General operator (virtual base class); operators derive from this. More...

#include <TensorOperator.hpp>

Inheritance diagram for DiracOperator::TensorOperator:

Public Member Functions
	TensorOperator (const TensorOperator &)=default

TensorOperator &	operator= (const TensorOperator &)=default

	TensorOperator (TensorOperator &&)=default

TensorOperator &	operator= (TensorOperator &&)=default

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

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

virtual double	angularCff (int, int) const
	Angular factor for f_a*f_b part of radial integral.

virtual double	angularCgg (int, int) const
	Angular factor for g_a*g_b part of radial integral.

virtual double	angularCfg (int, int) const
	Angular factor for f_a*g_b part of radial integral.

virtual double	angularCgf (int, int) const
	Angular factor for g_a*f_b part of radial integral.

virtual double	angularF (const int, const int) const =0
	angularF: links radiation integral to RME. RME = <a\|\|h\|\|b> = angularF(a,b) * radial_int(a,b)

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.

double	rme3js (const DiracSpinor &Fa, const DiracSpinor &Fb, 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

Protected Member Functions
	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
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

General operator (virtual base class); operators derive from this.

k is rank, c is multiplicative constant, d_order is derivative order,
pi is parity, may be Parity::even or odd.
RorI may be Realness::real or Realness::imaginary.
Note: You may not construct a TensorOperator. Instead, you must construct one of the derived 'operators' (there are some general ones); see operators.hpp for list of operators. Operators work by overrideing the angularCxx() functions and angularF().
c, v, and Cxx are included in radial integral.

Constructor & Destructor Documentation

◆ TensorOperator()

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`
	)

inlineprotected

Constructs a tensor operator description.

Initialises the basic properties of a tensor operator.

Parameters

rank_k	Tensor rank k of the operator.
pi	Parity of the operator (Parity::even or Parity::odd).
constant	Multiplicative constant c, included in the radial integral.
vec	Overall v=f(r) radial function, as std::vector array
RorI	Specifies whether the matrix element is real or imaginary (Realness::real or Realness::imaginary).
freq_dep	Indicates whether the operator depends on frequency (e.g., dynamic external fields).

Note: TensorOperator is a virtual base class and may not be constructed directly. It is intended to be initialised by derived operator classes.

Member Function Documentation

◆ isZero()

bool DiracOperator::TensorOperator::isZero	(	const int	ka,
		int	kb
	)		const

If matrix element <a|h|b> is zero, returns true.

◆ updateFrequency()

virtual void DiracOperator::TensorOperator::updateFrequency ( const double )

inlinevirtual

Update frequency for frequency-dependant operators.

Reimplemented in DiracOperator::E1v, DiracOperator::VEk_Len, DiracOperator::VEk, DiracOperator::VLk, DiracOperator::VMk, DiracOperator::Phik, DiracOperator::Sk, DiracOperator::AEk, DiracOperator::ALk, DiracOperator::AMk, DiracOperator::Phi5k, DiracOperator::S5k, DiracOperator::VMk_lowq, DiracOperator::Phik_lowq, DiracOperator::Sk_lowq, DiracOperator::AEk_lowq, DiracOperator::ALk_lowq, DiracOperator::AMk_lowq, DiracOperator::Phi5k_lowq, DiracOperator::S5k_lowq, and DiracOperator::M1.

◆ scale()

void DiracOperator::TensorOperator::scale ( double lambda )

Permanently re-scales the operator by constant, lambda.

◆ getv()

const std::vector< double > & DiracOperator::TensorOperator::getv ( ) const

inline

Returns a const ref to vector v.

◆ getc()

double DiracOperator::TensorOperator::getc ( ) const

inline

Returns a const ref to constant c.

◆ imaginaryQ()

bool DiracOperator::TensorOperator::imaginaryQ ( ) const

inline

returns true if operator is imaginary (has imag MEs)

◆ rank()

int DiracOperator::TensorOperator::rank ( ) const

inline

Rank k of operator.

◆ parity()

int DiracOperator::TensorOperator::parity ( ) const

inline

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

◆ symm_sign()

int DiracOperator::TensorOperator::symm_sign	(	const DiracSpinor &	Fa,
		const DiracSpinor &	Fb
	)		const

inline

returns relative sign between <a||x||b> and <b||x||a>

◆ name()

virtual std::string DiracOperator::TensorOperator::name ( ) const

inlinevirtual

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

◆ units()

virtual std::string DiracOperator::TensorOperator::units ( ) const

inlinevirtual

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

Reimplemented in DiracOperator::Ek, DiracOperator::fieldshift, DiracOperator::j, DiracOperator::l, DiracOperator::s, DiracOperator::E1v, DiracOperator::hfs, DiracOperator::jL, DiracOperator::M1, DiracOperator::M1nr, DiracOperator::PNCnsi, DiracOperator::Vrad, DiracOperator::VertexQED, DiracOperator::MLVP, DiracOperator::RadialF, and DiracOperator::dr.

◆ angularCff()

virtual double DiracOperator::TensorOperator::angularCff	(	int	,
		int
	)		const

inlinevirtual

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 in DiracOperator::VertexQED, DiracOperator::MLVP, DiracOperator::jL, DiracOperator::ig0g5jL, DiracOperator::ScalarOperator, DiracOperator::E1v, DiracOperator::VEk_lowq, DiracOperator::VMk_lowq, DiracOperator::VLk_lowq, DiracOperator::hfs, DiracOperator::g0jL, DiracOperator::ig5jL, DiracOperator::M1, and DiracOperator::NullOperator.

◆ angularCgg()

virtual double DiracOperator::TensorOperator::angularCgg	(	int	,
		int
	)		const

inlinevirtual

Angular factor for g_a*g_b part of radial integral.

Reimplemented in DiracOperator::VertexQED, DiracOperator::MLVP, DiracOperator::jL, DiracOperator::ig0g5jL, DiracOperator::ScalarOperator, DiracOperator::E1v, DiracOperator::VEk_lowq, DiracOperator::VMk_lowq, DiracOperator::VLk_lowq, DiracOperator::hfs, DiracOperator::g0jL, DiracOperator::ig5jL, DiracOperator::M1, and DiracOperator::NullOperator.

◆ angularCfg()

virtual double DiracOperator::TensorOperator::angularCfg	(	int	,
		int
	)		const

inlinevirtual

Angular factor for f_a*g_b part of radial integral.

Reimplemented in DiracOperator::E1v, DiracOperator::VEk_lowq, DiracOperator::VLk_lowq, DiracOperator::VertexQED, DiracOperator::MLVP, DiracOperator::jL, DiracOperator::ig0g5jL, DiracOperator::ScalarOperator, DiracOperator::VMk_lowq, DiracOperator::hfs, DiracOperator::g0jL, DiracOperator::ig5jL, DiracOperator::M1, and DiracOperator::NullOperator.

◆ angularCgf()

virtual double DiracOperator::TensorOperator::angularCgf	(	int	,
		int
	)		const

inlinevirtual

Angular factor for g_a*f_b part of radial integral.

Reimplemented in DiracOperator::E1v, DiracOperator::VEk_lowq, DiracOperator::VLk_lowq, DiracOperator::VertexQED, DiracOperator::MLVP, DiracOperator::jL, DiracOperator::ig0g5jL, DiracOperator::ScalarOperator, DiracOperator::VMk_lowq, DiracOperator::hfs, DiracOperator::g0jL, DiracOperator::ig5jL, DiracOperator::M1, and DiracOperator::NullOperator.

◆ angularF()

virtual double DiracOperator::TensorOperator::angularF	(	const int	,
		const int
	)		const

pure virtual

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

Implemented in DiracOperator::jL, DiracOperator::ig0g5jL, DiracOperator::ScalarOperator, DiracOperator::Ek, DiracOperator::E1v, DiracOperator::VEk_Len, DiracOperator::VEk, DiracOperator::VLk, DiracOperator::VMk, DiracOperator::Phik, DiracOperator::Sk, DiracOperator::AEk, DiracOperator::ALk, DiracOperator::AMk, DiracOperator::Phi5k, DiracOperator::S5k, DiracOperator::VEk_lowq, DiracOperator::VMk_lowq, DiracOperator::VLk_lowq, DiracOperator::Phik_lowq, DiracOperator::Sk_lowq, DiracOperator::AEk_lowq, DiracOperator::ALk_lowq, DiracOperator::AMk_lowq, DiracOperator::Phi5k_lowq, DiracOperator::S5k_lowq, DiracOperator::hfs, DiracOperator::ig5jL, DiracOperator::j, DiracOperator::l, DiracOperator::s, DiracOperator::M1, DiracOperator::VertexQED, DiracOperator::MLVP, and DiracOperator::M1nr.

◆ radial_rhs()

DiracSpinor DiracOperator::TensorOperator::radial_rhs	(	const int	kappa_a,
		const DiracSpinor &	Fb
	)		const

virtual

radial_int = Fa * radial_rhs(a, Fb) (a needed for angular factor)

By default, is defined as:

\[ \delta F_{\rm b} = C_{\rm overall}\,v(r) \begin{pmatrix} C_{ff}f_b(r) + C_{fg}g_b(r) \\ C_{gf}f_b(r) + C_{gg}g_b(r) \end{pmatrix} \]

\( C_{f/g} \) are angular coeficients - see TensorOperator::angularCff

◆ radialIntegral()

double DiracOperator::TensorOperator::radialIntegral	(	const DiracSpinor &	Fa,
		const DiracSpinor &	Fb
	)		const

virtual

Radial part of integral R_ab = (Fa|t|Fb).

<a||t||b> = angularF(a,b) * radialIntegral(a,b)

The 'radial' integral \(R_{ab}\) for operator \(t\) is defined as

\[ \langle a ||t|| b \rangle \equiv R_{ab} * A_{ab} \]

where \(A_{ab}\) is TensorOperator::angularF()

By default, is implemented as:

\[ R = \int_0^\infty F_a\cdot\delta F_{\rm b} \,{\rm d}r \]

where \( \delta F_{\rm b} \) is defined in TensorOperator::radial_rhs

So, if TensorOperator::radial_rhs is defined normally, we have:

\[ C_{\rm overall}\int_0^\infty v(r)\left( C_{ff}f_a(r)f_b(r) + C_{fg}f_a(r)g_b(r) + C_{gf}g_a(r)f_b(r) + C_{gg}g_a(r)g_b(r) \right)\,{\rm d}r \]

\( C_{f/g} \) are angular coeficients - see TensorOperator::angularCff

Warning

This is defined for the "standard" case, which doesn't always suit
TensorOperator::radial_rhs may be overridden for special cases
If radial_rhs is overridden, then radialIntegral must also be_

Reimplemented in DiracOperator::VEk_Len, DiracOperator::VEk, DiracOperator::VLk, DiracOperator::VMk, DiracOperator::Phik, DiracOperator::Sk, DiracOperator::AEk, DiracOperator::ALk, DiracOperator::AMk, DiracOperator::Phi5k, DiracOperator::S5k, DiracOperator::Phik_lowq, DiracOperator::Sk_lowq, DiracOperator::AEk_lowq, DiracOperator::ALk_lowq, DiracOperator::AMk_lowq, DiracOperator::Phi5k_lowq, DiracOperator::S5k_lowq, DiracOperator::jL, DiracOperator::M1nr, and DiracOperator::Vrad.

◆ rme3js() [1/2]

double DiracOperator::TensorOperator::rme3js	(	const int	twoja,
		const int	twojb,
		int	two_mb = `1`,
		int	two_q = `0`
	)		const

ME = rme3js * RME.

◆ rme3js() [2/2]

double DiracOperator::TensorOperator::rme3js	(	const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		int	two_mb = `1`,
		int	two_q = `0`
	)		const

inline

ME = rme3js * RME.

◆ reduced_rhs()

DiracSpinor DiracOperator::TensorOperator::reduced_rhs	(	const int	ka,
		const DiracSpinor &	Fb
	)		const

<a||h||b> = Fa * reduced_rhs(a, Fb) (a needed for angular factor)

◆ reduced_lhs()

DiracSpinor DiracOperator::TensorOperator::reduced_lhs	(	const int	ka,
		const DiracSpinor &	Fb
	)		const

<b||h||a> = Fa * reduced_lhs(a, Fb) (a needed for angular factor)

◆ reducedME()

double DiracOperator::TensorOperator::reducedME	(	const DiracSpinor &	Fa,
		const DiracSpinor &	Fb
	)		const

The reduced matrix element.

◆ fullME()

double DiracOperator::TensorOperator::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)

◆ matel_factor()

double DiracOperator::TensorOperator::matel_factor	(	MatrixElementType	type,
		int	twoJa,
		int	twoJb
	)		const

Converts reduced matrix element to different "type" (MatrixElementType)

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

DiracOperator/TensorOperator.hpp
DiracOperator/TensorOperator.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TensorOperator()

Member Function Documentation

◆ isZero()

◆ updateFrequency()

◆ scale()

◆ getv()

◆ getc()

◆ imaginaryQ()

◆ rank()

◆ parity()

◆ symm_sign()

◆ name()

◆ units()

◆ angularCff()

◆ angularCgg()

◆ angularCfg()

◆ angularCgf()

◆ angularF()

◆ radial_rhs()

◆ radialIntegral()

◆ rme3js() [1/2]

◆ rme3js() [2/2]

◆ reduced_rhs()

◆ reduced_lhs()

◆ reducedME()

◆ fullME()

◆ matel_factor()