Investigation Of High Spin States And Low-lying Spectrum In Odd-Odd Nucleus ¹²⁶Cs

Among all natural and synthetic nuclei,odd-odd nuclei are notably the least abundant.This scarcity stems from the coupling between an unpaired valence proton and an unpaired valence neutron,rendering the physical characteristics of odd-odd nuclei notably intricate and diverse.Consequently,investigating both the high spin band part and the low-lying excited state part proves challenging.The A～130 transition region is a hotspot in the study of high spin states of nuclei.Characterized as a prototypical"γ-soft"nuclear region,this region encompasses numerous physical phenomena associated with gamma deformation,including shape coexistence,chiral symmetry breaking,signature inversion,and band crossing.In this paper,we conduct a nuclear spectrographic analysis and theoretical calculation of the nuclear structure of the odd-odd nucleus ¹²⁶Cs within this mass region.The Fermi level of the proton resides in the lower segment of the h_11/2 subshell,while that of the neutron is situated in the middle to upper segment of the h_11/2 subshell.¹²⁶Cs exhibits a complex energy level structure,showing rich physical phenomena of high spin states.Based on the experimental and theoretical analysis of the original data obtained by Dr.Komatsubara et al.on the NORDBALL detector array at the Niels Bohr Institute,we delve into the energy structure of high spin states and study chiral problems in the odd-odd nucleus126Cs.Theγ-ray coincidence analysis method is used to enrich the energy level scheme of the positive parity part of the odd-odd nucleus ¹²⁶Cs,and it is found that it has multiple chiral doublets for the first time.It is proved experimentally and theoretically that four positive parity rotation bands are multiple chiral bands based on the same configuration.For the high spin negative parity rotational bands,various theoretical methods,such as TRS method and configuration-constrained PES,are used to calculate the corresponding deformation of each negative parity rotational band,and the projected shell model method is used for theoretical calculation,and the configuration is specified again.For the low-lying excited states,configuration-constrained PES is used for the first time to determine the ground state configuration and deformation of the ¹²⁶Cs.The energy level scheme is further improved,and the energies of the newly discovered energy levels are reproduced by using the projected shell model and the configuration is specified.The machine learning method is extended to the study of the low-lying excited states of odd-odd nuclei,and experimental excited energies of the first excited states of odd-odd nuclei are preliminarily predicted,which is expected to provide a reference for the subsequent research.The main results of this work are as follows:1.In this study,the energy level scheme of the high and low-lying excited states are further improved on the basis of verifying the positions of the excited states reported by predecessors,more than 20 newγ-transitions are added to the energy level scheme of ¹²⁶Cs nucleus.At the same time,the relative intensity,ADO ratio and the reduced transition probability B（M1）/B（E2）of eachγ-transition observed in ¹²⁶Cs is extracted.2.The configuration of the ground state 1⁺level of ¹²⁶Cs is specified as πg_7/2（?）vg_7/2 by using the configuration-constrained Potential-energy Surface（PES）method,and the configurations of the newly observed levels are specified by the projected shell model.3.A newly discovered chiral doublet band in ¹²⁶Cs is specified to have the same πh_11/2（?）vh_11/2 configuration as the first chiral doublet band reported before.The positive parity rotational band of ¹²⁶Cs is calculated and analyzed in detail by using the projected shell model,and the excited energy levels and electromagnetic transitions are well reproduced,these four bands are specified as multiple chiral doublets based on the same configuration.The chiral geometry of ¹²⁶Cs is studied for the first time,and the evolution of yrast band and its partner band from chiral vibration to chiral rotation is analyzed.4.The Total Routhian Surface（TRS）method,the configuration-constrained Potential energy Surface（PES）method and the projected shell model are used to reconstruct and analyze the negative parity rotational bands of ¹²⁶Cs.The deformations of the band head for these bands are given,and the excited energy and electromagnetic transition of the experiment are reconstructed theoretically according to the calculated deformation.The corresponding configuration of each rotational band is re-analyzed.The results of the projected shell model show that band A corresponds to one deformation（β=0.212,γ=1.449°）,while band C-E corresponds to another deformation（β=0.223,γ=26.828°）.5.The application of machine learning method in the study of low-lying excited states of nuclei is extended,and it is advanced to the calculation of low-lying excited states of odd-odd nuclei.The first excited states of odd-odd nuclei are predicted by using a single layer Bayesian neural network.The prediction effect of odd-odd nuclei with large and stable deformation is also good.Projected Hartree-Fock（PHF）method is projected to calculate the energy levels of the first excited states of some typical odd-odd nuclear isotope chains,and the accuracy of the machine learning method is estimated by comparing with projected Hartree-Fock（PHF）.Considering more appropriate physical quantities related to odd-odd nuclei,the prediction results can be closer to the experimental values.This method is expected to be used to predict the higher excited states of odd-odd nuclei.