameters	(	double	R_rms,
		double *	c,
		double *	a )

estimate parameters of the Fermi model using default formulas for 'c' and 'a'. return -1 if such estimate cannot be performed, 1 otherwise.

units: Fermi for R_rms, c, a.

Definition at line 65 of file grpp_nuclear_models.c.

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libgrpp_coulomb_potential_point()

double libgrpp_coulomb_potential_point	(	double	r,
		double	Z )

point charge

Definition at line 88 of file grpp_nuclear_models.c.

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libgrpp_charge_density_ball()

double libgrpp_charge_density_ball	(	double	r,
		double	Z,
		double	R_rms )

uniformly charged ball: density

Definition at line 93 of file grpp_nuclear_models.c.

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libgrpp_coulomb_potential_ball()

double libgrpp_coulomb_potential_ball	(	double	r,
		double	Z,
		double	R_rms )

uniformly charged ball: potential

formula from: L. Visscher, K. G. Dyall, Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions. Atomic Data and Nuclear Data Tables, 67, 207–224 (1997)

Definition at line 111 of file grpp_nuclear_models.c.

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libgrpp_charge_density_gaussian()

double libgrpp_charge_density_gaussian	(	double	r,
		double	Z,
		double	R_rms )

Gaussian charge distribution: density

Definition at line 124 of file grpp_nuclear_models.c.

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libgrpp_coulomb_potential_gaussian()

double libgrpp_coulomb_potential_gaussian	(	double	r,
		double	Z,
		double	R_rms )

Gaussian charge distribution: potential

formula from: L. Visscher, K. G. Dyall, Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions. Atomic Data and Nuclear Data Tables, 67, 207–224 (1997)

Definition at line 139 of file grpp_nuclear_models.c.

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libgrpp_charge_density_fermi()

double libgrpp_charge_density_fermi	(	double	r,
		double	Z,
		double	c,
		double	a )

Fermi charge distribution: density

Definition at line 148 of file grpp_nuclear_models.c.

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libgrpp_rms_radius_fermi()

double libgrpp_rms_radius_fermi	(	int	Z,
		double	c,
		double	a )

Fermi charge distribution: rms radius

Definition at line 159 of file grpp_nuclear_models.c.

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libgrpp_coulomb_potential_fermi()

double libgrpp_coulomb_potential_fermi	(	double	r,
		double	Z,
		double	c,
		double	a )

Fermi charge distribution: potential

formula from: N. S. Mosyagin, A. V. Zaitsevskii, A. V. Titov Generalized relativistic effective core potentials for superheavy elements Int. J. Quantum Chem. e26076 (2019) doi: https://doi.org/10.1002/qua.26076

Definition at line 182 of file grpp_nuclear_models.c.

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libgrpp_charge_density_fermi_bubble()

double libgrpp_charge_density_fermi_bubble	(	double	r,
		double	Z,
		double	c,
		double	a,
		double	k )

"Fermi bubble" charge distribution: density

Definition at line 221 of file grpp_nuclear_models.c.

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libgrpp_rms_radius_fermi_bubble()

double libgrpp_rms_radius_fermi_bubble	(	int	Z,
		double	c,
		double	a,
		double	k )

"Fermi bubble" charge distribution: rms radius

Definition at line 233 of file grpp_nuclear_models.c.

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libgrpp_coulomb_potential_fermi_bubble()

double libgrpp_coulomb_potential_fermi_bubble	(	double	r,
		double	Z,
		double	c,
		double	a,
		double	k )

"Fermi bubble" charge distribution: potential.

derivation of the formula is based on:

F. A. Parpia and A. K. Mohanty, Relativistic basis-set calculations for atoms with Fermi nuclei. Phys. Rev. A 46, 3735 (1992) doi: 10.1103/PhysRevA.46.3735

Definition at line 267 of file grpp_nuclear_models.c.

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