The role of the imaginary part in the microscopic description of (p,p′) scattering

A (p, p′) scattering experiment at E_p = 40 MeV was performed on the targets ⁹²Mo and ^{116, 120, 124}Sn. The addition of a simple collective imaginary from factor to the microscopic real form factor provides an important improvement in the agreement between calculated and experimental cross sections for the lowest 2⁺ and 3^? states. Results concerning the ΔT = 1 and ΔT = 0 contributions to the transitions are discussed.     

Behavior of the giant-dipole resonance in 120Sn and 208Pb at high excitation energy

The properties of the giant-dipole resonance (GDR) are calculated as a function of excitation energy, angular momentum, and the compound nucleus particle decay width in the nuclei ¹²⁰Sn and ²⁰⁸Pb, and are compared with recent experimental data. Differences observed in the behavior of the full-width-at-half-maximum of the GDR for ¹²⁰Sn and ²⁰⁸Pb are attributed to the fact that shell corrections in ²⁰⁸Pb are stronger than in ¹²⁰Sn, and favor the spherical shape at low temperatures. The effects shell corrections have on both the free energy and the moments of inertia are discussed in detail. At high temperature, the FWHM in ¹²⁰Sn exhibits effects due to the evaporation width of the compound nucleus, while these effects are predicted for ²⁰⁸Pb.     

An imaginary potential with universal normalization for dissipative processes in heavy-ion reactions

In this work we present new coupled channel calculations with the São Paulo potential (SPP) as the bare interaction, and an imaginary potential with system and energy independent normalization that has been developed to take into account dissipative processes in heavy-ion reactions. This imaginary potential is based on high-energy nucleon interaction in nuclear medium. Our theoretical predictions for energies up to ≈100 MeV/nucleon agree very well with the experimental data for the p,n+nucleus, ¹⁶O + ²⁷Al, ¹⁶O + ⁶⁰Ni, ⁵⁸Ni + ¹²⁴Sn, and weakly bound projectile ⁷Li + ¹²⁰Sn systems.     

The role of the imaginary form factor in the microscopic description of (p,p′) scattering from nuclei with one closed shell

The inelastic scattering of protons from the lowest 2⁺ and 3^? levels in ⁴⁰Ca, Ni, Sn and N = 50 isotopes is analyzed for different incident proton energies. The addition of a collective imaginary term to the microscopic real form factor very much improves the agreement between the calculated and experimental cross section angular distributions. The variation with energy of the relative contributions of the ΔT = 1 and gDT = 0 isospin parts of the transitions is discussed.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

Neutron elastic scattering from 116,118,120,122,124Sn

Accurate measurements of neutron differential elastic cross sections have been obtained from even isotopes of Sn. Data are presented for the elastic scattering of 11 MeV neutrons from ^{116, 118, 120, 122, 124}Sn, the elastic scattering for 24 MeV neutrons from ^{116, 118, 124}Sn and the neutron total cross section from ^{118, 120, 122, 124}Sn in the energy ranges 5.0–10.6 MeV and 20.0–26.0 MeV. The elastic scattering data are analyzed in terms of an empirical optical-model potential. The obtained optical-potential parameters are analyzed in terms of energy and isospin dependence and compared with those obtained from proton elastic scattering on even Sn isotopes.     

16, 18O induced transfer reactions on122, 120Sn

The reactions¹²⁰Sn+72 MeV¹⁸O and¹²²Sn+74 MeV¹⁶O were investigated with time of-flightΔE-E-telescopes. Data are presented for all quasi-elastic reaction channels. The two neutron stripping and pickup reactions (¹⁸O,¹⁶O), (¹⁸O,²⁰O) and (¹⁶O,¹⁸O) are analyzed in detail. It is shown that these heavy ion induced two neutron transfer reactions proceed with essentially the same type of selectivity as the corresponding light ion induced reactions. The differential cross sections for transfer reactions leaving the^{120, 122}Sn nuclei in their 2⁺ first excited states are shown to be influenced by interference effects due to additional inelastic excitations.     

Mean field and beyond in nuclei far from stability lines

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (¹²⁰Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v₁₄) in a Hartree-Fock basis. The resulting gap accounts for about half of the experimental gap. Going beyond the mean field in the particle-particle channel, the combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap. Examples for light, halo nuclei are also reported. The more studied effects of the particle-vibration coupling in the particle-hole channel are discussed for the low-lying quadrupole vibration in ¹²⁰Sn and the giant dipole resonance in the unstable oxygen isotopes and ¹³²Sn.     

Production of light nuclei in the reactions of protons with separated tin isotopes

The cross sections for the production of ⁷Be, ²²Na, ²⁴Na, ²⁸Mg, ³⁸S, ³⁸Cl, and ³⁹Cl nuclei from ¹¹²Sn, ¹¹⁸Sn, ¹²⁰Sn, and ¹²⁴Sn targets irradiated with 0.6-, 1.0-, and 8.1-GeV protons were measured by the method of induced activity. In analyzing resulting data, it was established that the above nuclei are produced in the fragmentation process and that the reaction cross section is a power-law function of the mass and charge numbers of fragmentation products. A strong dependence of the reaction cross section on the nucleonic composition of the targets and of the products is observed. The measured cross sections, together with data available in the literature, are discussed within various assumptions.     

Microscopic calculation of 58,64Ni + 124,132Sn sub-barrier fusion

The fusion cross-sections of ^58,64Ni + ^124,132Sn are investigated through a coupled-channel approach using a density- and energy-dependent effective Brueckner G-matrix interaction. Microscopic Skyrme-Hartree-Fock proton and neutron density distributions are used in the calculations. A good agreement with the experimental data of the fusion cross-sections of these neutron-rich systems has been obtained, which favors the present microscopic approach for calculating the interaction potentials and fusion cross-sections.     

Calculation of the 6He + p elastic scattering cross sections within the folding approach and the high-energy approximation for the optical potential

Data on cross sections for the ⁶He + p elastic scattering at energies of tens of MeV/nucleon are analyzed by calculating the microscopic optical potential (OP) (its real and imaginary parts). The effect produced on the cross section by the dependence of the nucleon-nucleon potential on the nuclear matter density, the role of the spin-orbit interaction, and the role of nonlinearity and renormalization of the microscopic OP are studied. A comparison with the experimental data allows sensitivity of cross sections to these effects to be tested.     

Folding model description of reactions with exotic nuclei

Microscopic folding calculations based upon the effective M3Y nucleon-nucleon interaction and the nuclearmatter densities of the interacting nuclei have been carried out to explain recently measured experimental data of the ⁶He+¹²⁰Sn elastic scattering cross section at four different laboratory energies near the Coulomb barrier. The extracted reaction cross sections are also considered.     

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.     

16, 18O induced transfer reactions on122, 120Sn

The reactions¹²⁰Sn+72 MeV¹⁸O and¹²²Sn+74 MeV¹⁶O were investigated with time of-flightE-E-telescopes. Data are presented for all quasi-elastic reaction channels. The two neutron stripping and pickup reactions (¹⁸O,¹⁶O), (¹⁸O,²⁰O) and (¹⁶O,¹⁸O) are analyzed in detail. It is shown that these heavy ion induced two neutron transfer reactions proceed with essentially the same type of selectivity as the corresponding light ion induced reactions. The differential cross sections for transfer reactions leaving the^{120, 122}Sn nuclei in their 2⁺ first excited states are shown to be influenced by interference effects due to additional inelastic excitations.     

Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles(nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The impacts of the isoscalar and isovector parts of the momentum dependent interaction on the emissions of isospin particles are explored, i.e., the mass splittings of m_n~*=m_p~* and m_n~* m_p~*(m_n~* m_p~*). The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of ~(112)Sn+~(112)Sn and ~(124)Sn+~(124)Sn at incident energies of 50 and 120 MeV/nucleon, respectively. It is found that both the effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail(larger than 20 Me V). The isospin splitting of nucleon effective mass slightly impacts the double ratio spectra at the energy of 50 MeV/nucleon. A soft symmetry energy with stiffness coefficient of γ_s =0.5 is constrained from the experimental data with the Fermi-energy heavy-ion collisions.     

Ionized impurity scattering in degenerate In2O3

Thin films of In₂O₃ are prepared by the spraying method. The concentration of charge carriers is changed from about 8×10¹⁹ cm^?3 to 5×10²⁰ cm^?3 by suitable doping with Sn. The optical effective mass is found to depend slightly on carrier concentration. Electrical and optical measurements indicate that electrons are scattered predominantly by charged impurity centres. Structural investigations show that grain boundary scattering can be neglected. The interpretation of the experimental results is mainly based on a paper by von Baltz and Escher, where analytical formulas for the imaginary part of the complex dielectric constant are given for the most important scattering mechanisms in (degenerate) semiconductors.     

Study of the one-neutron transfer reactions induced by polarized 7Li ON 26Mg and 120Sn

Angular distributions of the cross sections and analyzing powers up to third rank have been measured for the one-neutron transfer reactions ²⁶Mg(⁷Li,⁶Li)²⁷Mg, ¹²⁰Sn(⁷Li,⁶Li)¹²¹Sn and ¹²⁰Sn(⁷Li, ⁸Li)¹²⁹Sn initiated by polarized ⁷Li ions of 44 MeV. Third-rank analyzing power has been measured for the first time in transfer reactions. Coupled-channels calculations in which the ground and first excited states of ⁷Li are coupled together by collective interactions and one-neutron transfers are calculated in exact finite range explain the experimental data for low-lying states in final nuclei. Extracted spectroscopic factors are in good agreement with those obtained from other one-neutron transfer reactions on the same targets.