Superdeformation in Asymmetric N$>$Z Nucleus $^{40}$Ar

A rotational band with five $\gamma$-ray transitions ranging from 2$^{+}$ to 12$^{+}$ states was identified in $^{40}$Ar. This band is linked through $\gamma$ transitions from the excited 2$^{+}$, 4$^{+}$ and 6$^{+}$ levels to the low-lying states; this determines the excitation energy and the spin-parity of the band. The deduced transition quadrupole moment of 1.45$^{+0.49}_{-0.31} eb$ indicates that the band has a superdeformed shape. The nature of the band is revealed by cranked Hartree--Fock--Bogoliubov calculations and a multiparticle--multihole configuration is assigned to the band.

Until recently, the nuclear magic numbers have been considered to be robust and durable with respect to the shell structure of atomic nuclei. The nuclear shell model initiated by Mayer and Jensen (1) successfully accounts for the shell structure of nuclei on and near the β-stability line. However, recent experimental studies on neutron-rich nuclei far from the β-stability line have revealed disappearance of magic numbers (e.g., N = 8 (2; 3; 4; 5), 20 (6)) and appearance of new magic numbers (e.g., N = 16 (7)). The new N = 16 magic number comes from the reduction of the N = 20 shell gap.
One theoretical explanation (8; 9) for this phenomenon is that the attractive monopole part of the tensor force acting between the πd 5/2 and νd 3/2 orbitals reduces the N = 20 gap in nuclei with high N/Z ratios.
Another anomalous phenomenon discovered in neutron-rich nuclei is the occurrence of a strongly deformed ground state on and near the N = 20 magic nuclei in the Z ∼ 12 region, the so-called 'island of inversion' (10). Here, the intruder two-particle, two-hole (2p-2h) configuration occupying the fp shell and the normal 0p-0h configuration in the sd shell are inverted in energy, and the 2p-2h configuration dominates in the ground state. This is a new challenge to the nuclear shell model. The most convincing evidence for the large quadrupole collectivity of the nuclei in the 'island of inversion' was the measured low E(2 + 1 ) energy (11) and the high B(E2) strength (6) as well as the enhancement of the binding energy (12). The experimentally deduced large B(E2; 0 + g.s. →2 + 1 ) value indicates large deformation (β 2 = 0.512(44)) in 32 Mg (6). 34 Mg (N = 22) shows an even larger deformation (β 2 = 0.58(6)) (13). Monte Carlo shell model calculations (14) that include the effects of the narrowed shell gap at N = 20 and enhanced 2p-2h excitations reproduce the experimental values quite well (13).
On the other hand, such a multiparticle-multihole (mp-mh) excitation appears in the excited states of nuclei near the β-stability line. These states can be studied by the heavy-ion induced fusion-evaporation reaction of stable isotopes. In fact, an mp-mh excitation from the sd to fp shell produces superdeformation (SD) in N = Z light mass nuclei, such as 36 Ar (15), 40 Ca (16), and 44 Ti (17). These SD nuclei exhibit a large deformation of β 2 ∼ 0.5, which is about the same magnitude as the ground state deformation in the 'island of inversion'. The presence of SD in the three abovementioned nuclei can be also understood in terms of the SD shell gaps of N = Z = 18, 20, and 22, respectively (16). In this region, the spherical and SD magic numbers occur at similar particle numbers, which results in shape coexistence.
However, the existence of a SD shell structure in neutron-rich nuclei has not been experimentally confirmed yet.
In order to access the currently reachable neutron-richest SD states with asymmetric SD magic numbers, especially the nucleus with N = 22 corresponding to 34 Mg, we employed a proton emission channel (2p2n) in the fusion-evaporation reaction using the neutron-richest beam and target combination of stable isotopes obtained so far. Consequently, we successfully populated the high-spin states of the SD double magic Z = 18 and N = 22 nucleus, 40 Ar. In this Letter, we report experimental results on the SD states in 40 Ar associated with the mp-mh excitation between the sd and fp shells.
High-spin states in 40 Ar have previously been studied by proton-γ coincidence measurements using the 37 Cl(α, pγ) reaction (18). High-spin levels below 6.8 MeV were identified up to (8 + ) and spin-parity assignments up to the 6 + state were obtained from the particle-γ angular correlations. The parity of the 5 − state at 4.494 MeV was determined by the linear polarization of the 5 − →4 + transition at 1602 keV. The lifetimes of low-lying levels were measured by the Doppler-shift attenuation method. The high E2 strengths of the 6 + 2 →4 + 2 and 4 + 2 →2 + 2 transitions are respectively deduced to be 67 +38

−19
and 46 +15 −10 in Weisskopf units, which indicates the large collectivity of the band. However, the (8 + ) assignment was based solely on the similarity of the level structure to that in 42 Ca, but the γ − γ coincidence relations of the in-band transitions were not examined and the presence of the band structure was not unambiguously identified by experiment. Therefore, it is essential to find the higher-spin members of the rotational band and to confirm the coincidence relations between the in-band γ transitions. were segmented into two sections each, giving a total of 25 channels that were used to enhance the selectivity of multi charged-particle events. With a trigger condition of more than two Compton-suppressed Ge detectors firing in coincidence with charged particles, a total number of 6.6×10 8 events were collected.

High-spin states in
Based on the number of hits in the charged particle detectors, events were sorted into three types of E γ −E γ coincidence matrices for each evaporation channel. A symmetrized matrix was created and the RADWARE program ESCL8R (21) was used to examine the coincidence relations of γ rays. By gating on the previously reported γ rays, high-spin states in 40 Ar were investigated.
By gating on the known 1461, 1432, and 571 keV peaks of the 2 + →0 + , 4 + →2 + , and 6 + →4 + transitions respectively, several new levels were iden- To determine the deformation of the band, the transition quadrupole moment Q t was deduced. Lifetimes were estimated by the (22)  In order to compare the high-spin behavior of the rotational band in 40 Ar with the SD bands in 36 Ar and 40 Ca, the so-called 'backbending' plot of the SD bands is displayed in Fig. 4. The gradients of the plots correspond to the kinematic moments of inertia. Because 40 Ar has a similar gradient to 36 Ar and 40 Ca, the deformation size of the 40 Ar rotational band is expected to be as large as the deformation of the SD bands in 36 Ar and 40 Ca. Unlike 36 Ar, no backbending was observed in 40 Ar. Its behavior is rather similar to that of 40 Ca. Many theoretical models, including the shell model (15; 24; 25; 26) and various mean-field models (27; 28; 29), have been used to analyze 36 Ar.
All the calculations reveal that the strong backbending in 36 Ar is due to the simultaneous alignment of protons and neutrons in the f 7/2 orbital.
The pronounced difference in the high-spin behaviors of 36 Ar and 40 Ar implies that the addition of four neutrons to 36 Ar gives rise to a dramatic effect on its structure. In order to understand this structural change theoretically, cranked Hartree-Fock-Bogoliubov (HFB) calculations with the P+QQ force (29) were conducted. The evolution of the nuclear shape was treated in a fully self-consistent manner and the model space of the full sd-fp shell plus the g 9/2 orbital was employed. The calculation shows that β 2 = 0.57 at J = 0 and that the deformation gradually decreases to 0.45 at J = 12 .
Triaxiality is found to be almost zero (γ ≃ 0) throughout this angular momentum range. This result agrees with the experimental Q t value within the error bars.
The occupation number of each orbital was also calculated ( Table 1). The ground-state configuration is expressed as (sd) −2 (fp) 2 relative to the groundstate configuration of 40 Ca, where the Fermi levels for protons and neutrons lie at d 3/2 and f 7/2 , respectively. The self-consistently calculated second 0 + state has the (sd) −6 (fp) 6 configuration. Here, the fp shell is occupied by two protons and four neutrons, while the sd shell has four proton holes and two neutron holes. Considering the rise of the neutron Fermi level relative to that in 36 Ar, this excited configuration is essentially equivalent to the 4p-4h superdeformed configuration in 36 Ar.
Cranking is then performed to study high-spin states. In the proton sector, the behaviors of single-particle orbitals are similar to those of 36 Ar (29). For example, the occupation numbers in the πp 3/2 orbital monotonically decrease up to J = 16 while the πf 7/2 orbital starts to increase at J = 8 due to the disappearance of the pairing gap energy.
In the neutron sector, clear differences are observed from the 36 Ar case.
The occupation number in the νf 7/2 orbital is almost constant (∼3) against the total angular momentum; it is about 1.5 times larger than that for 36 Ar.
The νd 5/2 orbitals are almost fully occupied (≃ 5.5) from the low-to the high-spin regions. In the case of 36 Ar, the structural change involving the sharp backbending is caused by a particle feeding from the p 3/2 orbital to the f 7/2 orbital for both protons and neutrons. In the neutron sector of 40 Ar, this feeding happens from the p 3/2 to the many other single-particle orbitals. This is because the rise of the neutron Fermi level enhances the occupation numbers of the single-particle orbitals, particularly at the bottom end of the fp shell. For example, the f 7/2 is well occupied by ≃ 40%. This high occupation influences the response of the system to the Coriolis force. In general, low-Ω states tend to come down energetically lower, so that such states are the first to be "submerged" when the Fermi level rises. As a result, neutron states near the Fermi level in 40 Ar possess a higher Ω value and the rotational alignment is suppressed. In 36 Ar, many Ω = 1/2 states are vacant in the fp shell, so that it is possible to place particles in the Ω = 1/2 states during the feeding from the p 3/2 orbital to the f 7/2 orbital. However, in 40 Ar, such Ω = 1/2 states are filled due to the rise of the neutron Fermi level.
It is thus necessary to place neutrons in the Ω = 3/2 or 5/2 levels in order to generate angular momentum. But this way of feeding weakens the rotational alignment. This "Pauli blocking effect" is one of the reasons why 40 Ar does not backbend (at least, not in the spin region so far observed). It is also worth mentioning that because of the rise of the neutron Fermi level in 40 Ar, angular momentum generation is spread among the extra f 7/2 neutrons, in comparison with 36 Ar. This means that, unlike their neutron counterparts, the f 7/2 protons do not need to "work hard" to generate angular momentum.
As a result, simultaneous alignment of the f 7/2 protons and neutrons does not occur in 40 Ar. Our calculation confirms this picture.
In summary, a discrete-line superdeformed band has been identified in