Shell corrections with finite temperature covariant density functional theory

The temperature dependence of the shell corrections to the energy sEsell,entropy T8S sell,and free en-ergy oFshell is studied by employing the covariant density functional theory for closed-shell nuclei.Taking 144Sm as an example,studies have shown that,unlike the widely-used exponential dependence exp(-E*/Ed),8Eshell exhibits a non-monotonous behavior,ie.,first decreasing 20%approaching a temperature of 0.8 MeV,and then fading away exponentially.Shell corrections to both free energy 8F shell and entropy T8S shell can be approximated well using the Bohr-Mottelson forms T/sinh(t)and[rcoth(r)-1]/sinh(r),respectively,in which Tx T.Further studies on the shell corrections in other closed-shell nuclei,100Sn and 208 Pb,are conducted,and the same temperature dependen-cics are obtained.

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model（GLDM）, whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.

Investigating the fission dynamics of the following neutron shell closed nuclei within a stochastic dynamical approach:^(210)Po,^(212)Rn,and ^(213)Fr

The dissipative dynamics of nuclear fission is a well confirmed phenomenon that can be either described by a Kramers-modified statistical model or by a dynamical model employing the Langevin equation.Although dynamical models as well as statistical models incorporating fission delays have been found to explain the measured fission observables in several studies,they present conflicting results for shell closed nuclei in the mass region of 200.Notably,an analysis of the recent data on neutron shell closed nuclei in the excitation energy range of 40-80 MeV failed to provide a satisfactory description of the data,which was attributed to a mismatch with shell effects and/or entrance channel effects,without reaching a definite conclusion.In the present study,we demonstrate that a well established stochastic dynamical code can simultaneously reproduce the available data for pre-scission neutron multiplicities and fission and evaporation residue excitation functions for the following neutron shell closed nuclei^(210)Po and^(212)Rn and their isotopes^(206)Po and^(214,216)Rn without the need for including any extra shell or entrance channel effects.The relevant calculations are performed by using a phenomenological universal friction form factor with no ad-hoc adjustment of the model parameters.However,we note a significant deviation,beyond experimental errors,for some Frisotopes.

Binding energies of proton-rich nuclei determined from their mirror pairs

In addition to the Coulomb displacement energy,the residual differences between the binding energies of mirror nuclei(a pair of nuclei with the same mass number plus interchanged proton and neutron numbers)contribute to the shell effect via the valence scheme in this study.To this end,one linear combining type of valence nucleon number,namely,αNp+βNn,is chosen to tackle this shell correction,in which Npand Nnare the valence proton and neutron numbers with respect to the nearest shell closure,respectively.The mass differences of mirror nuclei,as the sum of the empirical Coulomb displacement energy and shell effect correction,are then used to obtain the binding energies of proton-rich nuclei through the available data of their mirror partners to explore the proton dripline of the nuclear chart.

An improved α-decay energy formula for heavy and superheavy nuclei

Based on the liquid-drop model and using the first derivative of the normalized Gaussian function to consider the shell correction,a simpleα-decay energy formula is proposed for heavy and superheavy nuclei.The values of corresponding adjustable parameters are obtained by fittingα-decay energies of 209 nuclei ranging from Z=90 to Z=118 with N≥140.The calculated results are in good agreement with the experimental data.The average and standard deviations between the experimental data and theoretical results are 0.141 and 0.190 Me V,respectively.For comparison,the reliable formulae proposed by Dong T K et al(2010,Phys.Rev.C 82,034320),Dong J M et al(2010,Phys.Rev.C 81,064309)and the WS3+nuclear mass model proposed by Wang N et al(2011,Phys.Rev.C 84,051303)are also used.The results indicate that our improved 7-parameter formula is superior to these empirical formulae and is largely consistent with the WS3+nuclear mass model.In addition,we extend this formula to predict theα-decay energies for nuclei with Z=117,118,119 and 120.The predicted results of these formulae are basically consistent.

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.

Released energy formula for proton radioactivity based on the liquid-drop model

In this work,based on the liquid-drop model and considering the shell correction,we propose a simple formula to calculate the released energy of proton radioactivity(Q_(p)).The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state.The standard deviation between the theoretical values and experimental ones is only 0.157 Me V.In addition,we extend this formula to calculate 51 proton radioactivity candidates in region 51≤Z≤83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q_(p)calculated by WS4 and HFB-29.The calculated results indicate that the evaluation ability of this formula for Q_(p)is inferior to WS4 while better than HFB-29.