Coulomb energies in 17 Ne and the ground state mass of 18

The low-lying negative-parity states of 17N [1] are reasonably well described as two sd-shell neutrons coupled to the 15N ground state (gs). Two different sets of wave functions within this space were used to analyze results from the 15N (t, p) reaction [2]. Both sets worked well, and comparison between experiment and calculations allowed several suggestions of J and a dominant configuration. One minor exception was the first 3/2− state, whose energy and strength in 18O(d,3He) [3] indicate about 10% configuration with a p3/2 hole (rather than p1/2). The states in 17Ne should be mirrors of those in 17N, but the different values of N, Z—together with significant occupancy of the 2s1/2 orbital—can produce appreciable differences in energy splittings in the two nuclei. We have computed Coulomb energies in 17Ne using one set of wave functions (labeled LSF) from Ref. [2] and a set from a recent shell-model (sm) calculation [4]. The LSF wave functions result from a pure two-nucleon calculation, using two-body matrix elements (Constrained II) from Ref. [5] and “local” (i.e., 16N) single-particle energies. The shell-model calculation uses the p-sd model space in which the wave functions for A = 17 have two particles in the sd shell and one hole in the p shell (p1/2 or p3/2). We use the WBP Hamiltonian that was obtained from the USD interaction for the sd-shell matrix elements and from fitted potential-model interactions for the p-shell and crossshell p-sd matrix elements. This Hamiltonian and the data considered for its determination are discussed in Ref. [4]. Our assumption is that the admixture coefficients in the wave functions are equal in 17N and 17Ne and that only the shape of the radial wave function is different for mirror levels. Such an approach worked well for Coulomb energies in 18Ne [6]. Our wave functions are computed in a Woods-Saxon potential (r0 = 1.25, a = 0.65 fm), plus angular momentum and Coulomb terms (uniform sphere) as appropriate. For the LSF wave functions (Table I), we couple s2, d2, and ds to the gs of 15N or 15O. For the newer sm set, we use sp spectroscopic factors (Table II) computed with the interaction of Ref. [4] TABLE I. Wave function amplitudes for 17N levels coupled to15N (gs) (LSF from Ref. [2]).