Here we focus our attention on terms up to first-order in the perturbative expansion eq. ( ) (i.e. the very first term on the right-hand side of eq. ( )). The energies are then determined by eq. ( ) with Hkk 0 = H kk 0 , and the variational optimization involves the diagonalization of a matrix of dimension (2J + 1) ⇥ (2J + 1) once the integrals in eqs. ( )-(45) are made explicit.