The energy dependent nucleus-nucleus optical potential in a nuclear matter approach

We calculated the energy dependent real and imaginary part of the nucleus-nucleus optical potential in a lab. energy domain between 50MeV and 225MeV per nucleon for the systems¹²C-¹²C and⁵⁸Ni-⁵⁸Ni. In our model we assume that the energetical behaviour of the colliding nucleons inside of the two overlapping nuclei is locally that of two colliding nuclear matter systems. Therefore the effective nucleon-nucleon interaction is calculated using a Bethe-Goldstone equation that includes the Pauli blocking caused by the two Fermi spheres and takes account of the presence of the other nucleons by their mean field. Neglecting finite range effects one can calculate the real and imaginary part by a folding procedure.     

Influence of momentum-dependent interactions on balance energy and mass dependence⋆

We aim to understand the role of momentum-dependent interactions in transverse flow as well as in its disappearance. For the present study, central collisions involving masses between 24 and 394 are considered. We find that the momentum-dependent interactions have different impact in lighter colliding nuclei compared to heavier colliding nuclei. In lighter nuclei, the contribution of the mean field towards flow is smaller compared to heavier nuclei where binary nucleon-nucleon collisions dominate the scene. The inclusion of momentum-dependent interactions also explains the energy of the vanishing flow in the ¹²C + ¹²C reaction which otherwise was not possible with the static hard equation of state. An excellent agreement of our theoretical attempt is found for balance energy with experimental data throughout the periodic table.     

Learning about the nuclear equation of state using flow

We present results for transverse flow, the balance energy, and elliptic flow for Ar+Sc, ⁵⁸Fe+⁵⁸Fe, ⁵⁸Ni+⁵⁸Ni, Kr+Nb, and Au+Au. We find that a soft equation of state is required to explain these results. We find that a momentum dependent formulation of the nuclear mean field is required. A 30% density dependent reduction of the in-medium nucleon-nucleon cross sections in BUU is required to reproduce the observed balance energies for light systems.     

Entrance-Channel Dependence of Isospin Effects on Double n/p Ratio in HIC

Within the hadronic transport model IBUU04, we investigate the effect of density-dependent symmetry energy on double neutron/proton (n/p) ratio of free nucleons in heavy ion collisions by taking four isotopic Sn+Sn reaction systems. Especially the entrance-channel asymmetry and impact-parameter dependence of the effect of symmetry energy are discussed. It is found that in both central and semi-central collisions the sensitivity of the double n/p ratio to the density-dependent symmetry energy is more pronounced in neutron-richer systems. Our results also indicate clearly that the effect of symmetry energy is stronger in central collisions than that in semi-central collisions.     

Angular momentum dependence of quasifission dynamics in the reaction <Superscript>48</Superscript>Ca+<Superscript>244</Superscript>Pu

The quasifission dynamics in the reaction ⁴⁸Ca+²⁴⁴Pu is investigated in the framework of time-dependent Hartree-Fock (TDHF) theory. The calculations are performed in three-dimensional Cartesian coordinate without any symmetry restrictions. The full Skyrme energy functional is incorporated in our TDHF implementation. The quasifission dynamics is quite sensitive to the angular momentum of colliding system. The contact time of quasifission decreases as a function of angular momentum and then forms a plateau with small oscillations. The quasifission process is accompanied by an important multi-nucleon transfer. The quantum shell effect plays a crucial role in the mass and charge of quasifission fragments. The mass-angle distribution of the fragments is calculated, which can be compared directly with future experiments.     

Isospin Effects of Threshold Energy of Radial Flow in Heavy Ion Collisions

The threshold energies of radial flow in reactions of ^40 Ca-^40Ca and ^48Ca＋ ^48Ca in central collisions are investigated within an isospin dependent quantum molecular dynamics model by using three different forms of symmetry energy. It is found that the neutron-rich system has smaller threshold energy of radial flow and this quantity depends on the form of symmetry potential. It is indicated that the threshold energy of radial flow can provide a new method to determine the symmetry energy of asymmetric nuclear matter.     

Measurement and hybrid-model analysis of proton-induced reactions with V,Fe and Co

On target elements V, Fe and Co (natural isotopic composition) proton-induced reactions were investigated in the energy region from 12 to 45 MeV using the stacked-foil technique. The product nuclides observed were ⁴⁸Cr, ⁴⁹Cr, ⁵¹Cr, ⁴⁸V, ^{46m + g}Sc, ⁴⁷Sc and ⁴⁸Sc from V, ⁵⁵Co, ⁵⁶Co, ⁵⁷Co, ^{58m + g}Co, ⁵²Fe, ^{52m + g}Mn, ⁵⁴Mn, ⁵¹Cr and ⁴⁸V from Fe, and ⁵⁶Ni, ⁵⁷Ni, ⁵⁶Co, ⁵⁷Co, ^{58m + g}Co, ⁵⁴Mn and ⁵⁶Mn from Co. The comprehensive set of excitation functions extending and improving earlier studies is compared with calculations considering equilibrium as well as preequilibrium reactions according to the hybrid model of Blann. The overall agreement between experiment and theory is good. Certain discrepancies, however, indicate the necessity to revise the hybrid model with respect to the emission of complex particles.     

中能Ca+Ca反应中的对称能效应

采用把重离子碰撞的动力学和统计衰变过程相结合的一个两步模型,再现了INDRA Collaborations 对入射能为35 AMeV40Ca+40Ca 和48Ca+48Ca 反应的实验结果。进而得到了反应碎块同位素分布的Isoscaling 参数α(Z) 和β(N),约化对称能系数ζ(Z) 及与平均场中的对称能强度系数Cs 之间的关系。结果表明,Isoscaling 参数强烈依赖于系统的丰中子程度。随着质子数的增大,ζ(Z) 在动力学阶段呈现平缓趋势但在衰变之后呈现上升趋势,且该结果不依赖于所选取的反应系统。对称能效应在统计衰变过程之后的末级碎块分布中有明显表现。A two-step model for combining the dynamical and statistical decay processes in heavy-ion collisions is used to reproduce the experimental results of the INDRA Collaborations on 40Ca+40Ca and 48Ca+48Ca reactions at 35 AMeV. We obtain the isoscaling parameters α(Z) and β(N) of isotopic distributions of the fragments, the reduced symmetry energy coefficient ζ(Z) and its dependence on the symmetry energy strength coefficient Cs in the mean field. Our results suggest that Isoscaling parameters strongly depend on the degree of neutron-rich. With the increasing atomic number, ζ(Z) represents a smoothly flat tendency during the dynamical process but shows the increasing tendency after decay, and such results are independent on the selected reaction systems. The effect of symmetry energy shows evidently in the isotopic distributions of fragments after statistical decay process.     

Inclusion of the Δ resonance in the optical potential between two nuclei and its application to medium energy12C-12C scattering

An energy dependent complex optical potential between two nuclei is calculated from the potential energy density for two colliding nuclear matters generated by solving the Bethe-Goldstone equation in whichNΔ and ΔΔ channels are explicitly coupled to theNN channel. By adding the contributions from the third and fourth order ring diagrams and the relativistic correction to the calculated potential energy density, the saturation property of a nuclear matter is reasonably well reproduced. This is used together with the kinetic energy density to calculate the optical potential for the¹²C+¹²C system in the energy density formalism with the local density approximation. The surface correction term and the symmetry energy term in the energy density functional are determined to reproduce the observed binding energy and the rms radius of¹²C. Using this potential, the differential cross sections for elastic¹²C-¹²C scattering atE _lab=1440 and 2400 MeV are calculated and compared with recent experimental data.     

Projectile fragmentation of <Superscript>40,48</Superscript>Ca and isotopic scaling in a transport approach

We investigate theoretically projectile fragmentation in reactions of ^40,48Ca on ⁹Be and ¹⁸¹Ta targets using a Boltzmann-type transport approach, which is supplemented by a statistical decay code to describe the de-excitation of the hot primary fragments. We determine the thermodynamical properties of the primary fragments and calculate the isotope distributions of the cold final fragments. These describe the data reasonably well. For the pairs of projectiles with different isotopic content we analyze the isotopic scaling (or isoscaling) of the final fragment distributions, which has been used to extract the symmetry energy of the primary source. The calculation exhibits isoscaling behavior for the total yields as do the experiments. We also perform an impact-parameter-dependent isoscaling analysis in view of the fact that the primary systems at different impact parameters have very different properties. Then the isoscaling behavior is less stringent, which we can attribute to specific structure effects of the ^40,48Ca pair. The symmetry energy determined in this way depends on these structure effects.     

Study of the excitation function fluctuations of the dissipative28Si+48Ti binary collision in the incident energy interval from 206.9 MeV to 213.8 MeV

It is shown that the Partially Overlapping Molecular Level Model (POMLM) accounts for the experimental results of the dissipative²⁸Si +⁴⁸Ti collision around 210 MeV incident energy. The general trend of the properties of the fluctuations as well as the average angular distributions are reproduced by the same set of main parameters. A general consistency is also found between the present data and the data obtained in previous work on the same colliding system performed at lower incident energy (around 123 MeV).     

同位旋相关的核子碰撞截面的不同形式与核子的集体流

在详细比较同位旋相关的核子-核子碰撞截面的几种常用形式的基础上,利用IBUU模型, 分别对具有相同质量的⁶⁰Ca+⁶⁰Ca和⁶⁰Ni+⁶⁰Ni的中能重离子碰撞进行了模拟计算,定量地分析了碰撞过程中不同形式的同位旋相关的核子-核子碰撞截面对于核子的快度分布和集体流的影响.结果显示: 不同形式的核子碰撞截面,可以给出相差较大的核子的快度分布和横向流, 但在同一种截面形式下,对称势的变化对横向流的影响较小.这表明在新的动量相关的对称势下, 中能重离子碰撞中集体流对于截面的敏感性依然成立;同时表明,在相同的碰撞截面和对称势形式下, 当入射能量在平衡能附近时,入射粒子的中质比对核子在平面流的影响较大,反之,影响较小.     

Isotope Dependence of Superheavy Nucleus Formation Cross Section

The dynamical process in the superheavy nucleus synthesis is studied on the basis of the two-dimensional Smoluchowski equation. Special attention is paid to the isotope dependence of the cross section for the superheavy nucleus formation by means of making a comparison among the reaction systems of ^54Re＋204pb, ^56Re ＋206Pb, and ^58Fe＋^208Pb. It is found by this comparison that the formation cross section is very sensitive to the conditional saddle-point height and the neutron separation energy of the compound nucleus. Reaction systems with lower height of conditional saddle-point and smaller neutron separation energy are more favourable for the synthesis of the superheavy nucleus.     

Assessment of multifragmentation under the effect of symmetry energy

We study the effect of symmetry energy on the fragment production for the reactions ₂₀ ¹⁰ Ne₁₀+ ₂₀ ¹⁰ Ne₁₀ and ₁₉₇ ⁷⁹ Au₁₁₈ + ₁₉₇ ⁷⁹ Au₁₁₈ for the incident energy range of 50–1000 MeV/nucleon using isospin-dependent quantum molecular dynamics (IQMD) model. Our study shows that the density-dependent symmetry energy plays a significant role in multiplicity of fragments produced at low energy. Moreover, sensitivity of density-dependent symmetry energy decreases with increase in neutron content of colliding system. We also compare the symmetry energy suggested by different groups. A comparative study of experimental results with theoretical calculations of IQMD shows that the density-dependent symmetry energy is a good probe to explain the multiplicity of the fragments at low energy.     

Direct comparison of phase-space distributions of K- and K+ mesons in heavy-ion collisions at SIS energies -- evidence for in-medium modifications of kaons?

The ratio of K^- to K⁺-meson yields has been measured in the systems ⁹⁶Ru + ⁹⁶Ru at 1.69 A GeV, ⁹⁶Ru+⁹⁶Zr at 1.69 A GeV, and ⁵⁸Ni+⁵⁸Ni at 1.93 A GeV incident beam kinetic energy. The yield ratio is observed to vary across the measured phase space. Relativistic transport-model calculations indicate that the data are best understood if in-medium modifications of the kaons are taken into account. Received: 30 November 1998 / Accepted: 20 December 2000     

中子晕核引起核反应中的同位旋效应

利用同位旋相关的量子分子动力学(IQMD)对中子晕核，⁸He和¹⁰He引起核反应中重要的同位旋效应和松散的中子晕结构影响的平均特征进行了研究.因为IQMD中的互作用势和介质中核子-核子碰撞截面灵敏地依赖于碰撞系统的密度分布.而扩展的中子晕密度分布包含了中子晕核的同位旋效应和松散的中子晕结构的平均特征，从而将这些信息通过动力学碰撞带入到反应机理中. 为了清楚地鉴别中子晕核带入反应机理重要的同位旋效应和松散中子晕结构的影响，通过比较中子晕核和相等质量稳定弹核在相同入射道条件下，所得物理观测量之间的差别加以确定.计算结果确实发现具有初始晕核信息的中子扩展密度分布将重要的同位旋效应和松散中子晕结构带入到各种物理观测量中.例如与相等质量稳定相比，中子晕核的晕特征引起了原子核阻止的降低；并明显地增加了核子发射中子-质子比和同位旋分馏比. 关键词： 中子晕核 原子核阻止 核子发射中子-质子比 同位旋分馏比     

Isotopic dependence of neutron emission from dinuclear system

Using the statistical approach, we study the isotopic dependence of the de-excitation of dinuclear systems formed in the entrance channel of heavy-ion reactions. The probabilities of neutron emission from the dinuclear systems ^62-73Ni + ²⁰⁸Pb are estimated and a possible experiment for the observation of this emission is discussed.     

Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon forpositive and negative Q-value systems using the proximity-type potential

A systematic survey of the accurate measurements of heavy-ion fusion cross sections at extreme sub-barrier energies is performed using the coupled-channels (CC) theory that is based on the proximity formalism. This work theoretically explores the role of the surface energy coefficient and energy-dependent nucleus-nucleus proximity potential in the mechanism of the fusion hindrance of 14 typical colliding systems with negative \begin{document}$Q$\end{document}-values, including ¹¹B+¹⁹⁷Au, ¹²C+¹⁹⁸Pt, ¹⁶O+²⁰⁸Pb, ²⁸Si+⁹⁴Mo, ⁴⁸Ca+⁹⁶Zr, ²⁸Si+⁶⁴Ni, ⁵⁸Ni+⁵⁸Ni, ⁶⁰Ni+⁸⁹Y, ¹²C+²⁰⁴Pb, ³⁶S+⁶⁴Ni, ³⁶S+⁹⁰Zr, ⁴⁰Ca+⁹⁰Zr, ⁴⁰Ca+⁴⁰Ca, and ⁴⁸Ca+⁴⁸Ca, as well as five typical colliding systems with positive \begin{document}$Q$\end{document}-values, including ¹²C+³⁰Si, ²⁴Mg+³⁰Si, ²⁸Si+³⁰Si, ³⁶S+⁴⁸Ca, and ⁴⁰Ca+⁴⁸Ca. It is shown that the outcomes based on the proximity potential along with the above-mentioned physical effects achieve reasonable agreement with the experimentally observed data of the fusion cross sections \begin{document}$\sigma_{\rm{fus}}(E)$\end{document}, astrophysical \begin{document}$S(E)$\end{document} factors, and logarithmic derivatives \begin{document}$L(E)$\end{document} in the energy region far below the Coulomb barrier. A discussion is also presented on the performance of the present theoretical approach in reproducing the experimental fusion barrier distributions for different colliding systems.     

Fusion-evaporation cross-sections for 48Ca + 154Sm near the Coulomb barrier

Measurements of fusion-evaporation cross-sections for the system ⁴⁸Ca + ¹⁵⁴Sm have been performed in the sub- and near-barrier energy range. Barrier-passing cross-sections have been obtained by adding recently measured capture-fission cross-sections at the same energies, and the barrier distribution for capture has been extracted. The data have been analyzed within a coupled-channel model, and a large subbarrier cross-section enhancement is observed, due to the ground-state prolate deformation of ¹⁵⁴Sm. The ⁴⁸Ca + ¹⁵⁴Sm capture cross-sections are compared to existing data on ¹⁶O + ¹⁸⁶W fusion, leading to the same CN, where a few higher-energy points have also been measured. The evaporation residue cross-sections for the two systems above the barrier indicate that complete fusion is inhibited for ⁴⁸Ca + ¹⁵⁴Sm by 40% in that energy region, with respect to ¹⁶O + ¹⁸⁶W.     

Angular anisotropy of the fusion-fission and quasifission fragments

The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the ¹⁶O + ²³⁸U , ¹⁹F + ²⁰⁸Pb and ³²S + ²⁰⁸Pb reactions is studied by analyzing the angular-momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of the axial symmetry axes of the colliding nuclei relative to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that there is a large contribution of the quasifission fragments in the ³²S + ²⁰⁸Pb reaction to the deviation of the experimental angular anisotropy from the statistical model results. Enhancement of anisotropy at low energies in the ¹⁶O + ²³⁸U reaction is connected with the quasifission of the dinuclear system having low temperature and relatively small effective moment of inertia.