Experimental study of the ${}^{66}\mathrm{Ni}(d,p) {}^{67}\mathrm{Ni}$ one-neutron transfer reaction

The quasi-SU(3) sequence of the positive parity $\nu g_{9/2},d_{5/2},s_{1/2}$ orbitals above the $N=40$ shell gap are assumed to induce strong quadrupole collectivity in the neutron-rich Fe $\left(Z=26\right)$ and Cr $\left(Z=24\right)$ isotopes below the nickel region. In this paper the position and strength of these single-particle orbitals are characterized in the neighborhood of ${}^{68}\mathrm{Ni} (Z=28,N=40)$ through the ${}^{66}\mathrm{Ni}(d,p){}^{67}\mathrm{Ni}$ one-neutron transfer reaction at 2.95 MeV/nucleon in inverse kinematics, performed at the REX-ISOLDE facility in CERN. A combination of the Miniball $\gamma$-array and T-REX particle-detection setup was used and a delayed coincidence technique was employed to investigate the 13.3-$\mu \mathrm{s}$ isomer at 1007 keV in ${}^{67}\mathrm{Ni}$. Excited states up to an excitation energy of 5.8 MeV have been populated. Feeding of the $\nu g_{9/2}$ (1007 keV) and $\nu d_{5/2}$ (2207 keV and 3277 keV) positive-parity neutron states and negative parity $\left(\nu pf\right)$ states have been observed at low excitation energy. The extracted relative spectroscopic factors, based on a distorted-wave Born approximation analysis, show that the $\nu d_{5/2}$ single-particle strength is mostly split over these two excited states. The results are also compared to the distribution of the proton single-particle strength in the ${}^{90}\mathrm{Zr}$ region $(Z=40,N=50)$.

Figure 1

Proton-$\gamma$ time difference between $\gamma$ rays detected in Miniball and protons detected by T-REX. The gray region defines the prompt proton-$\gamma$ time window; other events are referred to as random coincidences. The width of the prompt window is determined by the timing resolution of the low-energy $\gamma$ rays after the walk correction.

Figure 2

(a) Doppler corrected $\gamma$-ray spectrum in Miniball, delayed coincident with either 313 keV or 694 keV. Random-delayed events (see, e.g., Fig. 1 in Ref. [38]) and the delayed coincident background have been subtracted. (b) Delayed coincidence spectrum requiring a prompt proton-1201-keV event in Miniball. This spectrum was used to determine the delayed coincidence efficiency. See text for more information.

Figure 3

Doppler corrected Miniball $\gamma$-ray spectra, prompt proton coincident (black), and random proton coincident (red). See Fig. 1 for definition of Miniball timing windows. In the prompt spectrum most lines belonging to the $\gamma$ decay of ${}^{67}\mathrm{Ni}$ can be clearly identified, while only traces of the most intense lines remain in the random spectrum together with a broadened $\beta$-decay line around 1039 keV $\left({}^{66}\mathrm{Cu}\to {}^{66}\mathrm{Zn}\right)$. Energies of the most prominent $\gamma$ rays are indicated in keV.

Figure 4

Measured $\mathrm{\Delta }E\text{−}E$ signature in strip 7 (${\theta }_{\text{LAB}}$ between $42{}^{\circ }$ and $48{}^{\circ }$) of the barrel detector. Particles that are stopped in the $\mathrm{\Delta }E$ part of T-REX are rejected and not shown in this figure. The red events correspond to particles that are identified as deuterons based on their kinematical signature by the analysis software. Alternatively, the black dots are identified as protons.

Figure 5

Doppler corrected energy of $\gamma$ rays with respect to the original excitation energy of ${}^{67}\mathrm{Ni}$, deduced from proton kinematics. Events on the solid line correspond to direct ground-state $\gamma$ transitions after the transfer reaction.

Figure 6

(a) Proton-$\gamma \text{−}\gamma$ coincidences for the 1724-keV transition. The strongest coincidences at 483 and 1896 keV are clearly visible. (b) Corresponding incoming excitation energies in ${}^{67}\mathrm{Ni}$ deduced from coincident proton kinematics for 1724 keV and coincident $\gamma$ rays, efficiency corrected. See text for more information.

Figure 7

Level scheme constructed from the available $(d,p)$ data. Gamma and level energies are given in keV. Gamma-ray intensities relative to the 3621-keV transition.

Figure 8

Experimental excitation spectrum deduced from proton kinematics in singles (gray area) compared with a reconstructed feeding probability based on the proposed level scheme and $\gamma$-ray intensities (black line). The contribution of each individual state was drawn for completeness.

Figure 9

Angular distribution of elastically scattered deuterons. The DWBA calculations using optical potential paramaters from Refs. [63, 64, 65] are shown as the three lines.

Figure 10

Experimental angular distributions for different states in ${}^{67}\mathrm{Ni}$. The two or three best fits are presented for each case (solid line for best fit, dashed line for second best, and dotted-dashed for third best).

Figure 11

Sum of the $\nu p{}_{1/2},p{}_{3/2}$, and $f{}_{5/2}$ spectroscopic factors relative to $\nu g{}_{9/2}$. See text for discussion. Data from [79, 80].

Figure 12

Evolution of $C_S^2$ weighted centroid energies in the nickel isotopes with respect to the $\nu g_{9/2}$ level. Data taken from [53, 54, 55, 56, 57, 58, 59, 60] for ${}^{59-65}\mathrm{Ni}$.

Figure 13

Distribution of neutron single-particle strength in ${}^{67}\mathrm{Ni}$ (experimental and shell-model calculations) and proton-single particle strength in ${}^{89}\mathrm{Y}$. See text for additional information.