myfnsymbols** ††‡‡§§‖∥¶¶

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

M. Spieker  Corresponding author<EMAIL_ADDRESS>Department of Physics,
Florida State University, Tallahassee, Florida 32306, USA  L.T. Baby
Department of Physics, Florida State University, Tallahassee, Florida 32306,
USA  A.L. Conley  Department of Physics, Florida State University,
Tallahassee, Florida 32306, USA  B. Kelly  Department of Physics, Florida
State University, Tallahassee, Florida 32306, USA  M. Müscher  Institute for
Nuclear Physics, University of Cologne, 50937 Köln, Germany  R. Renom
Department of Physics, Florida State University, Tallahassee, Florida 32306,
USA  T. Schüttler  Institute for Nuclear Physics, University of Cologne, 50937
Köln, Germany  A. Zilges  Institute for Nuclear Physics, University of
Cologne, 50937 Köln, Germany

(August 28, 2024)

###### Abstract

The degree of collectivity of the Pygmy Dipole Resonance (PDR) is an open
question. Recently, Ries et al. have 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 $3\hbar$ $(l\leq 2)$. To further
investigate the microscopic structures causing the possible formation of a PDR
beyond the $N=28$ neutron shell closure, we performed a 61Ni$(d,p)$62Ni
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 62Ni,
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 58,60Ni provides evidence
that the $B(E1)$ strength shifts further down in energy. The $(d,p)$ data
clearly prove that $l=0$ strength, i.e., the neutron
$(2p_{3/2})^{-1}(3s_{1/2})^{+1}$ one-particle-one-hole configuration plays
only a minor role for $1^{-}$ states below the neutron-separation threshold in
62Ni.

###### pacs:

##  I Introduction

The present work is a continuation of studying the microscopic origin of the
low-lying electric dipole, $E1$, strength via one-neutron $(d,p)$ transfer
reactions Spieker  _et al._ (2020); Weinert  _et al._ (2021). This low-lying
$E1$ strength below, around, and partially above the neutron-separation
threshold, $S_{n}$, is also often referred to as Pygmy Dipole Resonance (PDR)
(see, e.g., the review articles Paar  _et al._ (2007); Savran  _et al._
(2013); Bracco  _et al._ (2015, 2019); Lanza  _et al._ (2023)). In a
simplified, macroscopic picture, the PDR is interpreted as the oscillation of
the neutron skin, mostly consisting of valence neutrons, against the nearly
isospin-saturated core Bartholomew (1961). This interpretation has been
controversially discussed though and we note beforehand that the term “PDR”
will be used without implying the neutron skin mode interpretation. There is
significant interest in the PDR as it can inform studies of the nuclear
equation of state Piekarewicz (2006); Tsoneva and Lenske (2008); Carbone  _et
al._ (2010); Piekarewicz (2011); Baran  _et al._ (2013); Roca-Maza and Paar
(2018), also used to describe neutron-star properties Thiel  _et al._ (2019);
Horowitz and Piekarewicz (2001a, b); Fattoyev and Piekarewicz (2012, 2013),
and as it can impact photodissociation and capture rates in stellar
environments (see, e.g., Refs. Goriely (1998); Litvinova  _et al._ (2009);
Tsoneva  _et al._ (2015); Tonchev  _et al._ (2017); Larsen  _et al._ (2019)).
For the latter, a precise understanding of its microscopic structure is
essential to pin down how the PDR contributes to the $\gamma$-ray strength
function ($\gamma$SF). The concept of the $\gamma$-ray strength function is
used in statistical Hauser-Feshbach approaches to calculate, e.g.,
$(n,\gamma)$ rates far off the valley of $\beta$ stability. An open question
is whether there is a dependence of the $\gamma$SF’s shape on excitation
energy, spin-parity quantum number, or even specific nuclear structure Angell
_et al._ (2012); Bassauer  _et al._ (2016); Guttormsen  _et al._ (2016);
Martin  _et al._ (2017); Campo  _et al._ (2018); Isaak  _et al._ (2019);
Simbirtseva  _et al._ (2020); Scholz  _et al._ (2020); Markova  _et al._
(2021, 2022); often referred to as the generalized Brink-Axel Hypothesis Bri ;
Axel (1962). Therefore, we want to stress again that in the PDR region states
with different isospin character have already been identified by comparing
experimental data obtained with hadronic probes at intermediate energies and
real-photon scattering (see, e.g., the review articles Savran  _et al._
(2013); Bracco  _et al._ (2015, 2019)). In heavier nuclei, two distinct groups
were observed, suggesting a splitting of the PDR into at least two groups of
different isospin character and underlining the presence of different
structures. Interestingly, only the group of states at lower energies was
observed in a recent study of 120Sn via the $(d,p\gamma)$ reaction Weinert
_et al._ (2021). Hundreds of $J=1$ states had previously been identified up to
the neutron-separation energy in real-photon scattering Müscher  _et al._
(2020). A detailed comparison to quasiparticle-phonon model (QPM) calculations
showed that the states, which were populated via $(d,p)$, were predominantly
of neutron one-particle-one-hole (1p-1h) character with transition densities,
which had a more pronounced contribution of neutrons at the surface Weinert
_et al._ (2021). This microscopic structure of the $J^{\pi}=1^{-}$ states
could explain why only the lower group of states was observed with the surface
sensitive 124Sn$(\alpha,\alpha^{\prime}\gamma)$ reaction at intermediate
energies Endres  _et al._ (2010); Lanza  _et al._ (2014). The presently
favored interpretation is that the higher-lying group of $1^{-}$ states has a
more complex structure with two-particle-two-hole (2p-2h) and three-particle-
three-hole (3p-3h) excitations contributing to the wavefunctions Spieker  _et
al._ (2020); Weinert  _et al._ (2021), which could also explain the suppressed
$\gamma$ decay to the ground state. The neutron 1p-1h components, mentioned
above, are of special importance as they have been identified as possible
doorway states shared between neutron and $\gamma$ channels in $(n,\gamma)$
reactions Lane (1971). This idea also connects to the open question to what
extent $(d,p)$ can be used as a proxy for $(n,\gamma)$ (see, e.g., Refs.
Escher  _et al._ (2012); Ratkiewicz  _et al._ (2019)).

To further understand the microscopic structures causing the formation of the
PDR, we have now started an experimental program to study $fp$-shell nuclei
around and beyond the $N=28$ shell closure at the Super-Enge Split-Pole
Spectrograph (SE-SPS) of the John D. Fox Superconducting Linear Accelerator
Laboratory at Florida State University fox  via one-neutron $(d,p)$ transfer.
The interest in this specific mass region is twofold. First, Ries et al. have
recently 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 apparently has its origin in a few-nucleon effect Ries  _et al._
(2019). This connects to the open question of how collective the PDR really
is. In general, collective phenomena emerge if a relatively large number of
constituent nucleons act coherently. Examples in atomic nuclei are giant
resonances Harakeh and van der Woude (2001) as well as vibrational and
rotational excitations at lower excitation energies Bohr and Mottelson (1998).
For the case of the PDR, it appears that coherence of different 1p-1h $E1$
matrix elements is observed in the isoscalar rather than in the isovector
channel (see, e.g., the discussion in Refs. Roca-Maza  _et al._ (2012);
Spieker  _et al._ (2020); Lanza  _et al._ (2023)). Second, Inakura et al.
showed for even-even nuclei with $8\leq Z\leq 40$ 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 shows a clear correlation with the
occupation of orbits with orbital angular momenta less than $3\hbar$ $(l\leq
2)$ Inakura  _et al._ (2011). It is intriguing that they do indeed predict the
pronounced $E1$ strength increase for $fp$-shell nuclei beyond $N=28$, which
Ries et al. observed for the Cr isotopes Ries  _et al._ (2019).

In this article, we report on the results of a 61Ni$(d,p)$62Ni experiment
performed at a deuteron beam energy of $E_{d}=16$ MeV ($Q=8371.2(6)$ keV Wang
_et al._ (2021)) at the FSU John D. Fox Laboratory. To test the predictions of
Inakura et al. Inakura  _et al._ (2011), 62Ni ($Z=28,N=34$) is particularly
suited as $J^{\pi}=1^{-}$ states would be populated through $l=0$ and $l=2$
angular momentum transfers from the $J^{\pi}=3/2^{-}$ ground state of 61Ni
ENSDF . This suggests that the associated neutron 1p-1h excitations in 62Ni
should be strongly coupled to the ground state via the corresponding $E1$
matrix elements. Previous $(d,p)$ studies, including the most recent one of
Ref. Karban  _et al._ (1981), exist Nichols  _et al._ (2012). The
spectroscopic information above 7 MeV of excitation energy is, however,
extremely sparse. Here, the current work adds significantly by providing data
for excited states of 62Ni up to the neutron-separation energy. Complementary
$(\gamma,\gamma^{\prime})$ experiments with real photons have already been
conducted and results will be communicated elsewhere Sch (2023). Information
from these experiments has, however, been used to identify possible
$J^{\pi}=1^{-}$ states populated in $(d,p)$ and will be discussed briefly. For
completeness, we mention that the isovector $E1$ strengths of 58,60,68,70Ni
have been studied experimentally in Refs. Bauwens  _et al._ (2000); Wieland
_et al._ (2009); Scheck  _et al._ (2013); Rossi  _et al._ (2013); Wieland  _et
al._ (2018). The isoscalar $E1$ strengths of 58,68Ni were measured and
discussed in Refs. Poelhekken  _et al._ (1992); Martorana  _et al._ (2018).

##  II Experimental Setup and Details

Figure 1: Particle identification with the SE-SPS. Data were taken at
$\theta_{\mathrm{SE-SPS}}=30^{\circ}$ 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 $\Delta\Omega=4.6$ msr corresponding to an angular acceptance
of about $\pm 1.7^{\circ}$. However, shapes like the one of the proton group
in the $\Delta E-E$ 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
$\theta_{\mathrm{SE-SPS}}=20^{\circ}$ 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 62Ni. For each
setting, position-dependent losses were observed in the region of lower
excitation energies. To correct for these, field settings were chosen such to
have large overlap regions. Excitation energies of observed levels are
indicated in the panels. The neutron-separation energy of $S_{n}=10595.9(4)$
keV ENSDF  has been added to the panel (c). Contaminants resulting from the
58Ni$(d,p)$59Ni reaction are identified with an asterisk in panel (a).

The 61Ni$(d,p)$62Ni experiment was performed at the John D. Fox
Superconducting Linear Accelerator Laboratory of Florida State University. The
Fox Laboratory operates a 9-MV Super-FN Tandem van-de-Graaff accelerator.
Deuterons were injected from a NEC SNICS-II cesium sputter ion source into the
Tandem and accelerated up to an energy of 16 MeV. For the experiment, we used
a 427-$\mu$g/cm2 thick, self-supporting 61Ni metal foil. The target was
provided by the Center for Accelerator Target Science at Argonne National
Laboratory. Protons were identified using the light-ion focal plane detection
system of the FSU Super-Enge Split-Pole Spectrograph (SE-SPS) goo (2020). A
sample particle identification plot is shown in Fig. 1. Offline gates are
applied to select the protons and generate position (excitation energy)
spectra, which are measured using the delay lines of the SE-SPS focal-plane
detector goo (2020). Like any spectrograph of the split-pole design Enge
(1979), the SE-SPS consists of two pole sections used to momentum-analyze
light-ion reaction products and focus them at the magnetic focal plane to
identify nuclear reactions and excited states. The split-pole design allows
approximate transverse focusing as well as maintaining second-order
corrections in the polar angle $\theta$ and azimuthal angle $\phi$, i.e.,
$(x/\theta^{2})\approx 0$ and $(x/\phi^{2})\approx 0$, over the entire
horizontal range Enge (1979). Examples of proton spectra measured in the SE-
SPS focal plane are shown in Fig. 2. The calibration was performed according
to the excitation energy, $E_{x}$, in 62Ni rather than the magnetic rigidity,
$B\rho$, as presented in Refs. Riley  _et al._ (2021, 2022). As in Ref. Karban
_et al._ (1981), a small 58Ni$(d,p)$59Ni contamination is observed (marked
with asterisks in Fig. 2). At present, this contamination cannot be quantified
precisely. The energy resolution in the focal plane depends on the solid
angle, target thickness and beam-spot size. It may, thus, vary from experiment
to experiment. In standard operation and with a global kinematic correction, a
resolution of 30-50 keV (FWHM) is routinely achieved. As a comparably thick
target was used, the average energy resolution in this experiment was around
59 keV. For reference, the energy loss in the target is between 5 keV and 15
keV depending on the scattering angle. The entrance slits to the spectrograph
were set such that the solid-angle opening corresponded to $\Delta\Omega=4.6$
msr. To determine the transferred angular momentum, $l$, in the $(d,p)$
reaction, differential cross sections, $d\sigma/d\Omega$, were measured at
seven different scattering angles, $\theta_{\mathrm{SE-SPS}}$, between
$10^{\circ}$ and $60^{\circ}$ for excited states of 62Ni. To cover the
excitation spectrum up to the neutron-separation energy, $S_{n}$, three
different magnetic settings between 7.2 kG and 9.0 kG were used for each
angle. The number of incoming deuterons was determined by measuring the beam
current with a Faraday cup at $0^{\circ}$ degree. Based on sample
measurements, a systematic uncertainty of 15 $\%$ is assumed for the current
integration.

##  III Results and Discussion

Figure 3: (Color online) First set of angular distributions measured for
excited states of 62Ni via 61Ni$(d,p)$62Ni. Experimental data (symbols) and
ADW 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 ENSDF . 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 kG and 7.8 kG
magnetic settings, data are shown with open and closed symbols, respectively.

In total, 79 excited states of 62Ni were identified; not counting the first
excited $J^{\pi}=2^{+}$ state. Out of these, 37 states were observed for the
first time. Information on the observed states is presented in Table
LABEL:tab:energy. The information includes the excitation (level) energy
determined in this work (also shown in Fig. 2), the proposed spin-parity
assignment $J^{\pi}$ based on the observed angular momentum $l$ transfer and
information from $(\gamma,\gamma^{\prime})$ Sch (2023), the angle-integrated
total cross section $\sigma_{\mathrm{total}}$, and the transfer configuration
used to calculate the model-dependent spectroscopic factors $S^{{}^{\prime}}$.
If no specific spin-parity assignment is provided, then
$S^{{}^{\prime}}=(2J_{f}+1)S$, where $J_{f}$ is the spin of the final
(populated) level and $S$ is the true spectroscopic factor. If a specific
spin-parity assignment is listed, then $S^{{}^{\prime}}=S$. In the latter
case, previously reported spectroscopic factors $S^{{}^{\prime}}$ have been
corrected accordingly. The measured angular distributions are shown in Figs.
3–6. For the angle-integrated cross section, $\sigma_{\mathrm{total}}$, the
stated uncertainty includes statistical uncertainties, a 15 $\%$ contribution
due to beam-current integration, and a systematic contribution coming from
position-dependent losses. To quantify the latter and benchmark the applied
corrections, measurements were performed at different magnetic field strength
settings, placing excited states at different positions in the focal plane. As
can be seen in Figs. 3–6, differential cross sections, measured at different
settings, do in almost all cases agree within uncertainties. To obtain parity
quantum number and spin-range assignments as well as model-dependent
spectroscopic factors, Adiabatic Distorted Wave Approximation (ADWA)
calculations were performed using the coupled-channels program chuck3 Kunz and
Comfort . To determine the deuteron optical-model parameters (OMPs), the
approach of Ref. Wales and Johnson (1976) was chosen, where the proton and
neutron OMPs were calculated using the global parameters of Ref. Koning and
Delaroche (2003). As in Refs. Riley  _et al._ (2021, 2022), the overlaps
between 62Ni and 61Ni$+n$ were calculated using binding potentials of Woods-
Saxon form whose depth was varied to reproduce the given state’s binding
energy. For the Volume Woods-Saxon part, we used geometry parameters of
$r_{0}=1.20$ fm and $a_{0}=0.67$ fm and a Thomas spin-orbit term of strength
$V_{so}=6$ MeV, which was not varied. In contrast to Refs. Riley  _et al._
(2021, 2022), we added a spin-orbit potential with geometry parameters
$r_{so}=1.02$ fm and $a_{so}=0.59$ fm. As no polarized deuteron beam is
available at the Fox Laboratory, we are not able to differentiate between
$l+1/2$ and $l-1/2$ components, i.e., we cannot tell whether the neutron is
transferred into, ${\it e.g.}$, the $2p_{3/2}$ or $2p_{1/2}$ orbital.
Calculations were, thus, performed assuming transfers to the $2p_{3/2}$,
$1f_{5/2}$, $1g_{9/2}$, and $2d_{5/2}$ neutron orbitals. For $l=1$ and $l=2$
transfers, spectroscopic factors for transfers to the $2p_{1/2}$ and
$2d_{3/2}$ neutron orbitals would be comparable, respectively. To determine
spectroscopic factors $S^{{}^{\prime}}$, calculated distributions were scaled
to data and the following figure of merit ($FOM$) minimized:

$FOM=\frac{\left(\frac{d\sigma_{exp}}{d\Omega}\left(\theta\right)-S^{{}^{\prime}}\frac{d\sigma_{ADWA}}{d\Omega}\left(\theta\right)\right)}{\frac{d\sigma_{exp}}{d\Omega}\left(\theta\right)}$
(1)

Only in two cases – for the excited states at 5325 keV and 5843 keV – the
$FOM$ was ambiguous. Here, both possible $l$ transfers are listed in Table
LABEL:tab:energy and Figs. 3–6. The results using a simple angle-averaged
scaling factor and the weighted average are shown in Figs. 3–6. Table
LABEL:tab:energy lists the angle-averaged scaling factors, where the quoted
uncertainty corresponds to the standard deviation between the individual
scaling factors. For many excited states, the agreement with previously
reported spectroscopic factors, $S^{{}^{\prime}}$, is good. For the first few
excited states, the agreement is excellent within uncertainties (see Table
LABEL:tab:energy). Some exceptions will be discussed.

Table 1: Experimental data for excited states of 62Ni observed in the 61Ni$(d,p)$62Ni reaction. Data are compared to adopted level energies, spin-parity assignments, as well as reported $l$ transfers and spectroscopic factors $S^{{}^{\prime}}$ Nichols  _et al._ (2012). If no specific spin-parity assignment is provided, then $S^{{}^{\prime}}=(2J_{f}+1)S$, where $J_{f}$ is the spin of the final (populated) level and $S$ is the true spectroscopic factor. If a specific spin-parity assignment is listed, then $S^{{}^{\prime}}=S$. In the latter case, previously reported spectroscopic factors $S^{{}^{\prime}}$ Nichols  _et al._ (2012) have been corrected accordingly. The quoted uncertainty corresponds to the standard deviation between the individual scaling factors determined at the corresponding scattering angles. The angle-integrated total cross section, $\sigma_{\mathrm{total}}$, as well as the transfer configuration, used to calculate the spectroscopic factor for an excited state, are also given. For $\sigma_{\mathrm{total}}$, the stated uncertainty includes statistical uncertainties, a 15 $\%$ contribution due to beam-current integration, and a systematic contribution coming from position-dependent losses. Note that for $l=2$ transfers a spin-parity assignments of $J^{\pi}=0^{-}-4^{-}$ is given as, in principle, both $2d_{5/2}$ and $2d_{3/2}$ are possible transfer configurations. As mentioned in the text, $2d_{5/2}$ was assumed to calculate the model-dependent spectroscopic factors. Cross sections for a $2d_{3/2}$ transfer configuration are, however, comparable. Level Energy [keV] |  | $J^{\pi}$ | $\sigma_{\mathrm{total}}$ |  $l$ transfer | Transfer | $S^{{}^{\prime}}$
---|---|---|---|---|---|---
This Work | Ref. Nichols  _et al._ (2012) |  | This Work | Ref. Nichols  _et al._ (2012) | [$\mu$b] | This Work | Ref. Nichols  _et al._ (2012) | configuration | This Work | Ref. Nichols  _et al._ (2012)
2052(7) | $2048.68(12)$ |  | 0+ | 0+ | 140(20) | 1 | 1 | $2p_{3/2}$ | 0.12(5) | 0.085
2302 | $2301.84(13)$ |  | 2+ | 2+ | 130(20) | 1 | $1+3$ | $2p_{3/2}$ | 0.020(14) | 0.007
2337 | $2336.52(14)$ |  | 4+ | 4+ | 91(12) | 3 | $1+3^{a}$ | $1f_{5/2}$ | 0.045(25) | 0.06
2889(3) | $2890.63(20)$ |  | 0+ | 0+ | 170(20) | 1 | 1 | $2p_{3/2}$ | 0.15(7) | 0.12
3057(5) | $3058.76(17)$ |  | $(2)^{+}$ | $3^{+}$ | 210(20) | 1 | $3^{b}$ | $2p_{3/2}$ | 0.04(2) | 0.37b
3154(4) | $3157.96(16)$ |  | $2^{+}$ | $2^{+}$ | 180(20) | 1 | $1+3$ | $2p_{3/2}$ | 0.032(17) | $0.02+0.04$
| $3257.6(2)$ |  |  | $2^{+}$ |  |  | $3$ | $1f_{5/2}$ |  | $1.1$
3268(3) | $3269.97(20)$ |  | $1^{+},2^{+}$ | $1,2^{+}$ | 480(40) | $1+3$ | $1+3$ | $2p_{3/2}$ | $0.12(3)$ | $0.076$
|  |  |  |  |  |  |  | $+1f_{5/2}$ | $+0.5(2)$ | $+0.82$
3368(4) | $3369.98(20)$ |  | $1^{+}$ | $1^{+}$ | 350(30) | 1 | 1 | $2p_{3/2}$ | 0.09(4) | 0.09
3520(3) | $3518.23(23)$ |  | $(2)^{+}$ | $2^{+}$ | 650(60) | 1 | 1 | $2p_{3/2}$ | 0.10(4) | 0.06
| $3522.54(18)$ |  |  | $2^{+},3^{+}$ |  |  |  |  |  |
| $3524.4(5)$ |  |  | $0^{+}$ |  |  |  |  |  |
3756(4) | $3756.5(3)$ |  | $3^{-}$ | $3^{-}$ | 190(20) | 4 | $4^{b}$ | $1g_{9/2}$ | 0.11(4) | 0.33b
3863(3) | $3859.6(4)$ |  | $1^{+},2^{+}$ | $1^{+},2^{+}$ | 780(70) | 1 | 1 | $2p_{3/2}$ | 0.18(5) | 0.13
3975(7) | $3972.9(4)$ |  | $2^{+}$ | $2^{+}$ | 330(30) | 1 | 1 | $2p_{3/2}$ | 0.046(16) | 0.015
4058(7) | $4062.4(5)$ |  | $1^{+},2^{+}$ | $1^{+},2^{+}$ | 170(20) | $1+3$ | 1 | $2p_{3/2}$ | $0.04(2)$ | 0.27
|  |  |  |  |  |  |  | $+1f_{5/2}$ | $+0.19(9)$ |
4165(8) | $4161.26(24)$ |  | $(5)^{-}$ | $(5^{-})$ | 440(50) | $4$ | $4^{b}$ | $1g_{9/2}$ | 0.12(5) | 0.75b
4206(6) | $4208.8(21)$ |  | $0^{+}-2^{+}$ |  | 300(30) | $1$ |  | $2p_{3/2}$ | 0.18(5) |
4423(4) | 4424(3) |  | $0^{+}-2^{+}$ |  | 120(20) | $1$ | $3$ | $2p_{3/2}$ | $0.07(2)$ | 0.28
4516(7) | 4503(4) |  | $(3)^{-}$ | $(3)^{-}$ | 106(12) | $4$ | $4^{b}$ | $1g_{9/2}$ | 0.06(4) | 0.14b
4643(3) | 4655(5) |  | $0^{+}-2^{+}$ | $3^{-}$ | 140(20) | $1$ |  | $2p_{3/2}$ | 0.9(6) |
4721(16) | $4719.9(7)$ |  | $(3)^{-}$ | $(3)^{-}$ | 300(40) | $4$ | $4^{b}$ | $1g_{9/2}$ | 0.08(2) | 0.67b
4873(9) | 4861(5) |  |  | $(2^{+})$ | 660(70) | $1+4$ |  | $2p_{3/2}$ | $0.09(3)$ |
| $4863.3(3)$ |  |  | $5^{-},6^{-}$ |  |  | $4^{b}$ | $+1g_{9/2}$ | +1.7(4) | 8.9b
4952(9) | 4949(7) |  | $3^{-}-6^{-}$ |  | 270(30) | $4$ |  | $1g_{9/2}$ | 0.8(3) |
| 4967(7) |  |  |  |  |  |  |  |  |
5004(10) | 4994(6) |  | $(3)^{-}$ | $3^{-}$ | 270(50) | $4$ |  | $1g_{9/2}$ | 0.10(2) |
5062(11) | 5041(10) |  |  | $(3^{-}-6^{-})$ | 310(30) | $1+4$ | $4$ | $2p_{3/2}$ | 0.10(3) | 9.2b
| 5071(10) |  |  |  |  |  |  | $+1g_{9/2}$ | +0.5(2) |
5240(10) | 5222(10) |  | $0^{+}-2^{+}$ |  | 78(9) | $1$ |  | $2p_{3/2}$ | 0.05(3) |
| 5233(10) |  |  |  |  |  |  |  |  |
5325(10) | 5331(10) |  | $0^{+}-2^{+}$ |  | 300(30) | $1$ |  | $2p_{3/2}$ | 0.17(6) |
|  |  | $(3)^{-}$ | $(3)^{-}$ |  | or $2$ | $2$ | or $2d_{5/2}$ | or 0.019(6) | 0.14b
5472(12) | 5465(6) |  | $(1)^{-c}$ |  | 280(30) | $2$ |  | $2d_{5/2}$ | 0.05(3) |
| 5488(10) |  |  |  |  |  |  |  |  |
5581(12) | 5587(10) |  | $0^{-}-4^{-}$ |  | 180(20) | $2$ |  | $2d_{5/2}$ | 0.09(4) |
| 5601(10) |  |  |  |  |  |  |  |  |
5632(12) | 5628(6) |  | $1^{+c}$ | $3^{-}$ | 190(20) | $1$ | $2$ | $2p_{3/2}$ | 0.035(14) | 0.05
5843(16) | 5834(10) |  | $0^{+}-2^{+}$ |  | 340(40) | $1$ |  | $2p_{3/2}$ | 0.21(14) |
|  |  | or $0^{-}-4^{-}$ |  |  | or $2$ | $2$ | or $2d_{5/2}$ | or 0.18(10) | 0.35b
| 5846(10) |  |  |  |  |  |  |  |  |
| 5859(10) |  |  |  |  |  |  |  |  |
5994(7) | 5993(10) |  | $0^{-}-4^{-}$ | $(1^{-},2^{-})$ | 140(20) | $2$ |  | $2d_{5/2}$ | 0.08(4) |
6096(7) | 6103(10) |  | $(1)^{-c}$ | $(1^{-}-4^{-})$ | 540(60) | $2$ | $2$ | $2d_{5/2}$ | 0.08(3) | 0.21
6179(4) | 6170(10) |  | $1^{-c}$ |  | 240(30) | $2$ |  | $2d_{5/2}$ | 0.038(14) |
6280(2) |  |  | $(1)^{-c}$ |  | 490(60) | $2$ |  | $2d_{5/2}$ | 0.08(3) |
6360(5) | 6320(25)d |  | $0^{-}-4^{-}$ |  | 300(40) | $2$ |  | $2d_{5/2}$ | 0.14(7) | 0.21
6417(12) |  |  | $0^{-}-4^{-}$ |  | 200(30) | $2$ |  | $2d_{5/2}$ | 0.10(5) |
6482(10) |  |  | $0^{-}-4^{-}$ |  | 200(30) | $2$ |  | $2d_{5/2}$ | 0.08(4) |
6549(8) | 6540(80) |  | $0^{-}-4^{-}$ | $1^{-},2^{-}$ | 400(50) | $2$ | $2$ | $2d_{5/2}$ | 0.18(6) | 0.29
6606(5) |  |  | $1^{+c}$ |  | 240(40) | $1$ |  | $2p_{3/2}$ | 0.026(15) |
6715(9) | 6750(80) |  | $1^{-c}$ | $1^{-},2^{-}$ | 200(30) | $2$ | $0$ | $2d_{5/2}$ | 0.04(2) |
6942(7) | 6900(25) |  | $1^{-c}$ | $(1^{-},2^{-})$ | 123(14) | $2$ | $(0)$ | $2d_{5/2}$ | 0.018(7) |
7042(8) | 7030 |  | $(1)^{-c}$ | $3^{-}$ | 160(20) | $2$ |  | $2d_{5/2}$ | 0.010(6) |
| 7080(30) |  |  |  |  |  |  |  |  |
7132(5) |  |  | $1^{-c}$ |  | 114(14) | $2$ |  | $2d_{5/2}$ | 0.017(7) |
7211(8) |  |  | $0^{-}-4^{-}$ |  | 240(30) | $2$ |  | $2d_{5/2}$ | 0.11(5) |
7263(11) | 7260 |  | $1^{-c}$ |  | 270(30) | $2$ |  | $2d_{5/2}$ | 0.04(2) |
7313(10) | 7300(25)d |  | $0^{-}-4^{-}$ | $1^{-}-4^{-}$ | 210(30) | $2$ | $2$ | $2d_{5/2}$ | 0.08(3) | 0.36
7398(5) |  |  | $0^{-}-4^{-}$ |  | 260(30) | $2$ |  | $2d_{5/2}$ | 0.11(3) |
7459(10) |  |  | $1^{+c}$ |  | 200(40) | $1$ |  | $2p_{3/2}$ | 0.030(9) |
7541(11) |  |  | $1^{-c}$ |  | 460(50) | $2$ |  | $2d_{5/2}$ | 0.06(3) |
7644(10) | $7645.6(4)$ |  | $1^{-}$ | $1^{-}$ | 370(40) | $2$ |  | $2d_{5/2}$ | 0.05(2) |
7703(8) | 7700 |  | $0^{-}-4^{-}$ |  | 500(60) | $2$ |  | $2d_{5/2}$ | 0.18(4) |
7774(12) | 7800(25) |  | $1^{-c}$ | $1^{-}-4^{-}$ | 450(60) | $2$ | $2$ | $2d_{5/2}$ | 0.06(2) | 0.37
7835(11) | 7800(25) |  | $1^{-c}$ | $1^{-}-4^{-}$ | 480(60) | $2$ | $2$ | $2d_{5/2}$ | 0.06(2) | 0.37
7886(11) |  |  | $0^{-}-4^{-}$ |  | 300(40) | $2$ |  | $2d_{5/2}$ | 0.11(5) |
7982(10) |  |  | $0^{-}-4^{-}$ |  | 640(70) | $2$ |  | $2d_{5/2}$ | 0.21(10) |
8072(5) |  |  | $1^{-c}$ |  | 940(110) | $2$ |  | $2d_{5/2}$ | 0.11(3) |
8118(4) | 8130(25) |  | $1^{-c}$ | $(1^{-}-4^{-})$ | 570(70) | $2$ | $(2)$ | $2d_{5/2}$ | 0.06(3) | 0.4
8217(5) |  |  | $1^{-c}$ |  | 450(70) | $2$ |  | $2d_{5/2}$ | 0.04(2) |
8340(8) |  |  | $1^{-c}$ |  | 590(110) | $2$ |  | $2d_{5/2}$ | 0.05(2) |
8396(5) |  |  | $0^{-}-4^{-}$ |  | 740(90) | $2$ |  | $2d_{5/2}$ | 0.27(6) |
8487(9) | 8460(25) |  | $0^{-}-4^{-}$ | $(2^{-}-5^{-})$ | 710(80) | $2$ | $(4)$ | $2d_{5/2}$ | 0.24(9) |
8650(4) |  |  | $0^{-}-4^{-}$ |  | 540(70) | $2$ |  | $2d_{5/2}$ | 0.18(9) |
8773(8) |  |  | $0^{-}-4^{-}$ |  | 840(150) | $2$ |  | $2d_{5/2}$ | 0.21(9) |
8872(9) |  |  | $0^{-}-4^{-}$ |  | 370(70) | $2$ |  | $2d_{5/2}$ | 0.10(5) |
8927(7) |  |  | $0^{-}-4^{-}$ |  | 280(60) | $2$ |  | $2d_{5/2}$ | 0.09(6) |
9070(5) |  |  | $0^{-}-4^{-}$ |  | 590(80) | $2$ |  | $2d_{5/2}$ | 0.18(9) |
9139(10) |  |  | $0^{-}-4^{-}$ |  | 550(90) | $2$ |  | $2d_{5/2}$ | 0.16(11) |
9186(10) |  |  |  |  | 790(110) |  |  |  |  |
9267(10) |  |  |  |  | 570(110) |  |  |  |  |
9309(16) |  |  |  |  | 750(150) |  |  |  |  |
9459(12) |  |  |  |  | 690(120) |  |  |  |  |
9526(9) |  |  |  |  | 910(140) |  |  |  |  |
9590(15) |  |  |  |  | 990(140) |  |  |  |  |
9694(15) |  |  |  |  | 880(120) |  |  |  |  |
9874(17) |  |  |  |  | 1100(230) |  |  |  |  |
10133(12) |  |  | $0^{-}-4^{-}$ |  | 440(90) | $2$ |  | $2d_{5/2}$ | 0.11(5) |
10242(15) |  |  |  |  | 440(90) |  |  |  |  |
10321(15) |  |  | $0^{-}-4^{-}$ |  | 320(60) | $2$ |  | $2d_{5/2}$ | 0.10(4) |
10491(17) |  |  | $0^{-}-4^{-}$ |  | 650(120) | $2$ |  | $2d_{5/2}$ | 0.11(2) |
10619(19) |  |  | $0^{-}-4^{-}$ |  | 450(70) | $2$ |  | $2d_{5/2}$ | 0.24(3) |
a Because of the $J^{\pi}=3/2^{-}$ ground state of 61Ni an $l=1$ transfer cannot populate a $J^{\pi}=4^{+}$ state. |
b Ref. Karban  _et al._ (1981). |
c 62Ni$(\gamma,\gamma^{\prime})$ intensity ratio indicative of a $J=1$ assignment Sch (2023). See also Fig. 8. |
d Reported in Ref. Nichols  _et al._ (2012) for previous $(d,p)$ experiment. |

###  III.1 Discussion of selected states and spectroscopic strengths

####  III.1.1 3059 keV

Figure 4: (Color online) Same as Fig. 3 but for the second set of angular
distributions measured for excited states of 62Ni via 61Ni$(d,p)$62Ni. For
states observed in both the 8.7 kG and 7.8 kG magnetic settings, data are
shown with open and closed symbols, respectively. For the excited states at
5325 keV and 5843 keV, the $FOM$ was ambiguous. Here, both $l=1$ (gray band)
and $l=2$ (red band) ADWA angular distributions are shown.

The first discrepancy between our measurement and previously available $(d,p)$
data is observed for the level at 3059 keV. Previous data suggested that an
$l=3$ transfer was observed in $(d,p)$ Karban  _et al._ (1981). This angular
momentum transfer would allow for the currently adopted $J^{\pi}=3^{+}$
assignment ENSDF ; Nichols  _et al._ (2012), which is based on an angular
distribution measurement performed in $(n,n^{\prime}\gamma)$ Chakraborty  _et
al._ (2011). We do, however, observe an $l=1$ transfer (see Fig. 3). This
limits the spin range to $J=0-2$ and positive parity for the 3059-keV level. A
previous $(p,t)$ experiment observed an $l=2$ transfer from the 64Ni
$J^{\pi}=0^{+}$ ground state to this level Kong-A-Siou and Nann (1975), which
is consistent with our data and would suggest a $J^{\pi}=2^{+}$ assignment.
When reexamining the data of Ref. Chakraborty  _et al._ (2011), this $J^{\pi}$
assignment also appears to be consistent with their data. We, thus, suggest to
reevaluate the information for this excited state.

####  III.1.2 4643 keV

Figure 5: (Color online) Same as Fig. 3 but for the third set of angular
distributions measured for excited states of 62Ni via 61Ni$(d,p)$62Ni. For
states observed in both the 7.8 kG 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 $E_{x}>9.2$ MeV corresponds to the differential cross sections
measured for the 9186-keV state scaled to the respective state’s angular
distribution. See Sec. III.1.9 for further discussion.

Currently, two states are adopted around an excitation energy of $4650$ keV.
The first is a tentatively assigned $J^{\pi}=(7^{-})$ at 4648.9(3) keV and the
second is a $J^{\pi}=3^{-}$ state at an energy of 4655(5) keV. The
$J^{\pi}=3^{-}$ assignment seems rather certain given the observation of the
$l=3$ angular momentum transfers in $(p,t)$ Kong-A-Siou and Nann (1975) and
$(\alpha,\alpha^{\prime})$ Kumabe  _et al._ (182), which are also listed in
the Nuclear Data Sheets Nichols  _et al._ (2012). Arguably, it is, however,
difficult to tell whether $l=2$ could not describe the measured distributions,
too. In our work, we observed a state at 4643(3) keV. The observed angular
distribution is well described by an $l=1$ angular momentum transfer, which
sets the possible spin range at $J=0-2$ and points at a positive parity
quantum number. So, the state populated here does not seem to correspond to
any of the previously observed states unless the $J^{\pi}=3^{-}$ assignment is
incorrect.

####  III.1.3 4873 keV

Figure 6: (Color online) Same as Fig. 3 but for the fourth set of angular
distributions measured for excited states of 62Ni via 61Ni$(d,p)$62Ni. States
were observed in the 7.4/7.2 kG magnetic setting. The gray, dashed line added
for states with $E_{x}>9.2$ MeV corresponds to the differential cross sections
measured for the 9186-keV state scaled to the respective state’s angular
distribution. See Sec. III.1.9 for further discussion.

Judging from the angular distribution, which can only be described with a
superposition of an $l=1$ and $l=4$ transfer, a doublet at an energy 4873(9)
keV could not be resolved in our $(d,p)$ measurement. Two excited states are
currently known at this energy; a tentatively assigned $J^{\pi}=2^{+}$ state
at an energy of 4861(5) keV and a level at 4863.3(3) keV with a spin-parity
assignment of $J^{\pi}=5^{-}$ or $6^{-}$ ENSDF ; Nichols  _et al._ (2012).
Reexamining the angular distribution presented in Ref. Karban  _et al._
(1981), it is quite clear that they also observed the doublet but only
reported an $l=4$ transfer for their $(d,p)$ data. This also explains the
discrepant spectroscopic factors. The angular distribution observed in our
work is consistent with the population of the tentatively assigned
$J^{\pi}=2^{+}$ state and the 4863-keV state with $J^{\pi}=5^{-},6^{-}$.

####  III.1.4 5062 keV

Also in this case it is quite likely that a doublet could not be resolved as
the angular distribution can only be fitted with a superposition of an $l=1$
and $l=4$ transfer. Ref. Karban  _et al._ (1981) reported a pure $l=4$
transfer. It is obvious though that an $l=1$ contribution is needed to
describe their data, too. Currently adopted levels at 5041(10) keV and
5071(10) keV are candidates for the unresolved doublet members, respectively.
The two different angular momentum transfers suggest that the two levels have
different parity quantum numbers.

####  III.1.5 5632 keV

An excited $J^{\pi}=3^{-}$ state is adopted at an energy of 5628(6) keV
Nichols  _et al._ (2012). The previous $(d,p)$ experiment of Karban et al.
observed a state at 5.63 MeV and reported an $l=2$ transfer Karban  _et al._
(1981), which would be consistent with the adopted spin-parity assignment.
However, our measured angular distribution favors an $l=1$ transfer [see Fig.
4]. In addition, a $J=1$ state was observed at 5634 keV in $(\gamma,\gamma’)$
Sch (2023) [see also Fig. 8 (d)]. The observed $l=1$ transfer in $(d,p)$ is
indicative of populating this $J^{\pi}=1^{+}$ state. A $J^{\pi}=3^{-}$ state
would not be directly populated in $(\gamma,\gamma’)$. It is possible that two
different states were observed.

####  III.1.6 6715 keV, 6942 keV and previously reported $l=0$ angular
momentum transfers

For states previously reported at excitation energies of 6750(80) keV and
6900(25) keV, respectively, $l=0$ transfers are listed to have been observed
in $(d,p)$ Karban  _et al._ (1981); Fulmer and McCarthy (1963); Nichols  _et
al._ (2012). Angular distributions to support these assignments are neither
shown in Karban  _et al._ (1981) nor Fulmer and McCarthy (1963). In fact, we
do not observe any $l=0$ transfer in our work. It, thus, appears that the
$3s_{1/2}$ spectroscopic strength would be observed above the neutron-
separation threshold. In our work, we observed states at 6715(8) keV and
6942(7) keV, whose measured angular distributions can both be described by
$l=2$ angular momentum transfers (see Fig. 4). This leads to a possible spin-
parity assignment of $J^{\pi}=0^{-}-4^{-}$ when considering the two possible
transfer configurations $2d_{5/2}$ and $2d_{3/2}$, respectively. As will be
discussed further in Sec. III.2, states at these energies were observed in
real-photon scattering, which suggests a $J^{\pi}=1^{-}$ assignment consistent
with our data.

####  III.1.7 8487 keV

A state at 8460(25) keV is currently adopted with a possible spin-parity
assignment of $J^{\pi}=2^{-}-5^{-}$ based on a possible $l=4$ transfer
observed in a previous $(d,p)$ experiment Karban  _et al._ (1981). A
supporting angular distribution is not shown in Ref. Karban  _et al._ (1981).
We do observe a state at 8487(9) keV, whose angular distribution can be
clearly described by an $l=2$ transfer (see Fig. 5). We, thus, propose to drop
the previous spin-parity assignment and to consider $J^{\pi}=0^{-}-4^{-}$
instead.

####  III.1.8 $1g_{9/2}$ spectroscopic strength $(l=4)$

The spectroscopic factors for $l=4$ transfers reported in Ref. Karban  _et
al._ (1981) appear too large. Even though still partially tentatively assigned
as $J^{\pi}=3^{-}$ states, the spectroscopic factors of the states at 3757
keV, 4503 keV, and 4720 keV would already sum up to 1.14 and, therefore,
exceed the expected spectroscopic strengths. A more recent evaluation of data
from one-nucleon adding reactions leading to the odd-$A$ Ni isotopes suggests
that only about 75 $\%$ of the spectroscopic strength are concentrated in one
$9/2^{+}$ state in 61Ni and that the rest of the strength is strongly
fragmented Schiffer  _et al._ (2013). In 63Ni, 75 $\%$ of the spectroscopic
strength are shared between two major fragments Schiffer  _et al._ (2013).
However, these values were only obtained after applying the normalization
discussed in Refs. Schiffer  _et al._ (2013, 2012). Otherwise, the summed
spectroscopic factor would be $\sim 0.39$ for $l=4$ strength in 61Ni Schiffer
_et al._ (2013). If we also consider the $3^{-}$ state at an energy of 4994(6)
keV, which very likely corresponds to the state observed at 5004(10) keV in
our work, a summed spectroscopic strength of 0.35(12) for resolved $3^{-}$
states of 62Ni can be determined. This is in agreement with the summed value
reported for the major $1g_{9/2}$ fragments in 61Ni Schiffer  _et al._ (2013).
From simple cross section scaling arguments, one could expect that $(2\times
3+1)/(2\times 5+1)=0.64$ of the spectroscopic strength going to $3^{-}$ states
should be observed for $5^{-}$ states. This leads to an estimated
spectroscopic strength (factor) of 0.22(8), which we should be able to
resolve. A spectroscopic factor of 0.12(5) is observed for the $J^{\pi}=5^{-}$
candidate at 4161 keV. If the previously discussed doublet member at 4863 keV
was a $5^{-}$ state, then the summed spectroscopic factor would indeed be
$\sim 0.23$ as expected. It is, however, extremely important to point out that
these values are strongly model-dependent. Ref. Schiffer  _et al._ (2013)
stressed the sensitivity of the predicted cross sections on the bound-state
parameters. For higher $l$ transfers like $l=4$, they explicitly showed the
pronounced dependence of the cross sections on the radius of the spin-orbit
term in the neutron-transfer channel. Variations of this radius by 20 $\%$ led
to cross-section varations of up to 50 $\%$. Ref. Schiffer  _et al._ (2013)
states that the radius of the spin-orbit term should be about $20-30$ $\%$
smaller than the radius of the real potential. Following the procedure
described above, we calculated a spin-orbit radius $r_{so}=1.02$ fm compared
to a real-well radius $r_{0}=1.20$ fm, i.e., 15 $\%$ smaller. For
completeness, we add that the summed spectroscopic factor for the $1g_{9/2}$
strength is $\sim 0.50$ in 63Ni if the normalization is not applied Schiffer
_et al._ (2013, 2012).

####  III.1.9 Group of states above 9 MeV

A group of states above an excitation energy of 9 MeV has been observed in
this work, which show remarkably similar $(d,p)$ angular distributions (see
Figs. 5–6). The gray, dashed line added for states with $E_{x}>9.2$ MeV
corresponds to the differential cross sections measured for the 9186-keV state
scaled to the respective state. However, no angular momentum transfer could be
found which matched the observed distributions; including $l=0$ ($3s_{1/2}$)
and $l=4$ ($1g_{7/2}$) transfers. These states are still below the neutron-
separation energy of $S_{n}=10.6$ MeV. It cannot be excluded though that their
distributions are altered by threshold effects or that more indirect processes
contribute. To show that the shape is different than the one predicted for an
$l=2$ transfer at these energies, the scaled 9186-keV angular distribution was
added to the panel for the 10133-keV state in Fig. 6. This state’s angular
distribution can be described with an $l=2$ transfer. Interestingly, the
10242-keV state’s angular distribution is again different.

####  III.1.10 $l=2$ strength distribution

Figure 7: (Color online) 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 $\mathrm{FWHM}=300$ 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.

Almost all of the states of 62Ni observed with excitation energies greater
than $5.5$ MeV were populated through $l=2$ angular momentum transfers. The
strength distribution for these states is shown in Fig. 7. A broad structure
with a centroid of approximately 8 MeV is observed. To better illustrate the
appearance of this broad structure, the angle-intergrated cross sections were
convoluted with a Lorentzian of $\mathrm{FWHM}=300$ keV and added. In addition
to this broader feature, a narrower structure is observed around 6.2 MeV.
While it is clear that both structures can be explained by $l=2$ transfers, we
can currently not determine whether one of them corresponds to
$(2p_{3/2})^{-1}(2d_{5/2})^{+1}$ and the other to
$(2p_{3/2})^{-1}(2d_{3/2})^{+1}$ neutron 1p-1h excitations. There is also no
intuitive reason why the $2d_{3/2}$ strength should be more fragmented besides
the fact that the level density generally increases towards higher excitation
energies.

###  III.2 Identification of possible PDR $J^{\pi}=1^{-}$ states

Figure 8: (Color online) (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 61Ni$(d,p)$62Ni and 62Ni$(\gamma,\gamma^{\prime})$. (d) intensity
ratios measured in 62Ni$(\gamma,\gamma^{\prime})$ Sch (2023). States observed
in $(d,p)$ and $(\gamma,\gamma^{\prime})$ are shown with black, open symbols.
A value of $\omega=0.73$ corresponds to a $0^{+}\rightarrow 1\rightarrow
0^{+}$ transition. Nuclear Resonance Fluorescence (NRF), i.e.,
$(\gamma,\gamma^{\prime})$ scattering cross sections $I_{S}$ for resolved
$J^{\pi}=1^{-}$ states of (d) 60Ni Scheck  _et al._ (2013) and (e) 58Ni Scheck
_et al._ (2013); Bauwens  _et al._ (2000). Red bars in panel (f) indicate that
the parity quantum number assignment is uncertain.

We now turn to a brief discussion of possible PDR states, i.e.,
$J^{\pi}=1^{-}$ states below and around the neutron-separation threshold
$S_{n}$. As mentioned earlier, the $(d,p)$ data will be discussed here. The
details of the 62Ni$(\gamma,\gamma^{\prime})$ experiment will be presented
elsewhere Sch (2023). As of now, $J=1$ assignments are available up to an
excitation energy of 8.5 MeV from 62Ni$(\gamma,\gamma^{\prime})$. Thus, at
this point, the discussion will be limited up to that energy. We used three
criteria to identify $1^{-}$ states: Their excitation energy must match the
one determined in $(\gamma,\gamma^{\prime})$ within uncertainties, their
angular distribution measured in $(\gamma,\gamma^{\prime})$ is indicative of a
$J=1$ assignment, and their $(d,p)$ angular distribution is described by an
$l=2$ (or $l=0$) transfer. These criteria provide rather unambiguous
$J^{\pi}=1^{-}$ assignments for 17 excited states up to an excitation energy
of 8.5 MeV (see Table LABEL:tab:energy). For four of these states, we list a
tentative spin-parity assignment as their $(\gamma,\gamma^{\prime})$ intensity
ratio is not entirely unambiguous. Fig. 8 presents the experimental data for
the $1^{-}$ states including the intensity ratios measured in
$(\gamma,\gamma^{\prime})$. For an explanation of the latter and of how these
ratios can be used to establish $J=1$ assignments, see, e.g., Refs. Müscher
_et al._ (2020); Kneissl  _et al._ (1996); Zilges  _et al._ (2022). Fig. 8
also shows the Nuclear Resonance Fluorescence (NRF), i.e.,
$(\gamma,\gamma^{\prime})$ scattering cross sections $I_{S}$ for 58,60Ni
determined for resolved $J^{\pi}=1^{-}$ states Scheck  _et al._ (2013);
Bauwens  _et al._ (2000). As can be seen in panels (e) and (f), the summed NRF
scattering cross section increases significantly from 58Ni $(N=30)$ to 60Ni
$(N=32)$. Since the NRF cross section is proportional to the $B(E1)$ strength,
this also indicates that the summed $B(E1)$ strength increases. Of course,
there is the caveat of possibly unobserved $\gamma$-decay branching when
calculating the $B(E1)$ strengths as also mentioned in Ref. Scheck  _et al._
(2013) and possibly unresolved strength. In addition to more strength being
observed for 60Ni, it is also clear that this strength shifts to lower
energies and that the density of states increases compared to 58Ni. Thus, it
does not seem unreasonable that we observe a further increase of the density
of $J=1$ states at lower energies in the $N=34$ isotope 62Ni [compare Fig. 8
(d) and (e)]. As the $(\gamma,\gamma^{\prime})$ data for 60Ni could indicate
the observation of two broader structures at $7.0-8.5$ MeV and $8.5-9.7$ MeV
(see Ref. Scheck  _et al._ (2013)), respectively, our $(d,p)$ data for 62Ni
might also hint at two broader structures with centroids at roughly 6.2 MeV
and 8 MeV [see Fig. 8 (a), (b) and compare to Fig. 7]. As also mentioned in
the previous section, we can currently not determine whether one of the
structures corresponds to $(2p_{3/2})^{-1}(2d_{5/2})^{+1}$ and the other to
$(2p_{3/2})^{-1}(2d_{3/2})^{+1}$ neutron 1p-1h excitations. To gain further
insight, detailed theoretical structure calculations, similar to the ones
performed for 208Pb Spieker  _et al._ (2020) and 120Sn Weinert  _et al._
(2021), are needed. A systematic comparison for 58-62Ni will then show whether
the strength increase and shift of the strength to lower energies is linked to
the $l=2$ spectroscopic strength also shifting down in energy. Such a
comparison will also allow to test the predictions of Inakura et al. Inakura
_et al._ (2011) in more detail. Inakura et al. had linked the strength
increase to the occupation of orbits with orbital angular momenta less than
$3\hbar$ $(l\leq 2)$ Inakura  _et al._ (2011). Based on our data, we can
already exclude that $l=0$ strength contributes significantly to the structure
of the $1^{-}$ states below the neutron-separation energy. If the connection
is true, the strength increase would, thus, need to be linked to the $l=2$
neutron 1p-1h strength.

##  IV Summary and Outlook

We presented new results for excited states of 62Ni up to the neutron-
separation energy. The data were obtained from a 61Ni$(d,p)$62Ni experiment
performed with the Super-Enge Split-Pole Spectrograph at the John D. Fox
Superconducting Linear Accelerator Laboratory of Florida State University.
Differential cross sections and angular distributions were measured for 79
excited states of 62Ni, of which 37 states were observed for the first time.
Besides discussing conflicting spin-parity assignments for a handful of
states, the $1g_{9/2}$ $(l=4)$ and $l=2$ spectroscopic strength in 62Ni, we
presented new experimental data for $J^{\pi}=1^{-}$ states obtained from the
$(d,p)$ and a complementary $(\gamma,\gamma^{\prime})$ experiment. The details
of the latter will be discussed elsewhere Sch (2023). A total of 17 excited
$J^{\pi}=1^{-}$ states were observed in both the $(d,p)$ and
$(\gamma,\gamma^{\prime})$ reaction below an excitation energy of 8.5 MeV. The
$(d,p)$ angular distributions for all of these states are described by $l=2$
angular momentum transfers suggesting that either
$(2p_{3/2})^{-1}(2d_{5/2})^{+1}$ or $(2p_{3/2})^{-1}(2d_{3/2})^{+1}$ neutron
1p-1h excitations contribute to their wavefunctions. Based on our new data, we
can exclude that $l=0$ strength, i.e., $(2p_{3/2})^{-1}(3s_{1/2})^{+1}$
neutron 1p-1h excitations contribute significantly to the structure of the
$1^{-}$ states below the neutron-separation energy. A look at the real-photon
scattering cross sections, which are already available for 58,60Ni, shows that
the $E1$ strength significantly increases in the Ni isotopes beyond $N=28$
Scheck  _et al._ (2013); Bauwens  _et al._ (2000); just as it did in the Cr
isotopes Ries  _et al._ (2019) and as it appears to increase in the Fe
isotopes Avigo  _et al._ (2020). Previously, Inakura et al. had linked this
strength increase to the occupation of orbits with orbital angular momenta
less than $3\hbar$ $(l\leq 2)$ Inakura  _et al._ (2011). An experimental test
of this prediction has, however, been missing so far. Our experimental study
provides the first step to start a rigorous test of this prediction based on
the neutron 1p-1h components of the wavefunctions.

The full analysis of the $(\gamma,\gamma^{\prime})$ data up to the neutron-
separation energy is ongoing. In the future, we plan to perform a systematic
study of the $B(E1)$ strengths of 58-62Ni, compare to quasiparticle-phonon
model (QPM) calculations, and use the QPM structure input to also calculate
the $(d,p)$ cross sections as done in Refs. Spieker  _et al._ (2020); Weinert
_et al._ (2021). We have already started the experimental study of other
nuclei in the $fp$ shell at the FSU SE-SPS. Particle-$\gamma$ coincidence
capabilities are also being established at the FSU SE-SPS, which will allow
detailed $(d,p\gamma)$ experiments in the future. Besides identifying possible
target contaminants, which might stay undetected in singles experiments and
lead to incorrect placement of excited states, additional information for
spin-parity assignments can be gained. Detailed studies of the $\gamma$-ray
strength function will also become possible.

###### Acknowledgements.

This work was supported by the National Science Foundation (NSF) under Grant
No. PHY-2012522 (WoU-MMA: Studies of Nuclear Structure and Nuclear
Astrophysics) and by the Deutsche Forschungsgemeinschaft under Contract No. ZI
510/10-1. The authors would like to thank G.W. McCann for helpful discussions
and his help with the data-analysis code. We thank P. Barber and B. Schmidt
for technical support prior to the experiment. M.S. also wants to thank P.D.
Cottle and K.W. Kemper for many informative discussions. A target provided by
the Center for Accelerator Target Science at Argonne National Laboratory was
used in this work.

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