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 a...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.展开更多
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...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.展开更多
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 dynamica...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.展开更多
Based on the Weizsacker-Skyrme(WS4)mass model,the fission barriers of nuclei are systematically studied.Considering the shell corrections,macroscopic deformation energy,and a phenomenological residual correction,the f...Based on the Weizsacker-Skyrme(WS4)mass model,the fission barriers of nuclei are systematically studied.Considering the shell corrections,macroscopic deformation energy,and a phenomenological residual correction,the fission barrier heights for nuclei with Z≥82 can be well described,with an rms deviation of 0.481 MeV with respect to 71 empirical barrier heights.In addition to the shell correction at the ground state,the shell correction at the saddle point and its relative value are also important for both deformed and spherical nuclei.The fission barriers for nuclei far from theβ-stability line and super-heavy nuclei are also predicted with the proposed approach.展开更多
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 ...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.展开更多
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...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.展开更多
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...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.展开更多
The barrier against the spontaneous fission has been determined within the Generalized Liquid Drop Model （GLDM） including the mass and charge asymmetry, and the proximity energy. The shell correction of the spherica...The barrier against the spontaneous fission has been determined within the Generalized Liquid Drop Model （GLDM） including the mass and charge asymmetry, and the proximity energy. The shell correction of the spherical parent nucleus is calculated by using the Strutinsky method, and the empirical shape-dependent shell correction is 6mp10yed during the deformation process. A quasi-molecular shape sequence has been defined to describe the whole process from one-body shape to two-body shape system, and a two-touching-ellipsoid is adopted when the superdeformed one-body system reaches the rupture point. On these bases the spontaneous fission barriers are systematically studied for nuclei from 2a^Th to 249 Cm for different possible exiting channels with the different mass and charge asymmetries. The double, and triple bumps are found in the fission potential energy in this region, which roughly agree with the experimental results. It is found that at around Sn-like fragment the outer fission barriers are lower, while the partner of the Sn-like fragment is in the range near l^SRu where the ground-state mass is lowered by allowing axially symmetric shapes. The preferable fission channels are distinctly pronounced, which should be corresponding to the fragment mass distributions.展开更多
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 ...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.展开更多
基金Supported by Naturnal Science Foundation of Henan Province(202300410480,202300410479)the National Natural Science Foundation of China(U2032141)+1 种基金the Foundation of Fundamental Research for Young Teachers of Zhengzhou University(UC 202041041)the Physics Research and Development Program of Zheng-zhou University(324102171)。
文摘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.
基金Supported by National Natural Science Foundation of China(11675066,11475050)the Fundamental Research Funds for the Central Universities(lzujbky-2017-ot04)Feitian Scholar Project of Gansu Province
文摘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.
基金D.A.acknowledges the financial support from the University Grants Commission(UGC),Government of India,received in the form of a research fellowship(Ref.No.19/06/2016/(i)EU-V,Sr.No.2061651303)。
文摘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.
基金Supported by the National Natural Science Foundation of China(12265006,U1867212)the Guangxi Natural Science Foundation(2017GXNSFGA198001)。
文摘Based on the Weizsacker-Skyrme(WS4)mass model,the fission barriers of nuclei are systematically studied.Considering the shell corrections,macroscopic deformation energy,and a phenomenological residual correction,the fission barrier heights for nuclei with Z≥82 can be well described,with an rms deviation of 0.481 MeV with respect to 71 empirical barrier heights.In addition to the shell correction at the ground state,the shell correction at the saddle point and its relative value are also important for both deformed and spherical nuclei.The fission barriers for nuclei far from theβ-stability line and super-heavy nuclei are also predicted with the proposed approach.
基金Supported by the National Natural Science Foundation of China(12075121 and 11605089)by the Natural Science Foundation of Jiangsu Province(BK20190067 and BK20150762)。
文摘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.
基金National Natural Science Foundation of China(Grant No.12175100)the construct program of the key discipline in Hunan province,the Research Foundation of Education Bureau of Hunan Province,China(Grant No.18A237)+1 种基金the Innovation Group of Nuclear and Particle Physics in USC,the Shandong Province Natural Science Foundation,China(Grant No.ZR2022JQ04)the Hunan Provincial Innovation Foundation For Postgraduate(Grant No.CX20210942 and No.CX20220993)
文摘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.
基金Supported by the National Natural Science Foundation of China(11790325,11875323,11875125,11947410,11705163,11790320,11790323,11961141003)the National Key R&D Program of China(2018 YFA0404404)+1 种基金the Continuous Basic Scientific Research Project(WDJC-2019-09,WDJC-2019-13,BJ20002501)of the funding of China Institute of Atomic EnergyChinese-Polish Joint project by the National Science Foundation of China(11961131010)。
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11175074,11120101005,11105035,and 10805061the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2012-5the Knowledge Innovation Project of the Chinese Academy of Sciences under Grant No.KJCX2-EW-N01
文摘The barrier against the spontaneous fission has been determined within the Generalized Liquid Drop Model （GLDM） including the mass and charge asymmetry, and the proximity energy. The shell correction of the spherical parent nucleus is calculated by using the Strutinsky method, and the empirical shape-dependent shell correction is 6mp10yed during the deformation process. A quasi-molecular shape sequence has been defined to describe the whole process from one-body shape to two-body shape system, and a two-touching-ellipsoid is adopted when the superdeformed one-body system reaches the rupture point. On these bases the spontaneous fission barriers are systematically studied for nuclei from 2a^Th to 249 Cm for different possible exiting channels with the different mass and charge asymmetries. The double, and triple bumps are found in the fission potential energy in this region, which roughly agree with the experimental results. It is found that at around Sn-like fragment the outer fission barriers are lower, while the partner of the Sn-like fragment is in the range near l^SRu where the ground-state mass is lowered by allowing axially symmetric shapes. The preferable fission channels are distinctly pronounced, which should be corresponding to the fragment mass distributions.
基金Supported by National Natural Science Foundation of China(Grant No.11205083 and No.11975132)the construct program of the key discipline in Hunan province,the Research Foundation of Education Bureau of Hunan Province,China(Grant No.18A237)+1 种基金the Innovation Group of Nuclear and Particle Physics in USC,the Shandong Province Natural Science Foundation,China(Grant No.ZR2019YQ01)the Hunan Provincial Innovation Foundation For Postgraduate(Grant No.CX20200909)。
文摘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.
