arc.alkali_atom_functions.AlkaliAtom.getReducedMatrixElementJ_asymmetric#

AlkaliAtom.getReducedMatrixElementJ_asymmetric(n1, l1, j1, n2, l2, j2, s=0.5)[source]#

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