E2 transitions in nuclei

Abstract

If one assumes a single major oscillator shell to describe the properties of low-lying nuclear states, shell-model calculations on single-closed-shell nuclei or nuclei with T z = 0 invariably predict the following result for doubly even nuclei: If one introduces an effective charge for the neutron and proton, the E2 transition rates between the lowest state with spin J i (denoted by J i (0)) and the lowest state with spin J f (denoted by J f (0)) are in good agreement with experiment. On the other hand, for ΔT = 0 the E2 transition rate between the state J i (0) and the state J f (k) is quite small when J i ≠ J f and k ≠ 0. (The superscript k denotes which of the many states with spin J f we refer to − k = 0 means the lowest one, k = 1 the second state etc.) In this note, it is shown that the lack of an E2 component in the gamma transition J i (0) → J f (k) ( J i ≠ J f, k ≠ 0) may be traced to an asymptotic selection rule which, although holding rigorously only when the nucleus has large deformation, persists to a high degree of approximation even when the nucleus is almost spherical. A strong E2 transition that violates this rule therefore indicates a form of core excitation different from that already included through the introduction of an effective charge. Thus, a measurement of B(E2) for such states provides a sensitive method of testing the “single major oscillator shell” assumption that goes into many shell-model calculations.