Description of nucleon-nucleus scattering in the Dirac-Brueckner method

Elastic scattering of protons from nuclei is studied based on the Dirac-Brueckner approach. Effective N-N interactions in the nuclear medium are obtained by solving the relativistic Brueckner-Bethe-Goldstone equation in infinite nuclear matter. Relativistic optical potentials for p-⁴⁰Ca scattering at 200 MeV are calculated in the improved local density approximation. It is found that medium effects other than Pauli blocking reduce the strengths of scalar and vector potentials very much. Differential cross section and spin observables are calculated and compared with experimental data.     

In-medium Nucleon-Nucleon Inelastic Scattering Cross Section(Ⅰ)

The explicit expressions for in-medium NN→N△ cross section are derived within the relativistic Boltzmann-Uehling-Uhlenbeck approach,which are given simultalleously with the other integrants of transport model such as the mean field, NN elastic scattering cross section as well as the transport equation itself based on the effective Lagrangian.Our results can reproduce the experimental data of free inelastic cross section nicely.The in-medium inelastic cross section is calculated up to twice nuclear matter density and is in agreement with the Dirac-Brueckner calculations.     

Quasimolecular nuclear optical potentials

A theory is presented to calculate potentials for the elastic nuclear heavy-ion scattering in a phenomenological way. The density properties of finite nuclei are derived with a schematic ansatz for the interaction energy between nuclear matter. The same interaction energy is applied to the calculation of the real part of the heavy-ion potential, which is of the quasimolecular type. The imaginary part is connected with the outflow time of nuclear matter out of compressed regions of overlapping nuclei. The resulting cross section for the elastic O¹⁶-O¹⁶ scattering reproduces the experiment up to 30 MeV quite well. An effective compression modulus of the S³² compound system can be deduced from the scattering experiment. It results to be about 200 MeV.     

Investigation of Self-Consistent Relativistic Microscopic Optical Potential

In Dirac-Brueckner calculations for nuclear matter,the average binding energy per nucleon versus density curve is not uniquely defined if coupling to anti-particle is neglected.According to the Hugenholtz-Van Hove theorem,a constraint requires that the nucleon separation energy equals to the fermi energy at saturation density.Choosing saturation energy as empirical value E_B/A=－15.8MeV,the self-consistent calculation leads to the saturation density k_f=1.41fm^－1 and effective mass m*=0.52m,in compressive coefficient k=208MeV.Applying the first law of thermodynamics,self-consistent effective mass (real scalar potential) and the binding energy per nucleon as function of the nuclear density can be obtained.With the realistic nucleon-nucleon interaction (Bonn potential),the vector potential can be obtained from solving the RBBG equation,which weakly depends on the momentum.The cross section and spin observables of the nucleon-nucleus scattering are studied with this new self-consistent relativistic microscopic optical potential.     

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.     

On the Dirac structure of the nucleon self-energy in nuclear matter

The relativistic structure of the self-energy of a nucleon in nuclear matter is investigated including the imaginary and real components which arise from the terms of first and second order in the NN interaction. A parameterized form of the Brueckner G-matrix is used for the NN interaction. The effects of the terms beyond the DBHF approximation on quasiparticle energies and the optical potential for nucleon-nucleus scattering are discussed.     

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.     

Theoretical analysis of <Superscript>6</Superscript>He + <Superscript>12</Superscript>C scattering by means of the model of microscopic optical potential

The ⁶He + ¹²C elastic scattering at E = 3.0, 38.3, and 41.6 MeV/nucleon is analyzed using the microscopic model of optical potential. According to this approach, two or three parameters are fitted that renormalize the depth of real, imaginary, and surface parts of the calculated optical potential. In this case, the ambiguity of the obtained sets of fitting parameters remains, but can be reduced by introducing an additional criterion of selection: the dependence of the volume integrals of the optical potential on the energy. The structure of the obtained optical potential, the role of the nuclear medium, the formation of the imaginary part of the optical potential, and the interconnection between the surface potential and the ⁶He breakup channels are discussed.     

格点核子-核子势在核物质中的相对论效应(英文)

利用最新的格点核子-核子势研究了核物质中的相对论效应。通过此格点核子-核子势场,首先我们构建一个包括π介子,σ介子以及ω介子的单玻色子交换势。势场中的介子-核子耦合常数以及截断动量通过拟合格点核力得到的核子-核子散射相移确定。随后采用非常成功的第一性原理多体计算方法Brueckner-Hartree-Fock模型,计算了核物质的基本性质。发现对称核物质的状态方程以及饱和性质在非相对论框架和相对论框架中有很明显的区别。在格点核力中,该相对论效应对核物质的结合能提供吸引的贡献。这与采用传统的核力计算得到的结果是相反的。The relativistic effect in nuclear matter is investigated with the latest lattice nucleon-nucleon (NN) potential. A one-boson-exchange potential (OBEP) including three mesons, pion, σ meson and ω meson was constructed based on the lattice NN potential. The meson-nucleon coupling constants and cutoff momentums are determined by fitting the phase shifts of NN scattering from lattice NN potential. The properties of nuclear matter with this OBEP from lattice potential are calculated by one very successful ab initio many-body method, Brueckner-Hartree-Fock model. The equations of state and saturation properties of symmetric nuclear matter present very obvious different behaviors in non-relativistic and relativistic frameworks. The relativistic effect plays attractive contributions with the components of S and D waves in lattice NN potential, which is opposite comparing to the relativistic effect from the conventional NN potential.     

Nuclear matter approach to the heavy-ion optical potential

An energy-dependent local potential for heavy-ion (HI) scattering is derived from Reid's softcore interaction using the Brueckner theory. The Bethe-Goldstone equation in momentum space is first solved with the outgoing boundary condition for two colliding systems of nuclear matter with the relative momentum K_r per nucleon. The Fermi distribution is assumed to consist of two spheres without double counting of their intersection separated by the relative momentum K_r. The angle-averaged Pauli projection function is given in the form of a one-dimensional integral. Secondly the optical potential for HI scattering is evaluated using the energy-density formalism. The energy density is calculated for two limiting cases: (i) the sudden approximation in which the spatial distribution of the two HI is described by an antisymmetrized cluster wave function, and (ii) the adiabatic limit represented by an antisymmetrized two-centre wave function. The complex HI potential is defined in terms of the energy density from nuclear matter so that both volume elements in the finite and the infinite systems have the same nucleon and kinetic energy density. This method is applied to the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O, and ⁴⁰Ca + ⁴⁰Ca potentials. The calculated results are compared with phenomenological potentials. Though in principle our approach can generate an imaginary part for the HI potential, the magnitude is too small. Reasons and possible improvements of this point are discussed.     

The reaction mechanism of heavy ion scattering at intermediate energies

The contribution to the real and imaginary nucleus-nucleus (N-N) optical potential from nucleon-nucleon scattering in the medium is calculated in a local density approximation from a two Fermi sphere nuclear matter picture for the N-N collision. This reaction mechanism is shown to be dominant for ¹²C + ¹²C scattering at all considered energies (160 MeV < E_lab < 2250 MeV) giving a weakly energy dependent reaction cross section of about 900 mb. Inclusion of the collective 2⁺, 3^? excitations in a coupled channel calculations gives good agreement for both the measured elastic and inelastic 2⁺ cross section at E_lab = 1016 MeV. This fully microscopic parameter free calculation indicates that the energy dependence of the reaction cross section for this system is mostly due to the decrease of the collective contribution with increasing energy contrary to current theoretical models.     

α-Cluster Optical Potential Model of <Superscript>40</Superscript>Ca

Elastic scattering of α + ⁴⁰Ca is analyzed in the framework of the optical model. We adopted an independent α-cluster model to generate the α-cluster and matter density of ⁴⁰Ca. We proposed a parametrized form for the α-cluster density and fixed its parameters according to the available experimental data about the α-particle and ⁴⁰Ca nuclei. The obtained α-cluster density of ⁴⁰Ca is used to generate the real part of the optical potential. The single folding procedure is used to generate this real optical potential with two different effective α–α interactions. The real calculated potential supplied with an imaginary Woods–Saxon squared potential is used to analyze 20 sets of experimental data in the energy range between 18 and 166 MeV. We found that our model is successful in reproducing the data for energies above 40 MeV and still doubtful for lower energies.     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

Heavy-ion optical potentials at finite temperature calculated using a complex effective interaction derived from a realistic force

Hot density distributions of heavy ions generated by a modified Thomas-Fermi calculation at finite temperature are used to calculate the optical potential using the double-folding method and a complex effective energy and density-dependent interaction deduced from a realistic NN (Reid soft-core) force in nuclear matter. The real and the imaginary part of the optical potential become more attractive when the temperature increases.     

Nuclear matter approach to the heavy-ion optical potential: (II). Imaginary part

The heavy-ion optical potentials are constructed in a nuclear matter approach, for the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O and ⁴⁰Ca + ⁴⁰Ca elastic scattering at the incident energies per nucleon E^lab/A ? 45 MeV. The energy density formalism is employed assuming that the complex energy density of colliding heavy ions is a functional of the nucleon density ?(r), the intrinsic kinetic energy density τ⁽²⁾(r) and the average momentum of relative motion per nucleon K_r(≦ 1.5 fm^?1). The complex energy density is numerically evaluated for the two units of colliding nuclear matter with the same values of ρ, τ⁽²⁾ and K_r. The Bethe-Goldstone equation is solved for the corresponding Fermi distribution in momentum space using the Reid soft-core interaction. The “self-consistent” single-particle potential for unoccupied states which is continuous at the Fermi surface plays a crucial role to produce the imaginary part. It is found that the calculated optical potentials become more attractive and absorptive with increasing incident energy. The elastic scattering and the reaction cross sections are in fair agreement with the experimental data.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

Microscopic optical model analysis of elastic scattering cross sections for nucleon-40Ca systems at low energy

Neutron and proton-⁴⁰Ca elastic scattering angular distributions and total reaction cross sections are calculated between 10 and 40 MeV using the microscopic optical potential derived by Bouyssy et al. within the nuclear structure approach. Direct comparison with experiment confirms that our calculation reproduces the imaginary potential at low energy for protons, but it gives insufficient absorption above the deuteron pick-up threshold. A renormalization of both the real and the imaginary parts of the potential leads to good agreement with the data. For both parts of the potential this renormalization is compatible with the renormalization factors obtained by Bouyssy et al. from a comparison of calculated and phenomenological volume integrals.