Isotope Shift in Magnesium

A theoretical investigation is made to see whether nuclear motion alone can account for observed fine structure in magnesium, especially for the lines $3{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, $3{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, $3{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$, $3{}_{}{}^3{}_{}{}^{}P-3\mathrm{}{}_{}{}^3{}_{}{}^{}D$, and the limit of the series $3{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}-n{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$. Both by calculation with explicit radial functions and by the choice of theoretical parameters to fit observed shifts, it is shown that the values of the core-valence parameters occurring in the theory are not at all negligible, so that a two-electron model would not be permissible. Calculations with explicit radial functions give correct signs for the specific shifts of all these lines except for the limiting shift of $3{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}-n{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$. In the case of the line $3{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ the correct sign is obtained only when one takes into account the perturbation of $\mathrm{}\left(3s\right)\mathrm{} \mathrm{}\left(3d\right)\mathrm{} {}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ by ${\mathrm{}\left(3p\right)\mathrm{}}^2{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$; however, greater accuracy in the solution of the perturbation problem could not improve the agreement very much as long as the present radial functions are used. The total shift of any member of $3{}_{}{}^3{}_{}{}^{}P-3\mathrm{}{}_{}{}^3{}_{}{}^{}D$ comes out much smaller than any of the other total shifts, in agreement with Meissner's...