arc.divalent_atom_functions.DivalentAtom.getReducedMatrixElementJ_asymmetric#

DivalentAtom.getReducedMatrixElementJ_asymmetric(n1, l1, j1, n2, l2, j2, s=0.5)#

Reduced matrix element in \(J\) basis, defined in asymmetric notation.

Note that notation for symmetric and asymmetricly defined reduced matrix element is not consistent in the literature. For example, notation is used e.g. in Steck 1 is precisely the oposite.

Note

Note that this notation is asymmetric: \(( j||e r ||j' ) \neq ( j'||e r ||j )\). Relation between the two notation is \(\langle j||er||j' \rangle=\sqrt{2j+1} ( j ||er ||j')\). This function always returns value for transition from lower to higher energy state, independent of the order of states entered in the function call.

Parameters

  • n1 (int) – principal quantum number of state 1

  • l1 (int) – orbital angular momentum of state 1

  • j1 (float) – total angular momentum of state 1

  • n2 (int) – principal quantum number of state 2

  • l2 (int) – orbital angular momentum of state 2

  • j2 (float) – total angular momentum of state 2

  • s (float) – optional, total spin angular momentum of state. By default 0.5 for Alkali atoms.

Returns

reduced dipole matrix element in Steck notation \(( j || er || j' )\) (\(a_0 e\)).

Return type

float

1

Daniel A. Steck, “Cesium D Line Data,” (revision 2.0.1, 2 May 2008). http://steck.us/alkalidata