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.