arc.alkali_atom_functions.AlkaliAtom.getQuadrupoleMatrixElement#

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

Radial part of the quadrupole matrix element

Calculates \(\int \mathbf{d}r~R_{n_1,l_1,j_1}(r)\cdot R_{n_1,l_1,j_1}(r) \cdot r^4\). See Quadrupole calculation example snippet .

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

quadrupole matrix element (\(a_0^2 e\)).

Return type

float