Microscopic structure of coexisting $0^{+}$ states in ${}^{68}\mathrm{Ni}$ probed via two-neutron transfer

The structure of low-spin states originating from shape-coexisting configurations in ${}_{40}{}^{68}\mathrm{Ni}_{28}$ was directly probed via the two-neutron transfer reaction ${}^{66}\mathrm{Ni}(t,p){}^{68}\mathrm{Ni}$ in inverse kinematics using a radioactive ion beam on a radioactive target. The direct feeding to the first excited $0^{+}$ state was measured for center-of-mass angles $4^{\circ }–{16}^{\circ }$ and amounts to an integral of 4.2(16)% relative to the ground state. The observed difference in feeding of the $0^{+}$ states is explained by the transfer of neutrons, mainly in the $pf$ shell below $N=40$ for the ground state, and across $N=40$ in the $g_{9/2}$ orbital for the $0_2^{+}$, based on second-order distorted-wave Born approximation calculations combined with state-of-the-art shell-model two-nucleon amplitudes. However, the direct feeding to the $2_1^{+}$ state [29(3)%] is incompatible with these calculations.

Figure 1

Excitation energy of ${}^{68}\mathrm{Ni}$ versus $\gamma$-ray energy in prompt coincidence with protons. The gray line is an indication for possible ground-state transitions. The numbers indicate (1) the ground-state transition from the first excited $2^{+}$ state and (2) random events from the Doppler-broadened background line of 1039 keV arising from the $\beta$ decay of ${}^{66}\mathrm{Cu}$.

Figure 2

Excitation energy spectrum of ${}^{68}\mathrm{Ni}$ deduced from protons detected in the CD detector. The numbers indicate feeding to (1) the ground state, (2) the second $0^{+}$ state, and (3) the first excited $2^{+}$ state. The nonshaded area of the figure shows all detected protons, and the light gray area shows the protons that were detected in prompt coincidence with a $\gamma$ ray. Known levels in ${}^{68}\mathrm{Ni}$ are indicated in the panel above the figure. The pointing arrow indicates the excitation energy above which states have been omitted.

Figure 3

Measured angular distributions together with DWBA calculations including direct and sequential transfer to the (a) ground state, (b) $0_2^{+}$, and (c) $2_1^{+}$ state in ${}^{68}\mathrm{Ni}$. Global optical model parameters are taken from Ref. [28, 29, 30]. DWBA calculations use different two-nucleon amplitudes, either from shell-model calculations with the A3DA-m interaction [15] (solid red line) or the JJ44pna interaction [31] (dashed blue line) or assuming pure two-neutron configurations (black lines). See text for details.

Figure 4

Top: Average orbital occupancies of (a) neutrons and (b) protons for $0_{1,2,3}^{+}$ and $2_1^{+}$ states in ${}^{68}\mathrm{Ni}$ calculated using the A3DA-m interaction [15] (see text for details). Bottom: Two-nucleon amplitudes between the ${}^{66}\mathrm{Ni}$ ground state and the $0_{1,2}^{+}$ states of ${}^{68}\mathrm{Ni}$ [(c) and (d)] calculated using two different shell-model interactions (A3DA-m [15] and JJ44pna [31]). All of the TNA contributions in panel (c) add coherently to the two-neutron transfer cross section.