Microscopic analysis of the energy dependence of the 6He, 6Li + 28Si total reaction cross sections in the energy range E = 5−50 A MeV

The experimental data on the total cross sections of the ^{4, 6}He, ^{6, 7}Li + ²⁸Si reactions at energies E=5−50 A MeV are reported. The data for the ⁶Li, ⁶He + ²⁸Si reactions have been analyzed within the microscopic model of double-folding optical potential, in which the real and imaginary parts are calculated at different densities of the projectile nucleus. The cross sections calculated with the microscopic double-folding Coulomb potential and the standard Coulomb potential for uniform charge distribution are compared with each other. Semimicroscopic potentials providing agreement with experimental data have been constructed on the basis of renormalized microscopic potentials and their derivatives, added to take into account collective effects. Original Russian Text ￠ K.V. Lukyanov, E.V. Zemlyanaya, V.K. Lukyanov, I.N. Kukhtina, Yu.E. Penionzhkevich, Yu.G. Sobolev, 2008, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2008, Vol. 72, No. 3, pp. 382–386.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

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.     

Elastic scattering of 33 MeV tritons and isospin dependence of mass-3 optical potential

Differential cross section data are presented for the elastic scattering of 33 MeV tritons from a range of nuclei from ¹²C to ²³²Th. These data have been analysed using a phenomenological optical model. Parameters are presented for three families of the real potential. A comparison of the triton optical model potential with those from a re-analysis of ³He scattering from fp shell nuclei has allowed the isospin dependence of the optical model potential for mass-3 projectiles to be obtained in this mass region.     

Influence of the transfer reactions on p + <Superscript>6</Superscript>He elastic scattering

We have studied an effect of neutron and triton transfer reactions on the p +^6He elasticscatteringat25 MeVbymeansofcoupled - reaction - channelcalculations.Itisfoundthatwhenthetransferreactionsareexplicitlyincludedinthecalculationstheimaginarypartoftheinput$p + $⁶He optical model potential has to be reduced by 52 percent while its real part enhanced by 15 percent in order to fit the elastic-scattering data. The effect of transfer channels on the real part of this potential is somewhat weaker than that of ⁶He breakup reported previously. However, for the imaginary part, the effect of transfer channels is dominant. It is concluded that while the breakup contribution to proton elastic scattering mainly affects the real part of the bare potential, the contribution of transfer channels affects mainly its imaginary part.     

Optical potential analysis of proton elastic scattering from <Superscript>12</Superscript>C based on the <Emphasis Type="Italic">α</Emphasis>-particle model

Based on an α-particle model of ¹²C, an optical potential for intermediate-energy proton- ¹²C scattering is presented in the framework of the KMT theory. The parameterized proton- ⁴He amplitude, the required basic input for constructing the optical potential, is obtained by fitting the proton- ⁴He scattering data. The differential cross-sections and analyzing powers of the proton- ¹²C elastic scattering at incident energies ranging from 0.2 to 1.0GeV have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross-section and the analyzing power can be satisfactorily described. The proton- ¹²C total cross-sections have also been calculated, and the results are in good agreement with the experimental data at energies below 0.6GeV but underestimate the data about 6% at higher energies.     

Phenomenological optical model for p-4He elastic scattering

The results of a Dirac equation optical model analysis of p-⁴He elastic scattering data are reported. The optical potential obtained at 1029 MeV reproduces the systematics of p-⁴He data over the energy range from 560 to 1730 MeV.     

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     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

Measurement of nuclear deformation parameters from elastic and inelastic scattering of α and 3He ions on Te isotopes

Cross sections for the elastic scattering of ⁴He by ^{122, 124, 126, 128}Te and ³He by ¹²⁸Te and for inelastic transitions to the lowest 2⁺ states of Te isotopes were measured for several scattering angles at bombarding energies in the vicinity of the Coulomb barrier. The data were analyzed in the framework of the optical model and the DWBA from which optical potential and deformation parameters were extracted. A detailed study of the fit procedure is presented with emphasis on the significance of the extracted parameters and the correlations among them.     

Anomalous 3He scattering in the Ca region

Elastic ³He scattering on ⁴⁰Ar, ³⁹K, ⁴¹K, ⁴⁰Ca and ⁴²Ca was investigated at $\text{E(}{}^3\text{He) = 28}\text{MeV}$. A comparison of the scattering on neighbouring nuclei shows differences in backward angle cross sections up to one order of magnitude. This variation is clearly outside the domain of the standard optical model. This anomalous backward angle scattering is discussed in connection with similar anomalies observed in elastic α-particle scattering.     

Pauli Correlation Effect for the Elastic Scattering of Protons by Different Nuclei at 800 MeV

The angular distributions of the elastic scattering of protons at an energy of 800 MeV by ¹⁶O and ²⁰Ne nuclei are described in terms of the optical model scattering theory. Single folding model is applied to calculate the optical potential taking the effective nucleon-nucleon interaction to be in two forms. One form includes the zero-range pseudo-potential term and the other includes a two-body Pauli correlation function. Analytical expressions for the real part of the optical potential are obtained for both forms. The imaginary part of the optical potential is taken to be of the Woods-Saxon's shape. It is found that introducing the Pauli correlation function improves the agreement with the experimental data for the elastic scattering differential cross-sections of protons with the target nuclei ¹⁶O and ²⁰Ne.     

Microscopic study on proton elastic scattering of light exotic nuclei at energies below than 100 MeV/nucleon

The proton elastic scattering data on some light exotic nuclei, namely, ^{6, 8}He, ^{9, 11}Li, and ^{10, 11, 12}Be, at energies below than 100MeV/nucleon are analyzed using the single folding optical model. The real, imaginary, and spin-orbit parts of the optical potential (OP) are constructed only from the folded potentials and their derivatives using M3Y effective nucleon-nucleon interaction. These OP parts, their renormalization factors and their volume integrals are studied. The surface and spin-orbit potentials are important to fit the experimental data. Three model densities for halo nuclei are used and the sensitivity of the cross-sections to these densities is tested. The imaginary OP within high-energy approximation is used and compared with the single folding OP. This OP with few and limited fitting parameters, which have systematic behavior with incident energy, successfully describes the proton elastic scattering data with exotic nuclei.     

Study of 3He + Nucleus Scattering with a Simplified Resonating-Group Method

 A simplified resonating-group method, called model K, is used to analyze ³He + nucleus scattering data for target nuclei with nucleon number ranging from 40 to 208 and for ³He energies ranging from 70 to 130 MeV. The results show that a rather satisfactory agreement between calculated and experimental differential-scattering cross sections can be obtained if one allows the value of the exchange-mixture parameter in the nucleon-nucleon potential to deviate somewhat from that in the corresponding N + nucleus case. With the model-K nonlocal interaction, an equivalent local internuclear potential is also constructed with a WKB procedure. Here it is found that, with a proper consideration of nucleon-exchange effects, one can explain nearly all of the energy dependence of the real part of the phenomenologically determined optical potential in ³He + nucleus scattering. Received May 31, 1999; revised November 9, 1999; accepted for publication December 20, 1999     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

Analyzing Power in Elastic Scattering of Polarized Protons from Neutron-rich Helium Isotopes

The vector analyzing power has been measured for the elastic scattering of neutron-rich ⁶He from polarized protons at 71 MeV/nucleon. Two approaches based on local one-body potentials were applied to investigate the spin-orbit interaction between a proton and a ⁶He nucleus. An optical model analysis revealed that the spin-orbit potential for ⁶He is characterized by a shallow and long-ranged shape compared with the global systematics of stable nuclei. A semi-microscopic analysis with a α + n + n cluster folding model suggests that the inclusion of realistic interaction between a proton and the α core is important in describing the p-⁶He elastic scattering.     

Optical model analysis of p+6He scattering over a wide range of energy

Optical-model analysis of proton elastic scattering from ⁶He has been carried out for eight sets of elastic scattering data at energies, 24.5, 25.0, 36.2, 38.3, 40.9, 41.6, 71.0 and 82.3 MeV/n respectively. The vector analyzing power and differential cross section for the elastic scattering of ⁶He nucleus from polarized protons at 71 MeV have been analyzed in the framework of the optical model potentials. The data are, first, analyzed in term of phenomenological potentials using the Woods-Saxon form for the real and imaginary parts supplemented by a spin-orbit potential of Thomas form. The analysis has been also performed using microscopic complex potentials.     

Scattering lengths of pionic 3He and 4He

Scattering lengths of pionic ³He and ⁴He and the charge exchange contribution to the 1s width of pionic ³He are calculated within the fixed scatterer approximation of the multiple scattering formalism. Particular attention is focussed on the nuclear physics part and on πN p-wave contributions. For the first time triple scattering and double-spin-flip contributions have been included. We find significant deviations from previous estimates and calculations. Good agreement is achieved with the experimental π^?3He scattering length, whereas in the case of ⁴He a repulsive dispersion contribution is clearly needed. We propose to use the measured 1s level shift of pionic ³He as a constraint to deduce a precise value of the isoscalar πN scattering length. Furthermore, we find that multiple scattering reduces the impulse approximation value for Γ_1s(π^?3He → π^{0 3}H) by more thsn 20 %. This result casts some doubt on impulse approximation calculations of radiative pion capture as well.