ΔS=±1 Magnetic Quadrupole Radiative Transitions in Atoms and Molecules

Abstract

The probabiliy of the spontaneous transition n₁→n₂ through the magnetic quadrupole moment Q_2m^(mg) is P_2m^(mg)(n₁→n₂)=(60πhε₀)⁻¹ω⁵|(n₁|Q_2m^(mg)|n₂)|²·Q_2m^(mg) is a tensor operator of order 2, and (Remark: Graphics omitted.), where ε₀ is the capacitivity of the vacuum, e and μ are electron charge and mass, respectively, r_i, s_i, and l_i are coordinate, spin, and orbital angular momenta, respectively, of i-th electron. When the total spin S is a good quantum number the magnetic quadrupole moment can produce ΔS=±1 radiative transitions. Selection rules are J+J′≥2≥|J−J′|, L+L′≥1≥|L−L′|, and parity change. In many cases the resulting transition probability competes with that by spin-orbit electric dipole moment. Numerical values of these transition probabilities are calculated for many atoms, ions, and molecules using simple wave functions. In atoms P₂^(mg) is about 10⁻³ sec⁻¹. In ions and molecules it is larger.