Mirror displacement energies and neutron skins

Abstract

A gross estimate of the neutron skin [0.80(5)(N − Z)/A fm] is extracted from experimental proton radii, represented by a four parameter fit, and observed mirror displacement energies (CDE). The calculation of the latter relies on an accurately derived Coulomb energy and smooth averages of the charge symmetry breaking potentials constrained to state of the art values. The only free parameter is the neutron skin itself. The Nolen Schiffer anomaly is reduced to small deviations (rms=127 keV) that exhibit a secular trend. It is argued that with state of the art shell model calculations the anomaly should disappear. Highly accurate fits to proton radii emerge as a fringe benefit. Recent experiments [1,2] have considerably added to our knowledge of neutron radii, the most elusive of the fundamental properties of nuclear ground states. The two sets of measures are consistent with one another, and a recognizable pattern emerges [1, Fig. 4], leading to an estimate for the neutron skin (ν ≡ neutrons, π ≡ protons, t = N − Z)A third-totally different-experiment [3] adds weight to this estimate: it deals with the sodium isotopes, lighter and far more exotic than the species studied in [1,2]. Nonetheless, their ∆ rνπ behaviour is very much the same, as seen in Fig. 1.

Oscillator parameters in nuclei

“…Although the analysis here uses directly the observed charge radii, rather than a fit to them, it is worth mentioning that the treatment in Ref. [12] includes an impressively precise few-parameter fit to a large number of measured charge radii, which could serve as the basis for an improved formula. The neutron excess N − Z plays a significant role in their analysis, while the deviations of the Blomqvist-Molinari formula from the extractedhω values in the present work show a fair amount of scatter on a scale of some 0.5 MeV, but no systematic behaviour, as a function of (N − Z)/A.…”

“…A similar approach to separate proton and neutron oscillator energy spacingshω was adopted by Duflo and Zuker [12] in their discussion of mirror displacement energies. They use Eqs.…”

Unusual Isospin-Breaking and Isospin-Mixing Effects in theA=35Mirror Nuclei

“…In this case, Cr is proportional to differences in the sum of neutron and proton orbital occupancies, weighted by the orbits' square radii. Taking the sum ensures that neutron and proton radii are about equal, as requested by experiment [23].…”

Mass and lifetime measurements of stored exotic nuclei

“…The theoretical models are indicated in the legend and are described in detail in Refs. [89,90,91,92]. The error bars, if not indicated, are within the symbol size.…”