Isotope Shift in Atomic Spectra

Abstract

In the spectrum of an atomic system consisting of a nucleus with proton number (atomic number) Z and neutron number N, in the nuclear ground state, surrounded by z electrons in states characterized by electron quantum numbers a, the transition energies IlE or the wave numbers 1T=IlEjhc of the lines depend approximately only upon Z, z, and a; but when studied more closely they an� found to depend also slightly upon N. The N-depen­ dence, or so-called isotope shift, is the subject of this review. If the (Z,N) nucleus has a non-zero angular momentum, the levels and lines in general exhibit hyperfine-structure splitting. In isotope shift studies the hyperfine structure itself need not be treated: each hyperfine-structure multiplet may be treated as a single level or line at the centroid (except that those few cases where fine and hyperfine structure separations are of the same order of magnitude need further, straightforward treatment). The most comprehensive compilation of isotope shift in atomic spectra is that of Brix & Kopfermann in Landolt-Bornstein (1), which covers the literature to 1950. The subject is discussed extensively in the revised edition of Kopfermann's book (2) and several general theoretical reviews have ap­ peared (3, 4, 5). One respect in which isotope shift studies differ markedly from most other spectroscopic studies is that the small energy differences under investigation occur between level pairs in different atoms, and any common reference point is purely arbitrary. In isotope shift studies involving more than one line, a convenient custom is to consider the spectra under consideration to be arbitrarily matched at a series limit appropriate to the lines under study, the limit usually, but not always, being the ground level of the next higher stage of ionization. The usual (but not universal) convention with respect to the sign of the shift, which is the one used in this review, is to consider the direc­ tion of the normal mass shift (discussed below) positive; thus the level shift is called positive when the level belonging to the heavier of two isotopes is farther below the reference series limit than the corresponding level of the lighter isotope, and the line shift is caJIed positive when, between correspond­ ing lines, that belonging to the heavier isotope has the higher wave number. The treatment of isotope shift can be carried out under two headings: mass effect and field effect. The former depends only upon the nuclear mass and the electron wave functions, while the latter depends upon details of the