Occurrence of a chiral-like pair band and a six-nucleon noncollective oblate isomer in 120I

a Department of Physics, Korea University, Seoul 02841, Republic of Korea b Faculty of Science, Hoseo University, Chung-Nam 31499, Republic of Korea c Department of Nuclear Physics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT 2601, Australia d iThemba LABS PO Box722, Somerset West 7129, South Africa e Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519-082, China

Nuclei close to the Z = 50 shell closure are good candidates for investigations of nuclear shell structure because isomeric states induced by a few particles (or holes) outside a closed core are abundant. The long-lived nature of isomers has been interpreted as arising from the shape coexistence, spin-trap, and K -trap isomerism [1][2][3]. Spin (or yrast) trap isomers are normally found near closed shells, e.g., in Sn, Sb, and I around Z = 50. The unique negative-parity neutron h 11/2 orbital, which lies close to the Fermi surface, is responsible for the spin-trap isomerism in this region. These unusual high-spin states are interpreted as being associated with the noncollective oblate state owing to an oblate mass distribution that is symmetric around the rotation axis.
Moreover, the neutron-deficient odd-odd I isotopes fall in a region where the h 11/2 proton (π h 11/2 ) and the h 11/2 neutron (νh 11/2 ) orbitals near the Fermi surface are of opposite particlehole character. This condition can lead to complicated dynamics and is the basis for the development of the so-called chiral bands * Corresponding author. in the mass A = 120 − 130 region. As described by Frauendorf and collaborators [4][5][6], the chiral mechanism comes from a combination of dynamics: the angular momentum involving two quasiparticles in the appropriate orbitals and geometry (i.e. the triaxial shape). Under this condition, high-j particles of one kind of nucleon and high-j holes of the other kind are combined with the triaxial deformed potential in odd-odd nuclei. One of experimental signatures of the chirality is the observation of a pair of I = 1 collective bands with the same parity and a small energy difference. To date, chiral-like doublet bands have been systematically observed in the mass A ∼ 130 region such as in Cs, La, Pr, and Pm [7][8][9][10][11].
In the present work, we report on observation of both a specific single-nucleon configurational state and a collective state in oddodd 120 I: a noncollective oblate isomer at a high-spin state and a pair of doublet bands, which are both unique in the Z = 53 oddodd system. It should be emphasised that the first observation of the doublet bands in 120 I was given in our previous report [12].
The experiment was conducted at the Heavy Ion Accelerator Facility of the Australian National University.   I were populated by the 118 Sn( 6 Li, 4n) reaction at a beam energy of 48 MeV. The beam, provided by the 14UD tandem accelerator, had a pulsed structure with a 1-ns pulse separated by periods of 1.7 μs. The 118 Sn target was a self-supporting foil with a thickness of 3.6 mg/cm 2 . γ rays emitted during the decay of excited states were detected by using the CAESAR array, which was composed of six Compton-suppressed hyper-purity germanium (HPGe) detectors and two low-energy photon spectrometer (LEPS) detectors. γ rays were collected both during the period that the beam was incident on the target and during the period without beam irradiation, allowing the detection of decays following isomeric states. Fig. 1(a) shows the γ -ray singles spectrum of 120 I within the delayed region in timing information. Retarded γ transitions induced by several isomeric states in 120 I are obtained and their energies are indicated. The peaks marked with & symbols are γ rays emitted from 120 Te, which is an another resultant nucleus from the reaction or a daughter nucleus after the β decay. The 72-keV isomeric decay with a half-life of 244(3) ns has been previously reported in [13,14]. This isomer is located at 72 keV and has a spin-parity of 3 + . The 80-and 124-keV transitions are delayed γ rays from the 7 − isomeric state at 290 keV with a half-life of 9.2 ns [13,14]. The 506-, 872-, 1067-, and 1091-keV peaks are from the high-spin isomer located at the top of the collective band with positive parity. γ rays belonging to Band 1 and Band 2 can be found in  dence analysis, γ transitions not only from Band 1 and Band 2 but also from weak inter-transitions between these two bands were successfully identified. The detailed full level scheme and the characteristics of γ -ray transitions can be found in the supplementary materials. It should be noticed that the present level scheme of 120 I differs from the result reported by Kaur et al. [15]. In Ref. [15], the dominant states, to which we assign positive parity, were assigned to be of negative parity with a band head of 9 − and interpreted as being associated with the π g 7/2 νh 11/2 configuration. However, we suggested [12,13] that Band 1 should be associated with the πh 11/2 νh 11/2 configuration for the following reasons: Firstly, the multipolarities of γ transitions were determined by the DCO (directional correlation of oriented states) analysis. For instance, in the full level scheme [13], two strong transitions with 565.5 and 571.1 keV, depopulating the 8 + and 9 + states, show E1 dipole character. Secondly, the level built on the 11/2 − state dominates the yrast sequence in adjacent odd-proton ( 119,121 I [16,17]), and odd-neutron ( 119 Te [18] and 121 Xe [19]) nuclides. Further, the excitation energy of the 10 + band-head state is systematically consistent with that of the negative-parity band-head state based on the h 11/2 orbital in the neighbouring odd-mass 119,121 I isotopes. Finally, to understand the origin of 9 + and 10 + , we performed theoretical calculations with a large-scale spherical shell model (SM) in the space of 50 < Z and N < 82 using the shell model code, K-SHELL [20]. It was found that the calculated 9 + and 10 + states, dominated by the πh 11/2 νh 11/2 configuration, comprising 49% and 60%, respectively, have been built at 1004 and 1003 keV. These levels are almost consistent with the observed 9 + and 10 + states.
Above Band 1, a high-spin isomer was found at 6418 keV. This observation was from an analysis of the time-correlated γ -ray spectrum data in which the 506-and 872-keV transitions appear to be delayed characters, as shown in Fig. 1(a). Fig. 1(c) shows the decay curve induced by the retarded transitions depopulating the observed isomer. The half-life of this isomer is estimated to be 49(2) ns by using the maximum likelihood method with an exponential decay function and a constant background. Li et al. [21] suggested that, by noticing the imbalanced intensities between transitions populating and depopulating the 6418-keV level, this 6418-keV level would be an isomeric state. Accordingly, the 506-keV transition was proposed to be an M3 transition. However, based on our further discussion, the 506-keV transition should have an E2 character and the isomer would be depopulated by an unobserved low-energy M1 transition. Given the low-energy detection efficiency of the LEPS, this low M1 transition may be below 30 keV. Consequently, this isomer is considered to be J π = 25 + at an energy of E < 30 keV above the 6418-keV state. , we can conclude that Band 2 is a candidate for a chiral-like pair band of Band 1. In Fig. 3(a), the energy separation between two bands and the signature splitting can be found. Band 2 is found to be lying higher in energy by ∼250 keV than the main πh 11/2 νh 11/2 band, Band 1. This energy separation is similar to values between the chiral doublet bands in odd-odd Cs, La, Pr, and Pm nuclei [7][8][9][10][11]. The observed similarity in the energy separation between Band 1 and Band 2 reflects their common underlying structure in the mass A ∼ 130 nuclei; therefore, Band 2 may be associated with the chiral partner band leading to a doubling of states for the πh 11/2 νh 11/2 configuration. Our suggestion can be further supported by discussing the B(M1) in /B(E2) in ratio. The B(M1) in /B(E2) in values for Band 1 and Band 2 are almost same as shown in Fig. 3(b). Various types of reduced transition ratios are summarised in Table 1. Fig. 3(c) shows the change of collective angular momentum geometries in two bands. For example, two lowest points in each band show their planar geometries at the band heads. However, as the spin increases, each band dramatically changes the angular momentum geometry into an aplanar geometry which causes the chiral doubling. The staggering parameter, S( J ), is also one of fingerprints for the chiral doubling. As shown in Fig. 3(d), S( J ) parameters exhibit the smooth variation which provides a good evidence for the chirality. However, the newly assigned chiral-like pair bands in 120 I have several differences from the known conditions needed to satisfy the chirality in the mass A ∼ 130 region. Firstly, the valence neutron in 120 I is not a hole in character, but should be treated as a quasiparticle. In the mass A ∼ 130 region, the coupling of a proton particle and a neutron hole in the h 11/2 orbital is one of optimal conditions, resulting in the occurrence of chiral pair bands. Secondly, the deformation in 120 I exhibits a rather different aspect from the known chirality. One of the requirements is the aplanar angular momentum geometry caused by the triaxial deformation [7]. Consequently, the best condition is known to form the triaxial deformed potential with |γ | = 30 • . As shown in Fig. 3(e), however, the TRS calculations for the πh 11/2 νh 11/2 configuration in 120 I indicate a γ -soft nucleus with a weak triaxial shape having γ ∼ 13 • . This result is insufficient for satisfying the known chiral geometry in the mass A ∼ 130 region. In summary, the chiral-like pair bands in 120 I satisfy neither the condition of a particle-hole configuration nor that of a triaxial deformation.
For studying the chirality built on the configuration of an h 11/2 proton and an h 11/2 neutron, Meng's group [23,24] investigated the angular momentum geometry in the framework of a particle rotor model with a quasi-proton and a quasi-neutron coupled with a triaxial rotor. After a detailed analysis, they found that the chiral geometry hold for away from the ideal case. The near-constant energy separation (∼200 keV) between the partner bands was interpreted as being due to either a deviation of the core shape from γ = −30 • or a deviation of the Fermi energy surface from a particle-hole configuration. This is an outstanding feature that agrees with the case of 120 I exhibiting a near-constant energy difference of 250 keV. However, our result still does not fully satisfy the theoretical predictions which require the γ condition as −40 • < γ < −20 • . Consequently, the observed doublet bands in 120 I are supposed to be the chiral-like pair bands induced by the weak triaxial core with the γ -softness that shows the most striking difference. It is also worth noting that the observation of the doublet bands based on the πh 11/2 νh 11/2 configuration in 120 I is the first case below Z = 55. Now we turn our attention to an isomeric state. We notice that the 16 + state at 5345 keV in 120 Te is located close to the 39/2 − state at 5186 keV in 119 Te and the 24 + state at 5410 keV relative to the 10 + state in 120 I. This 16 + level in 120 Te, being known to be an energetically favoured state, is a noncollective oblate shape built on the fully aligned four-quasiparticle π(g 7/2 d 5/2 ) 2 6 + ν(h 11/2 ) 2 10 + configuration. With this two-proton and two-neutron alignment in mind, we conclude that the 24 + level can be formed by the πh 11/2 νh 11/2 orbital coupled to the 16 + oblate structure, giving rise to an energetically favoured state with the π(g 7/2 ) 1 (d 5/2 ) 1 (h 11/2 ) 1 ν(h 11/2 ) 3 configuration. Moreover, the 526-keV transition de-exciting the 16 + level in 120 Te is almost Table 1 Summary of reduced transition ratios for Band 1 and Band 2. Intra-transitions and inter-transitions are notated as in and out, respectively. Uncertainties are given in parentheses.  identical to the 506-keV transition from 24 + to 22 + in 120 I. Nevertheless, the contrast is apparent in two transitions. In 120 Te, there is no evidence of an isomer with a half-life of a few or a few tens of nanoseconds but, in 120 I, there appears an isomer with a halflife of few tens of nanoseconds. Therefore, the best explanation of the presence of the isomeric state is to assume the existence of a 25 + level just above the 24 + level at 6418 keV. This unusual high-spin state can be regarded as a noncollective oblate state and is responsible for the spin-trap isomer [25]. Our scenario is consistent with results of the TRS calculations, as shown in Fig. 4(a). Based on the TRS calculations, this isomer with the π(g 7/2 ) 1 (d 5/2 ) 1 (h 11/2 ) 1 ν(h 11/2 ) 3 configuration, yielding J π = 25 + , has a minimum energy at β 2 = 0. 17  sult is certainly consistent with the TRS calculations. Consequently, these two types of calculations strongly support that the isomer originated from the π(g 7/2 ) 1 (d 5/2 ) 1 (h 11/2 ) 1 ν(h 11/2 ) 3 configuration with the noncollective oblate shape.
It is expected that an M1 transition, depopulating the 25 + isomer, should be so low in energy that is giving rise totally to a conversion electron emission. If we assume that the M1 transition has an energy between 5 and 30 keV, then the corresponding reduced transition rate lies between 3.6 W.u. (6.46μ 2 N ) and 0.016 W.u. (0.029μ 2 N ). In 152 Ho ( Z = 67, N = 85), the isomer at 28 − with a comparable half-life of 47 ns was found [26,27]. This isomer is known to be formed by six valence nucleon alignments, π(h 11/2 ) 3 ν( f 7/2 ) 1 (h 9/2 ) 1 (i 13/2 ) 1 , outside the semi-double shell closure of 146 Gd with Z = 64 and N = 82. These two isomers have their own magic shells of 50 and 82, respectively, and share a semi-magic shell closure value of 64. Consequently, the 25 + isomer is formed by six valence nucleon alignments, π(g 7/2 ) 1 (d 5/2 ) 1 (h 11/2 ) 1 ν(h 11/2 ) 3 , having valence three protons and three neutrons outside the semi-double shell closure of 114 Sn with Z = 50 and N = 64. We demonstrate the present high-angularmomentum isomeric structure in Fig. 4(b), which schematically illustrates the summed high-angular-momentum 25 + state formed by aligning individual valence nucleonic orbitals in 120 I together with the 28 − one in 152 Ho. Finally, we propose the existence of an isomer at J π = 26 − induced by the same physical phenomenon in gredient in understanding of proton-neutron interactions and the associated collectivity in nuclear many-body quantum systems.