On the transition rate for the two-electron one-phonon transition

By using different gauges, the relativistic rates for the $\text{K}{}_{\mathrm{\alpha \alpha 2}}\text{(1}\text{s}{}^{\mathrm{?2}}\text{→2}\text{s}{}^{\mathrm{?1}}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{) and the}\text{K}{}_{\mathrm{\alpha 2}}{}^{\mathrm{<mtext>h</mtext>}}\text{(1}\text{s}{}^{\mathrm{?2}}\text{→1}\text{s}{}^{\mathrm{?1}}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)}$ transitions are calculated for Ne, Ar, Ca, Fe and Cu. The problem in the use of the single configuration HF model is discussed.