Proton-Neutron Pairing Correlations in the Self-Conjugate NucleusK38Probed via a Direct Measurement of the Isomer Shift

Abstract

A marked difference in the nuclear charge radius was observed between the I^{π}=3^{+} ground state and the I^{π}=0^{+} isomer of ^{38}K and is qualitatively explained using an intuitive picture of proton-neutron pairing. In a high-precision measurement of the isomer shift using bunched-beam collinear laser spectroscopy at CERN-ISOLDE, a change in the mean-square charge radius of ⟨r_{c}^{2}⟩(^{38}K^{m})-⟨r_{c}^{2}⟩(^{38}K^{g})=0.100(6) fm^{2} was obtained. This is an order of magnitude more accurate than the result of a previous indirect measurement from which it was concluded that both long-lived states in ^{38}K have similar charge radii. Our observation leads to a substantially different understanding since the difference in charge radius is, moreover, opposite in sign to previously reported theoretical predictions. It is demonstrated that the observed isomer shift can be reproduced by large-scale shell-model calculations including proton and neutron excitations across the N,Z=20 shell gaps, confirming the significance of cross-shell correlations in the region of ^{40}Ca.

Changes in nuclear structure along the Mn isotopic chain studied via charge radii

“…Note that the difference in isomer and ground state charge radii is much larger on the neutron-deficient side. In the self-conjugate N = Z = 25 nucleus 50 Mn this can be understood in terms of the difference in isospin (T = 0 and T = 1), as was discussed previously for 38 19 K 19 [41]. A strong effect of the N = 28 shell closure is seen in all isotopic chains.…”

Collinear laser spectroscopy at ISOLDE: new methods and highlights

“…Recent mass measurements up to 54 Ca confirmed that result and 'unambiguously establishes a prominent shell closure at neutron number N=32' [83]. Furthermore, mass measurements up to 53 K confirmed the local 'doubly-magic' nature of 52 Ca [84]. However, in the mean square charge radii of the K isotopes, no clear evidence for a subshell closure at N=32 is observed [54].…”

“…We established firmly the ground state spin of all Mn isotopes and long-lived isomers up to 64 Mn [58,59]. All odd-A Mn isotopes, except for 53 Mn at N=28, have a ground state spin/parity 5/2 − , that deviates from the expected 7/2 − : this is a first signature for the non-spherical nature of these isotopes. A comparison of the magnetic and quadrupole moments with large scale shell model calculations in different model spaces shows that proton excitation across Z=28 as well as neutron excitation across N=40 and N=50 (into the g 9 2 and d 5 2 orbits) are needed to reproduce the observed values from N=36 onwards [58,61].…”

Shell-model computed cross sections for charged-current scattering of astrophysical neutrinos off Ar40

“…The wave functions of the initial and final nuclear states, and the one-body transition densities (OBTDs), related to the transitions, were calculated using the nuclear shell model. The calculations were done using the shell-model code NUSHELLX@MSU [14] in the 1s-0d 3/2 -0f 7/2 -1p 3/2 valence space using the Hamiltonian ZBM2M [8]. In Ref.…”

“…In Ref. [8], a new effective interaction was presented for the 1s-0d 3/2 -0f 7/2 -1p 3/2 model space. This interaction was created to explain the isomeric shift in 38 K m .…”