Impact of initial fluctuations and nuclear deformations in isobar collisions

Relativistic isobar^(96)_(44)Ru+^(96)_(44)Ru and^(96)_(40)Zr+^(96)_(40)Zrcollisions have revealed intricate differences in their nuclear size and shape,inspiring unconventional studies of nuclear structure using relativistic heavy ion collisions.In this study,we investigate the relative differences in the mean multiplicityR_(<Nch>)and the secondR_(ε2)and third-order eccentricityR_(ε3)between isobar collisions using initial state Glauber models.It is found that initial fluctuations and nuclear deformations have negligible effects on R_(<Nch>)in most central collisions,while both are important for the R_(ε2)and R_(ε3),the degree of which is sensitive to the underlying nucleonic or sub-nucleonic degree of freedom.These features,compared to real data,may probe the particle production mechanism and the physics underlying nuclear structure.

Structure of Hamiltonian Matrix and the Shape of Eigenfunctions：Nuclear Octupole Deformation Model

The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.

Nuclear dynamical octupole deformation in heavy-ion reactions

Within the quantum molecular dynamics （QMD） model, the dynamical octupole deformation is studied as a function of the central distance between the projectile and target in the approaching process of heavy-ion fusion reactions. The dependence of the maximum dynamical octupole defor- mations on tile incident energies is also investigated. The dynamical octupole deformations can be observed during the approaching process, and the maximum dynamical octupole deformations be- come more significant with decreasing incident energies. The distributions of the proton and neutron centers in the projectile and target are also investigated, respectively. In the approaching process of heavy-ion fusion reactions, the separation between proton centers for two nuclei is larger than that between neutron centers because of the strong Coulomb potential.

Transfer learning and neural networks in predicting quadrupole deformation

Accurately determining the quadrupole deformation parameters of atomic nuclei is crucial for understanding their structural and dynamic properties.This study introduces an innovative approach that combines transfer learning techniques with neural networks to predict the quadrupole deformation parameters of even-even nuclei.With the application of this innovative technique,the quadrupole deformation parameters of 2331 even-even nuclei are successfully predicted within the nuclear region defined by proton numbers 8≤Z≤134 and neutron numbers N≥8.Additionally,we discuss the impact of nuclear quadrupole deformation parameters on the capture cross-sections in heavy-ion fusion reactions,reconstructing the capture cross-sections for the reactions ^(48)Ca+^(244)Pu and ^(48)Ca+^(248)Cm.This research offers new insights into the application of neural networks in nuclear physics and highlights the potential of merging advanced machine learning techniques with both theoretical and experimental data,particularly in fields where experimental data are limited.

Deformation dependence of symmetry energy coefficients of nuclei

Based on the semi-classical Thomas-Fermi approximation together with the Skyrme energy-density functional, we study the deformation dependence of symmetry energy coefficients of finite nuclei. The symmetry energy coefficients of nuclei with mass number A = 40, 100, 150, 208 are extracted from two-parameter parabola fitting to the calculated energy per particle. We find that the symmetry energy coefficients decrease with the increase of nuclear quadrupole deformations, which is mainly due to the isospin dependence of the difference between the proton and neutron surface diffuseness. Large deformations of nuclei can cause the change of the symmetry energy coefficient by about 0.5 Me V and the influence of nuclear deformations on the symmetry energy coefficients is more evident for light and intermediate nuclei.

Nuclear structure study of some bubble nuclei in the light mass region using mean field formalism

We study the structural properties of some light mass nuclei using two different formalisms（i） a recently developed simple effective interaction in the frame work of microscopic non-relativistic Hartree-Fock method and（ii）the well-known relativistic mean field approach with NL3 parameter set. The bulk properties like binding energy, root mean square radii and quadrupole deformation parameter are estimated and compared with the available experimental data. The predicted results of both the formalisms are well comparable with the experimental observations. The analysis of density profiles of these light mass nuclei suggest that22 O,23F,34 Si and46Ar have bubble like structure.

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper,the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles.For axially deformed nuclei,two different types of density profiles are used to describe their charge distributions.For the same charge distributions expanded with different basis functions,the corresponding longitudinal form factors are derived and compared with each other.Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions.Further numerical calculations of longitudinal form factors of^（12）C indicates that the C_0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions.For deformed nuclei,their charge RMS radii can also be determined accurately by the C_0 measurement.The studies in this paper examine the model-independent properties of electron scattering,which are useful for interpreting electron scattering experiments on exotic deformed nuclei.

High-K multi-particle bands and pairing reduction in 254No

The multi-particle states and rotational properties of the two-particle bands in 254No are investigated by the cranked shell model with pairing correlations treated by the particle number conserving method. The rotational bands on top of the two-particle Kπ= 3+, 8- and 10+ states and the pairing reduction are studied theoretically in 254No for the first time. The experimental excitation energies and moments of inertia of the multi-particle states are reproduced well by the calculations. Better agreement with the data is achieved by including the high-order deformation ε6,J（1） in these two-particle bands compared with the ground state band is attributed to the pairing reduction due to the Pauli blocking effect.

Driving potential and fission-fragment charge distributions

We propose an efficient approach to describe the fission-fragment charge yields for actinides based on the driving potential of the fissioning system.Considering the properties of primary fission fragments at their ground states,the driving potential,which represents the potential energies of the system around scission configuration and closely relates to the yields of fragments,can be unambiguously and quickly obtained from the Skyrme energy-density functional together with the Weizs?cker-Skyrme mass model.The fission-fragment charge distributions for thermal-neutron-induced fission and spontaneous fission of a series of actinides,especially the odd-even staggering in the charge distributions,can be well reproduced.Nuclear dynamical deformations and pairing corrections of fragments play an important role in the charge distributions.

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field （RMF） theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov （HFB-14） model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.

Projected Shell Model Description for the Proton Emitters

Proton radioactivity is an important decay mode for nuclei near the proton drip-line. Studies of this decay mode can reveal valuable information on exotic nuclear structure and provide important information on the stucture of nuclei in extreme conditions. The new experimental data can let us understand the interactions in exotic systems, which motivate further theoretical development. The most recent application of the projected shell model(PSM) for proton emitters is represented. We study the rotational bands of the deformed proton emitter141 Ho by using the PSM. The experimental data are well reproduced. Strongly suppressed γ transition from the low-lying I~π= 3/2+state makes this state isomeric. Variations in the dynamical moment of inertia are discussed due to band crossings using the band diagram. The calculated results for proton emitter ^(151)Lu shows it is oblately deformed.

Understanding the isoscaling relationship in the fissioning system with evaluated data

The isoscaling parameters aevai in the fissioning systems,i.e.,those extracted from the Evaluated Nuclear Data Library(ENDF/B-VIII.O)and the Joint Evaluated Fission and Fusion File(JEFF-3.3),show an obvious difference from simple statistic model prediction where only the symmetry energy plays the dominant role.To explain the aeVai as a function of the charge number of the fission fragment,a statistic scission point model is adopted.Our analysis shows that the effects of the shell correction,nuclear shape deformation,and intrinsic temperature of fission fragments are indispensable as well as the symmetry energy.Furthermore,an alternative method for extracting the intrinsic temperatures of fission fragments is proposed based on the isoscaling relationship in fission fragments.The intrinsic temperatures of the light fragments are higher than those of the heavy fragments.