Separation of Mass and Field Shifts in Optical Isotope Shifts

Abstract

The isotope shift is to a very good approximation the sum of the mass shift and the field shift $$ IS = MS + FS $$ (6.1) Eq. (3.13) is, when generalized to the many-electron case, $$ MS_{\infty ,M} = \frac{{\left\langle {\sum\nolimits_i {p_i^2 } } \right\rangle }} {{2\left( {M + m} \right)}} + \frac{{\left\langle {\sum\nolimits_{i > j} {p_i \cdot p_j } } \right\rangle }} {{M + m}} $$ (6.2) where MS >∞,M is the mass shift between isotopes with nuclear masses ∞ and M. Eq. (6.2) can be written as $$ MS_{\infty ,M} = \frac{K} {{M + m}} $$ (6.3) where K is a constant that is independent of the mass M.