Present address: ]Department of Physics, Florida State University,
Tallahassee, Florida 32306, USA

# Nature of yrast excitations near $N=40$: Level structure of 67Ni

S. Zhu  R. V. F. Janssens  M. P. Carpenter  Physics Division, Argonne National
Laboratory, Argonne, Illinois 60439, USA  C. J. Chiara  Physics Division,
Argonne National Laboratory, Argonne, Illinois 60439, USA  Department of
Chemistry and Biochemistry, University of Maryland, College Park, Maryland
20742, USA  R. Broda  Institute of Nuclear Physics, Polish Academy of
Sciences, PL-31342 Krakow, Poland  B. Fornal  Institute of Nuclear Physics,
Polish Academy of Sciences, PL-31342 Krakow, Poland  N. Hoteling  Physics
Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
Department of Chemistry and Biochemistry, University of Maryland, College
Park, Maryland 20742, USA  W. Królas  Institute of Nuclear Physics, Polish
Academy of Sciences, PL-31342 Krakow, Poland  T. Lauritsen  Physics Division,
Argonne National Laboratory, Argonne, Illinois 60439, USA  T. Pawłat
Institute of Nuclear Physics, Polish Academy of Sciences, PL-31342 Krakow,
Poland  D. Seweryniak  Physics Division, Argonne National Laboratory, Argonne,
Illinois 60439, USA  I. Stefanescu  Physics Division, Argonne National
Laboratory, Argonne, Illinois 60439, USA  Department of Chemistry and
Biochemistry, University of Maryland, College Park, Maryland 20742, USA  J. R.
Stone  Department of Chemistry and Biochemistry, University of Maryland,
College Park, Maryland 20742, USA  Department of Physics, University of
Oxford, OX1 3PU Oxford, UK  W. B. Walters  Department of Chemistry and
Biochemistry, University of Maryland, College Park, Maryland 20742, USA  X.
Wang  [  Physics Division, Argonne National Laboratory, Argonne, Illinois
60439, USA  Physics Department, University of Notre Dame, Notre Dame, Indiana
46556, USA  J. Wrzesiński  Institute of Nuclear Physics, Polish Academy of
Sciences, PL-31342 Krakow, Poland

###### Abstract

Excited states in 67Ni were populated in deep-inelastic reactions of a 64Ni
beam at 430 MeV on a thick 238U target. A level scheme built on the previously
known 13-$\mu$s isomer has been delineated up to an excitation energy of 5.3
MeV and a tentative spin and parity of (21/2-). Shell model calculations have
been carried out using two effective interactions in the $f_{5/2}pg_{9/2}$
model space with a 56Ni core. Satisfactory agreement between experiment and
theory is achieved for the measured transition energies and branching ratios.
The calculations indicate that the yrast states are associated with rather
complex configurations, herewith demonstrating the relative weakness of the
$N=40$ subshell gap and the importance of multi particle-hole excitations
involving the $g_{9/2}$ neutron orbital.

###### pacs:

23.20.Lv, 21.60.Cs, 27.50.+e, 25.70.Lm

##  I INTRODUCTION

The presence of shell gaps with magic numbers of nucleons is a cornerstone of
nuclear structure. Over the past decade it has increasingly become clear that
magic numbers are not immutable, but depend on the ratio of protons and
neutrons Sorlin and Porquet (2008); Janssens (2009). In discussions of magic
numbers, neutron number $N=40$ has historically been a subject of debate,
especially in the case of the Ni isotopes. Proton number $Z=28$ is magic, and,
for neutrons, a sizable energy gap at $N=40$ is thought to separate the $pf$
shell from the intruder $g_{9/2}$ state, potentially making $Z=28$, $N=40$
68Ni a doubly-magic nucleus. Experimentally, the occurrence of shell closures
in 68Ni was first suggested based on the observation of a 1770-keV
0${}_{2}^{+}$ level as the lowest excited state, followed by a 2${}_{1}^{+}$
state of relatively high excitation energy (2034 keV) Bernas et al. (1982);
Broda et al. (1995). The discovery of several isomeric states in 68Ni and in
neighboring nuclei Grzywacz et al. (1998); Ishii et al. (2000) supported the
case for its magic character further, as did the results from Coulomb
excitation measurements indicating a $B(E2,2_{1}^{+}\rightarrow 0^{+})$
reduced transition probability roughly three times smaller than the
corresponding value for ${}^{56}_{28}$Ni28 Sorlin et al. (2002); Bree et al.
(2008). However, based on recent high-precision mass measurements in the
neutron-rich Ni isotopes (up to 73Ni), the $N=40$ shell closure appears to be
more doubtful when inferred from changes in the two-neutron separation
energies Guénaut et al. (2007); Rahaman et al. (2007). It has been argued in
the literature that the apparent contradiction between the $B(E2)$ value and
the separation energy is a consequence of the parity change across the $N=40$
gap, with a sizable fraction of the low-lying $B(E2)$ strength residing in
excited states around 4 MeV, and the 2${}_{1}^{+}$ level being associated
predominantly with a neutron-pair excitation Sorlin et al. (2002); Langanke et
al. (2003). The size of the $N=40$ gap is then of the order of 2 MeV only and
the corresponding discontinuity in the sequence of orbitals corresponds at
most to a subshell closure.

Beta-decay studies Hannawald et al. (1999); Mueller et al. (1999); Sorlin et
al. (2003); Gaudefroy et al. (2005) and in-beam investigations at intermediate
beam energies Aldrich et al. (2008); Gade et al. (2010); Ljungvall et al.
(2010); Rother et al. (2011) provide evidence for the onset of collectivity
and strong polarization of the 68Ni core in neighboring nuclei of the region.
For example, the 2${}_{1}^{+}$ levels in $N=40$ 64Cr Gade et al. (2010) and
66Fe Hannawald et al. (1999) are located at excitation energies as low as 420
and 573 keV, respectively. More generally, the available low-spin level
structures in these nuclei suggest sizable admixture of spherical and deformed
components in the configurations near their ground states. These observations,
combined with the large $B(E2,2_{1}^{+}\rightarrow 0^{+})$ value measured for
70Ni42 Perru et al. (2006), lead to the conclusion that any “island” of nuclei
with indications of a significant $N=40$ gap is rather localized. A main
contributor to this situation is the monopole tensor force Otsuka et al.
(2001, 2005) between protons in the $pf$ shell and $g_{9/2}$ neutrons, where
the occupation of the latter orbital leads to the onset of deformation, as
evidenced, for example, by the presence of rotational bands in neutron-rich
55-57Cr and 59-61Fe nuclei Deacon et al. (2005); Zhu et al. (2006); Deacon et
al. (2011, 2007); Hoteling et al. (2008). On the other hand, couplings of
protons and/or neutrons to the 68Ni core do not always result in a large
polarization of the core. For example, the first excited state above the
(19/2-) isomer in 71Cu is located 2020 keV higher in energy, herewith
mirroring the location of the 2${}_{1}^{+}$ level in 68Ni Stefanescu et al.
(2009).

From the considerations above, it is clear that a satisfactory description of
nuclear structure in this mass region is still lacking. This is also reflected
in on-going theoretical efforts to determine the most appropriate interactions
for use in the calculations. In this context, the present data on the neutron-
hole nucleus 67Ni provide an opportunity to test the most modern interactions
while investigating the nature of yrast excitations up to moderate spin.

At present, only limited information is available on the low-lying structure
of 67Ni. Using deep-inelastic reactions of a 64Ni beam at 350 MeV on a thick
208Pb target, Pawłat et al. Pawłat et al. (1994) identified a 1008-keV
isomeric state with a half-life of T${}_{1/2}>0.3$ $\mu$s decaying through
coincident 314- and 694-keV transitions towards the 67Ni ground state. The
presence of the isomer was later confirmed in a fragmentation measurement
where a 13.3(2)-$\mu$s half-life was determined Grzywacz et al. (1998).
Feeding of the isomer in 67Co $\beta$ decay was subsequently reported Weissman
et al. (1999). These three studies Grzywacz et al. (1998); Pawłat et al.
(1994); Weissman et al. (1999) proposed spin and parity quantum numbers of
9/2+ for the long-lived state and associated this level with the occupation of
the $g_{9/2}$ orbital by a single neutron. With the NMR/ON technique, the
magnetic dipole moment of the 1/2- ground state was measured to be +0.601(5)
$\mu_{N}$, a value differing only slightly from the $\nu p_{1/2}$ single-
particle value; a fact regarded as evidence for the strength of the $N=40$
shell closure Rikovska et al. (2000). For the isomer, a quenched $g$-factor
value of $|g|$=0.125(6) was reported in Ref. Georgiev et al. (2002) and was
interpreted as evidence for a 2% admixture of a
$\pi(f^{-1}_{7/2}f_{5/2})_{1+}\nu g_{9/2}$ configuration involving a proton
excitation across the $Z=28$ gap into the supposedly pure $\nu g_{9/2}$ state.

Prior to the present work, no transitions feeding the isomeric state had been
reported. Here, despite the long half-life, eight new states have been placed
above the isomer from an investigation of prompt-delayed coincidence events in
a deep-inelastic reaction with a pulsed beam.

##  II EXPERIMENT

A number of experiments have demonstrated that the yrast states of hard-to-
reach neutron-rich nuclei can be populated in deep-inelastic processes at beam
energies $15\%-25\%$ above the Coulomb barrier Janssens et al. (2002); Fornal
et al. (2005); Broda (2006), allowing experimental access to high-spin
structures in regions inaccessible with conventional heavy-ion induced,
fusion-evaporation reactions.

The experiment was carried out with a 64Ni beam delivered by the ATLAS
superconducting linear accelerator at Argonne National Laboratory. The 430-MeV
beam energy was chosen to correspond roughly to an energy of 20$\%$ above the
Coulomb barrier in the middle of a 55-mg/cm2 thick 238U target. The beam was
pulsed with a 412-ns repetition rate, each beam pulse being $\sim$$0.3$ ns
wide. Gammasphere Lee (1990), with 100 Compton-suppressed HPGe detectors, was
used to collect events with three or more $\gamma$ rays in coincidence. The
data were sorted into two-dimensional ($E_{\gamma}-E_{\gamma}$ matrices) and
three-dimensional ($E_{\gamma}-E_{\gamma}-E_{\gamma}$ cubes) histograms under
various timing conditions. The prompt $\gamma\gamma\gamma$ cube (PPP cube) was
incremented for $\gamma$ rays observed within $\pm$20 ns of the beam burst
while, in the delayed $\gamma\gamma\gamma$ cube (DDD cube), the transitions
were required to occur in an interval of $\sim$40 to $\sim$800 ns after the
prompt time peak (excluding the subsequent beam pulse), but within $\pm$20 ns
of each other. In this way, events associated with isomeric deexcitations
could be isolated and identified. The prompt-delayed-delayed (PDD) and prompt-
prompt-delayed (PPD) cubes were incremented by combining prompt and delayed
events. These proved critical in identifying prompt $\gamma$ rays feeding
isomeric levels as they revealed themselves in double-gated spectra on the
known transitions below the isomer in the PDD cubes. The relations between
these prompt $\gamma$ rays were subsequently established by examining proper
double coincidence gates in the PPD and PPP cubes. Examples and further
details of this technique can be found in Refs. Hoteling et al. (2008);
Stefanescu et al. (2009).

The spins and parities of the levels were deduced from an angular-correlation
analysis. In addition, considerations based on the fact that the reactions
feed yrast states preferentially, and/or on comparisons with shell-model
calculations, were also taken into account. The projectile-like products of
deep-inelastic reactions are usually characterized by no, or very little,
alignment. Therefore, the analysis of $\gamma$$\gamma$ angular correlations
for selected pairs of transitions is required Fornal et al. (2005); Hoteling
et al. (2006). In practice, in order to avoid as much as possible ambiguities
in the spin assignments, at least one known stretched transition was included
in the analysis.

##  III RESULTS

In previous studies Pawłat et al. (1994); Grzywacz et al. (1998); Weissman et
al. (1999), the 314- and 694-keV transitions deexciting the 13.3(2)-$\mu$s
isomer in 67Ni were assigned to the
$9/2^{+}$$\rightarrow$$5/2^{-}$$\rightarrow$$1/2^{-}$ cascade and no
transition above this long-lived state was reported. As stated above,
transitions feeding the isomer were initially identified in the present work
by using the PDD coincidence data. A coincidence spectrum from this PDD cube
with double gates placed on the 314- and 694-keV transitions is presented in
Fig. 1. Besides a 1345-keV line belonging to the $2^{+}\rightarrow 0^{+}$
transition in 64Ni, three $\gamma$ rays are clearly visible at 1210, 1655, and
1667 keV. The 1345-keV line originates from Coulomb excitation of the 64Ni
beam, and is attributed to random coincidences. By double gating the PDD cube
with one of the newly discovered prompt $\gamma$ rays and one of the delayed
transitions, their mutual coincidence relationships can be verified further.
The results, displayed in Fig. 2, establish the feeding of the 67Ni isomer by
the 1210- and 1655-keV transitions. Finally, additional evidence was provided
by the analysis of the PPD cube, where a double gate on the prompt 1655- and
1667-keV $\gamma$ rays yields a delayed spectrum in which the 314- and 694-keV
lines appear, consistent with the expected coincidence relationships for
$\gamma$ rays across the isomer. This observation also implies that the 1655-
and 1667-keV transitions are in mutual, prompt coincidence.

Levels above the 67Ni isomer were investigated further in the PPP cube with
the newly-observed 1210-, 1655- and 1667-keV transitions as a starting point.
A double gate on the latter two $\gamma$ rays reveals the presence of three
additional lines at 63, 172, and 708 keV (see Fig. 3). The 1655- and 1210-keV
transitions are not in mutual coincidence, herewith establishing the presence
of parallel decay sequences. Exploiting additional coincidence relationships,
such as those displayed in Fig. 4, it was possible to propose the level scheme
of Fig. 5. Thus, states at 2218, 2663, 3530, 3913, 4330, and 4502 keV were
firmly established through the various competing decay paths. The ordering of
the highest levels at 4565 and 5273 keV is based on the measured $\gamma$-ray
intensities. The presence of a low-energy transition of 63 keV might suggest a
longer half-life for the 4565-keV state. Unfortunately, at this energy, the
timing signal of the large-volume germanium detectors is rather poor. This
fact, combined with the rather small intensity, made it impossible to obtain
firm information on the level lifetime. However, time spectra gated on the
transitions below the 4502-keV state do not provide evidence for a measurable
lifetime and an upper limit of $\sim$15 ns can be given for the 4565-keV
level.

Angular correlations were used to determine the multipolarity of some of the
newly identified transitions. Because the yield of the 314- and 694-keV
isomeric cascade was sufficient, the relevant coincidence intensities were
grouped into 12 different angles $\theta$. The measured angular-correlation
pattern for this pair strongly favors a sequence with two stretched quadrupole
transitions, as can be seen from the comparison with the theoretical
prediction of Fig. 6(a), which agrees with a
9/2+$\rightarrow$5/2-$\rightarrow$1/2- cascade. In view of the smaller
intensities, the correlation between the 1655- and the 1667-keV lines was
grouped into five angles [Fig. 6(b)]. It is consistent with a quadrupole-
dipole sequence. To be consistent with the decay pattern of the 2663-keV
level, the 1655-keV $\gamma$ ray is proposed as a quadrupole transition,
leading to a 13/2+ assignment for this state, and 15/2+ quantum numbers for
the level at 4330 keV.

Due to the lack of statistics, the correlation data for other transitions were
regrouped into the two angles of 33∘ (from 20∘ to 42∘ in Gammasphere) and 77∘
(69∘ to 87∘). Intensity ratios were obtained for the 1655-1250, 1655-172, and
1210-1695 keV pairs of transitions. The ratio of 0.81(9) measured for the
1655-1250 keV cascade points to a dipole character for the 1250-keV $\gamma$
ray, resulting in a 15/2+ assignment to the 3913-keV level. With this 15/2+
assignment and the measured 1.8(3) ratio indicating a quadrupole-dipole
cascade for the 1210-1695 keV pair where the dipole transition has a large
$E2/M1$ mixing ratio, a consistent picture emerges with the proposed 11/2+
spin and parity for the 2218-keV state. Note that the mixed-dipole character
for the 1210-keV transition is also consistent with the expectations of shell-
model calculations, as will be discussed below. A 17/2 spin assignment to the
4502-keV state was derived from the 0.85(4) correlation ratio measured for the
1655-172 keV pair. Even though correlation data could not be extracted for the
1210-1312 keV cascade, the 13/2+ assignment to the 3530-keV level is supported
by the presence of the weak, 2522-keV decay branch towards the 9/2+ isomer.
Finally, the general agreement between these assignments and the results of
shell-model calculations was used to tentatively propose 19/2- and 21/2-
assignments to the two highest states. The experimental information on levels
in 67Ni is summarized in Table 1.

Table 1: List of levels with the spin-parity assignments and $\gamma$ rays identified in 67Ni, including intensities and placements. Ei | J${}_{i}^{\pi}$ | J${}_{f}^{\pi}$ | Eγ | Iγ
---|---|---|---|---
(keV) |  |  | (keV) |
0 | 1/2- |  |  |
694.3(2)111Observed only with beam off | 5/2- | 1/2- | 694.3(2) |
1008.1(3)111Observed only with beam off | 9/2+ | 5/2- | 313.8(2) |
2218.0(4) | 11/2+ | 9/2+ | 1210.0(3) | 66(9)
2662.8(4) | 13/2+ | 11/2+ | 444.9(3) | 13(2)
|  | 9/2+ | 1654.7(2) | 100(8)
3530.3(4) | 13/2+ | 11/2+ | 1312.3(3) | 16(3)
|  | 9/2+ | 2522(1) | 2.0(5)
3913.0(4) | 15/2+ | 13/2+ | 382.7(2) | 16(3)
|  | 13/2+ | 1250.0(3) | 29(5)
|  | 11/2+ | 1695.1(5) | 7(1)
4330.1(4) | 15/2+ | 13/2+ | 1667.3(2) | 50(7)
4501.9(4) | 17/2(-) | 15/2+ | 171.8(2) | 48(6)
|  | 15/2+ | 588.8(2) | 52(6)
4564.7(5) | (19/2-) | 17/2(-) | 62.8(2) | 31(6)
5273.1(7) | (21/2-) | (19/2-) | 708.4(5) | 20(3)
| (21/2-) | 17/2(-) | 771(1) |  $<$3

##  IV DISCUSSION

At first glance, the level structure on top of the 9/2+ isomer in 67Ni appears
to be of single-particle character. The yrast sequence does not exhibit any
regularity in the increase in excitation energy with angular momentum, as
would be expected in the presence of collectivity, and states of opposite
parity compete for yrast status. Moreover, in the absence of any notable
Doppler shift for any of the observed transitions, the combined feeding and
level lifetimes must be at least of the order of the stopping time of the
reaction products in the thick uranium target; i.e. 1 ps or longer. It should
also be noted that the sequence of levels above the 9/2+ isomer exhibits
similarities with the structure found above the corresponding 9/2+ long-lived
state in 65Ni. The latter structure was interpreted in terms of single-
particle excitations - see Ref. Pawłat et al. (1994) for details. These
observations would argue in favor of a subshell closure at $N=40$.

In order to gain further insight into the nature of the observed 67Ni states,
large-scale calculations were carried out with the shell-model code ANTOINE
Caurier and Nowacki (1999); Caurier (1989-2004) using both the jj44b Brown
and the JUN45 Honma et al. (2009) effective interactions. Both Hamiltonians
were restricted to the $f_{5/2}$, $p_{3/2}$, $p_{1/2}$, and $g_{9/2}$ valence
space and assume a 56Ni core. However, the required two-body matrix elements
and single-particle energies were obtained from fits to different sets of
data. Specifically, the JUN45 interaction was developed by considering data in
nuclei with $Z\sim 32$ and $N\sim 50$, and excludes explicitly the Ni and Cu
isotopes as the 56Ni core is viewed as being rather “soft” Honma et al.
(2009). In contrast, experimental data from $Z=28-30$ isotopes and $N=48-50$
isotones were incorporated in the fits in the case of the jj44b interaction
Brown .

The results of the calculations are compared with the experimental data in
Fig. 5. With both interactions, the energy of the 9/2+ state is predicted
lower than the measured value. This can be viewed as an indication that the
adopted single-particle energy of the $g_{9/2}$ neutron orbital is too low in
the two Hamiltonians. It is worth noting that the jj44b interaction calculates
this state to lie within 192 keV of the data and indicates about a 25%
admixture of the $\nu g_{9/2}^{3}$ configuration into the 9/2+ wave function.
With the JUN45 interaction, the level is predicted to lie 498 keV lower than
in the data with roughly 33% of the wave function involving three neutrons in
the $g_{9/2}$ orbital. This is possibly the result of the location of the
$g_{9/2}$ orbital at a lower energy in the JUN45 Hamiltonian, as compared to
that used in the jj44b case, which leads to larger configuration mixing in the
wave function of the $9/2^{+}$ state.

Overall, the calculated spectrum with both interactions appears somewhat
compressed when compared to the data, as illustrated on the right side of Fig.
5. Note that for reasons of clarity, only the calculated yrast and near-yrast
excitations are shown; i.e., the states with a likely corresponding level in
the data are plotted. The correspondence between data and calculations is
rather satisfactory when the computed excitation energies are expressed
relative to the 9/2+ isomer as is done on the left-hand side of Fig. 5.
Indeed, both interactions predict close-lying 11/2+ and 13/2+ levels,
separated from the next 13/2+ excitation by roughly 1 MeV, in agreement with
the proposed level scheme. A pair of close-lying 15/2+ levels is also computed
to be located directly above the 13/2${}_{2}^{+}$ state, as seen in the data.
Both interactions also predict a first excited 17/2+ state more than 300 keV
above the 15/2${}_{2}^{+}$ excitation with higher-spin, positive-parity states
another 1.3 MeV or more above this. In contrast, negative-parity levels are
present at lower excitation energies with both effective interactions, leading
to the proposed assignments of 17/2(-), (19/2-), and (21/2-) for the 4502-,
4565-, and 5273-keV states in Fig. 5. As indicated in the figure, these
assignments should be viewed as tentative, especially in the case of the 17/2
level, where calculated 17/2 states of both parities are separated only by
$\sim$200 and $\sim$400 keV, depending on the interaction.

It is of interest to identify in the calculations the main components of the
wave functions of the observed states. For the 11/2+ level, and the non-yrast
13/2${}_{2}^{+}$ and 15/2${}_{2}^{+}$ states, both Hamiltonians result in wave
functions in which the $\nu f_{5/2}^{5}p_{3/2}^{4}p_{1/2}^{1}g_{9/2}^{1}$
configurations dominate with a contribution of the order of 50%. Perhaps
surprisingly, the 13/2${}_{1}^{+}$ and 15/2${}_{1}^{+}$ states are computed to
be more fragmented, with respective main contributions by the $\nu
f_{5/2}^{5}p_{3/2}^{4}p_{1/2}^{1}g_{9/2}^{1}$ and $\nu
f_{5/2}^{4}p_{3/2}^{4}p_{1/2}^{2}g_{9/2}^{1}$ configurations of $\sim$30%
only. In addition, the JUN45 interaction results in a $\sim$10% admixture of
the $\nu g_{9/2}^{3}$ configuration into the wave functions of these two
levels. This contribution is of the order of 5% with the jj44b interaction.
With this Hamiltonian the wave functions of all the negative-parity states are
mixed with only the 17/2- level having a contribution from the $\nu
f_{5/2}^{4}p_{3/2}^{4}p_{1/2}^{1}g_{9/2}^{2}$ of the order of 50%. In
contrast, with the JUN45 interaction, where the ordering of states is computed
in better agreement with the data [see the
15/2${}_{2}^{+}$—17/2(-)—(19/2-)—(21/2-) sequence in Fig. 5], the wave
function of every negative-parity state is characterized by a 40-50% component
from the $\nu f_{5/2}^{4}p_{3/2}^{4}p_{1/2}^{1}g_{9/2}^{2}$ configuration.

Table 2: Relative branching ratios depopulating the 13/2${}_{1}^{+}$, 13/2${}_{2}^{+}$, and 15/2${}_{1}^{+}$ levels derived from experimental measurements, and calculated results using the JUN45 and jj44b effective interactions. J${}_{i}^{\pi}$ | J${}_{f}^{\pi}$ | Measurements | JUN45111Branching ratios are obtained with calculated transition energies. | jj44b111Branching ratios are obtained with calculated transition energies. | JUN45222Branching ratios are obtained with measured transition energies. | jj44b222Branching ratios are obtained with measured transition energies.
---|---|---|---|---|---|---
13/2${}^{+}_{1}$ | 11/2+ | 13(2) | 6 | 23 | 36 | 67
| 9/2+ | 100(8) | 100 | 100 | 100 | 100
13/2${}^{+}_{2}$ | 13/2${}^{+}_{1}$ |  $<$3 | 0 | 166 | 0 | 96
| 11/2+ | 100(20) | 100 | 100 | 100 | 100
| 9/2+ | 11(4) | 9 | 105 | 7 | 92
15/2${}^{+}_{1}$ | 13/2${}^{+}_{2}$ | 57(9) | 33 | 11 | 95 | 40
| 13/2${}^{+}_{1}$ | 100(15) | 100 | 100 | 100 | 100
| 11/2+ | 23(2) | 15 | 5 | 28 | 7

In the absence of lifetime information on the 67Ni levels above the isomer,
additional tests of the shell-model calculations are possible by considering
the branching ratios for transitions competing in the deexcitation of specific
levels. For the computation of the $B(E2)$ transition probabilities, proton
and neutron effective charges $e_{p}=1.5e$ and $e_{n}=0.5e$ were adopted as is
usual for nuclei in this region. Comparisons between computed branchings for
the two Hamiltonians and the data are presented in Table 2. Only cases for
which the coincidence yields were sufficient to allow gating on the
transitions directly feeding a state of interest were considered for Table 2.
Note that this table provides shell-model results using either the calculated
or the measured transition energies. The latter values effectively remove the
dependence of the ratios on the transition energies. From the table, it is
clear that calculations with the JUN45 Hamiltonian are consistently in better
agreement with the measured branching ratios. It is also worth pointing out
that both Hamiltonians also compute a $11/2^{+}\rightarrow 9/2^{+}$ transition
of strongly mixed $E2/M1$ character ($|\delta|>0.5$), in agreement with the
angular-correlation data for the 1210-1695 keV cascade (see Section III).

From the discussion above, it is concluded that the levels above the 9/2+
isomeric state can be understood as neutron excitations, with contributions of
protons across the $Z=28$ gap playing a minor role at best. Calculations with
both interactions are in fair agreement with the data. They attribute a
significant role to the $g_{9/2}$ neutron orbital for every state observed in
this measurement. In fact, in most cases, significant $\nu g_{9/2}^{2}$ and
$\nu g_{9/2}^{3}$ configurations are part of the wave functions. Similar
observations have been made for other nuclei close to 68Ni; see, for example,
recent comparisons between calculations with the same jj44b and JUN45
interactions and data for 65,67Cu in Ref. Chiara et al. (2008). From these
findings, it is concluded that even in a nucleus only one neutron removed from
$N=40$, the impact of a neutron shell closure is rather modest. As the
$g_{9/2}$ neutron orbital is shape driving, multi particle-hole excitations
involving this state may be expected to be associated with enhanced
collectivity and it would be of interest to investigate the latter in future
measurements.

##  V CONCLUSIONS

A level scheme above the known 13-$\mu$s isomer in 67Ni was established for
the first time by exploring prompt and delayed coincidence relationships from
deep-inelastic reaction products. Spin and parity quantum numbers for the
newly observed states were deduced from an angular-correlation analysis
whenever sufficient statistics was available. Shell-model calculations have
been carried out with two modern effective interactions, JUN45 and jj44b, for
the $f_{5/2}pg_{9/2}$ model space with 56Ni as a core. Satisfactory agreement
between experiment and theory was achieved. Even though the level structure of
67Ni appears to exhibit a single-particle character based on comparisons
between the measured level properties, including branching ratios, with the
results of shell-model calculations, it is suggested that the yrast and near-
yrast states are associated with rather complex configurations. In fact,
calculations indicate that the wave functions of the yrast states involve a
large number of configurations without a dominant ($\sim$50%) specific one;
the latter being more prevalent in the near-yrast levels. It is hoped that the
present data will stimulate additional theoretical work such as comparisons
with calculations using other effective interactions or a different model
space. Further experimental work aimed at the evolution of the degree of
collectivity with spin and excitation energy is highly desirable as well.

###### Acknowledgements.

The authors thank the ATLAS operating staff for the efficient running of the
accelerator and J.P. Greene for target preparation. This work was supported by
the U.S. Department of Energy, Office of Nuclear Physics, under Contract No.
DE-AC02-06CH11357 and Grant No. DE-FG02-94ER40834, by Polish Scientific
Committee Grant No. 2PO3B-074-18, and by Polish Ministry of Science Contract
No. NN202103333.

## References

  * Sorlin and Porquet (2008) O. Sorlin and M.-G. Porquet, Progress in Particle and Nuclear Physics 61, 602 (2008).
  * Janssens (2009) R. V. F. Janssens, Nature 459, 1069 (2009).
  * Bernas et al. (1982) M. Bernas, Ph. Dessagne, M. Langevin, J. Payet, F. Pougheon, and P. Roussel, Phys. Lett. B 113, 279 (1982).
  * Broda et al. (1995) R. Broda et al., Phys. Rev. Lett. 74, 868 (1995).
  * Grzywacz et al. (1998) R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998).
  * Ishii et al. (2000) T. Ishii, M. Asai, A. Makishima, I. Hossain, M. Ogawa, J. Hasegawa, M. Matsuda, and S. Ichikawa, Phys. Rev. Lett. 84, 39 (2000).
  * Sorlin et al. (2002) O. Sorlin et al., Phys. Rev. Lett. 88, 092501 (2002).
  * Bree et al. (2008) N. Bree et al., Phys. Rev. C 78, 047301 (2008).
  * Guénaut et al. (2007) C. Guénaut et al., Phys. Rev. C 75, 044303 (2007).
  * Rahaman et al. (2007) S. Rahaman et al., Eur. Phys. J. A 34, 5 (2007).
  * Langanke et al. (2003) K. Langanke, J. Terasaki, F. Nowacki, D. J. Dean, and W. Nazarewicz, Phys. Rev. C 67, 044314 (2003).
  * Hannawald et al. (1999) M. Hannawald et al., Phys. Rev. Lett. 82, 1391 (1999).
  * Mueller et al. (1999) W. F. Mueller et al., Phys. Rev. Lett. 83, 3613 (1999).
  * Sorlin et al. (2003) O. Sorlin et al., Eur. Phys. J. A 16, 55 (2003).
  * Gaudefroy et al. (2005) L. Gaudefroy et al., Eur. Phys. J. A 23, 41 (2005).
  * Aldrich et al. (2008) P. Aldrich et al., Phys. Rev. C 77, 054306 (2008).
  * Gade et al. (2010) A. Gade et al., Phys. Rev. C 81, 051304 (2010).
  * Ljungvall et al. (2010) J. Ljungvall et al., Phys. Rev. C 81, 061301(R) (2010).
  * Rother et al. (2011) W. Rother et al., Phys. Rev. Lett. 106, 022502 (2011).
  * Perru et al. (2006) O. Perru et al., Phys. Rev. Lett. 96, 232501 (2006).
  * Otsuka et al. (2001) Takaharu Otsuka, Rintaro Fujimoto, Yutaka Utsuno, B. Alex Brown, Michio Honma, and Takahiro Mizusaki, Phys. Rev. Lett. 87, 082502 (2001).
  * Otsuka et al. (2005) Takaharu Otsuka, Toshio Suzuki, Rintaro Fujimoto, Hubert Grawe, and Yoshinori Akaishi, Phys. Rev. Lett. 95, 232502 (2005).
  * Deacon et al. (2005) A. N. Deacon et al., Phys. Lett. B 622, 151 (2005).
  * Zhu et al. (2006) S. Zhu et al., Phys. Rev. C 74, 064315 (2006).
  * Deacon et al. (2011) A. N. Deacon et al., Phys. Rev. C 83, 064305 (2011).
  * Deacon et al. (2007) A. N. Deacon et al., Phys. Rev. C 76, 054303 (2007).
  * Hoteling et al. (2008) N. Hoteling et al., Phys. Rev. C 77, 044314 (2008).
  * Stefanescu et al. (2009) I. Stefanescu et al., Phys. Rev. C 79, 034319 (2009).
  * Pawłat et al. (1994) T. Pawłat et al., Nucl. Phys. A574, 623 (1994).
  * Weissman et al. (1999) L. Weissman et al., Phys. Rev. C 59, 2004 (1999).
  * Rikovska et al. (2000) J. Rikovska et al., Phys. Rev. Lett. 85, 1392 (2000).
  * Georgiev et al. (2002) G. Georgiev et al., J. Phys. G: Nucl. Part. Phys. 28, 2993 (2002).
  * Janssens et al. (2002) R. V. F. Janssens et al., Phys. Lett. B 546, 55 (2002).
  * Fornal et al. (2005) B. Fornal et al., Phys. Rev. C 72, 044315 (2005).
  * Broda (2006) R. Broda, J. Phys. G: Nucl. Part. Phys. 32, R151 (2006).
  * Lee (1990) I-Y. Lee, Nucl. Phys. A520, 641c (1990).
  * Hoteling et al. (2006) N. Hoteling et al., Phys. Rev. C 74, 064313 (2006).
  * Caurier and Nowacki (1999) E. Caurier and F. Nowacki, Acta Phys. Pol. B 30, 705 (1999).
  * Caurier (1989-2004) E. Caurier, shell-model code antoine, IRES, Strasbourg (1989-2004).
  * (40) B. A. Brown, private communication; see also Ref. [28] in B. Cheal et al., Phys. Rev. Lett. 104, 252502 (2010).
  * Honma et al. (2009) M. Honma, T. Otsuka, T. Mizusaki, and M. Hjorth-Jensen, Phys. Rev. C 80, 064323 (2009).
  * Chiara et al. (2008) C. J. Chiara et al., Phys. Rev. C 85, 024309 (2012).

Figure 1: Partial spectrum with double coincidence gates set on the 314- and
694-keV cascade below the 67Ni 9/2+ isomer in the PDD cube. The spectrum shows
three strong transitions feeding the 9/2+ state; the 1345-keV $\gamma$ ray of
64Ni is due to random coincidences (see text for detail).

Figure 2: Partial coincidence spectra with different gates in the PDD cube
establishing the feeding of the 9/2+ isomeric state, see text for details.
Note the change in energy scales between panels (a, b) and (c, d).

Figure 3: Partial coincidence spectrum with double gates set on the 1655- and
1667-keV lines in the PPP cube showing the transitions from the states with
highest excitation energy observed in the present work.

Figure 4: Partial spectra with different gates in the PPP cube demonstrating
various coincidence relationships used to establish the level scheme of Fig.
5.

Figure 5: The proposed level scheme of 67Ni. Results of the shell-model
calculations with the JUN45 and jj44b effective interactions are shown for
comparison. The set of calculations to the left is identical to that on the
right, except that the excitation energies were offset such that the 9/2+
isomeric state matches the data.

Figure 6: Measured angular correlations for $\gamma\gamma$ cascades in 67Ni.
Dashed lines in the figure correspond to expected patterns associated with
pairs of stretched quadrupole-quadrupole transitions (panels a and b), while
the dot-dashed line is associated with a stretched quadrupole-dipole pair of
$\gamma$ rays (panel b).