Spectroscopy of ${}^{70}\mathrm{Kr}$ and isospin symmetry in the $T=1 fpg$ shell nuclei

The recoil-$\beta$ tagging technique has been used in conjunction with the ${}^{40}\mathrm{Ca}({}^{32}\mathrm{S},2n)$ reaction at a beam energy of 88 MeV to identify transitions associated with the decay of the $2^{+}$ and, tentatively, $4^{+}$ states in the nucleus ${}^{70}\mathrm{Kr}$. These data are used, along with previously published data, to examine the triplet energy differences (TED) for the mass 70 isobars. The experimental TED values are compared with shell model calculations, performed with the JUN45 interaction in the $fpg$ model space, that include a $J=0$ isospin nonconserving (INC) interaction with an isotensor strength of 100 keV. The agreement is found to be very good up to spin 4 and supports the expectation for analog states that all three nuclei have the same oblate shape at low-spin. The $A=70$ results are compared with the experimental and shell model predicted TED and mirror energy differences (MED) for the mass 66 and 74 systems. The comparisons clearly demonstrate the importance of the isotensor INC interaction in replicating the TED data in this region. Issues related to the observed MED values and their interpretation within the shell model are discussed.

Figure 1

$\gamma$-ray spectra obtained with JUROGAM II for different tagging conditions. (a) requires that a $\beta$-decay event occurs within 400 ms of the correlated recoil ion implant, that it has a high-energy positron ($>2$ MeV) recorded in the GREAT planar detector and that no coincident charged particles were recorded in UoYTube; (b) has the same gating conditions as (a) except that the $\beta$-ion correlation time in this case was up to 100 ms, (c) has the same conditions as (b) plus a time restriction on the DSSSD-planar coincidence times to select the medium-energy $\beta$ particles. This reduced the ${}^{70}\mathrm{Br}$ events in the spectrum—see text for details; (d) same as (c) but with one charged particle explicitly demanded in UoYTube.

Figure 2

Natural logarithm, $ln(\mathrm{\Delta }t)$, of decay data gated on the 870 and 997 keV transitions assigned to ${}^{70}\mathrm{Kr}$, where $\mathrm{\Delta }t$ is the time difference in ms between the recoils associated with the two $\gamma$ rays and their subsequent $\beta$ decays. All correlated events within the 500 ms tagger time range were accepted. In addition to the $\gamma$ ray gates listed above the spectrum shown required a $\beta$-particle energy $>2$ MeV in the planar Ge detector and had a time gate on the DSSSD-planar coincidence times to select the medium energy $\beta$ particles. The solid red line represents the Schmidt (log likelihood) method [33] fit to the data. The centroid of the fit yields the mean lifetime (${44}_{-10}^{+19}$ ms), which can then be converted to a half-life of $31{}_{-7}^{+13}\mathrm{ms}$. See text for comments on the error analysis.

Figure 3

Triplet energy differences as a function of spin, $J$, for the $A=66,70,74$, and 78 triplets. Black squares show the experimental values for the $A=66$ and 74 systems, blue squares show the new experimental values for the $A=70$ triplet, whilst the solid (open) red circles show the results from shell model calculations with (without) the INC term.

Figure 4

Mirror energy differences as a function of spin, $J$, for the $A=66$, 70, and 74 mirror pairs. Black squares show the experimental values for the $A=66$ and 74 systems, blue squares show the new experimental values for the $A=70$ mirror pair, while the solid (open) red circles show the results from shell model calculations with (without) the INC interaction included.