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Considering energy dependence of the barrier radius in heavy-ion fusion reactions, a modified Siwek-Wilczy\'{n}ski (MSW) fusion cross section formula is proposed. With the MSW formula, the fusion barrier parameters for 367 reaction systems are systematically extracted, based on 443 datasets of measured cross sections. We find that the fusion excitation functions for about $60\%$ reaction systems can be better described by introducing the energy dependence of the barrier radius which is due to the dynamical effects at energies near and below the barrier. Considering both the influence of the geometry radii and that of the reduced de Broglie wavelength of the colliding nuclei, the barrier heights are well reproduced with only one model parameter. The extracted barrier radius parameters linearly decrease with the effective fissility parameter, and the width of the barrier distribution relates to the barrier height and as well as the reduced de Broglie wavelength at energies around the Coulomb barrier., Comment: 9 figures, 1 table, accepted for publication in Atomic Data and Nuclear Data Tables

Pre-neutron fragment mass yields in the vicinity of the thermal neutron energy are highly important for applications because of the larger fission cross sections of the U(n, f) and Pu(n, f) reactions. In this paper, pre-neutron fragment mass yields at incident energies from thermal up to 20 MeV are systematically studied using an empirical fission potential (EFP) model, the potential parameters of which are obtained from the measured data. The energy dependences of the peaks and valleys of the pre-neutron fragment mass yields are described by exponential and linear functions for the U(n, f) and Pu(n, f) reactions, respectively. The energy dependences of the evaporation neutrons, which play a crucial role in the reasonable description of pre-neutron fragment mass yields, are also obtained from the fission cross sections. The pre-neutron fragment mass yields in this study are not only consistent with the results of previous studies in regions of several MeVs but also agree well with existing measured data at incident energies from thermal up to 20 MeV. The results show that the feasibility of this EFP model is verified in this extended energy region.

The intensity interferometry is applied as a chronometer of the particle emission of hydrogen isotopes from the intermediate velocity source formed in $^{40}$Ar+$^{197}$Au reactions at 30 MeV/u. The dynamic emission order of τp>τd>τt is evidenced via the correlation functions of nonidentical particle pairs. Assuming the similar source size, the same emission order is inferred from the correlation functions of identical particle pairs, where τp≈100fm/c is extracted by the fit of Koonin-Pratt equation to p-p correlation function. Transport model simulations demonstrate that the dynamic emission order of light charged particles depends on the stiffness of the nuclear symmetry energy.

The energy dissipation processes in multinucleon transfer reactions of $^{136}$Xe+$^{198}$Pt at incident energies Elab=5.59 and 7.98 MeV/nucleon are investigated by using the improved quantum molecular dynamics model. The total-kinetic-energy-mass (TKE-Mass) distributions, the total kinetic energy loss (TKEL) distributions, and the excitation energy distributions of the primary binary products under different contact time scales of the reaction partners are analyzed. It shows that the value of the energy dissipation has an increasing trend over contact time. The quasielastic, the deep-inelastic, and the quasifission events can be roughly distinguished by the contact time. By analysing the correlation between the isotopic cross sections and the contact time, we find that the neutron-rich nuclei are produced in the deep-inelastic collisions.

We propose a method for extracting the properties of the isobaric mass parabola based on the total double -decay energies of isobaric nuclei. Two important parameters of the mass parabola, the location of the most -stable nuclei and the curvature parameter , are obtained for 251 A values, based on the total double -decay energies of nuclei compiled in the AME2016 database. The advantage of this approach is that the pairing energy term caused by the odd-even variation can be removed in the process, as well as the mass excess of the most stable nuclide for the mass number A, which are employed in the mass parabolic fitting method. The Coulomb energy coefficient MeV is determined by the mass difference relation for mirror nuclei, and the symmetry energy coefficient is also studied by the relation .

Dynamical nuclear shell effect is introduced to the improved quantum molecular dynamics model in interaction potential energy in the process of fusion reactions. The dynamical shell correction energy of the system is calculated and applied to dynamical process of fusion reactions with a switch function employed to connect the shell correction energy of the projectile and target with that of the compound nucleus. It is found that the shell effect enhances the fusion barrier and the calculated fusion (capture) cross-sections decrease for subbarrier fusion reactions which both projectile and target are doubly magic nuclei. The experimental data of the fusion cross-sections for four systems 40 Ca + 48 Ca , 48 Ca + 48 Ca , 16 O + 208 Pb and 48 Ca + 208 Pb can be reproduced better with the shell effect being considered by using the ImQMD model.

Angular distributions of fragments have been studied for 197 Au +197 Au ternary reactions at bombarding energy 15 A MeV by an improved quantum molecular dynamics model. The calculated results are qualitatively in agreement with the experimental data. Through analyzing the angular distributions of fragments, it is shown that in semi-peripheral collisions 197 Au +197 Au interacting system often reseparates into three massive fragments which are almost aligned in space along the separation axis. The anisotropic distribution in azimuthal angle ϕ shows that the projectile-like fragment (PLF) or target-like fragment (TLF) breaks up violently, reflecting nonequilibrium effects in the consecutive reseparation. The time scale elapsing from the scission of the binary PLF+TLF system to the secondary scission of PLF or TLF is estimated to be of about 80 fm /c. It is found that the distribution in Θ cm depends on the impact parameter, and its peak seems to be moving and narrowing with increasing impact parameter. Its asymptotic peak value is in agreement with the grazing angle. The shift of the peak value of Θ cm implies that the collective energy dissipation depends on impact parameter and decreases with impact parameter increasing since the exchange of nucleons becomes less frequent during the reaction process.

Collisions of very heavy nuclei197Au +197Au at the energy of 15A MeV has been studied with the improved quantum molecular dynamics model. The experimental mass distributions of ternary fission fragments for the system197Au +197Au are reproduced well. The direct and sequential ternary fission modes are studied by the time dependent snapshots of typical ternary events. The analysis of deviation from Viola systematics indicates the nonstatistical feature of the ternary fission in these reactions.

Intermediate energy proton-induced spallation reactions with various targets are studied by the improved quantum molecular dynamics (ImQMD05) model incorporated with the statistical decay model. The influences of the different Skyrme interactions on the mechanism of spallation reaction and the double differential cross sections of emitted neutrons are studied. It is found that the different Skyrme interactions influence the low energy part of spectrum of emitted neutrons. This effect decreases as incident energy becomes higher. The double differential cross sections of emitted neutrons are found to be in good agreement with experimental data when the Skyrme parameter set SkP is adopted.

Based on the semi-classical extended Thomas-Fermi approach, we study the mass dependence of the symmetry energy coefficients of finite nuclei for 36 different Skyrme forces. The reference densities of both light and heavy nuclei are obtained. Eight models based on nuclear liquid drop concept and the Skyrme force SkM* suggest the symmetry energy coefficient $a_{\rm sym}=22.90 \pm 0.15 $ MeV at $A=260$, and the corresponding reference density is $\rho_A\simeq 0.1$ fm$^{-3}$ at this mass region. The standard Skyrme energy density functionals give negative values for the coefficient of the $I^4$ term in the binding energy formula, whereas the latest Weizs\"acker-Skyrme formula and the experimental data suggest positive values for the coefficient., Comment: 6 figures, accepted for publication in Phys. Rev. C

The nuclear symmetry energy coefficient (including the coefficient $a_{\rm sym}^{(4)}$ of $I^{4}$ term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei. It is found that the extracted symmetry energy coefficient $a^{*}_{\rm sym}(A,I)$ decreases with increasing of isospin asymmetry $I$, which is mainly caused by Wigner correction, since $e^{*}_{\rm sym}$ is the summation of the traditional symmetry energy $e_{\rm sym}$ and the Wigner energy $e_{\rm W}$. We obtain the optimal values $J=30.25\pm0.10$ MeV, $a_{\rm ss}=56.18\pm1.25$ MeV, $a_{\rm sym}^{(4)}=8.33\pm1.21$ MeV and the Wigner parameter $x=2.38\pm0.12$ through the polynomial fit to 2240 measured binding energies for nuclei with $20 \leq A \leq 261$ with an rms deviation of 23.42 keV. We also find that the volume symmetry coefficient $J\simeq 30$ MeV is insensitive to the value $x$, whereas the surface symmetry coefficient $a_{\rm ss}$ and the coefficient $a_{\rm sym}^{(4)}$ are very sensitive to the value of $x$ in the range $1\leq x\leq 4$. The contribution of $a_{\rm sym}^{(4)}$ term increases rapidly with increasing of isospin asymmetry $I$. For very neutron-rich nuclei, the contribution of $a_{\rm sym}^{(4)}$ term will play an important role., Comment: 14 pages, 5 figures, Submitted to Chinese Physics C

The nuclear symmetry energy coefficients of finite nuclei are extracted by using the differences between the masses of isobaric nuclei. Based on the masses of more than 2400 nuclei with A = 10‐270, we investigate the modeldependenceintheextractionofthesymmetryenergycoefficient.Wefindthattheextractionofthesymmetry energy coefficients is strongly correlated with the forms of the Coulomb energy and the mass dependence of the symmetry energy coefficient adopted. The values of the extracted symmetry energy coefficients increase by about 2 MeV for heavy nuclei when the Coulomb correction term is involved. The values of the bulk symmetry energy coefficient S0 and the surface-to-volume ratio κ are simultaneously investigated based on the extracted symmetry energy coefficients.

To investigate the influence of nuclear finite-size effects on the fragmentation in heavy-ion collisions, the fragment charge distributions of ${}^{40}$Ca+${}^{40}$Ca, ${}^{197}$Au+${}^{197}$Au, ${}^{120}$Xe+${}^{129}$Sn, and ${}^{58}$Ni+${}^{48}$Ca at intermediate incident energies are studied by using the improved quantum molecular dynamics model. Both the width of the wave packet at the coordinate space and the surface energy term strongly affect the formation and stability of fragments at intermediate-low energies. The wave-packet width influences the stability and the central densities of the initial nuclei. With increase of incident energies, the influence of the detail in description of individual nucleons and of their interaction via mean field on the fragment distributions weakens gradually.

The improved Kelson-Garvey (ImKG) mass relations are proposed from the mass differences of mirror nuclei. The masses of 31 measured proton-rich nuclei with $7\leq A\leq41$ and $-5\leq (N-Z)\leq-3$ can be remarkably well reproduced by using the proposed relations, with a root-mean-square deviation of 0.398 MeV, which is much smaller than the results of Kelson-Garvey (0.502 MeV) and Isobar-Mirror mass relations (0.647 MeV). This is because many more masses of participating nuclei are involved in the ImKG mass relations for predicting the masses of unknown proton-rich nuclei. The masses for 144 unknown proton-rich nuclei with $6\leq A\leq74$ are predicted by using the ImKG mass relations. The one- and two-proton separation energies for these proton-rich nuclei and the diproton emission are investigated simultaneously., 23 Pages,7figures,to be published in Phys. Rev. C

The fusion probability in "hot" fusion reactions leading to the synthesis of super-heavy nuclei is investigated systematically. The quasi-fission barrier influences the formation of the super-heavy nucleus around the "island of stability" in addition to the shell correction. Based on the quasi-fission barrier height obtained with the Skyrme energy-density functional, we propose an analytical expression for the description of the fusion probability, with which the measured evaporation residual cross sections can be reproduced acceptably well. Simultaneously, some special fusion reactions for synthesizing new elements 119 and 120 are studied. The predicted evaporation residual cross sections for 50Ti+249Bk are about 10-150fb at energies around the entrance-channel Coulomb barrier. For the fusion reactions synthesizing element 120 with projectiles 54Cr and 58Fe, the cross sections fall to a few femtobarns which seems beyond the limit of the available facilities., 5 figures, 1 table

Based on the improved quantum molecular-dynamics (ImQMD) model, the incident energy dependence of dynamic potential barriers is investigated in the entrance channel of fusion reactions. The height of the dynamic barrier increases with the incident energy at energies around the Coulomb barrier. The calculated lowest dynamic barrier approaches to the adiabatic barrier, while the highest one goes up to the sudden potential barrier. To understand the energy dependence of the dynamical barrier we study the neck formation and shape evolution of the system which causes the dynamic lowering of the barrier.

Strongly damped reactions of (238)U+(238)U, (232)Th+(250)Cf at E(c.m.)=680-1880 MeV have been studied based on the improved quantum molecular dynamics model. The formation and properties of the transiently formed composite system during the reaction process are carefully studied. We find that at a certain energy region, the entrance channel potential is weakly repulsive, and the dissipation is very strong after touching configuration. These two effects delay the re-separation time for a composite system. The single-particle potential well of the transiently formed composite system has a Coulomb barrier about 15-20 MeV high at the surface, which causes the excited unbound protons still embedded in the potential well to move in a common mono-single-particle potential for a period of time and thus restrains the quick decay of the composite system. The incident-energy dependence of the lifetime of the composite system and how the lifetime correlates with the shape configuration, the momentum distribution of the composite system, and the angular distribution of primary fragments are carefully investigated. The results indicate that the longest average lifetime for the transient composite system of U+U can reach about 1200 fm/c at properly selected incident energies.

The improved quantum molecular dynamics model is further developed by introducing new parameters in interaction potential energy functional based on Skyrme interaction of SkM(*) and SLy series. The properties of ground states of selected nuclei can be reproduced very well. The Coulomb barriers for a series of reaction systems are studied and compared with the results of the proximity potential. The fusion excitation functions for a series of fusion reactions are calculated and the results are in good agreement with experimental data.

The recent GSI data for proton-induced spallation reactions by using inverse kinematics are analyzed by the improved quantum molecular dynamics model (ImQMD05) merged with the generalized evaporation model (GEM2) and GEMINI model. We find that the model of ImQMD05+GEM2 reproduces the experimental data of mass and charge distributions for proton-induced spallation reactions on heavy targets (208Pb, 238U and 197Au) well and the model of ImQMD05+GEMINI reproduces the ones on light targets (56Fe) well. The experimental data for double differential cross sections of emitted neutrons and protons in intermediate energy proton-induced spallation reactions can also be reproduced well with the same models and this shows that they are not very sensitive to the merged statistical model.