qspec.a_einstein_m1  (  f ,  j_l = 0 ,  j_u = 0 ,  ls = (0, 0) ,  jj_l = None ,  jj_u = None  )[source]

The Einstein coefficient of an M1 transition $$ A_\mathrm{ul} = \frac{2\mu_0(2\pi f)^3}{3hc^3} \frac{|\langle J_\mathrm{l}|\vec{\mu}|J_\mathrm{u}\rangle|^2}{2J_\mathrm{u} + 1}, $$ where $\mu_0$ is the vacuum permeability, $\vec{\mu}$ is the electronic magnetic moment operator in units of the Bohr magneton, $h$ is the Planck constant, and $c$ is the speed of light. This calculation neglects spin-orbit couplings, as $\Delta S = \Delta L = 0$ holds strictly. Consequently, M1 transition rates of transition such as $^3\mathrm{S}_1\rightarrow\, ^1\mathrm{S}_0$ cannot be calculated with this function.

Parameters:

farray_like

The frequency $f$ of a transition (MHz).

j_lquant_like

The electronic total angular momentum quantum number $J_\mathrm{l}$ of the lower state.

j_uquant_like

The electronic total angular momentum quantum number $J_\mathrm{u}$ of the upper state.

lsquant_like | Iterable

A list [(l_c, s_c), (l_o, l_c)] or a single pair (L, S) of electronic angular momentum and spin quantum numbers $(l, s)$ valid for both the lower and upper state. If this is a list of ls-pairs, the first pair specifies $l$ and $s$ of the core electron(s) and the second pair those of the outer electron(s). In this case, also a tuple of $(j_\mathrm{c}, j_\mathrm{o})$ quantum numbers needs to specified for the parameters jj_l and jj_u.

jj_lquant_like | Iterable

A tuple of electronic total angular momentum quantum numbers $(j_\mathrm{c}, j_\mathrm{o})$ of the lower state. Only needs to be specified if ls is a list of ls-pairs.

jj_uquant_like | Iterable

A tuple of electronic total angular momentum quantum numbers $(j_\mathrm{c}, j_\mathrm{o})$ of the upper state. Only needs to be specified if ls is a list of ls-pairs.

Returns:

A_ulndarray

The Einstein coefficient $A_\mathrm{ul}$ of an M1 transition, neglecting spin-orbit couplings (MHz).