Shell Correction Method Based On The Relativistic Mean-Field Theory

Shell-correction method is an efficient way to study the nuclear mass and shape.Combined with the liquid-drop model,the nuclear mass and fission barriers could be accurately calculated.Meanwhile,temperature is a crucial variable in the study of nuclear structure and nuclear reaction.In the study of J.C.Pei,thermal effects could lead to a 10 orders of magnitude variation of the half life of compound nuclei.Therefore,the study of temperature dependent shell corrections is important to the thermal nuclear fission.The temperature dependent Strutinsky's shell corrections of nuclei ranging from light mass to heavy mass have been systematically studied based on the single-particle levels obtained in the Finite-Temperature Relativistic Mean-Field?FTRMF?theory.These shell-correction quantities are related with the total binding energy and the fission barrier.Firstly,we study the temperature dependence of shell corrections of doubly magic nuclei ⁴⁰Ca,⁷⁸Ni,¹³²Sn,and ²⁰⁸Pb.Different from the traditional used exponential decay approximation,results show that with the increase of temperature,the energy shell corrections_shell first get large then decay.This can be deduced from the compeptition between the sum of single-particle energies_sum and its smoothed counterpart?.In the fitting part,we find the Bohr-Mottelson equation could nicely describe their behaviors,especially for the nuclei ¹³²Sn and ²⁰⁸Pb.Then,we study the temperature dependent energy shell correction_shell??of Sn,and Pb isotopic chains.There exist shell effects on_shell??for the shell closure nuclei,i.e.=82,126.Such effects get weak at¹.6MeV.The last part of this study is about the temperature dependence of the shell corrections of the equilibrium points and saddle points of ²⁴⁰Pu.Results show that the fission barrier get lower when nucleus get warmer.The shell corrections at zero temperature approach to zero,which can be omitted,but when temperature increases,they also increase.As a further study of the Relativistic Mean-Field?RMF?theory and a complement of this paper.We introduce the study of spin and pseudospin symmetries in the single-particle spectra within the meson-exchange version of RMF framework in the last part of this work.