Determine both electro-dipole and magneto-dipole transitions

Question

Assignment:

Assuming that the system is illuminated by a monochromatic electromagnetic wave propagating along y-axis and polarized along z-axis, find the allowed transitions between two-electron states and find their respective transition rates. Consider both electro-dipole and magneto-dipole transitions. The perturbation Hamiltonian for magneto-dipole transitions has the following form

Vˆ_md = e/2m_e B(0,t) n_B [(Lˆ1 + 2Sˆ₁)+ (Lˆ2 + 2Sˆ₂)] ,

where B(0, t) is the magnetic field of the light and you have to determine the direction of the magnetic field, n_B. using Maxwell equations. The lower indexes 1 and 2 at the angular momentum and spin operators refer to the particle one or two. The electric-dipole perturbation potential also includes summation over the two particles:

Vˆ_ed = -e (r₁ + r₂) E