Type II shell evolution in A = 70 isobars from the N ≥ 40 island of inversion

The level structures of 70 Co and 70 Ni, populated from the β decay of 70 Fe, have been investigated using β -delayed γ -ray spectroscopy following in-ﬂight ﬁssion of a 238 U beam. The experimental results are compared to Monte-Carlo Shell-Model calculations including the pf + g 9 / 2 + d 5 / 2 orbitals. The strong population of a ( 1 + ) state at 274 keV in 70 Co is at variance with the expected excitation energy of ∼ 1 MeV from near spherical single-particle estimates. This observation indicates a dominance of prolate- deformed intruder conﬁgurations in the low-lying levels, which coexist with the normal near spherical states. It is shown that the β decay of the neutron-rich A = 70 isobars from the new island of inversion

to the Z = 28 closed-shell regime progresses in accordance with a newly reported type of shell evolution, the so-called Type II, which involves many particle-hole excitations across energy gaps. In exotic nuclei, which have an increasingly unbalanced number of neutrons (N) and protons ( Z ), new aspects, such as neutronhalo or skin structures [1,2], magicity loss [3][4][5][6], and new magic numbers [7][8][9][10][11][12][13] have been discovered. These findings have provided pivotal information on single-particle energies and the resultant shell structure far from stability, helping to better understand the role of the tensor, spin-orbit, central, and three-body components of the nucleon-nucleon interaction [14,15].
The variation of the proton or neutron number is a longstanding recognized cause of shell evolution, yet particular particle-hole excitations in exotic nuclei have shown to alter significantly the shell structure owing to the monopole properties of the central and tensor forces [16,17]. This is a new, almost unexplored microscopic mechanism of shell evolution (called Type II) that is to be distinguished from the better known shell evolution due to varying neutron or proton number (called Type I) [18,19].
Shape-transitional phenomena are indicators of alterations in the normal-order configuration of protons and neutrons. For exotic nuclei, they may prelude the discovery of new nuclear regions in which the ground states are dominated by deformed intruder configurations, the so-called "islands of inversion" [20][21][22]. Similarly to the N = 20 deformation region in the vicinity of 32 Mg, the abrupt fall of the 2 + 1 state in the N = 40 isotones, from 2034 keV in 68 Ni to 574 keV in 66 Fe and 430 keV in 64 Cr [23], indicates an increase of collectivity. The fact that these nuclei are well deformed has been confirmed in a Coulomb excitation experiment at intermediate energy [24]. Later systematic studies of 2 + 1 and 4 + 1 states in 70 Fe, 72 Fe, and 66 Cr have revealed that the new island of inversion spreads beyond N = 40 [25,26]. In this context, the discovery of new deformed structures in neighboring nuclei is important to better model the deformation-driving forces approaching the N = 50 shell closure.
Shape transitions can also take place with excitation energy or angular momentum, leading to the coexistence of different shapes within the same nucleus [27]. An exemplary case is 68 Ni, which has a j-j (spin-orbit) closed shell at Z = 28 and a L-S (harmonicoscillator) shell closure at N = 40. In this nucleus three 0 + states below 3 MeV are related to spherical, prolate, and oblate shapes [18,[28][29][30]. In 70 Ni, a second 0 + level has recently been observed at a lower excitation energy than in 68 Ni [31], consistently with a prediction of a deeper local minimum at prolate deformation [18]. In fact, the advanced Monte Carlo Shell-Model (MCSM) calculations [18] have indicated that a combined effect of the protonneutron tensor force and changes of major configurations is crucial for driving and stabilizing the shape coexistence in the neutronrich Ni isotopes, as referred to as Type II shell evolution [19] in contrast to the more conventional Type I shell evolution [11].  [26]. Selection rules of the β decay process allow for the population of low-spin states in 70 Co while high spin isomeric states in 70 Co could not be effectively populated, as suggested by [28,32]. Results are compared to MCSM calculations, which predict the inversion of the intruder prolate structure with the normal near-spherical configuration in 70 Co.
The experiment was performed at the Radioactive Isotope Beam Factory (RIBF) in RIKEN, Japan. A 238 U primary beam at 345 MeV/nucleon, with an average intensity of 10 pnA, collided onto a Be target of 3 mm thickness. Fission fragments with A ∼ 70 were separated and identified in flight in the BigRIPS spectrometer through the E-Bρ-TOF method [34], using position, time, and energy-loss detectors at the focal planes for the measurement of the mass-to-charge ratio A/Q and the atomic number Z. The cocktail beam was implanted in the Wide-range Active Silicon Strip Stopper Array for Beta and ion detection (WAS3ABi) [35]. About 1.8 × 10 5 nuclei of 70 Fe were registered in WAS3ABi.
WAS3ABi consisted of a compact row of 5 highly pixelated double-sided silicon strip detectors of dimensions 60 ×40 ×1 mm 3 , with 2400 pixels of 1 mm 2 pitch each. The energy, position, and time of implanted nuclei and electrons were recorded in WAS3ABi. These information were used offline to correlate them through their positions and times. The β-decay half-lives of the implanted nuclei and their decay successors were determined from these correlations. Resulting values (61.4(7) ms for 70 Fe and 508(7) ms for the low-spin β-decaying state of 70 Co) are in reasonable agreement with previous measurements [28,36,37,31]. Energy and time of coincident γ rays were obtained with the EURICA γ -ray spectrometer [38], made of 12 7-element HPGe cluster detectors with an addback efficiency of 11% at 662 keV. More details on the geometry of the setup and analysis procedure are published in Refs. [25,[39][40][41].
The level structure of the decay successors was investigated through high-precision β-delayed γ spectroscopy.  [32,37]. In the present work, a total of 19 transitions have been placed in the level scheme of 70 Co after analyzing their coincidence relations and energy matchings (see Fig. 2). In the granddaughter nucleus 70 Ni 17 transitions are identified, about half of which are reported in Refs. [42,31]. The level scheme of 70 Ni is also shown in Fig. 2. Transitions shown as dashed lines are placed in the level scheme based only on energy-matching constraints but not on γ -γ coincidence relations.
Apparent β feedings and calculated log f t values are reported on the left side of the level schemes. They must be considered as upper and lower limits, respectively, due to possible missed feeding from higher-lying states.
In 70 Co, the strong β feeding to the states at 274 and 1696 keV indicates the occurrence of allowed Gamow-Teller transitions from the 0 + ground state of 70 Fe. Based on this, we tentatively assign them spin and parity (1 + ). It is to note that the low-lying levels of 70 Co will have negative parity as a result of the coupling of a single proton hole in the π f 7/2 orbital to the unpaired ν g 9/2 neu- tron, if these orbitals are well isolated from the adjacent sub-shells with the presence of sizable spherical shell gaps at Z = 20, 28 and N = 40, 50. Meanwhile, the first spherical 1 + state will arise from the π f 7/2 ⊗ ν f 5/2 multiplet. Its energy is expected to be around 1 MeV based on the energy difference between the (9/2 + ) ground state and the (5/2 − ) level in the N = 43 isotone 71 Ni [43], which are interpreted in terms of a single neutron in the g 9/2 and f 5/2 orbitals, respectively.
For a deformed nucleus, the 2 j + 1 degeneracy of the spherical orbitals is solved with respect to the projection of the singleparticle angular momentum j on the symmetry axis, . The deformed single-particle levels are labeled by the asymptotic quantum number π [Nn z ] in the Nilsson model [44]. In the odd-even isotopes 65 Co 38 and 67 Co 40 , the respective lowest-lying (1/2 − ) states at 1095 and 492 keV are ascribed to a downsloping intruder 1/2 − [321] proton orbit [45], indicating an evolution of the nuclear shape towards prolate deformation. In the neighboring odd-odd isotopes, a low-lying deformed 1 + state most likely involves a neutron in the 1/2 − [301] orbit coupled to the aforementioned proton intruder state [46,47]. Thus, the observation of the 1 + state at 274 keV in 70 Co provides evidence for the existence of a deformed-shape configuration. Theoretically, this deformed lowlying 1 + state of 70 Co is a consequence of many particle-hole excitations across the Z = 28 and N = 40 shell gaps induced by effect of Type II shell evolution [19]. Conversely, it may not arise in a simple single-particle picture based on a spherical shape. The experimental β-decay level schemes are interpreted with the help of the MCSM calculations based on the A3DA Hamiltonian [49]. The model space includes the full pf shell and the 0g 9/2 , 1d 5/2 orbitals for both protons and neutrons. The calculated levels are shown in Fig. 2. The results predict that the low-lying states of 70 Co, including a J π = 1 + level at 357 keV and the ground state, are dominated by strongly prolate configurations with deformation parameter β 2 ∼ 0.27. States characterized by small deformation, β 2 ∼ 0.15, appear at about 900 keV and above. The theoretical B(GT; 0 + → 1 + ) and the corresponding log f t values, evaluated as f t = 6147/[(g A /g V ) 2 B(G T )] with coupling constant ratio g A /g V = −1.266 [50], for the 70 Fe→ 70 Co decay are listed in the first column of Table 1, while those referring to the 70 Co→ 70 Ni decay are listed in the second, third and fourth columns. The calculation indicates an abundance of population of two excited 1 + levels, along with a highly hindered β feeding to the deformed 1 + ground state. This prediction is consistent with both the observed decay pattern to the states at 274 and 1696 keV, and the weak population of the low-spin β-decaying state, which can be understood as the ground state in the MCSM interpretation. Fig. 3 exhibits potential energy surface (PES) plots for 70 Fe and 70 Co in terms of the quadrupole moments Q 0 and Q 2 calculated by the constrained Hartree-Fock (CHF) method for the current Hamiltonian. The location and size of the circles on the PESs represent the intrinsic shape of each MCSM basis state and its significance in the eigenstate being considered, respectively, as called T -plot [18]. It can be seen in Fig. 3(a)  dominantly of the π f −1 7/2 ⊗ ν f −1 5/2 g +4 9/2 component. Hence, the apparent β feeding measured to the (1 + ) experimental candidate at 1696 keV can be attributed to the allowed Gamow-Teller transition ν f 5/2 → π f 7/2 . On the contrary, the 1 + 1,2 states mainly involve proton excitations from f 7/2 to p 3/2 and f 5/2 , and neutron excitations from f 5/2 and p 1/2 to g 9/2 . Such multiple particle-hole excitations across the Z = 28 and N = 40 shell gaps (Type II shell evolution) drive the 1 + 1,2 states towards a strongly prolate-deformed shape, leading to the enhancement of shape coexistence [18,19]. The observed energy difference between the near spherical (1 + 3 ) candidate and the lowest-lying deformed state is larger than the MCSM prediction by 800 keV. This difference may imply that the isolated prolate local minimum is more stabilized than expected by the model. Despite very similar occupancies, there is a discrepancy in β-decay strength between the 1 + 1 and 1 + 2 states of 70 Co (see Table 1 B(GT) (multiplied by a standard quenching factor of 0.74 2 [48]) and log f t values calculated by the MCSM calculations for selected levels in the β decay of 70 Fe and 70 Co.   the left column in Table 1). This can be explained by decompos- The subsequent β decay to 70 Ni is governed by the large β feeding to the 2 + 1,2 states, pointing to a J π = 1 + , 2 + , or 3 + assignment for the long-lived state of 70 Co. According to the MCSM calculations, the 70 Co→ 70 Ni decay would proceed via a strong transition to the (4 + 2 ) state at 2508 keV [42] if the β decay took place from a deformed 3 + 1 level, see the right column in Table 1. Since this is at variance with the present experimental results, a J π = 3 + assignment is discarded. The calculated 1 + 1 and 2 + 1 levels of 70 Co decay preferentially to the 2 + 2 and 2 + 4 states of 70 Ni with small logft values, which are comparable to log f t = 5.76(7) and 6.13 (8) observed for the (2 + 2 ) and (2 + 4 ) states, respectively (see Fig. 2). These arguments indicate that the T 1/2 = 508 ms β-decaying state of 70 Co has a spin and parity of 1 + or 2 + . Experimentally, the (2 + 1 ) state is as strongly populated as the (2 + 2 ) level. The MCSM calculations predict a near spherical shape for the 0 + 1 and 2 + 1 levels of 70 Ni, while prolate-deformed configurations stabilized by effect of Type II shell evolution dominate its 0 + 2 and 2 + 2,4 levels, and the low-lying states of 70 Co. Thus, it is natural that the (2 + 2 ) level shows a higher feeding ratio than the (2 + 1 ) level. A more quantitative analysis, however, needs more precise log f t values, as they are obtained presently from observed γ -ray intensities, indicating only lower limits.  In 70 Ni, four new excited states at about 6 MeV are populated with log f t ∼ 5.7 from the low-spin state of 70 Co. They preferentially feed the (2 + 2 ) state (see Fig. 2), suggesting a similar deformed structure. These decay patterns can be naively explained using the argument based on the DSO. For Q 0 200 fm 2 corresponding to the prolate local minimum in the PES of 70 Ni (see Fig. 3 in Ref. [18]), the highest | p | = 1/2 − and 3/2 − proton orbitals locate 6-7 MeV above the second lowest | p | = 1/2 − orbit, which is included in the deformed 1 + 1 configuration in 70 Co as discussed previously. Since the major components of these DSOs are the π p 1/2 (∼80%) and π p 3/2 (∼70%) spherical orbitals, respectively, it is expected that the | n | = 1/2 − neutron can transform to them through strong Gamow-Teller transitions, giving rise to proton two-quasiparticle configurations with J π = 0 + , 1 + , 2 + around 6 MeV.
In conclusion, the properties of the 70 Fe→ 70 Co→ 70 Ni decay chain are interpreted in terms of advanced MCSM calculations. The results provide first evidence of strongly prolate-deformed shapes for the low-lying levels in 70 Co, including the ground state which preferentially decays towards similarly deformed structures in 70 Ni. This decay path can be clearly distinguished from the one passing through nearly spherical levels following the β decay of the high-spin state of 70 Co, as reported in Ref. [31]. Thus, it turns out that the shape coexistence occurs in the A = 70 isobaric chain due to type II shell evolution. A challenge for future radioactive ion-beam facilities will be determining if the deformed-intruder dominance of the ground state is extended to the N = 50 isotones below 78 Ni.
The excellent work of the RIKEN accelerator staff for providing a stable and high intensity 238 U beam is acknowledged. We acknowledge the EUROBALL Owners Committee for the loan of germanium detectors and the PreSpec Collaboration for the readout electronics of the cluster detectors. Part of the WAS3ABi was supported by the Rare Isotope Science Project (RISP) of the Institute for Basic Science (IBS), funded by the Ministry of Sci-