Experimental study of excited states of ${}^{62}\mathrm{Ni}$ via one-neutron $(d,p)$ transfer up to the neutron-separation threshold and characteristics of the pygmy dipole resonance states

The degree of collectivity of the pygmy dipole resonance (PDR) is an open question. Recently, Ries et al. suggested the onset of the PDR beyond $N=28$ based on the observation of a significant $E1$ strength increase in the Cr isotopes and proposed that the PDR has its origin in a few-nucleon effect. Earlier, Inakura et al. had predicted by performing systematic calculations using the random-phase approximation (RPA) with the Skyrme functional SkM* that the $E1$ strength of the PDR strongly depends on the position of the Fermi level and that it displays a clear correlation with the occupation of orbits with orbital angular momenta less than $3\hslash (l\le 2)$. To further investigate the microscopic structures causing the possible formation of a PDR beyond the $N=28$ neutron shell closure, we performed a ${}^{61}\mathrm{Ni}(d,p){}^{62}\mathrm{Ni}$ experiment at the John D. Fox Superconducting Linear Accelerator Laboratory of Florida State University. To determine the angular momentum transfer populating possible $J^{\pi }=1^{-}$ states and other excited states of ${}^{62}\mathrm{Ni}$, angular distributions and associated single-neutron transfer cross sections were measured with the Super-Enge Split-Pole Spectrograph. A number of $J^{\pi }=1^{-}$ states were observed below the neutron-separation threshold after being populated through $l=2$ angular momentum transfers. A comparison to available $(\gamma ,{\gamma }^{\prime })$ data for ${}^{58,60}\mathrm{Ni}$ provides evidence that the $B\left(E1\right)$ strength shifts further down in energy. The $(d,p)$ data clearly prove that $l=0$ strength, i.e., the neutron ${\left(2p_{3/2}\right)}^{-1}{\left(3s_{1/2}\right)}^{+1}$ one-particle–one-hole configuration, plays only a minor role for $1^{-}$ states below the neutron-separation threshold in ${}^{62}\mathrm{Ni}$.

Figure 1

Particle identification with the SE-SPS. Data were taken at ${\theta }_{\mathrm{SE}\text{−}\mathrm{SPS}}={30}^{\circ }$ and a magnetic field of 8.6 kG. The energy loss was measured by the rear anode wire and the rest energy by the plastic scintillator of the light-ion focal-plane detector. The proton group is marked. The specific shape of the proton group is partly caused by the combined effects of angle-dependent energy losses in the target and in the isobutane gas of the focal-plane detector. For the experiment, the solid-angle acceptance was $\mathrm{\Delta }\mathrm{\Omega }=4.6\mathrm{msr}$, corresponding to an angular acceptance of about $\pm 1.7^{\circ }$. However, shapes like the one of the proton group in the $\mathrm{\Delta }E\text{−}E$ matrix change with the applied magnetic field, anode and cathode voltages, as well as with the gas pressure in the detector. The other particle groups correspond to deuterons, tritons, and $\alpha$ particles.

Figure 2

Proton spectra measured with the SE-SPS at a scattering angle ${\theta }_{\mathrm{SE}\text{−}\mathrm{SPS}}={20}^{\circ }$ for three different magnetic settings [(a) 8.7 kG, (b) 7.8 kG, and (c) 7.4 kG]. The position of protons in the focal plane was calibrated according to the excitation energy in ${}^{62}\mathrm{Ni}$. For each setting, position-dependent losses were observed in the region of lower excitation energies. To correct for these, field settings were chosen such that they have large overlap regions. Excitation energies of observed levels are indicated in the panels. The neutron-separation energy of $S_n=10595.9\left(4\right)\mathrm{keV}$ [50] is added in panel (c). Contaminants resulting from the ${}^{58}\mathrm{Ni}(d,p){}^{59}\mathrm{Ni}$ reaction are identified with an asterisk in panel (a).

Figure 3

First set of angular distributions measured for excited states of ${}^{62}\mathrm{Ni}$ via ${}^{61}\mathrm{Ni}(d,p){}^{62}\mathrm{Ni}$: Experimental data (symbols) and ADWA calculations performed with the coupled-channels program chuck3 (lines). Calculated distributions were scaled to data. The results using a simple average scaling factor (red, solid line) and the weighted average (blue, dashed line) are shown. The gray-shaded area corresponds to the standard deviation of the scaling factors. In cases where two different angular-momentum transfers were needed, the individual contributions are shown with black- and gray-dashed lines, respectively. The superposition is presented as a green, solid line. The uncertainty band is presented in light green. If the identification of the excited state is unambiguous, the adopted excitation energy and spin-parity assignment are given [50]. Otherwise, the excitation energy determined in this work is listed. The preferred angular momentum transfer is indicated. For states observed in both the 8.7 and 7.8 kG magnetic settings, data are shown with open and closed symbols, respectively.

Figure 4

Same as Fig. 3 but for the second set of angular distributions measured for excited states of ${}^{62}\mathrm{Ni}$ via ${}^{61}\mathrm{Ni}(d,p){}^{62}\mathrm{Ni}$. For states observed in both the 8.7 and 7.8 kG magnetic settings, data are shown with open and closed symbols, respectively. For the excited states at 5325 and 5843 keV, the FOM was ambiguous. Here, both $l=1$ (gray band) and $l=2$ (red band) ADWA angular distributions are shown.

Figure 5

Same as Fig. 3 but for the third set of angular distributions measured for excited states of ${}^{62}\mathrm{Ni}$ via ${}^{61}\mathrm{Ni}(d,p){}^{62}\mathrm{Ni}$. For states observed in both the 7.8 and 7.4/7.2 kG magnetic settings, data are shown with open and closed symbols, respectively. The gray, dashed line added for states with $E_x>9.2\mathrm{MeV}$ corresponds to the differential cross sections measured for the 9186-keV state scaled to the respective state's angular distribution. See Sec. 3a9 for further discussion.

Figure 6

Same as Fig. 3 but for the fourth set of angular distributions measured for excited states of ${}^{62}\mathrm{Ni}$ via ${}^{61}\mathrm{Ni}(d,p){}^{62}\mathrm{Ni}$. States were observed in the 7.4/7.2 kG magnetic setting. The gray, dashed line added for states with $E_x>9.2\mathrm{MeV}$ corresponds to the differential cross sections measured for the 9186-keV state scaled to the respective state's angular distribution. See Sec. 3a9 for further discussion.

Figure 7

Model-independent, angle-integrated $(d,p)$ cross sections ${\sigma }_{\mathrm{total}}$ for states which were populated through an $l=2$ angular momentum transfer (symbols). To illustrate the appearance of at least two groups, the cross sections of individual states were convoluted with a Lorentzian of $\mathrm{FWHM}=300\mathrm{keV}$ and added (blue line). The summed Lorentzian convolution has been scaled with a factor of 150. The FWHM and scaling factor are arbitrary and were chosen entirely for illustrative purposes.

Figure 8

(a) Model-independent, angle-integrated $(d,p)$ cross sections ${\sigma }_{\mathrm{total}}$, (b) model-dependent spectroscopic factors $S^{\prime }$ assuming a $2d_{5/2}$ transfer configuration, and (c) summed spectroscopic strength $\sum S_i^{\prime }$ for $J^{\pi }=1^{-}$ states observed in ${}^{61}\mathrm{Ni}(d,p){}^{62}\mathrm{Ni}$ and ${}^{62}\mathrm{Ni}(\gamma ,{\gamma }^{\prime })$. (d) Intensity ratios measured in ${}^{62}\mathrm{Ni}(\gamma ,{\gamma }^{\prime })$ [53]. States observed in $(d,p)$ and $(\gamma ,{\gamma }^{\prime })$ are shown with black, open symbols. A value of $\omega =0.73$ corresponds to a $0^{+}\to 1\to 0^{+}$ transition. Nuclear Resonance Fluorescence (NRF), i.e., $(\gamma ,{\gamma }^{\prime })$ scattering cross sections $I_S$ for resolved $J^{\pi }=1^{-}$ states of (d) ${}^{60}\mathrm{Ni}$ [56] and (e) ${}^{58}\mathrm{Ni}$ [54, 56]. Red bars in panel (f) indicate that the parity quantum number assignment is uncertain.