Scalar multipole operator: \( S_K = t^K(q)\gamma^0 \). More...

#include <EM_multipole.hpp>

Inheritance diagram for DiracOperator::Sk:

Public Member Functions
	Sk (const Grid &gr, int K, double omega, const SphericalBessel::JL_table *jl=nullptr)

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

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

void	updateFrequency (const double omega) override final
	nb: q = alpha*omega!

	Sk (const Sk &other)

Sk &	operator= (const Sk &other)

Public Member Functions inherited from DiracOperator::EM_multipole
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

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.

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

Additional Inherited Members
Protected Member Functions inherited from 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')
	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 inherited from DiracOperator::EM_multipole
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

Scalar multipole operator: \( S_K = t^K(q)\gamma^0 \).

nb: q = alpha*omega, so "omega" = c*q
Implements the scalar multipole operator whose radial factor is e^{i q r} (represented via spherical Bessel functions j_L(q*r)). The operator includes the gamma^0 Dirac matrix structure.
The constructor takes an optional const SphericalBessel::JL_table *jl to enable lookup from a precomputed table for improved performance.
Note: The q value for jL(qr) will be the nearest to the requested q
- you should ensure the lookup table is close enough, or this can lead to errors.

Member Function Documentation

◆ radial_rhs()

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

finaloverridevirtual

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::Sk::radialIntegral	(	const DiracSpinor &	Fa,
		const DiracSpinor &	Fb
	)		const

finaloverridevirtual

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 from DiracOperator::TensorOperator.

◆ updateFrequency()

void DiracOperator::Sk::updateFrequency ( const double omega )

finaloverridevirtual

nb: q = alpha*omega!

Reimplemented from DiracOperator::TensorOperator.

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

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

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ radial_rhs()

◆ radialIntegral()

◆ updateFrequency()