arc.alkali_atom_functions.AlkaliAtom.getRadialMatrixElement#

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

Radial part of the dipole matrix element

Calculates \(\int \mathbf{d}r~R_{n_1,l_1,j_1}(r)\cdot R_{n_1,l_1,j_1}(r) \cdot r^3\).

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 1. By default 0.5 for Alkali atoms.

  • useLiterature (bool) – optional, should literature values for dipole matrix element be used if existing? If true, compiled values stored in literatureDMEfilename variable for a given atom (file is stored locally at ~/.arc-data/), will be checked, and if the value is found, selects the value with smallest error estimate (if there are multiple entries). If no value is found, it will default to numerical integration of wavefunctions. By default True.

Returns

dipole matrix element (\(a_0 e\)).

Return type

float