Relativistic Effects in the Hyperfine Structure ofSn117,119

Abstract

The atomic-beam magnetic-resonance technique has been used to measure the magnetic-dipole hyperfine-interaction constants $A$ for the 8613-${\mathrm{cm}}^{-1\mathrm{}}$ ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ metastable atomic state of ${\mathrm{Sn}}^{117,119}$. The results are $A({\mathrm{Sn}}^{117},{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{})=-1269.\mathrm{}650\left(3\right)\mathrm{}$ MHz and $A({\mathrm{Sn}}^{119},{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{})=-1328.\mathrm{}745\left(4\right)\mathrm{}$ MHz. These results, together with the previous measurements of $A$ for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ states, are considered (a) nonrelativistically, (b) relativistically, with Casimir correction factors, and (c) with relativistic Hartree-Fock radial wave functions. Procedure (c) is shown to be relatively successful in accounting for the hfs observations, and leads to a predicted mixing coefficient for the states ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ which is within 13% of the mutually consistent values found (i) by consideration of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ energy separation and (ii) from the precisely measured $g_J$ values for the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ states.