First observation of excited states in 120La and its impact on the shape evolution in the A ≈ 120 mass region

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ First observation of excited states in 120La and its impact on the shape evolution in the A ≈ 120 mass region © 2024 the Authors Published version Jodidar, P.M.; Petrache, C.M.; Lawrie, E.A.; Astier, A.; Guo, S.; Lv, B.F.; Zheng, K.K.; Auranen, K.; Briscoe, A.D.; Grahn, T.; Greenlees, P.T.; Illana, A.; Joukainen, H.; Julin, R.; Louko, J.; Luoma, M.; Jutila, H.; Ojala, J.; Pakarinen, J.; Plaza, A.M.; Rahkila, P.; Ruotsalainen, P.; Sarén, J.; Tolosa-Delgado, A.; Uusitalo, J.; Zimba, G.; Kuti, I.; Krakó, A.; Andreoiu, C.; Joss, D.T.; Page, R.D.; Cederlöf, E.A.; Ertoprak, A. Jodidar, P.M., Petrache, C.M., Lawrie, E.A., Astier, A., Guo, S., Lv, B.F., Zheng, K.K., . Auranen, K., Briscoe, A.D., Grahn, T., Greenlees, P.T., Illana, A., Joukainen, H., Julin, R., . Louko, J., Luoma, M., Jutila, H., Ojala, J., Pakarinen, J., . . . Ertoprak, A. (2024). First observation of excited states in 120La and its impact on the shape evolution in the A ≈ 120 mass region. Physics Letters B, 855, Article 138806. https://doi.org/10.1016/j.physletb.2024.138806 2024 Phys. Lett. B 855 (2024) 138806 Available online 20 June 2024 0370-2693/© 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Letter First observation of excited states in 120La and its impact on the shape evolution in the 𝐴 ≈ 120 mass region P.M. Jodidara,∗, C.M. Petrachea,∗, B.F. Lvb,c,∗, E.A. Lawried, A. Astiera, S. Guob,c, K.K. Zhengb,c, K. Auranene, A.D. Briscoee,f, T. Grahne, P.T. Greenleese, A. Illanae, H. Joukainene, R. Juline, J. Loukoe, M. Luomae, H. Jutilae, J. Ojalae, J. Pakarinene, A.M. Plazae,f, P. Rahkilae, P. Ruotsalainene, J. Saréne, A. Tolosa-Delgadoe, J. Uusitaloe, G. Zimbae, I. Kutig, A. Krakóg, C. Andreoiuh, D.T. Jossf, R.D. Pagef, E.A. Cederlöfi, A. Ertopraki aUniversité Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France bKey Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China cSchool of Nuclear Science and Technology, University of Chinese Academy of Science, Beijing 100049, China diThemba LABS, Natural Research Foundation, PO Box 722, 7129 Somerset West, South Africa eAccelerator Laboratory, Department of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland fOliver Lodge Laboratory, Department of Physics, University of Liverpool, Liverpool L69 7ZE, United Kingdom gInstitute for Nuclear Research (Atomki-ELKH), 4001 Debrecen, Hungary hDepartment of Chemistry, Simon Fraser University, Burnaby, BC V5A 1S6, Canada iKTH Department of Physics, S-10691 Stockholm, Sweden A R T I C L E I N F O A B S T R A C T Editor: B. Blank Keywords: Nuclear reaction: 58Ni(64Zn,pn)120La E= 255 MeV Measured 𝛾𝛾𝛾-coincidences E𝛾 I𝛾 Angular correlations Recoil gated prompt coincidences 120La deduced levels Spin and parity Model calculation Excited states have been observed for the first time in the very neutron-deficient odd-odd nucleus 120 57 La63. The observed 𝛾rays have been assigned based on coincidences with lanthanum X rays measured with the JUROGAM 3 array and with 𝐴 = 120 fusion-evaporation residues measured with the MARA separator. The observed 𝛾rays form a rotational band which decays to the ground state via a cascade of four low-energy transitions. Based on the systematic comparisons with the heavier odd-odd La isotopes we assign spin-parity 4+to the ground state and a 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 configuration to the rotational band. The nuclear shape has been investigated by the cranked Nilsson-Strutinsky model. Two quasiparticle plus triaxial rotor model calculations including the 𝑛𝑝 interaction nicely reproduce the spin of the inversion between the even- and odd-spin cascades of 𝐸2transitions, giving credit to the 𝑛𝑝 interaction as an important parameter responsible for the mechanism inducing the inversion. The position of the Fermi levels, in particular for neutrons, also has a strong impact on the observed inversion in the chain of lanthanum nuclei. The study of the lightest nuclei in the 𝐴 ≈ 120 mass region is confronted with the increasing difficulty of populating high-spin states using fusion-evaporation reactions due to the limited choice of projectiletarget combinations and the small cross sections for neutron evaporation. The existing experimental information on excited states in very proton-rich nuclei is therefore increasingly scarce. Excited states have been identified in the extremely proton-rich odd-odd cesium nuclei up to the proton emitter 112Cs [1,2], while the odd-even Cs nuclei have been the subject of investigations devoted to the evolution of the structure and collectivity far from stability [3–7]. The recent studies of the * Corresponding authors. E-mail addresses: [email protected] (P.M. Jodidar), [email protected] (C.M. Petrache), [email protected] (B.F. Lv). odd-odd cesium nuclei have been mainly focused on chirality which was observed over a long sequence from 122Cs to 132Cs [8], and on signature inversion [9–14]. The odd-odd lanthanum isotopes with 𝑁<82 have also been extensively studied, with focus on chirality from 128La to 134La [8], and with at least two bands identified in each nucleus from 122La to 138La [15]. Several bands have been also observed in each of the proton-rich oddeven La nuclei, the lightest known spectroscopically being 121La [15]. Two proton emitters have been discovered, 116La and 117La [16,17]. However, the spectroscopic information on nuclei between the proton https://doi.org/10.1016/j.physletb.2024.138806 Received 20 February 2024; Received in revised form 29 April 2024; Accepted 12 June 2024 Physics Letters B 855 (2024) 138806 2 P.M. Jodidar, C.M. Petrache, B.F. Lv et al. emitters and those known spectroscopically is missing: 118La and 119La are completely unknown, while 120La has been synthesized but no spectroscopic information is known. Of particular interest are the 𝜋ℎ11∕2 ⊗𝜈ℎ11∕2 bands in the odd-odd Cs and La nuclei, not only because they can have chiral partners, but also because they can exhibit the so-called signature inversion at low spin. The signature is defined as the symmetry in the intrinsic frame of the nucleus of the wave function which transforms as symmetric or antisymmetric with respect to 180◦rotation about a principal axis. There exists a correspondence between the signature quantum number 𝛼which is 0 for even-spin and 1 for odd-spin sequences of states in the laboratory frame, but only for nuclei rotating about a principal axis of the nuclear shape. However, most often the nuclei with a collective core and active nucleons rotate or precess around an axis which is tilted relative to the principal axes of the intrinsic frame. In such cases the signature quantum number is not well defined and it is more appropriate to refer to rotational bands as built of two sequences of 𝐸2transitions between states with odd and even spins, respectively, which, depending on the relative energies of the even- and odd-spin sequences can also be connected by dipole transitions. This is relevant for most odd-odd nuclei where the total angular momentum has significant components on all three nuclear axes. The 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 bands observed experimentally in the odd-odd Cs and La isotopes are composed of two branches (cascades) of 𝐸2transitions, one between states with even spins and one between states with odd spins, which are connected by dipole 𝑀1∕𝐸2 transitions. In this work we will not use the term “signature”, but will refer to the even- and odd-spin branches of the band, because our analysis suggests that the nuclear shape of 120La is triaxial, and therefore the term “signature” is not applicable. Consequently, instead of the commonly used terms of “signature splitting” and “signature inversion” we will discuss the energy splitting and the inversion of the favored and unfavored branches at the crossing point. The experimental energy splitting between the even- and odd-spin branches of a given band can be expressed as 𝑆(𝐼) =[𝐸(𝐼) −𝐸(𝐼− 1)]∕(2𝐼)or 𝑆(𝐼) =[𝐸(𝐼) −𝐸(𝐼−1)] −[𝐸(𝐼+1) −𝐸(𝐼) +𝐸(𝐼−1) − 𝐸(𝐼− 2)]∕2. We will use the first simpler formula which involves the energies of only two states and can be extracted for more members of the band. One can draw two 𝑆(𝐼)curves, one for odd spins and one for even spins. When 𝑆(𝐼)of the favored branch is lower than that of the unfavored one, like for the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 bands at high spin, there is normal splitting. When the opposite is true, there is inversion, like for the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 bands at low spin. 𝑆(𝐼)depends on the band-head spin, which is often difficult to establish because the de-excitation of the band to low-lying states is not known. Liu et al. [18,19] critically analyzed and reassigned spins of bands in the 118−132Cs and 124−134La nuclei in the 1990s, revealing the presence of low-spin inversion in all of these doubly-odd nuclei. Since then, new experimental results have been obtained for 116,118Cs [9–11]and 122La [20], extending further the range of nuclei which show low-spin inversion. The inversion of the two branches observed in 𝐴 ≈ 130 and 𝐴 ≈ 160 nuclei with bands based on the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 and 𝜋ℎ11∕2 ⊗𝜈𝑖 13∕2 configurations, respectively, has been investigated theoretically using different models, aiming to unveil the mechanism at the origin of this phenomenon [21–36]. Hamamoto and Matsuzaki investigated the longrange proton-neutron interaction [21,30], Semmes and Ragnarsson [31] and Tajima [32] investigated the residual 𝑛𝑝 contact force with a spinspin interaction using the particle-rotor model, Hara and Sun [33] obtained the inversion within the projected shell model in 𝐴 ≈ 160 nuclei, Xu, Satula and Wyss showed that the inversion in 𝐴 ≈ 130 and 𝐴 ≈ 160 nuclei can appear in axially symmetric shapes due to the contribution of the (𝜆𝜇) = (22) component of the quadrupole-pairing interaction to the mean-field potential in the Total Routhian Surface (TRS) framework [34,35]. More recently, Gao, Chen and Sun obtained excellent results in the 𝐴 ≈ 130 mass region, in particular for Cs isotopes, and interpreted the inversion phenomenon as determined by the triaxiality of the nuclear shape, while the residual interactions impact the spin of the inversion point. They also noted the manifestation of a dynamical drift of the total angular momentum toward the intermediate axis [36]. It was initially proposed [22]that inversion occurs in nuclei with triaxial shape rotating around their short axis (𝛾>0◦in Lund convention), however alternative interpretations based on rotation around the intermediate axis [32,36,37], or around the long axis [38]were also proposed. In addition, there is no consensus on the primary quantity which governs the inversion, its amplitude, its inversion spin, and its gradual evolution along different isotopic and isotonic chains, including the La isotopes. The most recently obtained experimental information on the lightest Cs [9,11]and La [20,37]nuclei, together with the present new results on 120La extend the range of odd-odd nuclei exhibiting low-spin inversion, and offer the challenging opportunity to test the accuracy with which different theoretical models describe the evolution of the spin and amplitude of the inversion as a function of neutron number. The present work reports excited states in 120La. One rotational band composed of 𝑀1∕𝐸2dipole and 𝐸2crossover transitions was observed on top of the 8+state. It decays to the newly established 4+ground state via four low-energy dipole transitions. The spins and parities of most observed states are determined based on the systematics of the 𝜋ℎ11∕2 ⊗𝜈ℎ11∕2 bands in La nuclei and the measured angular correlation ratios. Calculations using the two quasiparticle plus triaxial rotor model including the 𝑛𝑝 interaction [31,32]reproduced very well the spin of the inversion. The 120La nucleus has been investigated using the 58Ni(64Zn,pn) fusion-evaporation reaction, and the JUROGAM 3 [39]plusMARA (Mass Analysing Recoil Apparatus) [40]setup at the Accelerator Laboratory of the University of Jyväskylä, Finland (see Fig. 1. A self-supporting enriched 58Ni foil of 0.95 mg/cm2thickness was bombarded with a 64Zn beam of 255 MeV delivered by the K130 cyclotron. The fusionevaporation residues were separated as a function of 𝐴∕𝑞and identified using the in-flight double-focusing recoil mass separator MARA [41]. Three BEGe and one clover detectors surrounding the MARA focal-plane detection system were used to detect 𝛾rays emitted by long-lived isomers and daughters of the 𝛽decay of the implanted recoils. All detector signals were recorded by the trigger-less Total Data Readout (TDR) data acquisition system, and time stamped by a global 100 MHz clock which allowed both temporal and spatial correlations to be established between recoils and events obtained with the rest of the focal plane and JUROGAM 3 arrays [40,42]. Prompt 𝛾rays were detected at the target position using the JUROGAM 3 array consisting of 24 Euroball clover [43]and 15 Eurogam Phase I-type [44] escape-suppressed germanium detectors, with an efficiency of ≈6%at 1.3 MeV. The clover detectors were arranged symmetrically relative to the direction perpendicular to the beam (twelve at 75.5◦and twelve at 104.5◦), while the Phase I detectors were placed at backward angles with respect to the beam direction (five at 157.6◦and ten at 133.6◦). The data were sorted using the GRAIN code [45]. In a first step the newly identified bands were assigned to 120La using recoil-gated prompt coincidences and the presence of x rays in the spectra. Following this identification, the analysis of the higher statistics prompt 𝛾𝛾𝛾 coincidences without recoil gating enabled construction of the level scheme. Fully symmetrized, three-dimensional (𝐸𝛾-𝐸𝛾-𝐸𝛾) matrices were analyzed using the radware [46,47] package. A total of 3.3 ×10 9prompt 𝛾-ray coincidence events with fold ≥3 were collected. The multipolarities of the 𝛾rays were extracted using the directional correlation from oriented states ratios (R𝐷𝐶𝑂) and two-point angular correlation (anisotropy) ratios 𝑅𝑎𝑐 [48,49]. The R𝐷𝐶𝑂 values (𝑅𝐷𝐶𝑂 =𝐼𝛾(157.6◦, ≈90 ◦)/𝐼𝛾(≈90 ◦, 157.6◦)) were extracted from a 𝛾-𝛾matrix, constructed by sorting prompt coincidence events with the detectors at 157.6◦versus those at (75.5◦, 104.5◦). Typical R𝐷𝐶𝑂 values obtained by gating on a stretched quadrupole transition are ≈1 for stretched quadrupole and ≈0.46 for dipole transitions, while those obtained by gating on a stretched dipole transition are ≈1for Physics Letters B 855 (2024) 138806 3 P.M. Jodidar, C.M. Petrache, B.F. Lv et al. Fig. 1. Schematic drawing of the MARA+JUROGAM 3 setup employed in the present experiment. Fig. 2. a) Level scheme of 120La. The arrow thickness is proportional to the relative intensity of the transition. b) Spectrum showing the observed transitions in 120La obtained by double-gating on the selected transitions 76-, 80-, 81-, 103-, 165-, 106-keV. c), d) Spectra showing the energy difference between the 80.3- and 80.8-keV transitions, obtained by double-gating as follow: c) on the left tail or d) on the right tail of the 81-keV peak, and on the 272-, 165-, 103-keV peaks. e) Mass spectra obtained by gating on selected transitions of 118Xe, 119Cs, 120Ba and 120La. The four peaks of 120La are labeled with the charge state of the ions detected by the MWPC at the MARA focal plane. f) Excitation energy systematics of states with I ≤22ℏrelative to the 10+state corresponding to the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 bands in 120La (present work) and 122−134La [15]. a dipole and ≈2.1for a quadrupole transition. The 𝑅𝑎𝑐 values (𝑅𝑎𝑐 = 𝐼𝛾(133.6◦+157.6◦)/𝐼𝛾(75.5◦+104.5◦)) had typical values of 0.8 and 1.4 for stretched dipole and quadrupole transitions, respectively. The level scheme of 120La, a double-gated spectrum showing the observed transitions, and a zoom on double-gated spectra showing the evidence for the 80.3-keV and 80.8-keV transitions forming a doublet peak are given in Fig. 2. Experimental information on the 𝛾-ray transitions is listed in Table 1. The 𝛾rays have been unambiguously assigned to 120La based on their prompt coincidence with the 𝐾𝛼1+𝐾𝛼2(33.4 keV) and 𝐾𝛽1(37.8 Physics Letters B 855 (2024) 138806 4 P.M. Jodidar, C.M. Petrache, B.F. Lv et al. Fig. 3. a), b) Parameter 𝐽(1), c) splitting 𝑆(𝐼), and d) ratios of reduced transition probabilities 𝐵(𝑀1)∕𝐵(𝐸2), for the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 bands in 120La (present work), 122−130La [20,37,51–53]. Filled symbols are for even spins and open symbols are for odd spins. The blue and red lines in c) are to guide the eye through the inversion points. The mixing ratio (𝛿) for the M1 transitions is assumed to be 0. Note that the 𝐵(𝑀1)∕𝐵(𝐸2) values for 126La have been calculated based on the intensities reported in Ref. [51], in which the 12+→10+transition should be 441.7 keV instead of 411.7 keV and the 𝐵(𝑀1)∕𝐵(𝐸2) values in panel (b) of Fig. 4 of Ref. [51] should be corrected accordingly. Table 1 Experimental information including energies 𝐸𝛾, relative intensities 𝐼𝛾, angular correlation 𝑅𝑎𝑐 and 𝑅𝐷𝐶𝑂 ratios, spin-parity of the connected states of the 𝛾rays assigned to 120La. Tentative spins and parities are given in parentheses. E(keV) 𝐼𝛾a𝑅𝑎𝑐 b𝑅𝐷𝐶𝑂 I𝜋 𝑓←→ 𝐼𝜋 𝑖 76.3(5) 70(14) 0.7(1) 1.0(1)𝑏5+←→ 4+ 80.3(5) 70(14) 0.7(1) 1.0(1)𝑏6+←→ 5+ 80.8(5) 70(14) 0.7(1) 1.0(1)𝑏7+←→ 6+ 103.1(5) 100(15) 0.7(1) 1.1(1)𝑏8+←→ 7+ 106.0(5) 46(8) 0.6(1) 0.9(1)𝑏10+←→ 9+ 165.2(5) 89(12) 0.7(2) 0.9(1)𝑏9+←→ 8+ 177.2(5) 22(6) 0.6(2) 12+←→ 11+ 238.7(5) 68(9) 0.9(2) 11+←→ 10+ 271.5(5) 103(12) 1.4(2) 1.4(2)𝑏10+←→ 8+ 284(1) 10(2) (14+←→ 13+) 288.0(5) 45(8) 0.6(1) 13+←→ 12+ 308.6(5) 33(5) 1.1(1) 15+←→ 14+ 345.1(5) 16(3) 1.5(3) 11+←→ 9+ 415.8(5) 110(16) 1.4(2) 12+←→ 10+ 465.3(5) 25(4) 1.6(3) 13+←→ 11+ 573.0(5) 70(10) 1.5(3) 14+←→ 12+ 593.0(5) 40(6) 1.5(3) 15+←→ 13+ 717(1) 50(15) 1.5(3) 16+←→ 14+ 718(1) 29(15) 1.5(3) 17+←→ 15+ 827(1) 58(18) 1.3(3) 18+←→ 16+ 843(1) <40 (19+←→ 17+) 924(1) <40 (20+←→ 18+) 953(1) <40 (21+←→ 19+) 1012(1) <40 (22+←→ 20+) 1090(1) <40 (24+←→ 22+) aRelative intensities corrected for efficiency, normalized to the intensity of the 103.1-keV transition. The intensities 𝐼𝛾were obtained from a combination of those measured from the total projection and gated spectra. bGated on the dipole 80-keV transition. keV) X rays of lanthanum, and on the mass spectrum measured at the MARA focal plane tagged by selected uncontaminated 𝛾rays measured at the focus of the JUROGAM 3 array (see Fig. 2a, 2e). The mass spectrum tagged by uncontaminated 𝛾rays assigned to 120La exhibits peaks at the same positions as those of 120Ba, and clearly distinct from the positions of the masses 118 and 119. In order to assign the spin and parity to the ground state, which could be the long-lived 𝑇1∕2 =2.8s isomer assigned to 120La from the observation of 𝛽-delayed protons in coincidence with 119Ba X rays [50], we first analyzed the systematics of the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 bands of La isotopes. As one can see in Fig. 2f, the expected gradual evolution of the level energies can only be obtained by assigning the observed band to the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 configuration and the band head to 𝐼𝜋=8 +. The energies of the even-spin levels above 10+exhibit a gradual decrease with decreasing neutron number, have a minimum for 122La and slightly increase for 120La, while those of the odd-spin levels are nearly flat or decrease from 122La to 120La. This induces a significant difference between the 𝐽(1)(𝐼)parameters which are related to moments of inertia (MOI) of the odd- and even-spin states in 120La (see the following), being higher for the odd-spin states (see Fig. 3a, 3b). The spin and parity of the ground state is then determined by the electromagnetic characters of the 103-, 81-, 80- and 76-keV transitions depopulating in cascade the 8+band head to the ground state. We established the electromagnetic characters of the four transitions by analyzing their total intensities in spectra obtained by gating on 𝛾rays above the 8+state, which should be equal after correction for internal conversion. As the intensities of the four transitions are comparable (see Table 1and Fig. 2a), but the conversion coefficients are very different for 𝐸1(≈0.5) and 𝑀1(≈2) characters, the four transitions should all be 𝐸1or all be 𝑀1∕𝐸2transitions, otherwise the intensity balance of at least one state would not be achieved. The 𝐸1character is excluded by the fact that the conversion coefficient extracted from gated spectra are consistent with 𝑀1∕𝐸2character, and the asymmetry in conversion coefficients expected for an 𝐸1transition is not observed. Furthermore, as no enhanced low-energy electric transitions are expected in this mass region, an 𝐸1character of all four transitions can be discarded. The order of the four 103-, 81-, 80- and 76-keV transitions cannot be firmly established. By gating on the 80-keV peak we find the 76-keV peak stronger than the 103-keV one after correcting for internal conversion, which suggests that the position of the 76-keV transition is below the 103-keV transition, or below the 80-keV doublet. The order of the 80- and 81-keV transitions could not be established; we tentatively put the 80-keV transition below the 81-keV one, and the 76-keV transition the lowest lying. In any case, we can then safely conclude that all four transitions of the cascade de-exciting the 8+state have an 𝑀1∕𝐸2character leading to a spin-parity assignment of 4+for the ground state. From the level energies we can extract the parameter 𝐽(1)(𝐼) = 𝐼∕𝜔(𝐼)related to the kinematic moment of inertia of the core and to the contributions of the valence nucleons, which are dominant at low spin. The 𝐽(1) parameter shown in panels a) and b) of Fig. 3exhibits a down-sloping trend, indicating that realignments of the odd nucleons play a significant role. However, the decreasing slope becomes smaller Physics Letters B 855 (2024) 138806 5 P.M. Jodidar, C.M. Petrache, B.F. Lv et al. Fig. 4. a) CNS potential energy surface plot for the 8+state of the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 band in 120La. The contour lines are 250 keV apart. b) Excitation energies, c) splitting 𝑆(𝐼)and d) 𝐵(𝑀1)∕𝐵(𝐸2) ratios calculated with TQTRM (red triangles) and experimental (black circles) for the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 band in 120La. The lines are drawn to guide the eyes. Open symbols are for odd spins and filled symbols for even spins. with increasing spin and stabilizes at spin around 20, beyond which the collective component prevails. One can distinguish three groups in the 𝐽(1) plots: the 𝐽(1) values of 120,122La which are distinctly larger than those of 124,126,128La especially for odd spins, and those of 130,132La which are significantly lower than the others. The difference between 𝑆(𝐼)for odd and even spins shown in Fig. 3c is largest in 122La at spin 12, and decreases gradually in the heavier isotopes. The spin of the inversion increases nearly linearly with increasing neutron number. The inversion persists up to the highest observed spin for 130La, and for 132La, 134La which are not shown in Fig. 3c. Similar behavior is present in the odd-odd Cs isotopes [9]. From the transitions intensities we extracted the ratios of reduced transition probabilities 𝐵(𝑀1)∕𝐵(𝐸2) in the rotational band of 120La, which are shown together with those of the heavier La isotopes in Fig. 3d. Different to the heavier isotopes, 120La exhibits a pronounced staggering over the entire observed spin range, in phase with that of the splitting 𝑆(𝐼)shown in Fig. 3c, similar to those observed in the 118−128Cs isotopes [15], but different from those of the heavier La nuclei where the regular staggering is not observed. Before discussing the configuration assignment to the observed nuclear states we should mention that despite their common use the Nilsson quantum numbers are not very accurate for the La isotopes, as the model assumes axially symmetric nuclear shape, while the deformations of these nuclei are triaxial. On the other hand, the axial asymmetry in 120La is moderate, thus in the following we will use the Nilsson labels as an indication of the dominant component in the wave function. The spin-parity 4+assigned to the ground state of 120La can be simply explained by coupling of a proton in the 𝜋3∕2+[422] Nilsson orbital to a neutron in 𝜈5∕2+[413], leading to the {𝜋3∕2+[422] ⊗𝜈5∕2+[413]}4+ configuration. The same reasoning can explain the spin-parity 2+assigned to the ground state of 122La, which can be obtained by coupling a proton in the 𝜋1∕2+[420] orbital (which is slightly above the 𝜋3∕2+[422] orbital occupied in 120La) to a neutron in the same 𝜈5∕2+[413] orbital, leading to the {𝜋1∕2+[420]⊗𝜈5∕2+[413]}2+configuration. The occupation of the same 𝜈5∕2+[413] neutron orbital in both 120La and 122La can be understood from the Nilsson diagram, in which the flat 𝜈5∕2+[413] orbital is crossed by the down-sloping 𝜈5∕2−[532] orbital at a deformation around 𝜀2=0.3: on the left side of the crossing (𝜀2<0.3), the occupation of the 𝜈5∕2−[532] orbital corresponds to 𝑁=63, that is to 120La, while on the right side of the crossing (𝜀2>0.3), the occupation of that orbital corresponds to 𝑁=65and 122La. Concerning the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 band in 120La, the involved Nilsson orbitals are clearly 𝜋1∕2−[550] and 𝜈5∕2−[532], leading to the 𝜋1∕2−[550] ⊗𝜈5∕2−[532] configuration. While the ground state the spin can be calculated by summing the projections Ω𝑝+Ω 𝑛 within the strong-coupling limit, such consideration is not applicable for the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 band, because here the nucleons show considerable alignment. The band-head spin is consistent with the assumption of a nearly orthogonal coupling of the proton two single-particle angular momenta, with that of the proton nearly completely aligned with the rotation axis and that of the neutron less aligned. In the 𝜋ℎ11∕2 ⊗𝜈ℎ11∕2 bands of the heavier La nuclei the proton occupies the same Nilsson orbital, that is 𝜋1∕2−[550], while the neutron successively occupies orbitals of the ℎ11∕2 sub-shell with increasing Ωwhen the neutron number increases: 𝜈5∕2−[532] in 120,122La (𝑁= 63, 65), 𝜈7∕2−[523] in 124,126,128La (𝑁=67, 69, 71), 𝜈9∕2−[514] in 130,132La (𝑁= 73, 75), and 𝜈11∕2−[505] in 134La (𝑁=77). The occupation of these neutron orbitals is supported by the band-head spins of the singleparticle bands observed in the odd-even Ba isotones of the La nuclei, which are 5∕2−in 119,121Ba, 7∕2−in 123,125,127Ba, 9∕2−in 129,131Ba, and 11∕2−in 133Ba [15]. As the occupied proton orbital remains unchanged in the chain of La nuclei, one is tempted to explain the evolution of the inversion spin with increasing neutron number through the successive occupation of the neutron Nilsson orbitals. From the 𝐽(1) and 𝑆(𝐼)systematics shown in Fig. 3a, 3b, 3c, we can deduce the following: the largest 𝐽(1) are those of 120,122La in which the orbital with Ω =5∕2is occupied (𝜈5∕2−[532]), having therefore the angular momentum closest to the intermediate axis, which is the axis with largest moment of inertia in triaxial nuclei; the 𝐽(1) values of 124,126,128La are clustered together and are smaller than those of 120,122La because the occupied orbital has larger Ω =7∕2 (𝜈7∕2−[523]), and therefore is more tilted relative to the intermediate axis; the 𝐽(1) values of 130,132La are even smaller because the occupied orbital has larger Ω =9∕2(𝜈9∕2−[514]) and therefore more tilted relative to the intermediate axis; the 𝐽(1) of 134La, not shown in the figure, is the smallest because the occupied 𝜈11∕2−[505] orbital has the largest Ω = 11∕2 possible in the ℎ11∕2 sub-shell. The magnitude and variation of 𝐽(1) with neutron number can be directly related to the overlap of the density distribution of the occupied neutron orbital with that of the core, which depends on the orientation of the single-particle angular momentum relative to that of the nuclear axes: the orbitals with small Ω contribute more to 𝐽(1) because of the larger overlap with the core. For the heavy La nuclei, for which the quadrupole deformation is smaller and the triaxiality is larger, the valence neutron occupies orbitals with higher Ωvalues in the ℎ11∕2 sub-shell, inducing a strong coupling of the odd neutron with the core, and setting up favorable conditions for chiral rotation to occur. To get a deeper insight in the mechanism responsible for the inversion, we performed two types of calculations: cranked Nilsson-Strutinsky (CNS) [54]to study the nuclear shape, and two quasiparticle plus triaxial rotor model (TQTRM) [31]to study the inversion. The yrast rotational bands with positive parity were calculated with CNS using standard parameters for the potential [55]. The configurations near the proton Fermi level with ℎ11∕2 nature involve 3 protons and 5 neutrons in the corresponding ℎ11∕2 sub-shells. The potential energy surface for the yrast band and for I = 8+is shown in Fig. 4. The absolute minimum suggests nuclear deformation of 𝜀2= 0.29, and 𝛾 = -19◦for both branches, which is similar to that used with the corequasiparticle coupling model for 124La (𝛽2= 0.28, and 𝛾= -13◦) [37]. The deduced nuclear shape indicates that rotation around the intermediate nuclear axis is favored. For 𝐼≈10the CNS calculations predict small energy difference between the two branches of the 𝜋ℎ11∕2 ⊗𝜈ℎ11∕2 band, which increases with increasing spin. However, the experimentally ob- Physics Letters B 855 (2024) 138806 6 P.M. Jodidar, C.M. Petrache, B.F. Lv et al. served inversion at low spins is not reproduced. Thus, additional effects, such as simultaneous rotation around more than one nuclear axis, and neutron-proton interactions, may possible play an important role in the observed inversion phenomenon. We then carried out two quasiparticle plus triaxial rotor model calculations. We employed the two quasiparticle plus triaxial rotor model (TQTRM) of Semmes and Ragnarsson [31]with standard parameters for the Nilsson potential [55]and for the pairing gaps, resulting in Δ𝑝=1.242 MeV and Δ𝑛=1.113 MeV. The Fermi level for protons is lying near the lowest-energy ℎ11∕2 orbital (dominant Ω𝓁=1∕2) and for neutrons between the second and third ℎ11∕2 orbitals (dominant Ω𝓁=3∕2, 5∕2). Calculations included large configuration spaces comprising four (five) negative-parity orbitals near the proton (neutron) Fermi level. The orbitals have mostly ℎ11∕2 nature. The Fermi level for protons is lying near the lowest-energy ℎ11∕2 orbital (dominant Ω𝓁=1∕2) and for neutrons between the second and third ℎ11∕2 orbitals (dominant Ω𝓁=3∕2, 5∕2). The TQTRM moments of inertia follow the irrotational flow model dependence with respect to 𝛾, an assumption that is supported by empirical evaluations [56]. The choice of the magnitude of the moment of inertia was guided by the energy of the 2+state of the even-even core and no variable MOI was used. A Coriolis attenuation factor of 0.7 was adopted, as in previous works in this mass region [32]. The model includes residual neutron-proton interaction in the form 𝑉𝑛𝑝 =√8𝜋3(ℏ 𝑚𝜔 ) 3 2𝛿(𝑟𝑝−𝑟𝑛)(𝑢0+𝑢1𝜎𝑝⋅𝜎𝑛), with parameters 𝑢0=−7.2MeV and 𝑢1=−0.8MeV, which were previously established for the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 configuration [12,31]. Results from the TQTRM calculations carried out with quadrupole deformation of 𝜀2=0.28 and 𝛾=16 ◦are shown in Fig. 4, where one can see that both the calculated excitation energies and the inversion spin were very well reproduced. It is known that the inversion is a result of multiple effects, such as the position of the Fermi levels (in particular if they are close to an Ω=1/2 orbital), triaxiality of the nuclear shape, and residual neutronproton interactions. For 120La the present calculations suggest that most important for the observed inversion is the position of the Fermi levels, in particular the neutron Fermi level. Significant inverse splitting was found specifically for wave-function contributions where the second lowest-energy 𝜈ℎ11∕2 orbital was involved. Transition probabilities were calculated using effective spin and core 𝑔factors of 𝑔𝑠,𝑒𝑓 𝑓 = 0.8 𝑔𝑠,𝑓 𝑟𝑒𝑒 and 𝑔𝑐=𝑍∕𝐴, respectively. The model calculates macroscopically the electric quadrupole moment assuming that the nucleus is a deformed rigid object with a sharp surface. It is known that this assumption is a simplification. In the present calculations it resulted in an overestimation of the reduced 𝐵(𝐸2) values for the intra-band transitions, for instance a theoretical value of 𝐵(𝐸2; 10+→8+)= 216 W.u. was obtained in the calculations, while typical values of ∼100 W.u. are expected, similar to the measured 𝐵(𝐸2; 2+→0+)= 113(5), 94(4) W.u. in the neighboring 124,126Ba, and 𝐵(𝐸2; 2+→0+)= 138(24) W.u. in 126Ce, [15]. Thus, to reduce the theoretical electric quadrupole moment we used an effective electric charge 𝑒𝑒𝑓𝑓 = 0.8𝑒, which resulted in a reasonable 𝐵(𝐸2; 10+→8+)= 97 W. u. There is a very good agreement between the calculated 𝐵(𝑀1)∕ 𝐵(𝐸2) ratios and the experimental observations. In particular the staggering, which is clearly seen at low spin only in 120La, is very well reproduced, both in its phase and magnitude, see Fig. 4c. It is caused by a staggering in the 𝐵(𝑀1) values, which are very sensitive to the triaxial deformation. It is interesting to note that the calculated 𝐵(𝑀1) staggering decreases for larger triaxiality, which could explain the experimentally observed lack of staggering for the heavier La isotopes, where larger triaxial deformation is expected. Summarizing, the present work reports for the first time spectroscopic data in 120La, the lightest La isotope in which a collective rotational band built on the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 configuration has been observed. The band properties are theoretically investigated with the cranked Nilsson-Strutinsky model, and the two quasiparticle plus triaxial rotor model including the 𝑛𝑝 interaction. An excellent agreement is obtained for the spin where the inversion between the 𝐸2cascades of the 𝜋ℎ11∕2 ⊗𝜈ℎ 11∕2 band occurs, giving credit to the 𝑛𝑝 interaction as an important parameter responsible for the inversion. The calculations also suggest that the position of the Fermi levels, in particular for neutrons, have a strong impact on the observed inversion. Significant inverted splitting was found when the second lowest-energy neutron orbital from the ℎ11∕2 sub-shell was involved. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgements The work is based on research supported in part by the National Research Foundation of South Africa (Grant Number 150650); by the National Natural Science Foundation of China (Grants No. 12305128), by the Hubert Curien Partnership (PHC) “Cai Yuanpei Project”, by the International Partnership Program of Chinese Academy of Sciences for Future Network (Grants No. 016GJHZ2023024FN); by the Academy of Finland under the Finnish Centre of Excellence Programme (2012- 2017); by the EU 7th Framework Programme Project No. 262010 (ENSAR); by the United Kingdom Science and Technology Facilities Council through grant numbers ST/P004598/1 and ST/V001027/1, by the National Research, Development and Innovation Fund of Hungary (Project No. K128947), as well as by the European Regional Development Fund (Contract No. GINOP-2.3.3-15-2016-00034); by the Polish National Science Centre (NCN) Grant No. 2013/10/M/ST2/00427; by the Swedish Research Council under Grant No. 2019-04880; and by the National Natural Science Foundation of China (Grants No. 11505242, No. 11305220, No. U1732139, No. 11775274, and No. 11575255). 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