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Rank-0 (scalar) tensor operator; derives from TensorOperator with k=0.

Convenience base for scalar operators. angularF() returns \( \sqrt{2|\kappa|} \) when \( |\kappa_a|=|\kappa_b| \) , and zero otherwise. The four C_xy coefficients default to (1,0,0,1) (diagonal ff+gg), but can be set via in_g for operators with large/small component mixing (e.g., PNC operators).

#include <TensorOperator.hpp>

Inheritance diagram for DiracOperator::ScalarOperator:

Public Member Functions
	ScalarOperator (Parity pi, double in_coef, const std::vector< double > &in_v={}, const std::array< int, 4 > &in_g={1, 0, 0, 1}, Realness rori=Realness::real)
	General scalar operator constructor. in_g = {C_ff, C_fg, C_gf, C_gg}.

	ScalarOperator (const std::vector< double > &in_v={}, double in_coef=1.0)
	Convenience constructor: even-parity, real, diagonal (C_ff=C_gg=1, C_fg=C_gf=0) scalar operator.

virtual double	angularF (const int ka, const int kb) const override
	Angular factor A_ab linking the radial integral to the RME.

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
	Returns true if the operator is frequency-dependent (requires updateFrequency() calls).

bool	isZero (int ka, int kb) const
	Returns true if <a\|h\|b> = 0 by rank/parity selection rules.

bool	isZero (const DiracSpinor &Fa, const DiracSpinor &Fb) const
	Overload taking DiracSpinors; forwards to isZero(ka, kb).

bool	selectrion_rule (int twoJA, int piA, int twoJB, int piB) const
	Returns true if the matrix element is non-zero by angular momentum and parity selection rules (arguments are 2j and pi as integers).

virtual void	updateFrequency (const double)
	Updates the operator for a new frequency omega.

virtual void	updateRank (int)

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

double	getc () const
	Returns the "overall" constant c.

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 as a string (usually au, may be MHz, etc.)

double	angularCxy (uint8_t x, uint8_t y, int kappa_a, int kappa_b) const
	Dispatches to angularCff/fg/gf/gg based on component indices x, y.

virtual std::unique_ptr< TensorOperator >	clone () const
	Returns a polymorphic copy of the operator at its current state, or nullptr if cloning is not supported by the derived class.

virtual DiracSpinor	radial_rhs (const int kappa_a, const DiracSpinor &Fb) const
	Computes the right-hand spinor dF_b for the radial integral.

virtual double	radialIntegral (const DiracSpinor &Fa, const DiracSpinor &Fb) const
	Radial integral R_ab, defined by RME = angularF(a,b) * radialIntegral(a,b).

double	rme3js (int twoja, int twojb, int two_mb=1, int two_q=0) const
	3j-symbol factor linking the full ME to the RME.

double	rme3js (const DiracSpinor &Fa, const DiracSpinor &Fb, int two_mb=1, int two_q=0) const
	Overload of rme3js taking DiracSpinors.

DiracSpinor	reduced_rhs (const int ka, const DiracSpinor &Fb) const
	Returns angularF(ka,kb) * radial_rhs(ka,Fb); spinor-valued RME action on Fb, used in perturbation theory/TDHF.

DiracSpinor	reduced_lhs (const int ka, const DiracSpinor &Fb) const
	As reduced_rhs but for the conjugate direction; Fb * reduced_lhs(ka, Fb) = <b\|\|h\|\|a>.

double	reducedME (const DiracSpinor &Fa, const DiracSpinor &Fb) const
	Returns the reduced matrix element <a\|\|h\|\|b> = A_ab * R_ab.

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
	Returns the factor to convert a reduced ME to a different form (Reduced, Stretched, or HFConstant); see MatrixElementType.

double	matel_factor (MatrixElementType type, const DiracSpinor &Fa, const DiracSpinor &Fb) const
	Overload of matel_factor taking DiracSpinors.

Protected Member Functions
virtual double	angularCff (int, int) const override
	Angular coefficient C_ff for the f_a*f_b term of the radial integral.

virtual double	angularCgg (int, int) const override
	Angular coefficient C_gg for the g_a*g_b term of the radial integral.

virtual double	angularCfg (int, int) const override
	Angular coefficient C_fg for the f_a*g_b term of the radial integral.

virtual double	angularCgf (int, int) const override
	Angular coefficient C_gf for the g_a*f_b term of the radial integral.

Protected Member Functions inherited from DiracOperator::TensorOperator
	TensorOperator (int rank_k, Parity pi, double constant=1.0, const std::vector< double > &vec={}, Realness RorI=Realness::real, bool freq_dep=false)
	Constructs a specific tensor operator. Called by derived classes.

Additional Inherited Members
Protected Attributes inherited from DiracOperator::TensorOperator
int	m_rank

Parity	m_parity

Realness	m_Realness

bool	m_freqDependantQ {false}

double	m_constant

std::vector< double >	m_vec

Constructor & Destructor Documentation

◆ ScalarOperator() [1/2]

DiracOperator::ScalarOperator::ScalarOperator	(	Parity	pi,
		double	in_coef,
		const std::vector< double > &	in_v = `{}`,
		const std::array< int, 4 > &	in_g = `{1, 0, 0, 1}`,
		Realness	rori = `Realness::real`
	)

inline

General scalar operator constructor. in_g = {C_ff, C_fg, C_gf, C_gg}.

◆ ScalarOperator() [2/2]

DiracOperator::ScalarOperator::ScalarOperator	(	const std::vector< double > &	in_v = `{}`,
		double	in_coef = `1.0`
	)

inline

Convenience constructor: even-parity, real, diagonal (C_ff=C_gg=1, C_fg=C_gf=0) scalar operator.

Member Function Documentation

◆ angularF()

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

inlineoverridevirtual

Angular factor A_ab linking the radial integral to the RME.

All derived operators must implement this. It gives the purely angular part of the reduced matrix element:

\[ \langle a \| \hat{h} \| b \rangle \equiv A_{ab} \cdot R_{ab} \]

where \( R_{ab} \) is returned by radialIntegral(). For most operators, \( A_{ab} \) is a product of Clebsch-Gordan / 3j coefficients and depends only on \( \kappa_a, \kappa_b \) (and the rank \( k \) and parity \( \pi \) of the operator).

Note: This is a pure virtual function – every derived operator must provide an implementation.

Implements DiracOperator::TensorOperator.

◆ angularCff()

virtual double DiracOperator::ScalarOperator::angularCff	(	int	kappa_a,
		int	kappa_b
	)		const

inlineoverrideprotectedvirtual

Angular coefficient C_ff for the f_a*f_b term of the radial integral.

The default radial integral is structured as:

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

These coefficients are often constants, but may depend on \( \kappa_a, \kappa_b \) for operators with angular-momentum-dependent coupling between large and small components (e.g., spin-dependent operators). Override in derived classes as needed.

Parameters