Effective VertexQED operator. More...

#include <QED.hpp>

Inheritance diagram for DiracOperator::VertexQED:

Public Member Functions
	VertexQED (const TensorOperator *const h0, const Grid &rgrid, double a=1.0, double b=1.0)

std::string	name () const override final
	Returns "name" of operator (e.g., 'E1')

std::string	units () const override final
	Returns units of operator (usually au, may be MHz, etc.)

double	angularF (const int ka, const int kb) const override final
	angularF: links radiation integral to RME. RME = <a\|\|h\|\|b> = angularF(a,b) * radial_int(a,b)

double	angularCff (int ka, int kb) const override final
	Angular factor for f_a*f_b part of radial integral.

double	angularCgg (int ka, int kb) const override final
	Angular factor for g_a*g_b part of radial integral.

double	angularCfg (int ka, int kb) const override final
	Angular factor for f_a*g_b part of radial integral.

double	angularCgf (int ka, int kb) const override final
	Angular factor for g_a*f_b part of radial integral.

	VertexQED (const DiracOperator::VertexQED &)=delete

VertexQED &	operator= (const DiracOperator::VertexQED &)=delete

Public Member Functions inherited from DiracOperator::TensorOperator
bool	freqDependantQ () const

bool	isZero (const int ka, int kb) const
	If matrix element <a\|h\|b> is zero, returns true.

bool	isZero (const DiracSpinor &Fa, const DiracSpinor &Fb) const

bool	selectrion_rule (int twoJA, int piA, int twoJB, int piB) const

virtual void	updateFrequency (const double)
	Update frequency for frequency-dependant operators.

void	scale (double lambda)
	Permanently re-scales the operator by constant, lambda.

const std::vector< double > &	getv () const
	Returns a const ref to vector v.

double	getc () const
	Returns a const ref to constant c.

int	get_d_order () const

bool	imaginaryQ () const
	returns true if operator is imaginary (has imag MEs)

int	rank () const
	Rank k of operator.

int	parity () const
	returns parity, as integer (+1 or -1)

int	symm_sign (const DiracSpinor &Fa, const DiracSpinor &Fb) const
	returns relative sign between <a\|\|x\|\|b> and <b\|\|x\|\|a>

virtual DiracSpinor	radial_rhs (const int kappa_a, const DiracSpinor &Fb) const
	radial_int = Fa * radial_rhs(a, Fb) (a needed for angular factor)

virtual double	radialIntegral (const DiracSpinor &Fa, const DiracSpinor &Fb) const
	Radial part of integral R_ab = (Fa\|t\|Fb).

double	rme3js (const int twoja, const int twojb, int two_mb=1, int two_q=0) const
	ME = rme3js * RME.

DiracSpinor	reduced_rhs (const int ka, const DiracSpinor &Fb) const
	<a\|\|h\|\|b> = Fa * reduced_rhs(a, Fb) (a needed for angular factor)

DiracSpinor	reduced_lhs (const int ka, const DiracSpinor &Fb) const
	<b\|\|h\|\|a> = Fa * reduced_lhs(a, Fb) (a needed for angular factor)

double	reducedME (const DiracSpinor &Fa, const DiracSpinor &Fb) const
	The reduced matrix element.

double	fullME (const DiracSpinor &Fa, const DiracSpinor &Fb, std::optional< int > two_ma=std::nullopt, std::optional< int > two_mb=std::nullopt, std::optional< int > two_q=std::nullopt) const
	Returns "full" matrix element, for optional (ma, mb, q) [taken as int 2*]. If not specified, returns z-component (q=0), with ma=mb=min(ja,jb)

double	matel_factor (MatrixElementType type, int twoJa, int twoJb) const
	Converts reduced matrix element to different "type" (MatrixElementType)

double	matel_factor (MatrixElementType type, const DiracSpinor &Fa, const DiracSpinor &Fb) const

Static Public Member Functions
static double	a (double z)
	Fitting factor for hyperfine. Default a(Z)

static std::vector< double >	vertex_func (const Grid &rgrid, double a, double b, std::vector< double > v={})
	Takes existing radial vector, multiplies by:

Additional Inherited Members
Protected Member Functions inherited from DiracOperator::TensorOperator
	TensorOperator (int rank_k, Parity pi, double constant=1.0, const std::vector< double > &vec={}, int diff_order=0, Realness RorI=Realness::real, bool freq_dep=false)
	Constructs a tensor operator description.

Protected Attributes inherited from DiracOperator::TensorOperator
int	m_rank

Parity	m_parity

int	m_diff_order

Realness	opC

bool	m_freqDependantQ {false}

double	m_constant

std::vector< double >	m_vec

Detailed Description

Effective VertexQED operator.

Takes in any TensorOperator (DiracOperator) h, and forms the corresponding effective QED vertex operator, defined:

\[ \hat h_{\rm vertex} = A \alpha \exp(-b r / \lambda_c) \]

where

\[ \lambda_c = 1/ \alpha \approx 137 \]

A and b are fitting factors; typically b=1

Member Function Documentation

◆ name()

std::string DiracOperator::VertexQED::name ( ) const

inlinefinaloverridevirtual

Returns "name" of operator (e.g., 'E1')

Reimplemented from DiracOperator::TensorOperator.

◆ units()

std::string DiracOperator::VertexQED::units ( ) const

inlinefinaloverridevirtual

Returns units of operator (usually au, may be MHz, etc.)

Reimplemented from DiracOperator::TensorOperator.

◆ angularF()

double DiracOperator::VertexQED::angularF	(	const int	,
		const int
	)		const

inlinefinaloverridevirtual

angularF: links radiation integral to RME. RME = <a||h||b> = angularF(a,b) * radial_int(a,b)

Implements DiracOperator::TensorOperator.

◆ angularCff()

double DiracOperator::VertexQED::angularCff	(	int	,
		int
	)		const

inlinefinaloverridevirtual

Angular factor for f_a*f_b part of radial integral.

Often constant, though sometimes depends on \(\kappa_a,\kappa_b\)
\[ \int_0^\infty v(r)\left( C_{ff}f_a(r)f_b(r) + C_{fg}f_a(r)g_b(r) + C_{gf}g_a(r)f_b(r) + C_{gg}g_a(r)g_b(r) \right)\,{\rm d}r \]

Reimplemented from DiracOperator::TensorOperator.

◆ angularCgg()

double DiracOperator::VertexQED::angularCgg	(	int	,
		int
	)		const

inlinefinaloverridevirtual

Angular factor for g_a*g_b part of radial integral.

Reimplemented from DiracOperator::TensorOperator.

◆ angularCfg()

double DiracOperator::VertexQED::angularCfg	(	int	,
		int
	)		const

inlinefinaloverridevirtual

Angular factor for f_a*g_b part of radial integral.

Reimplemented from DiracOperator::TensorOperator.

◆ angularCgf()

double DiracOperator::VertexQED::angularCgf	(	int	,
		int
	)		const

inlinefinaloverridevirtual

Angular factor for g_a*f_b part of radial integral.

Reimplemented from DiracOperator::TensorOperator.

◆ a()

static double DiracOperator::VertexQED::a ( double z )

inlinestatic

Fitting factor for hyperfine. Default a(Z)

◆ vertex_func()

static std::vector< double > DiracOperator::VertexQED::vertex_func	(	const Grid &	rgrid,
		double	a,
		double	b,
		std::vector< double >	v = `{}`
	)

inlinestatic

Takes existing radial vector, multiplies by:

a(Z) * a0 * exp( - b * r / a0). a0 = alpha = 1/137. b=1 by default. A should be fitted. a(Z) = 1.0 + 28.5/Z nb: can give it an empty vector, to just get the exponential function

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

DiracOperator/Operators/QED.hpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ name()

◆ units()

◆ angularF()

◆ angularCff()

◆ angularCgg()

◆ angularCfg()

◆ angularCgf()

◆ a()

◆ vertex_func()