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.     

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.     

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.     

Analysis of scattering and reactions of aligned7Li-nuclei in a double folding model

Previously measured angular distributions of the differential cross section and the tensor analyzing powerT ₂₀ for the scattering of⁷Li from⁵¹V in the energy range from 10 to 18 MeV were analyzed with the double folding model using the effective nucleon-nucleon interaction M3Y as well as a zero range effective nucleon-nucleon interaction. Due to the spectroscopic deformation of the⁷Li-nucleus the interaction potential contains a central and aT _R -tensor part. The latter one is the origin of the observed tensor analyzing powers. Within the same model the scattering of aligned⁷Li-nuclei from⁵⁸Ni at 14.2 and 20.3 MeV is well described. The strength of theT _R -tensor potential in relation to the spectroscopic mass deformation of⁷Li is discussed. Using the real interaction potential obtained by the double folding model the energy dependence of the total reaction cross sectionσ ^r and its tensor analyzing powerT ₂₀ ^r for the system⁷Li?⁵¹V is well described within a barrier penetration model.     

Generator-coordinate study of 3He+3He elastic scattering with a semirealistic nucleon-nucleon potential

The elastic scattering of ³He by ³He is studied in the framework of the generator coordinate method, using a new semirealistic nucleon-nucleon potential. All components of this potential have a soft core in the sense that they can be used in calculations where short-range correlations between nucleons are not taken into account. With this potential, a good agreement between calculated and measured cross sections and polarizations is obtained. The tensor component of the potential is found to be essential to explain the J-dependence of the empirical phase shifts, although the calculated polarizations are insensitive to the strength of the tensor potential.     

An application of the multichannel cluster model theory to the elastic proton-α scattering

In the framework of the cluster model reaction theory a calculation for the elastic α-p scattering below 30 MeV was performed. The nucleon-nucleon potential, which contains spin orbit and tensor forces, has been succesfully used in reaction calculations for other light nuclei. The calculated α-p cross section and polarization values are in quantitative agreement with experimental data.     

Energy dependence of nucleon-deuteron elastic scattering observables and its bearing on the3 P J nucleon-nucleon interactions

The energy dependence of neutron-deuteron elastic scattering observables has been calculated from 5 to 45 MeV via rigorous three-nucleon calculations using the Bonn B nucleon-nucleon interaction. The goal of these calculations was to identify energy and angular regions that may be investigated experimentally to study the question of charge-symmetry breaking in the³ P _J nucleon-nucleon forces and/or Coulomb interactions. It was found that the measurement of the neutron-deuteron elastic analyzing power at 16 and 22.7 MeV and its comparison to proton-deuteron data obtained at the same incident energy is the most promising case for studying the issue of charge-symmetry breaking in the³ P _J nucleon-nucleon forces and/or Coulomb interactions.     

6Li与核弹性散射的微观光学势

从基本的Dirac-Brueckner-Hartree-Fock微观理论出发,得到同时包含实部和虚部的核子-核散射的微观光学势,并利用折叠模型直接获得了核-核散射参数无关的整体微观光学势.考虑到核-核散射去弹过程高级项的贡献和⁶Li的碎裂效应,在微观光学势的实部和虚部中引入了修正因子N_R,N_I.系统研究了入射粒子⁶Li与靶核¹²C,²⁸Si,关键词： 弹性散射 Dirac-Brueckner-Hartree-Fock方法 折叠模型 微观光学势     

Microscopic interpretation of 7Li+24Mg inelastic scattering at 34 MeV

Theoretical differential cross sections for ⁷Li+²⁴Mg inelastic scattering have been calculated in the DWA using a double folding model. The projectile and target transition densities are matched to electron scattering data and the nucleon-nucleon interaction is chosen to reproduce the real part of the optical potential at the distance $\text{D}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ where there is 50 % transmission in the elastic channel. There are no free parameters in the calculations. The agreement between the theoretical results and the available experimental data is good which serves to establish a consistency between elastic and inelastic scattering. The cross section for a mutual transition which leaves both the projectile and target in their first excited states is found to come mainly from relative L_r = 4 transfer. It is speculated that a quadrupole term in the optical potential might make important contributions at backward angles in the elastic cross section.     

The three-nucleon system near the N-d threshold

The three-nucleon system is studied at energies a few hundred keV above the N-d threshold. Measurements of the tensor analyzing powers T₂₀ and T₂₁ for p-d elastic scattering at E_c.m. = 432 keV are presented together with the corresponding theoretical predictions. The calculations are extended to very low energies since they are useful for extracting the p-d scattering lengths from the experimental data. The interaction considered here is the Argonne V18 potential plus the Urbana three-nucleon potential. The calculation of the asymptotic D- to S-state ratio for ³H and ³He, for which recent experimental results are available, is also presented.     

Parametrization of woods-saxon potential for heavy-ion systems

Several elastic scattering angular distributions of ~(12)C from target nuclei of A ≥39 are analyzed to extract the Woods-Saxon potential parameters with the fixed imaginary potential and Coulomb radius parameters.Using the best fitted diffuseness parameters,the correlations of the real part parameters with A_1~(1/3)+ A_2~(1/3) and incident energy are revealed, and the systematic Woods-Saxon potential parameters are presented for nucleus-nucleus interaction.The proposed potential parameters can reproduce not only the elastic scattering angular distributions induced by ~(12)C,but also many elastic scattering angular distributions induced by the projectiles other than ~(12)C,thus providing important inputs for the study of nuclear reactions of heavy-ion systems.     

Discrepancy between three-nucleon calculations and neutron-deuteron elastic analyzing power data at 8.5 MeV

The analyzing power A_y(θ) in neutron-deuteron elastic scattering was measured at Eⁿ = 8.5 MeV. Comparison of the data with realistic three-nucleon calculations reveals a pronounced difference at the maximum of A_y(θ), which is most likely due to either an inadequate knowledge of the ³P components of the nucleon-nucleon interaction or to three-body effects in the three-nucleon system.     

Glauber Monte Carlo program for NICA/MPD and CBM experiments

A program code widely applied at RHIC and LHC for calculations of geometrical properties of nucleus-nucleus interactions is adapted for NICA/MPD and CBM energies. A parameterization of pp elastic scattering amplitude earlier proposed by the authors and valid at √s ≥ 3 GeV is used for a setting of the nucleon-nucleon collision profile. An approach well known in physics of low and intermediate energies is used for a determination of nuclear parameters. The code is enlarged by a possibility to account for the Gribov inelastic screening.     

Analytic approach to the problem of constructing effective nucleon-nucleon potentials in the region of low and intermediate energies

A new relativistic approach to the problem of constructing effective local hadron-hadron potentials is proposed on the basis of analytic S-matrix theory and Gelfand-Levitan-Marchenko-Martin methods for solving the inverse quantum scattering problem. An effective potential is defined as a local operator in a partial-wave equation of the quasipotential type such that it generates an on-shell relativistic (Feynman) scattering amplitude that has required discontinuities at dynamical cuts. The method is used to construct nucleon-nucleon potentials in the ¹ S ₀-and ³ S ₁-wave states. The dynamical discontinuities of partial-wave amplitudes for nucleon-nucleon scattering are calculated on the basis of the one-bosonexchange model that takes into account the exchanges of π, σ, ρ, ω, η, and α ₀ mesons. It is shown that the nonlinear relation between the discontinuities of partial-wave scattering amplitudes at dynamical cuts and interaction operators generates additional short-range repulsion not associated with omega-meson exchange. The experimental energy dependences of phase shifts in the channels of nucleon-nucleon scattering that are considered here are faithfully reproduced by the results of the calculations up to the projectile-nucleon kinetic energies in the range T = 1.5–2.0 GeV.     

Elastic scattering of 56 MeV polarized deuterons on 4He

The differential cross section and the vector and tensor analyzing powers A_y, A_xx, A_yy and A_xz were measured for the d-⁴He elastic scattering at 56 MeV. The measurement of A_xz was performed using a deuteron beam polarized in the horizontal plane. An optical-model analysis of the experimental data was carried out. The magnitude of the tensor analyzing powers could not be reproduced without the tensor potential. By including the T_R type tensor potential, the optical-model calculations give a reasonable reproduction of the experimental data at θ_c.m. < 120°. The obtained T_R tensor potential was much stronger than that predicted by the folding model. The strength of the real T_R potential was roughly in accordance with that obtained from the optical-model analysis of d-⁴He elastic scattering at 20.2 MeV.     

Nuclear quadrupole-quadrupole interaction in the inelastic scattering of aligned deuterons from deformed nuclei

The 2 ₁ ⁺ -excitation of deformed nuclei by tensor polarized deuterons provides an alignment of both nuclei and thus a means to study specifically the quadrupole-quadrupole interaction between both nuclei. The tensor analyzing powerA _xz (θ) has been measured for the elastic and inelastic scattering on²⁴Mg and²⁸Si. The coupled channel analysis including a deformed tensor potential reveals a clear signature of the quadrupole-quadrupole part of the nuclear projectile-target interaction.     

The absorptive pion-nucleus optical potential

We calculate s-wave and p-wave absorptive pion-nucleus optical potentials assuming that a pion is absorbed by a pair of nucleons. Employing a model which takes into account both a single nucleon absorption with nucleon-nucleon correlations and rescattering, we obtain simple analytic expressions for Im B₀ sid Im C₀ of the pion-nucleus optical potential. The off-shell effect on the s-wave pion absorption is examined and shown to be strongly modified by short range correlations. The result for the p-wave absorptive part Im C₀ clearly shows the importance of the tensor correlations. The enhanced nn emission after π^? absorption is shown to be related with a large p-wave πN scattering length a₃₃ via the tensor correlations.     

Scattering of polarized 7Li by 120Sn and projectile-target spin-dependent interactions

Scattering of ⁷Li by ¹²⁰Sn targets at E_lab = 44 MeV is investigated in the coupled-channel frame by taking account of the projectile virtual excitations to the lowest three excited states. Calculations are performed by the cluster-folding (CF) interactions and the double-folding (DF) one. Both interactions reproduce very well the experimental data on the cross section, the vector analyzing power, the second-rank tensor ones and the third-rank tensor one in elastic and projectile inelastic scattering, although some differences are found between the CF results and the DF ones. In the calculation, the virtual excitations of the projectile are important for most of the analyzing powers and the spin-orbit interaction is indispensable for the vector analyzing power. These features are in contrast to those in ⁷Li-⁵⁸Ni scattering at 20 MeV and are interpreted as over-Coulomb-barrier effects. The scattering amplitudes and the analyzing powers are investigated by the invariant amplitude method, which provides a key connecting the spin-dependent interactions to the analyzing powers. The method proposes an important relationship between the tensor analyzing powers, which is useful in analyses of both theoretical and experimental results. Finally, it is found that in the elastic scattering the second-rank tensor analyzing powers are proportional to the strength of the second-rank tensor interaction and the vector and third-rank tensor analyzing powers to the square or cube of the strength of this interaction, while in the inelastic scattering the cross section is proportional to the square of the strength of the tensor interaction, other quantities being weakly dependent on the strength.