Probing the nuclear structure in the vicinity of 78Ni

Theoretical and experimental studies of neutron-rich nuclei have shown that the general concept of shell structure is not as robust and universal as earlier thought, but can exhibit significant changes as a function of neutron excess. New magic numbers appear and some other conventional ones disappear mainly because of a different ordering of the single-particle orbitals. In the present contribution, recent experimental studies of neutron-rich Cu isotopes, performed at RIKEN using β decay and one-proton knockout reactions, will be discussed. Neutron-rich nuclei near 78Ni were populated through in-flight fission of 238U on thick 9Be targets in both experiments. In the β-decay study, 75,77Ni nuclei were implanted into the WAS3ABi silicon array, while γ rays from excited states in 75,77Cu emitted after β decay of the implanted ions were detected with the EURICA Ge detector array that was surrounding the active stopper. In a second experiment within the SEASTAR campaign at RIKEN, the same 75,77Cu nuclei were produced in (p,2p) knockout reactions from 76,78Zn beam particles at around 250 MeV/nucleon impinging onto the MINOS liquid hydrogen target. In the latter experiment the DALI2 NaI array was used to detect de-excitation γ rays measured in coincidence with Cu nuclei identified in the Zero Degree Spectrometer. Both studies are complimentary and greatly contribute to our understanding on the nuclear structure in the 78Ni region.


Introduction
Over the last two decades, investigations at radioactive ion beam facilities have revealed that atomic nuclei undergo significant changes in their shell structure when moving towards neutron-rich isotopes. This so-called shell evolution for nuclei with large neutron-to-proton asymmetry is due to specific properties of the nucleon-nucleon interaction, which can lead to a different ordering of singleparticle orbitals and, hence, to the appearance or disappearance of shell gaps. The phenomenon is by now well established in lighter mass regions with Z < 28 and N < 40.
As an example, Figure 1a shows the energies of the first excited 2 + states, E(2 + 1 ), as a function of neutron number N for isotopes of Si, S, Ar, and Ca. One can clearly see the disappearance of the neutron N = 28 shell gap in 42 Si [1], 44 S [2], and 46 Ar [3], as evidenced by their low E(2 + 1 ) energies. On the other hand, the excitation energies for 52,54 Ca are very high, indicating the appearance of new shell gaps at N = 32 and 34. The shell gap at N = 34 appears to be rather robust, as illustrated by the high excitation energy of the 2 + 1 state in 52 Ar [4]. The reduction or even collapse of shell closures when going far away from stability is connected with an onset of deformation. The phenomenon where deformation is favored due to particle-hole excitations across major shells has been * e-mail: eda.sahin@fys.uio.no termed "island of inversion". In general, the coexistence of intruder and normal configurations leads to shape coexistence, which consequently can be expected in regions of disappearing shell closures. As an illustrative example 44 S can be mentioned, where a prolate 0 + 1 ground state coexists with a spherical excited 0 + 2 state [5]. In this case the reduction of the N = 28 shell gap enables quadrupole excitations from the 1 f 7/2 to the 2p 3/2 orbitals.
In the light of these results, questions arise concerning the robustness of the N = 50 shell gap for neutron-rich nuclei, the magic character of 78 Ni, and possible intruder states and an onset of deformation in the region around 78 Ni. Experimental information in this region of the nuclear chart is very sparse due to the extreme proton-toneutron ratio, which makes production of these nuclei difficult and experimental studies in general very challenging. The energy of the 2 + 1 state in 78 Ni was only very recently measured to be 2.6 MeV [6]. This high energy supports the notion of doubly magic character for 78 Ni and the persistence of the Z = 28 and N = 50 shell gaps (see Figure 1b). However, detailed studies on the evolution of single-particle orbitals in this mass region are still very much incomplete. The aim of the experiments that are presented here was to contribute to a more quantitative understanding of the shell structure near 78 Ni. More specifically, the evolution of the proton single-particle energies will be discussed as a function of neutron number, together with the consequences for the occupation of intruder configurations and the onset of deformation and collectivity.

Evolution of the Z=28 shell gap
Changes in the single-particle structure are strongly related to certain properties of the (residual) interactions between nucleons. In particular the tensor component of the monopole interaction was found to be responsible for the changes in the single-particle energies (SPEs) [8]. The tensor force is attractive between two orbits with relative spin orientations j > = l + 1/2 and j < = l − 1/2 (or j < = l − 1/2 and j > = l + 1/2) and repulsive between those with spin orientations j > and j > (or j < and j < ). The evolution of the Z = 28 shell gap was previously investigated by systematically studying the properties of the Ni isotopes from 68 Ni (N = 40) to 78 Ni (N = 50). Figure 2 shows the resulting proton SPEs as a function of neutron number from shell model calculations for the Ni isotopes [9]. Note that the SPEs change more dramatically when including the tensor component of the monopole interaction (solid lines), while the relative changes are less pronounced when the tensor component is not included (dashed lines). According to these calculations, the changes in the proton SPEs lead to an inversion of the π2p 3/2 and π1 f 5/2 orbitals with increasing number of neutrons in the ν1g 9/2 orbital. The crossing of the π2p 3/2 and π1 f 5/2 orbitals is consistent with the measured 5/2 − spin-parity for the ground state in 75 Cu [10]. Furthermore, the calculations predict a reduction for the Z = 28 shell gap as a result of the attraction between the π1 f 5/2 and the ν1g 9/2 and the repulsion between the π1 f 7/2 and ν1g 9/2 orbitals.

Beta-decay of 75,77 Ni
Cu nuclei have been studied in detail up to 73 Cu via different reaction mechanisms such as β-decay, Coulomb excitation, and single-and multi-nucleon transfer reaction studies [13][14][15][16][17][18][19][20][21]. For the heavier isotopes 75 Cu and 77 Cu, only the spin and parity of the ground state was known [10], and, in case of 75 Cu, two low-lying isomeric states [22,23]. To identify low-lying states and establish the level schemes for 75 Cu and 77 Cu, β-decay experiments were carried out at RI Beam Factory (RIBF) of the RIKEN Nishina Center [24]. The secondary beam particles near 78 Ni were produced via fission reaction of the 238 U primary beam on a thick 9 Be target. After particle identification in atomic number (Z) and mass-to-charge ratio (A/Q) using the T OF − Bρ − ∆E technique [25] in the BigRIPS fragment separator [26,27], the ions were delivered to the experimental setup through the ZeroDegree Spectrometer (ZDS) [27] and implanted in a stack of eight highly pixelised double-sided silicon strip detectors (WAS3ABI [28]). Each DSSSD had 60 horizontal and 40 vertical strips of 1 mm pitch, respectively. Surrounding the implantation detector was the EURICA germanium detector array [28,29] for the detection of γ rays emitted after β decay of the implanted ions.  The level structure of 75,77 Cu was investigated through γ-ray spectroscopy following the β decay of 75,77 Ni. The implanted Ni ions were correlated on an event-by-event basis in time and position with β decays detected in WAS3ABI. It was required that the β-decay electrons were detected in the same DSSSD within a correlation area that covered up to two pixels away from the implantation position. The time correlation between β-decay events and detected γ rays was used to identify γ-ray transitions as originating from 75,77 Cu or their respective daughter decays. Due to the high efficiency of EURICA it was possible to analyze γ-γ coincidences and use the coincidence relationships to build level schemes up to around 4 MeV excitation energy for both nuclei. A total of 28 new excited states were identified in 75 Cu [33] and 12 in 77 Cu [32]. Tentative spin-parity values were assigned for all states in 77 Cu based on the β-decay feeding (log( f t) values) and γdecay properties, whereas this was only possible for the lowest states in 75 Cu. Figure 3 shows the level scheme for 77 Cu obtained from the present data together with results from state-of-the-art Monte Carlo Shell Model calculations [30,31]. The calculations used the A3DA interaction [30] with rather large valence space, i.e. the full f p shell (1 f 7/2 , 1 f 5/2 , 2p 3/2 , 2p 1/2 ) plus the 1g 9/2 and 2d 5/2 orbitals outside a 40 Ca core.
There is rather good agreement between the experimental results and the results from the shell model calculations, in particular for the states up to 2 MeV excitation energy. All low-lying states are explained as having either single-particle, core-coupled, or intruder character as explained above. With new experimental results available, the shell model calculations have been refined compared to the previous results shown in Figure 2. The SPEs from the new shell model calculations are shown in Figure 4. The results indicate that the inversion of the π2p 3/2 and π1 f 5/2 orbitals does not occur at N = 46 ( 75 Cu), as was reported in 2010 in the work of Otsuka et al. [9], but occurs instead at N = 48 ( 77 Cu). The fact that the 5/2 − state is lower than the 3/2 − state already in 75 Cu is explained by correlation effects due to multipole interaction, which are stronger for the 5/2 − state than for the 3/2 − state [32]. Furthermore, with the crossing of these two orbits found to occur later than previously thought, the reduction of the Z = 28 shell gap is also smaller than in previously calculations. As one of the main results from the present βdecay study it can be concluded that the size of the Z = 28 shell gap is reduced from 6.5 MeV at N = 40 to 5 MeV at N = 50 [32]. More detailed discussions, together with extended results on 75 Cu and their comparison to the largescale shell-model calculations, will be presented in a forthcoming article [33].

Proton excitations across Z = 28
The β-decay experiment discussed above gave insight into the single-particle properties in the 78 Ni region based on comparisons with shell model calculations. It also gave a first indication for a 7/2 − intruder state based on a proton excitation across the Z = 28 shell gap (see Figure 4). Complementary experiments using direct reaction mechanism such as one-proton knockout selectively populate excited states arising from single-proton excitations. Such experiments can give a more direct identification of singleparticle states based on 2p 3/2 and 1 f 5/2 protons, and, in particular, of the (π1 f 7/2 ) −1 particle-hole excitation across the Z = 28 shell gap. As the interpretation of the 7/2 − states found in the β-decay experiment is less straightforward as compared to the other low-lying states, complementary knock-out experiments can provide essential information on the evolution of the shell structure close to 78 Ni. The location of the 7/2 − 2p − 1h intruder state along the chain of the Cu isotopes is important to provide sensitive information on the expected shape coexistence and onset of deformation in the 78 Ni region [31].

One-proton removal reaction
Experiments to study neutron-rich Cu isotopes in knockout reactions were performed within the SEASTAR col-laboration and campaign at RIKEN. The 75,77 Cu nuclei were produced through one-proton knockout of 76,78 Zn beam particles. In terms of reaction mechanism, the oneproton knockout strength is expected to be largest for the 1f 7/2 orbital since there are almost 8 protons in the groundstate configuration of the 76,78 Zn isotopes, while the remaining single-particle strength due to 2 protons above Z = 28 will be mostly shared between the 1f 5/2 , 2p 3/2 , and 1p 1/2 orbitals. As a consequence, the cross section to populate the 7/2 − particle-hole state is expected to be large, and the corresponding state can be clearly identified.
The experiment used again an intense primary beam of 238 U and a primary 9 Be target. The BigRIPS separator was optimized to select neutron-rich Zn isotopes. Identification of the incoming projectiles and outgoing reaction products was performed on event-by-event basis similar to the technique mentioned in Sect. 2.1. For the purpose of one-proton knockout, a reaction target of 10 cm thick liquid hydrogen, surrounded by the active target time projection chamber MINOS [34], was exploited during the experiment. The DALI2 array [35], coupled to the MI-NOS device, was used for the detection of the γ rays emitted from the reaction products. The setup allowed performing event-by-event Doppler correction of the γ rays detected in DALI2 using the reaction vertex information reconstructed in MINOS. Details of the procedure can be found in Ref. [36].  (Figure 5b). The knowledge of the level schemes of 75 Cu and 77 Cu from the β-decay experiments was of great help for the identification of transitions in the spectra following the knock-out reactions. In fact, all γ-ray transitions indicated in Figure 5 were also seen following the β decay of 75 Ni and 77 Ni, respectively [32,33].
The transition at 290 keV lies in the low-energy region where a large atomic background makes its identification difficult. The spectrum shown in the inset of Figure 5b was obtained using only DALI2 detectors at forward angles. Due to a relatively long lifetime of the (3/2 − ) state at 290 keV excitation energy, its decay transition appears shifted to 260 keV under these conditions. Using the lineshape of this transition depopulating the level at 290 keV, a lower limit of about 0.5 ns for the half life of the (3/2 − ) state could be extracted in the present experiment. Figure 6 shows examples of the coincidence spectra gated on the 530-and 490-keV transitions in 75 Cu. The coincidence relation between 530 keV and 880 keV and 950 keV and between 490 keV and 990 keV γ-ray transitions confirms the level scheme obtained in Ref. [33]. The similar analysis has been performed for 77 Cu and confirms the level scheme reported in Ref. [32] 2.1 Gamma single spectra Gamma-single spectra for 75 Cu are obtained for the (p, 2p) channel by gating on 76 Zn before and on 75 Cu after the target. The spectra are doppler corrected and with addback. TimeO↵setted gates are set to reduce the bg for better looking spectra (these gates are removed when the exclusive cross sections are calculated). Figure 1 and Figure 2 show the doppler-corrected spectra for 75 Cu and 77 Cu, respectively, for mult=All and mult=1 . Gamma-single spectra for 77 Cu are obtained for the (p, 2p) channel by gating on 78 Zn before and on 77 Cu after the target. The spectra are doppler corrected and with addback. TimeO↵setted gates are set to reduce the bg for better looking spectra. Figure 2 shows the doppler-corrected spectrum for mult=1.

Gamma coincidence examples
Coincidence data are su cient for 75 Cu. We are using gates with exponential bg subtraction. Figures 3a and b show the gated spectra satisfying the level scheme constructed in the beta-decay work using EURICA. The matrix and the projection on one axis accordingly were produced for mult= 2+3.
In the case of the spectrum gated on 950 keV in Figure 3a, we believe that under the peak at 530 keV there is a contribution from 490 keV which is in coincidence with 990 keV, close to the value of 950 keV. Figure 3b shows the relation between the transitions 490 and 990 keV. Like the case above, here there is a contribution from 530 keV under the peak area of 490 keV due to the fact that 950-and 990-keV peaks are lying closer than the resolution limit of DALI. The same applies to the gated spectrum on 490 keV in which 880+950 keV is slightly visible as 490 keV is lying close to 530 keV.

Gamma coincidence examples
Coincidence data are su cient for 75 Cu. We are using gates with exponential bg subtraction. Figures 3a and b show the gated spectra satisfying the level scheme constructed in the beta-decay work using EURICA. The matrix and the projection on one axis accordingly were produced for mult= 2+3.
In the case of the spectrum gated on 950 keV in Figure 3a, we believe that under the peak at 530 keV there is a contribution from 490 keV which is in coincidence with 990 keV, close to the value of 950 keV. Figure 3b shows the relation between the transitions 490 and 990 keV. Like the case above, here there is a contribution from 530 keV under the peak area of 490 keV due to the fact that 950-and 990-keV peaks are lying closer than the resolution limit of DALI. The same applies to the gated spectrum on 490 keV in which 880+950 keV is slightly visible as 490 keV is lying close to 530 keV.

Gamma coincidence examples
Coincidence data are su cient for 75 Cu. We are using gates with exponential bg subtraction. Figures 3a and b show the gated spectra satisfying the level scheme constructed in the beta-decay work using EURICA. The matrix and the projection on one axis accordingly were produced for mult= 2+3.
In the case of the spectrum gated on 950 keV in Figure 3a, we believe that under the peak at 530 keV there is a contribution from 490 keV which is in coincidence with 990 keV, close to the value of 950 keV. Figure 3b shows the relation between the transitions 490 and 990 keV. Like the case above, here there is a contribution from 530 keV under the peak area of 490 keV due to the fact that 950-and 990-keV peaks are lying closer than the resolution limit of DALI. The same applies to the gated spectrum on 490 keV in which 880+950 keV is slightly visible as 490 keV is lying close to 530 keV.

Gamma coincidence examples
Coincidence data are su cient for 75 Cu. We are using gates with exponential bg subtraction. Figures 3a and b show the gated spectra satisfying the level scheme constructed in the beta-decay work using EURICA. The matrix and the projection on one axis accordingly were produced for mult= 2+3.
In the case of the spectrum gated on 950 keV in Figure 3a, we believe that under the peak at 530 keV there is a contribution from 490 keV which is in coincidence with 990 keV, close to the value of 950 keV. Figure 3b shows the relation between the transitions 490 and 990 keV. Like the case above, here there is a contribution from 530 keV under the peak area of 490 keV due to the fact that 950-and 990-keV peaks are lying closer than the resolution limit of DALI. The same applies to the gated spectrum on 490 keV in which 880+950 keV is slightly visible as 490 keV is lying close to 530 keV.

Gamma coincidence examples
Coincidence data are su cient for 75 Cu. We are using gates with exponential bg subtraction. Figures 3a and b show the gated spectra satisfying the level scheme constructed in the beta-decay work using EURICA. The matrix and the projection on one axis accordingly were produced for mult= 2+3.
In the case of the spectrum gated on 950 keV in Figure 3a, we believe that under the peak at 530 keV there is a contribution from 490 keV which is in coincidence with 990 keV, close to the value of 950 keV. Figure 3b shows the relation between the transitions 490 and 990 keV. Like the case above, here there is a contribution from 530 keV under the peak area of 490 keV due to the fact that 950-and 990-keV peaks are lying closer than the resolution limit of DALI. The same applies to the gated spectrum on 490 keV in which 880+950 keV is slightly visible as 490 keV is lying close to 530 keV.  From Figure 5 it is evident that the transitions at around 1.5 MeV in 75 Cu and 2 MeV in 77 Cu are more strongly populated compared to the other transitions seen in the spectra. Accordingly, the state at 1483 keV in 75 Cu and at 2068 keV in 77 Cu will have the largest population through the (p,2p) reaction and, hence, can be assigned as the states based on the (π1 f 7/2 ) −1 particle-hole excitation. The detailed analysis including extraction of the exclusive cross sections and spectroscopic factors will be reported in another forthcoming article [37].
The preliminarily results from the one-proton knockout and beta-decay experiments at RIKEN can be translated into systematics of the excited states along the Cu chain. Figure 7 shows the energy of the low-lying states of the Cu isotopes as a function of the neutron number. From the systematics we can make the following observations: • An increase in the energy of the 3/2 − single-particle state (green full dots) and a decrease in the 5/2 − singleparticle state (red full squares) state is clearly visible as a result of the monopole tensor interaction, which is re-4 EPJ Web of Conferences 223, 01054 (2019) https://doi.org/10.1051/epjconf/201922301054 NSD2019 low 500 keV, the spectra in Fig.1a and b sing DALI2 detectors at forward angles y equal to one. Figure 1c shows these nuclei in which a 293-keV γ transition 3/2 ) state in 77 Cu is visible and shifted . A lower limit of about 0.5 ns for the e extracted for the state at 293 keV use of the γ-ray transition depopulating obtained value is in a good agreement of 1.5 ns from the MCSM calculations e 3/2 state in 77 Cu to be dominated by e-proton configuration [32]. Instead, the ion decaying from the 3/2 state in 75 Cu served in the present measurement due y and long half-life, 149(6) ns [29].
ntal spectra in Fig.1a and b were fitted square method (red solid lines) to obntensities. The previously measured γatios from Ref. [31,32] were used in the e. The response function of DALI2 for le solid lines) and a combination of two ctions for the background (blue dashed emented in the fit as done previously in [35,40]. Simulated energy (E ) and the (I ) for both Cu nuclei are summarized main sources of the uncertainties in the ies come from the energy calibration (5 gies) and from the statistical uncertainue to the presence of the long-lived 8 , a fraction of ions could reach the secthe isomeric state instead of the ground eric ratio was measured during the exper-URICA array to be 7.7(8) %. Although l schemes are known from the beta-decay , 32], the γ-γ coincidence data helped to artial level schemes for both Cu isotopes ork. The insets in Fig.1 show examples ce spectra gated on the 530-and 490in 75 Cu and on the 940-and 1740-keV Cu. Figure 2 shows the level schemes of etermined in the present γ-γ coincidence nown states observed in the recent meawith those reported in Ref. [ 15.0(7) mb and 11.5(8) mb, respecto 7.9(2) mb for the 80 Zn(p, 2p) 79 Cu rein Ref. [35]. A rather high ICS obtained pulsive between the π2p 3/2 and ν1g 9/2 and strongly attractive between the π1 f 5/2 and ν1g 9/2 orbitals, respectively.
• The particle-core coupled states (orange full diamonds) dominate the higher-energy regions. For the lighter isotopes from N = 36 to 44 one observes 7/2 − and 11/2 − states based largely on the 2p 3/2 ⊗2 + 1 coupling, while for the heavier isotopes from N = 46 to 48 one observes 9/2 − and 13/2 − states based largely on the 1 f 5/2 ⊗2 + 1 coupling. All these core-coupled states follow very closely the trend of the 2 + 1 and 4 + 1 states in the corresponding (A−1) Ni core.
• The 7/2 − "intruder" state (blue full triangle) exhibits a parabolic behavior indicating a possible existence of shape coexistence along the copper chain from N = 40 to N = 50. Similar parabolic behaviors have been observed in different mass regions such as the Hg (Z=80), Pb (Z=82), and Sn (Z=50) isotopic chains [38,39].

Conclusion
In conclusion, the status of the current spectroscopic studies for 75 Cu and 77 Cu performed at RIKEN has been discussed. Level schemes up to around 4 MeV were constructed for both nuclei from the β-decay studies of 75 Ni and 77 Ni within the EURICA campaign. The singleparticle character of the low-lying states was identified more selectively via one-proton knockout reactions of 76 Zn and 78 Zn projectiles on a proton target within the SEASTAR campaign. The results were compared to largescale shell model calculations, yielding information about the single-particle structure in the 78 Ni region in general and the size of the Z = 28 shell gap in particular. The results allow a significant extension of the systematics along the chain of Cu isotopes. The identification of intruder states suggest that deformation and shape coexistence are important for the 78 Ni region. Further results and more detailed discussions will be presented in forthcoming publications.