ExternalField Namespace Reference

Calculates many-body corrections (RPA) to matrix elements of external field. More...

Classes
struct	MEdata
	Small struct to store calculated matrix elements. More...
class	CorePolarisation
	Virtual Core Polarisation class, for <a||dV||b>. See TDHF, DiagramRPA, etc. More...
class	DiagramRPA
	RPA correction to matrix elements, using Diagram technique. More...
class	DiagramRPA0_jL
	RPA correction to matrix elements, using Diagram technique. More...
class	TDHF
	Uses time-dependent Hartree-Fock method to include core-polarisation (RPA) corrections to matrix elements of some external field operator. More...
class	TDHFbasis
	Similar to the time-dependent Hartree-Fock method, but expands dPsi corrections using a basis to include core-polarisation (RPA) corrections to matrix elements of some external field operator. More...

Enumerations
enum class	Method {   TDHF , basis , diagram , none ,   Error }
enum class	dPsiType { X , Y }
enum class	StateType { bra , ket }

Functions
std::vector< MEdata >	calcMatrixElements (const std::vector< DiracSpinor > &b_orbs, const std::vector< DiracSpinor > &a_orbs, DiracOperator::TensorOperator *const h, CorePolarisation *const dV, double omega, bool each_freq, bool diagonal, bool off_diagonal, bool calculate_both)
Coulomb::meTable< double >	me_table (const std::vector< DiracSpinor > &a_orbs, const std::vector< DiracSpinor > &b_orbs, const DiracOperator::TensorOperator *h, const CorePolarisation *dV=nullptr, const MBPT::StructureRad *srn=nullptr, std::optional< double > omega={})
	Fills me_table with MEs, <a||h||b> and <b||h||a>. Required to set omega for freq. dependent operators initially.
std::unique_ptr< CorePolarisation >	make_rpa (const std::string &method, const DiracOperator::TensorOperator *h, const HF::HartreeFock *vhf, bool print, const std::vector< DiracSpinor > &basis, const std::string &identity)
std::vector< MEdata >	calcMatrixElements (const std::vector< DiracSpinor > &orbs, DiracOperator::TensorOperator *const h, CorePolarisation *const dV=nullptr, double omega=0.0, bool each_freq=false, bool diagonal=true, bool off_diagonal=true, bool calculate_both=false)
Coulomb::meTable< double >	me_table (const std::vector< DiracSpinor > &a_orbs, const DiracOperator::TensorOperator *h, const CorePolarisation *dV=nullptr, const MBPT::StructureRad *srn=nullptr, std::optional< double > omega={})
	Fills me_table with MEs. Required to set omega for freq. dependent operators initially.
Method	ParseMethod (std::string_view str)
DiracSpinor	solveMixedState (const DiracSpinor &Fa, double omega, const std::vector< double > &vl, double alpha, const std::vector< DiracSpinor > &core, const DiracSpinor &Fs, double eps_target=1.0e-9, const MBPT::CorrelationPotential *const Sigma=nullptr, const HF::Breit *const VBr=nullptr, const std::vector< double > &H_mag={})
	Solves Mixed States (TDHF) equation, inhomogenous equation, with Hartree-Fock Hamiltonian, including exchange. More...
void	solveMixedState (DiracSpinor &dF, const DiracSpinor &Fa, double omega, const std::vector< double > &vl, double alpha, const std::vector< DiracSpinor > &core, const DiracSpinor &Fs, double eps_target=1.0e-9, const MBPT::CorrelationPotential *const Sigma=nullptr, const HF::Breit *const VBr=nullptr, const std::vector< double > &H_mag={})
	Solves Mixed States (TDHF) equation, inhomogenous equation, staring from existing approximate solition, dF. More...
DiracSpinor	solveMixedState (const DiracSpinor &Fa, double omega, const DiracSpinor &Fs, const HF::HartreeFock *const hf, double eps_target=1.0e-9, const MBPT::CorrelationPotential *const Sigma=nullptr)
	Solves Mixed States (TDHF) equation. Overload; takes hf object.
void	solveMixedState (DiracSpinor &dF, const DiracSpinor &Fa, double omega, const DiracSpinor &Fs, const HF::HartreeFock *const hf, double eps_target=1.0e-9, const MBPT::CorrelationPotential *const Sigma=nullptr)
	Solves Mixed States (TDHF) equation. Overload; takes hf object.
DiracSpinor	solveMixedState_basis (const DiracSpinor &Fa, const DiracSpinor &hFa, double omega, const std::vector< DiracSpinor > &basis)
	Directly findes dF = \sum_n |n><n|hFa> / (ea - en + omega) - mainly for tests.

Variables
constexpr bool	print_final_eps = false
constexpr bool	print_each_eps = false

Detailed Description

Calculates many-body corrections (RPA) to matrix elements of external field.

External field: Mixed-states + Core Polarisation.

Function Documentation

solveMixedState() [1/2]

DiracSpinor ExternalField::solveMixedState	(	const DiracSpinor &	Fa,
		double	omega,
		const std::vector< double > &	vl,
		double	alpha,
		const std::vector< DiracSpinor > &	core,
		const DiracSpinor &	Fs,
		double	eps_target = 1.0e-9,
		const MBPT::CorrelationPotential *const	Sigma = nullptr,
		const HF::Breit *const	VBr = nullptr,
		const std::vector< double > &	H_mag = {}
	)

Solves Mixed States (TDHF) equation, inhomogenous equation, with Hartree-Fock Hamiltonian, including exchange.

Solves

\[ (H_{\rm HF} - \epsilon - \omega)\delta\phi + F_S = 0 \]

for \(\delta\phi\) (dF). Typically

\[ F_S = (\hat h + \delta V_h - \delta \varepsilon) \phi. \]

Requires unperturbed orbital, Fa, a local potential (vl = vnuc + vdir), set of core electrons (for exchange). kappa (Dirac Q. number) of solution will have that of Fs. Note sign on hFa (this is \(\hat h \phi\), not \(-\hat h \phi\)). eps_target is convergance goal for solving the inhomogenous dif. equation. Can optionally include Sigma (correlations), Breit, and Magnetic part of QED radiative potential (electric part should be included in vl).

solveMixedState() [2/2]

void ExternalField::solveMixedState	(	DiracSpinor &	dF,
		const DiracSpinor &	Fa,
		double	omega,
		const std::vector< double > &	vl,
		double	alpha,
		const std::vector< DiracSpinor > &	core,
		const DiracSpinor &	Fs,
		double	eps_target = 1.0e-9,
		const MBPT::CorrelationPotential *const	Sigma = nullptr,
		const HF::Breit *const	VBr = nullptr,
		const std::vector< double > &	H_mag = {}
	)

Solves Mixed States (TDHF) equation, inhomogenous equation, staring from existing approximate solition, dF.

As above [solveMixedState], but starts with existing solution dF (may be 'zero'). If the existing solution is already approximate solution, this allows equation to be solved much quicker.