Magnetic dipole operator: <a||M1||b> More...
#include <M1.hpp>
Inheritance diagram for DiracOperator::M1:
Public Member Functions | |
| M1 (const Grid &gr, const double alpha, const double omega=0.0) | |
| M1 & | operator= (const M1 &)=delete |
| M1 (const M1 &)=default | |
| 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, int) const override final |
| Angular factor for f_a*f_b part of radial integral. | |
| double | angularCgg (int, int) const override final |
| Angular factor for g_a*g_b part of radial integral. | |
| double | angularCfg (int, int) const override final |
| Angular factor for f_a*g_b part of radial integral. | |
| double | angularCgf (int, int) const override final |
| Angular factor for g_a*f_b part of radial integral. | |
| void | updateFrequency (const double omega) override final |
| Update frequency for frequency-dependant operators. | |
| 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 |
| 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 |
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
Magnetic dipole operator: <a||M1||b>
\[ <a||M1||b> = R (k_a + k_b) <-k_a||C^1||k_b> \]
\[R = \frac{-3}{\alpha^2\omega} \int (f_ag_b+g_af_b) j_1(kr) \, dr\]
\( k = \omega/c = \omega*\alpha \). Negative sign (and alpha) puts into units |mu_B|. For k<<1 (static case): j1(kr) -> (r*k)/3,
\[R = \frac{-1}{\alpha} \int (f_ag_b+g_af_b) r \, dr\]
Be careful with this operator - compare with: U. I. Safronova, M. S. Safronova, and W. R. Johnson, Phys. Rev. A 95, 042507 (2017).
Member Function Documentation
◆ name()
|
inlinefinaloverridevirtual |
Returns "name" of operator (e.g., 'E1')
Reimplemented from DiracOperator::TensorOperator.
◆ units()
|
inlinefinaloverridevirtual |
Returns units of operator (usually au, may be MHz, etc.)
Reimplemented from DiracOperator::TensorOperator.
◆ angularF()
|
inlinefinaloverridevirtual |
angularF: links radiation integral to RME. RME = <a||h||b> = angularF(a,b) * radial_int(a,b)
Implements DiracOperator::TensorOperator.
◆ angularCff()
|
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()
|
inlinefinaloverridevirtual |
Angular factor for g_a*g_b part of radial integral.
Reimplemented from DiracOperator::TensorOperator.
◆ angularCfg()
|
inlinefinaloverridevirtual |
Angular factor for f_a*g_b part of radial integral.
Reimplemented from DiracOperator::TensorOperator.
◆ angularCgf()
|
inlinefinaloverridevirtual |
Angular factor for g_a*f_b part of radial integral.
Reimplemented from DiracOperator::TensorOperator.
◆ updateFrequency()
|
inlinefinaloverridevirtual |
Update frequency for frequency-dependant operators.
Reimplemented from DiracOperator::TensorOperator.
The documentation for this class was generated from the following file:
- DiracOperator/Operators/M1.hpp
