Intermediate abstract base class for all EM relativistic multipole operators. More...

#include <EM_multipole_base.hpp>

Inheritance diagram for DiracOperator::EM_multipole:

Public Member Functions
const SphericalBessel::JL_table *	jl () const
	Returns the precomputed Bessel table pointer (may be nullptr).

std::string	name () const override
	Returns a human-readable label, e.g. "T^E_1", "T^M5_2", "t_1", "P_1".

double	angularF (const int ka, const int kb) const override
	Angular factor linking the radial integral to the reduced matrix element: \( \langle a \\| h \\| b \rangle = F(\kappa_a,\kappa_b) \cdot \int \! dr \).

void	updateRank (int new_K) override
	Updates the tensor rank and adjusts parity accordingly.

std::unique_ptr< TensorOperator >	clone () const override
	Creates a fully independent copy of this operator at its current (rank, frequency) state via the MultipoleOperator factory.

	EM_multipole (const EM_multipole &)=default

EM_multipole &	operator= (const EM_multipole &)=default

	EM_multipole (EM_multipole &&)=default

EM_multipole &	operator= (EM_multipole &&)=default

Public Member Functions inherited from DiracOperator::TensorOperator
	TensorOperator (const TensorOperator &)=default

TensorOperator &	operator= (const TensorOperator &)=default

	TensorOperator (TensorOperator &&)=default

TensorOperator &	operator= (TensorOperator &&)=default

bool	freqDependantQ () const

bool	isZero (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	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 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 (int twoja, 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
	EM_multipole (int rank_k, Parity pi, double constant, const std::vector< double > &vec, Realness RorI, bool freq_dep, const Grid grid, char type, char comp, bool low_q, const SphericalBessel::JL_table jl=nullptr, char form='V')
	Initialise the EM_multipole base layer.

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
const Grid *	m_grid {nullptr}

double	m_omega
	Current frequency; cached by each derived updateFrequency().

char	m_type {}

char	m_comp {}

bool	m_low_q {}

char	m_form {}

const SphericalBessel::JL_table *	m_jl {nullptr}

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

Intermediate abstract base class for all EM relativistic multipole operators.

These are the \( t^K_Q \tilde\gamma \), \( T^{(\sigma)}_{KQ} \tilde\gamma \) operators from the vector expansion:

\[ \begin{align} e^{i\vec{q}\cdot\vec{r}} &= \sqrt{4\pi}\sum_{KQ}\sqrt{[K]} \, i^K \, {Y^*_{KQ}}{(\hat q)} \, t^K_Q(q,r),\\ \vec{\alpha} \, e^{i\vec{q}\cdot\vec{r}} & = \sqrt{4\pi} \sum_{KQ\sigma} \sqrt{[K]} \, i^{K-\sigma} \, \vec{Y}_{KQ}^{(\sigma)*}(\hat{{q}}) \, T^{(\sigma)}_{KQ}, \end{align} \]

with \( \tilde\gamma = 1,\) \( \gamma^5, \) \( \gamma^0, \) \( i\gamma^0\gamma^5 \) for vector (V), axial(pseudo)-vector (A), scalar (S), or pseudoscalar (P).

Stores the construction parameters needed to reconstruct the concrete operator via the MultipoleOperator factory, enabling type-erased cloning without the caller knowing the derived type.

Specifically, the stored parameters are: a pointer to the radial grid, the current frequency omega (updated by each derived class's updateFrequency()), the Lorentz type character m_type, the component character m_comp, the low-q flag m_low_q, an optional Bessel table pointer m_jl (shallow-owned; shared between original and clone), and a form character m_form (used to distinguish the length-form electric operator VEk_Len from the velocity-form VEk).

All concrete EM multipole operators VEk, VMk, VLk, Phik, Sk, AEk, ALk, AMk, Phi5k, S5k, and their low-q counterparts derive from this class.

Note: This class does not implement angularF() and so remains abstract. Operators must be constructed via the concrete derived types or the MultipoleOperator factory.

Constructor & Destructor Documentation

◆ EM_multipole()

DiracOperator::EM_multipole::EM_multipole	(	int	rank_k,
		Parity	pi,
		double	constant,
		const std::vector< double > &	vec,
		Realness	RorI,
		bool	freq_dep,
		const Grid *	grid,
		char	type,
		char	comp,
		bool	low_q,
		const SphericalBessel::JL_table *	jl = `nullptr`,
		char	form = `'V'`
	)

inlineprotected

Initialise the EM_multipole base layer.

Called exclusively from derived-class constructors.

Parameters

rank_k	Tensor rank of the operator.
pi	Parity.
constant	Overall multiplicative constant.
vec	Radial vector (usually gr.r(), sometimes empty).
RorI	Real or imaginary matrix elements.
freq_dep	True if the operator is frequency-dependent.
grid	Pointer to the radial Grid (stored for clone()).
type	Lorentz type: 'V', 'A', 'S', or 'P'.
comp	Component: 'E', 'M', 'L', or 'T'.
low_q	True for the low-momentum (long-wavelength) approximation.
jl	Optional pointer to a precomputed Bessel table.
form	'V' (velocity/V-form) or 'L' (length-form, VEk_Len only).

Member Function Documentation

◆ jl()

const SphericalBessel::JL_table * DiracOperator::EM_multipole::jl ( ) const

inline

Returns the precomputed Bessel table pointer (may be nullptr).

◆ name()

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

inlineoverridevirtual

Returns a human-readable label, e.g. "T^E_1", "T^M5_2", "t_1", "P_1".

Reimplemented from DiracOperator::TensorOperator.

◆ angularF()

double DiracOperator::EM_multipole::angularF	(	const int	ka,
		const int	kb
	)		const

inlineoverridevirtual

Angular factor linking the radial integral to the reduced matrix element: \( \langle a \| h \| b \rangle = F(\kappa_a,\kappa_b) \cdot \int \! dr \).

Returns \( C^K(\kappa_a, \kappa_b) \) or \( C^K(\kappa_a, -\kappa_b) \) depending on the Lorentz structure. The flipped form applies to: vector-magnetic (VM), all axial components except axial-magnetic (AE, AL, AT), and pseudoscalar (P).

Note: \( C^K(\kappa_a,-\kappa_b) = C^K(-\kappa_a,\kappa_b) \).; VMk_lowq overrides this with an extra \((_a+_b)\) prefactor.

Implements DiracOperator::TensorOperator.

Reimplemented in DiracOperator::VMk_lowq.

◆ updateRank()

void DiracOperator::EM_multipole::updateRank ( int new_K )

inlineoverridevirtual

Updates the tensor rank and adjusts parity accordingly.

Parity follows the tensor rank: even K gives even parity for most operators, but is flipped (even K odd parity) for vector-magnetic, all axial components except axial-magnetic, and pseudoscalar operators. The same flip rule as angularF() applies.

Note: Must be followed by a call to updateFrequency() to recompute the radial Bessel vectors for the new rank.

Reimplemented from DiracOperator::TensorOperator.

◆ clone()

std::unique_ptr< TensorOperator > DiracOperator::EM_multipole::clone ( ) const

overridevirtual

Creates a fully independent copy of this operator at its current (rank, frequency) state via the MultipoleOperator factory.

The Bessel table pointer m_jl is shallow-copied (the clone shares the same external table), but all computed radial vectors are regenerated independently on the first updateFrequency() call.

Returns: A std::unique_ptr<TensorOperator> to the cloned operator.

Reimplemented from DiracOperator::TensorOperator.

Member Data Documentation

◆ m_omega

double DiracOperator::EM_multipole::m_omega

protected

Initial value:

{

0.0}

Current frequency; cached by each derived updateFrequency().

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

DiracOperator/Operators/EM_multipole_base.hpp
DiracOperator/Operators/EM_multipole.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ EM_multipole()

Member Function Documentation

◆ jl()

◆ name()

◆ angularF()

◆ updateRank()

◆ clone()

Member Data Documentation

◆ m_omega