Identification of deformed intruder states in semi-magic ${}^{70}\mathrm{Ni}$

The structure of semi-magic ${}_{28}^{70}{\mathrm{Ni}}_{42}^{}$ was investigated following complementary multinucleon-transfer and secondary fragmentation reactions. Changes to the higher-spin, presumed negative-parity states based on observed $\gamma$-ray coincidence relationships result in better agreement with shell-model calculations using effective interactions in the neutron $f_{5/2}p{g}_{9/2}$ model space. The second $2^{+}$ and $\left(4^{+}\right)$ states, however, can only be successfully described when proton excitations across the $Z=28$ shell gap are included. Monte Carlo shell-model calculations suggest that the latter two states are part of a prolate-deformed intruder sequence, establishing an instance of shape coexistence at low excitation energies similar to that observed recently in neighboring ${}^{68}\mathrm{Ni}$.

Figure 1

Level scheme of ${}^{70}\mathrm{Ni}$ deduced from the multinucleon-transfer and secondary fragmentation reactions. The energies of $\gamma$ rays and states are given in keV. Spin-parity assignments in parentheses are tentative. The widths of the arrows represent the relative transition intensities. The half-life of the $8^{+}$ state is adopted from Ref. [25].

Figure 2

Background-subtracted, double-gated $\gamma$-ray coincidence spectra recorded with Gammasphere following ${}^{70}\mathrm{Zn}$+ ${}^{208}\mathrm{Pb}$ multinucleon-transfer reactions. (a) Sum of double gates on each pair of the 1260-, 970-, and 448-keV transitions in the delayed data. [(b)–(e)] Double gates in the prompt data on (b) 1260 and 970 keV, (c) 448 keV with either 1260 or 970 keV, (d) 1080 keV with either 1260 or 970 keV, and (e) one gate on 1260 or 970 keV and the other on 234 or 683 keV. Peaks assigned to ${}^{70}\mathrm{Ni}$ are labeled with their $\gamma$-ray energies in keV. Transitions that appear weakly in a given panel, but were found to have supporting evidence from other coincidence gates, are labeled in parentheses.

Figure 3

Angular correlations for members of the ${}^{70}\mathrm{Ni}$ yrast sequence gated on the coincident 1260-keV $2^{+}\to 0^{+}$ transition in the delayed Gammasphere data. The expected curve for an $E2-E2$ correlation is also plotted, scaled to each set of measurements.

Figure 4

Prompt $\gamma$ rays recorded with GRETINA in coincidence with ${}^{70}\mathrm{Ni}$ recoils following secondary reactions, Doppler corrected for $v/c=0.374$. (a) Singles spectrum. [(b)–(d)] Background-subtracted coincidence spectra gated on (b) 1259, (c) 968, (d) 609, and (b, inset) 1950 keV.

Figure 5

Experimental levels (exp.) in ${}^{70}\mathrm{Ni}$ compared with shell-model calculations using a number of effective interactions in the neutron $f_{5/2}p{g}_{9/2}$ model space (jj44bpn, jj44pna, and JUN45) and MCSM calculations using the A3DA interaction in the full $fp{g}_{9/2}{d}_{5/2}$ space for both protons and neutrons. A tentative $\left(0_2^{+}\right)$ level is drawn for ${}^{70}\mathrm{Ni}$ based on the scenario discussed in the text of a 384-keV decay from the 1868-keV $2^{+}$ state.

Figure 6

Experimental levels (exp.) in $N=42$ ${}^{70}\mathrm{Ni}$ and the valence-mirror nucleus $Z=42$ ${}^{92}\mathrm{Mo}$ compared with shell-model calculations using the jj44bpn effective interaction. The data for ${}^{92}\mathrm{Mo}$ are taken from Ref. [52]. A tentative $\left(0_2^{+}\right)$ level is drawn for ${}^{70}\mathrm{Ni}$ based on the scenario discussed in the text of a 384-keV decay from the 1868-keV $2^{+}$ state. Experimental levels in ${}^{68}\mathrm{Ni}$ are also shown, with dashed lines to their counterparts in ${}^{70}\mathrm{Ni}$ indicating the trend of decreasing excitation energies for levels associated with prolate deformation.

Figure 7

Potential-energy surfaces for (a) ${}^{68}\mathrm{Ni}$ and (b) ${}^{70}\mathrm{Ni}$ as a function of quadrupole deformation, obtained from constrained Hartree-Fock calculations for the A3DA Hamiltonian.

Figure 8

Potential-energy surfaces for ${}^{70}\mathrm{Ni}$ as a function of quadrupole deformation, obtained from constrained Hartree-Fock calculations for the A3DA Hamiltonian. Circles represent the size of the overlap between the wave function calculated for a given level, indicated by its spin and parity on each panel, and the basis states having quadrupole moments $Q_0$ and $Q_2$.

Figure 9

Occupancies and energies of proton and neutron orbitals near the Fermi surface for the $0_{1,2}^{+}$ levels in ${}^{70}\mathrm{Ni}$. The same line styles are used in all panels, as labeled in (c).