Collectivity of neutron-rich Cr and Fe toward N = 50

Within the SEASTAR project at RIKEN-RIBF, 66Cr and 70,72Fe have been produced via protonknockout reactions, and their first excited 2 and 4 states have been discovered. The combination of the liquid-hydrogen target and TPC system MINOS has been used in combination with the DALI2 detector array for the first time. A 345 MeV/u 238U beam with a mean intensity of about 12 pnA impinged on a Be target. Fission fragments were separated and identified using the BigRIPS spectrograph, and reaction products were analyzed using the ZeroDegree spectrograph. A plateau of excitation energies, with a small change in the systematic trends past N = 44, reveals an extension of the N = 40 region of collectivity toward N = 50. Hence, the isotopes of interest are located within the N = 40 island of inversion. An interpretation of the observed trends is offered through large scale shell model calculations.


Introduction
Of central interest in contemporary nuclear structure studies is the evolution of shell structure across the nuclear chart.In-medium nucleon-nucleon interactions may shift the energies of individual, or certain subsets of orbitals, such that new shell gaps may open, or vanish, as occupation numbers vary.Starting from the well-known magic numbers, marking significant shell gaps, such behavior has been found as a function of proton and neutron numbers.For example, the N=20 and N=28 magic numbers have been observed to disappear for neutron-rich nuclei in the region of 32 Mg [1][2][3], giving rise to a so-called island of inversion -that is, a sequential filling of proton or neutron orbitals not in the "normal" order, due to two-particle two-hole (2p-2h) configurations, favored because of quadrupole correlations [4][5][6].
A commonly used first indicator for the existence of shell gaps, and the evolution of collectivity within major nuclear shells, is the energy of the first excited 2 + state in even-even nuclei.A sudden rise in the 2 +  1 energy, typically on the order of one or few MeV, gives a strong hint on magicity, whereas 2 + 1 energies drop significantly with the onset of collectivity typically to hundreds of keV for vibrators, to tens of keV for well-deformed rotors.Although the absolute energy scale depends on the overall mass region, and may be influenced by other structural properties (e.g., effects of triaxiality or single magicity), the evolution of the E(2 + 1 ) over a series of isotopes is often A new project has now been started at RIKEN-RIBF, called "Shell Evolution And Search for Two-plus states At RIBF" (SEASTAR), with the aim of extending our knowledge on the location of 2 + 1 states as far as possible into neutron-rich regions accessible at the RIKEN-RIBF facility.The reach is aided by the novel combination of the DALI2 [8] and MINOS [9] systems, which will be described below, resulting in an excellent experimental sensitivity.Several experiments within the SEASTAR campaigns (first in spring 2014, second in spring 2015) already targeted specific isotopes, or isotopic chains, for which discussions with respect to their underlying shell structure are ongoing.One of these cases addresses the isotopes between N = 40−50, below the Ni chain, which will be the topic of this report.In more general, an extension of data into so-far unexplored regions may serve to guide the choice of specific new experiments, where deviations of energy trends from simple model assumptions, hence, potential changes in shell structures, appear.
In the following we will focus on the evolution of collectivity below the Z = 28 (Ni) shell closure, specifically on the 66 Cr and 70,72 Fe isotopes, for which 2 + 1 and 4 + 1 energies are determined for the first time [10].

Fe and Cr isotopes with N ≥ 40
Figure 1 shows the existing data on Cr-Ni isotopes in the mass region, where the high 2 + 1 energy in 68 Ni marks the closure of the p f neutron shell [11] and suggests a shell gap to the neutron g 9/2 orbital.However, below the Z = 28 shell closure, that is, for Fe and Cr isotopes, no such rise in E(2 + 1 ) has been observed.In contrast, 2 + 1 energies drop at N = 40 in those cases, rather indicating an increase of collectivity than the occurrence of a sub-shell closure when removing only two protons from the f 7/2 orbital.An increase of collectivity in Fe and Cr isotopes has also been deduced from recent B(E2) measurements [12,13], which show a modest rise of B(E2) values at N = 40.Hence, a new island of inversion has been suggested for the Fe and Cr isotopes at N = 40 [14].
This unexpected onset of deformation at N=40 below Z=28 has successfully been reproduced by large-scale shell model calculations [15] within a p f valence space for protons and a p f gd valence space for neutrons, explicitly taking into account the d 5/2 orbital beyond the N=50 magic shell closure.The term "island of inversion" infers an early filling of higher-lying orbitals, which, within this space, is given through quadrupole correlations between the 1g 9/2 and 2d 5/2 neutron orbitals, leading to the occurrence of particle-hole excitations.In contrast, with missing quadrupole correlations between the p f and the g sub-shells, the ground state of 68 Ni is rather uncorrelated [15].In that case, particle-hole excitations are strong in excited, intruder structures.Similar predictions were made from beyond-mean field calculations based on a collective Hamiltonian [16,17], where the 68 Ni is driven to sphericity by the proton shell closure at Z = 28 [16].
Of further interest is the evolution of collectivity toward the N = 50 major shell closure and to test its stability below Z = 28.Should N = 50 disappear, a situation akin to that in the heavier Mg isotopes could be present, with the merger of an island of inversion with a deformed region [3].The aim of the present work [10], within the first SEASTAR campaign, has been to obtain data on the most neutron-rich accessible members of the Fe and Cr isotopic chains.

Beam production and identification
A primary beam of 238 U was provided by the RIBF accelerators, with an energy of 345 MeV/u and an average The number of events is color-coded, given as function of Z and mass-over-charge (A/Q).intensity of 12 pnA.Impinging on a 3-mm thick 9 Be primary target, fission fragments were produced at high velocities, and secondary beams of interest were separated out by the BigRIPS separator [18].Two beam settings were chosen, tuned for 67 Mn and 71,73 Co, respectively, and secondary beam ions reaching the secondary target were identified through Bρ reconstruction, time of flight and energy-loss measurements in BigRIPS.Therefore, 8-mm and 2-mm thick aluminum wedges were used at two dispersive planes.The total intensities of 67 Mn and 71,73 Co at the entrance of the secondary target were 12 s −1 , 45 s −1 , and 6 s −1 , respectively, at energies of about 260 MeV/u.
Outgoing reaction residues or unreacted beam were identified by the ZeroDegree spectrometer (ZDS) [19].As an example, Fig. 2 shows the particle-identification data of BigRIPS and the ZDS from the Co setting.The reaction channel of primary interest was (p, 2p), hence, gates were set on incoming 67 Mn and 71,73 Co isotopes, which were sufficiently abundant in the beam, and outgoing 66 Cr and 70,72 Fe isotopes, respectively.

Target and detection setup
Proton-knockout (p, 2p) reactions occurred on a 1 H secondary target of 735(8) mg/cm 2 thickness, which was surrounded by a time projection chamber, both comprising the new MINOS device [9].MINOS was surrounded by the DALI2 NaI detector array [8] for γ-ray detection, thus, composing the SEASTAR setup for the first time.Further details on the target and detection systems can be found in Ref. [10] and references therein.
The SEASTAR setup led to a luminosity gain of about 3.5 compared to the use of a solid Be target with the same energy loss.In addition, the position information from MI-NOS allowed to compensate for the Doppler broadening.Since the hydrogen target was extended with a length of 102(1) mm, the MINOS TPC was used not only to select reactions with outgoing protons, but furthermore to reconstruct the reaction vertex by tracking the outgoing protons from the reaction, event-by-event.
The projectile velocity was determined from the reaction vertex, assuming a linear stopping within the hydrogen target.The efficiency for detection and reconstruction of one or two protons was 95 %, and a vertex position resolution along the beam axis better than 5 mm was achieved [20].With this spatial resolution the Doppler broadening of γ-rays from the uncertainty in the location of an event approximately matched the Doppler broadening due to solid angle of the DALI2 detectors.
The DALI2 array was composed of 186 NaI detectors, covering an angular range from 7 to 115 degrees with respect to the beam axis.The γ-ray detection efficiency was estimated to be 20 % at 1 MeV, and energy calibrations were performed using standard sources.In order to restore events where the γ-ray scattered between DALI2 detectors, an addback procedure was performed for γ-ray energies greater than 200 keV.

Results
The obtained γ-ray spectra from 66 Cr and 70,72 Fe have been binned to 20 keV/channel and the optimum addback conditions have been determined.Figure 3 shows a sample spectrum from the analysis of 70 Fe.At least one proton was required to be detected in MINOS.In case that only one proton was detected, the vertex was constructed from the proton track and the beam axis.Clearly two peaks from γ-ray transitions are observed.At different levels of statistics this has been the case for all three isotopes of interest.
Enough data was obtained in order to perform a γγcoincidence analysis, and the two transitions were found to be mutually coincident in all cases.In order to reduce background, a maximum multiplicity of 4 has been applied to DALI2. Figure 4 shows the resulting total projection of a γγ matrix for 70 Fe, as well as a projection after gating on the higher-lying transition, clearly leaving a signal at the energy of the lower-lying transition.Random background has been subtracted when setting the gate.From these observations and energy systematics, we assign a 2 + 1 → 0 + 1 transition to the lower-lying, more intense, transition in each isotope, and a 4 + 1 → 2 + 1 transition to the respective other, higher-lying transition.Transition energies have been obtained from a fit considering the detector response to the spectra, folding possible lifetime effects into the uncertainty.The procedure can be found in Ref. [10].Although the spin assignments cannot be made from transition energies only, the made assignment is the most likely with respect to observed intensities, similar observations in other isotopes where the respective states are already known, and the likelihood to populate a J = 4 state from knocking a proton out of the f 7/2 orbital.Therefore, we assign excited states in 66 Cr and 70,72 Fe as summarized in Table 1.The results of the final analysis can be found in Ref. [10].

Discussion
The new data extends the energy systematics in the Cr chain up to N = 42, and in the Fe chain up to N = 46.Since both, the 2 + 1 and 4 + 1 states were observed, we include the ratio R(4/2) = E(4 + 1 )/E(2 + 1 ) in the discussion, which is directly derived from observed transition energies.R(4/2) has limiting values of 2 for spherical harmonic vibrators and 3.33 for well-deformed rigid rotors.Lower values of R(4/2) are typically interpreted as less collectivity, vice versa (see Fig. 3 of Ref. [10]).
The Cr isotopic chain is located in the middle of the proton p f shell and, hence, is expected to display the highest collectivity in the region.The energy of the 2 + 1 state is lowered toward N = 42, indicating a further rise of collectivity beyond N = 40.An increase of collectivity is also supported by the corresponding rise in the R(4/2) value.
A small, but notable change in the energy systematics in the Fe isotopic chain is observed at N = 44, where E(2 + 1 ) minimizes and R(4/2) maximizes with R(4/2) = 2.8, before both values revert their trends.This behavior would typically be interpreted as a signature for maximum collectivity at N = 44, and could arise from the filling of the proton 1g 9/2 orbital, which is half-filled N = 45.The valence space for even-even nuclei in such an isolated g 9/2 shell would be maximized at N = 44, 46.In view of previous discussions on extended valence spaces including the 2d 5/2 orbital as in Refs.[15,16], however, such interpretation seems curious.
In order to obtain a better handle on the underlying microscopic mechanisms leading to the observed trends, shell model calculations were carried out in the same valence space as in Ref. [15].This valence space comprises the p f proton orbitals, and the p 1/2 , f 5/2 , g 9/2 , and d 5/2 neutron orbitals.In the LNPS-m interaction used in the present work, minor modifications were applied to the LNPS interaction from Ref. [15], namely on the monopole and pairing parts of the effective Hamiltonian.Calculations using the original LNPS interaction were found to underestimate the 2 + 1 energies of the most neutron-rich isotopes of interest.Therefore, in the LNPS-m interaction, an additional gd-gd monopole strength was introduced, leading to stronger intruder configurations in the ground states of these isotopes, and to a better overall agreement between theory and available data in the region.More details on the calculations and their results are shown in Ref. [10], and will be subject of a forthcoming publication.
The modifications to the Hamiltonian do not change the results obtained at N = 40 using the original LNPS interaction.The amount of np-nh configurations (up to n = 6) is at maximum in the N = 40 isotope 64 Cr.This indicates that the actual maximum of quadrupole collectivity is found in this isotope, at a maximum deformation EPJ Web of Conferences of β ≈ 0.33.Occupation numbers are found to be similar for states within the ground state band.A similar situation occurs for the Fe isotopes at N = 40.
The calculations also yield the largest B(E2) strength and quadrupole moment at N = 40, but variations thereafter are rather small.The latter goes along with the down sloping (up sloping), however, near-constant trends of E(2 + 1 ) (R(4/2)) values, which are well-reproduced in the LNPS-m calculation.This seemingly contradicts the conclusions drawn from np-nh configurations indicating the maximum collectivity at N = 40.In that case, a stronger peaking of B(E2) strengths and energies could be expected.
Pairing correlations may be one reason for this behavior, which is observed, both, in experiment and calculation.One may consider that, in a simple picture, the first 2 + state is generated by breaking a pair of nucleons.Should, in addition, the pairing strength be stronger in the 0 + ground state than in the 2 + state, the ground-state would be lowered more in energy than the excited state.Hence, the energy difference between both would rise -not due to its quadrupole collectivity.
The pairing expectation values of the multipole Hamiltonian for the ground and first excited states have been extracted from the shell model calculation, and reveal [10] that the minimum in 2 + 1 energies at N = 44 is, in fact, due to a smaller pairing correlations difference between the ground state and the 2 + 1 state.Hence, the observed detailed behavior of excitation energies is a consequence of a delicate interplay between quadrupole and pairing correlations.
The revised 2 + 1 energy systematics for the Cr and Fe chains are compared to their counterpart in the Ne and Mg isotopes around N = 20, including new data from [3,21], in Fig. 5.In both cases, a drop of 2 + 1 energies appears where (sub-)shell closures have originally been expected, that is at N = 40 and N = 20, respectively.Like in the Mg isotopic chain a rather constant behavior of the energies toward the next shell closures, that is N = 50 and N = 28, respectively, is found.In case of the Mg isotopes, from this trend a quenching of the N = 28 shell closure was speculated.This may also be the case for the N = 50 shell closure below Z = 28.

Summary
We have measured the energies of the 2 + 1 and 4 + 1 states of the neutron-rich 66 Cr and 70,72 Fe isotopes through their γ-ray decays after proton-knockout reactions.In this experiment, we employed for the first time the MINOS device, comprised of a liquid-hydrogen target and a TPC,

Figure 2 .
Figure 2. (Color online) Particle identification plots from BigRIPS (left) and the ZDS (right) for the beam setting tuned for Co isotopes.The number of events is color-coded, given as function of Z and mass-over-charge (A/Q).

Figure 3 .Figure 4 .
Figure 3. (Color online) Total DALI2 spectrum of 70 Fe with addback, but no multiplicity cuts on DALI2 data, and requiring at least one proton to be detected in MINOS.

Figure 5 .
Figure 5. (Color online) Systematics of E(2 + 1 ) in the Fe and Cr isotopes, across N = 40 toward N = 50, including the new data (top), and in the Mg and Ne isotopes, across N = 20 toward N = 28 (bottom).
in conjunction with the DALI2 NaI detector array at the RIKEN-RIBF facility.Although quadrupole collectivity is maximized at N = 40, excitation energies vary little beyond N = 40, as a consequence of pairing correlations.Within the shell model, this is interpreted as an extension of the N = 40 island of inversion toward N = 50.However, a test whether this island of inversion actually extends to N = 50, which would imply the disappearance of the N = 50 shell closure below 78 Ni, is not possible to date.In addition, B(E2) values are needed as a more direct test of the collectivity across N = 40, and toward N = 50.

Table 1 .
Excited state energies assigned in the present work.