MBPT::StructureRad

Calculates Structure Radiation + Normalisation of states, using diagram method. More...

#include <StructureRad.hpp>

Public Member Functions
	StructureRad (const std::vector< DiracSpinor > &basis, double en_core, std::pair< int, int > nminmax={0, 999}, const std::string &Qk_fname="", const std::vector< double > &fk={}, const std::vector< double > &etak={})
const std::vector< DiracSpinor > &	core () const
const std::vector< DiracSpinor > &	excited () const
const Coulomb::YkTable &	Yk () const
const std::optional< Coulomb::QkTable > &	Qk () const
std::pair< double, double >	srTB (const DiracOperator::TensorOperator *const h, const DiracSpinor &w, const DiracSpinor &v, double omega=0.0, const ExternalField::CorePolarisation *const dV=nullptr) const
	Returns sum of Top+Bottom (SR) diagrams, reduced ME: <w||T+B||v>. Returns a pair: {TB, TB+dV}: second includes RPA (if dV given)
std::pair< double, double >	srC (const DiracOperator::TensorOperator *const h, const DiracSpinor &w, const DiracSpinor &v, const ExternalField::CorePolarisation *const dV=nullptr) const
	Returns Centre (SR) diagrams, reduced ME: <w||C||v>. Returns a pair: {C, C+dV}: second includes RPA (if dV given)
std::pair< double, double >	norm (const DiracOperator::TensorOperator *const h, const DiracSpinor &w, const DiracSpinor &v, const ExternalField::CorePolarisation *const dV=nullptr) const
	Returns Normalisation of states, reduced ME: <w||h||v>_norm. Returns a pair: {N, N+dV}: second includes RPA (if dV given).
std::pair< double, double >	srn (const DiracOperator::TensorOperator *const h, const DiracSpinor &w, const DiracSpinor &v, double omega=0.0, const ExternalField::CorePolarisation *const dV=nullptr) const
	Returns sum of SR+Norm diagrams, reduced ME: <w||T+B+C+N||v>. Returns a pair: {SRN, SRN+dV}: second includes RPA (if dV given)
double	f_root_scr (int k) const
	Effective screening factor for Coulomb lines.
double	eta_hp (int k) const
	Effective hole-particle factor for polarisation loops.
std::pair< double, double >	BO (const DiracOperator::TensorOperator *const h, const DiracSpinor &w, const DiracSpinor &v, const ExternalField::CorePolarisation *const dV=nullptr, double fw=1.0, double fv=1.0) const
	Returns Brueckner orbital contribution to the, reduced ME: <w||h||v>_norm. Returns a pair: {N, N+dV}: second includes RPA (if dV given). More...
Coulomb::meTable< std::pair< double, double > >	srn_table (const DiracOperator::TensorOperator *const h, const std::vector< DiracSpinor > &as, const std::vector< DiracSpinor > &tbs={}, double omega=0.0, const ExternalField::CorePolarisation *const dV=nullptr) const
	constructs an me table of {srn, srn+dv} for each pair or {a,b}

Detailed Description

Calculates Structure Radiation + Normalisation of states, using diagram method.

Three functions: srTB(), srC(), norm(). Structure radiation is sum of srTB()+srC(); norm() gives normalisation of states.

• Typically, one should use splines for the 'legs' (outer states) of diagrams. However, code is written such that {w,v} (the valence states) always appear as the first state in the Q integrals; thus those states are always directly integrated (other states may use the existing y^k integrals, which were calculated using the spline states) * unless using QkTable (see below).
• For using spline states as legs: This means you must typically ensure basis is large enough to make relevant valence states "physical"
• The user should check if the zeroth order <w|t|v> matches closely between valence/spline states. If not, basis/cavity is too small and SR+N probably meaningless
• Option to use QkTable to calculate SR+N. Otherwise, calculates Coulomb integrals on-the-fly. If QkTable is used, leads to ~10x speed-up, but uses large amount of memory. Also, using QkTable means spline states are used for "legs" of diagrams.
• Formulas are presented in (for example): W. R. Johnson, Z. W. Liu, and J. Sapirstein, At. Data Nucl. Data Tables 64, 279 (1996). doi:10.1006/adnd.1996.0024

Constructor & Destructor Documentation

StructureRad()

MBPT::StructureRad::StructureRad	(	const std::vector< DiracSpinor > &	basis,
		double	en_core,
		std::pair< int, int >	nminmax = {0, 999},
		const std::string &	Qk_fname = "",
		const std::vector< double > &	fk = {},
		const std::vector< double > &	etak = {}
	)

en_core: is defined such that states with e < en_core are in the core, while states with e > en_core are not. Typcially: en_core = max(e_core)-min(e_valence) = wf.FermiLevel(). nminmax is a pair{min, max}: we only used core states with n>=min, and only uses excited states with n<=nmax in the summations. Qk_fname is filename for QkTable - if given it will read/write QkTable to this file, and use QkTable to calculate SR. This ldeads to ~10x speedup in calculation, at cost of using much more memory

Member Function Documentation

BO()

std::pair< double, double > MBPT::StructureRad::BO	(	const DiracOperator::TensorOperator *const	h,
		const DiracSpinor &	w,
		const DiracSpinor &	v,
		const ExternalField::CorePolarisation *const	dV = nullptr,
		double	fw = 1.0,
		double	fv = 1.0
	)		const

Returns Brueckner orbital contribution to the, reduced ME: <w||h||v>_norm. Returns a pair: {N, N+dV}: second includes RPA (if dV given).

from 10.1006/adnd.1996.0024

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The documentation for this class was generated from the following files:

• MBPT/StructureRad.hpp
• MBPT/StructureRad.cpp