A Comprehensive Theoretical Analysis of <Superscript>6,7</Superscript>Li + <Superscript>64</Superscript>Zn Elastic Scattering in a Wide Angular Range Around the Coulomb Barrier

In this paper, the elastic scattering angular distributions of ^6,7Li on ⁶⁴Zn have been investigated by using various nuclear potentials. For this, we use the phenomenological Woods-Saxon potential, the real double folding potential with the density-independent M3Y effective interaction supplemented with an imaginary part in Woods-Saxon form and the double folding potentials multiplied with a normalization factor of the real and imaginary parts via the density-independent and CDM3Y6 density-dependent versions of the M3Y effective interaction have been used. The results have been compared with each other as well as with the experimental data. It has been observed that the agreement between the theoretical results and earlier reported data is perfect. Finally, the change of the total reaction cross sections with energy has been investigated.     

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N²LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.     

The finite size effects in fusion of deformed nuclei at incident energies near the barrier

By the end of the last century, the precision of heavy-ion-fusion cross-section measurement had been increased up to 1%. This allowed the measured cross sections to be converted into experimental fusion-barrier distributions. In the experimental analysis, the barrier distributions were analyzed using a Woods-Saxon shape for the nuclear part of the bare nucleus-nucleus potential. This potential was defined along the line joining the centers of the two nuclei (“centerline potential”), which, for deformed nuclei, contradicts the short-range character of the nucleon-nucleon (N N) nuclear interaction. We present the results of our theoretical study of the significant deviations of the simplified potential from a “realistic” nuclear potential. The finite-size effects on the potential for deformed nuclei were first investigated in an approximate geometrical way. Then a more rigorous approach, namely, a semimicroscopic double-folding model, was applied to calculate the nucleus-nucleus potential. The angle-dependent fusion barriers calculated with a simple delta-function-like exchange term of the N N M3Y interaction was found to be very similar to those calculated with a finite-range expression. This circumstance enables us to perform rather quick calculations of the fusion cross sections and the corresponding barrier distributions. Comparison of the results with the experimental data showed that the finite-size effects are substantial and cannot be ignored in a quantitative analysis of experimental fusion cross sections and barrier distributions. The text was submitted by the authors in English.     

Folding model analysis of the nucleus–nucleus scattering based on Jacobi coordinates

This paper presents the results of scattering of ¹⁶O+²⁰⁹Bi interaction near the Coulomb barrier. The interaction potential between two nuclei is calculated using the double folding model with the effective nucleon–nucleon (NN) interaction. The calculations of the exchange part of the interaction were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. Also the results are compared with the zero-range approximation. All these calculations are done using the wave functions of the two colliding nuclei in place of their density distributions. The wave functions are obtained by the D-dimensional wave equation using the hyperspherical calculations on the basis of Jacobi coordinates. The numerical results for the interaction potential and the differential scattering are in good agreement with the previous works.     

Low energy α+<Superscript>16</Superscript>O scattering in the orthogonality condition model

The orthogonality condition model (OCM) is used to describe α+¹⁶O scattering at low energies. A double folding potential with density-dependent effective NN interactions is used as the local potential of the model. The energies and widths of α-cluster resonances and differential cross sections are calculated. The results are compared to one obtained using the standard potential approach, without the nonlocal interaction of the OCM.     

Finite-range DWBA analyses of (dt) and (d3He) reactions on 64Zn at Ed = 13 MeV

Exact finite-range DWBA analyses of ($\text{d}\text{, t}\text{)}$ and $\text{(}\text{d}\text{d}$, ³He) reactions have been performed for an ⁶⁴Zr target at an incident deuteron energy of 13.0 MeV, leading to the ground states of the residual nuclei. The microscopic overlap functions for (d, t) and (d, ³He) systems obtained by using the Phillips triton wavefunctions have been used as projectile form factors into the calculation. The results are compared with zero-range DWBA calculations taking the finite-range effects into account by means of a local energy approximation. The results obtained by finite-range and zero-range calculations for differential cross sections as well as vector and tensor analysing powers are compared with the experimental data. The range of validity of the local energy approximation is discussed.     

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.     

Exact finite range calculations of light-ion induced two-neutron transfer reactions

Exact finite-range (EFR) distorted-wave Born approximation calculations were performed for light-ion induced two-neutron transfer reactions, by using a technique to calculate the form factors rather fast. The use of this method made it possible to carry out calculations even when realistic light-ion wave functions and multi-configurational two-neutron wave functions were used and large transferred angular momenta were considered. It was found that, at lower bombarding energies, the predictions of the EFR and zero-range calculations agree very closely both in angular distributions and relative magnitudes of the cross sections, though they differ significantly in absolute magnitude. As the bombarding energy increases, the discrepancy between the predicted absolute magnitude becomes still larger, and noticeable differences are seen even in relative cross sections. For all the energies considered, the EFR calculations predicted the absolute magnitudes of the experimental cross sections to within a factor of several units.     

Energy dependence of the zero-range DWBA normalization of the 58Ni(3He, α) 58Ni reaction

Strong transitions in the ⁵⁸Ni(³He, α)⁵⁷Ni reaction were analyzed using both the zero-range and exact finite-range DWBA. Data considered covered a range of bombarding energies from 15 to 205 MeV. The zero-range DWBA described all data well when finite-range and non-locality corrections were included in the local energy approximation. Comparison of zero-range and exact finite-range calculations showed the local energy approximation correction to be very accurate over the entire energy region. Empirically determined D₀ values showed no energy dependence. A theoretical D₀ value calculated using an α wave function which reproduced the measured α rms charge radius and the elastic electron scattering form factor agreed well with the empirical values. Comparison was made between these values and D₀ values quoted previously in the literature.     

Effect of Gaussian Potential on the Differential Cross Sections of Alpha Transfer Reactions

The differential cross sections of different alpha transfer reactions have been investigated by using the exact finite-range DWBA calculations. The double-folding density-dependent model is used for the real and imaginary nucleus-nucleus potential in the initial and final channels. The effective nucleon-nucleon interaction is assumed to be the double-Gaussian potential. The Yukawa interaction is found reasonable and exhibits a slight better agreement at energies above the barrier region. The obtained values of the extracted normalization factors are reasonable.     

Elastic and inelastic scattering of 58Ni +90,94Zr

Pure elastic and inelastic scattering cross sections have been measured for the systems ⁵⁸Ni +^90,94Zr at energies near the Coulomb barrier where not only quasi-elastic and fusion but also deep-inelastic process come into play. Coupled channels calculations including both projectile and target inelastic excitations can successfully explain the elastic and inelastic scattering angular distributions with an energy-independent semi-empirical bare potential. The calculation reproduces also the sum of the total quasi-elastic, fusion and deep-inelastic cross sections. Received: 14 September 1998 / Revised version: 21 October 1998     

Fusion probability of symmetric heavy,nuclear systems determined from evaporation-residue cross sections

Cross sections were measured for the formation of evaporation residues in ⁴⁸Ca-, ⁸⁶Kr- and ¹²⁴ Sn-induced reactions with Yb, Sb and Zr isotopes. For the nearly symmetric systems, the energy dependence of the fusion probability in central collisions was determined. The fusion probability at the expected fusion barrier as calculated from a one-dimensional heavy-ion potential was found to be reduced by several orders of magnitude. The fusion cross sections increase gradually, and only at energies appreciably above the expected fusion barrier the major part of the cross section of central collisions leads to fusion. The observed hindrance of the fusion process is compared with model predictions.     

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (⁶He), cluster (⁶Li and ⁷Li), and loosely bound (³He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.     

Finite-range calculation of two-neutron transfer reactions in deformed nuclei

Finite-range DWBA calculations have been done for the reaction ¹⁵⁴Sm(p, t)¹⁵²Sm. The results have been compared with those of the zero-range DWBA calculations. It is found that the finite-range effects are considerably large to the shapes of the angular distributions, but are small to the relative magnitude of the cross section for the 2⁺ and 4⁺ ground-band members to the ground-state transition.     

Measurement and interpretation of heavy ion fusion excitation functions

Fusion excitation functions for ³²S induced reactions on ²⁴Mg, ²⁷Al, ⁴⁰Ca and ⁵⁸Ni are reported at incident ³²S ion energies of 65 to 132.5 MeV. Measurements were made using counter-telescopes with beams from Van de Graaff accelerators. From these data barrier heights and radii for fusion are extracted. These results are interpreted in terms of the nuclear diftuseness, and the nuclear attractive potentials at the fusion radii are deduced. Relative density overlaps at the fusion radius are estimated from electron scattering density distributions. Several parameterizations for the fusion radii and barrier heights are presented. Fusion cross sections are compared with reaction cross sections based on elastic scattering measurements coupled with optical model analysis. It is found that for the systems investigated, 90±10 % of the reaction cross section results in fusion.     

Effective interactions in the proton optical-model potential

A six-parameter optical model is developed in which the real central part is calculated by folding several effective nucleon-nucleon interactions into matter distributions which reproduce single-particle binding energies and electron scattering data. A simple local approximation is made to take into account the exchange term. It is concluded that the density-dependent effective interactions derived from nuclear-structure calculations are also appropriate for nucleon-nucleus scattering. Off-shell effects are apparent from the worsening of the quality of fit for light nuclei.     

Finite-range nucleon-nucleon interaction in the radiative capture of fast nucleons

The direct-semidirect model for nucleon radiative capture has so far been formulated assuming a zero-range nucleon-nucleon interaction. An extension of the theory to finite-range forces is proposed here. The usual δ-function in the interaction is replaced by a range-dependent gaussian function and then the radial form factor in the particle-vibration coupling (responsible for excitation of the E1 and E2 giant resonance states) is derived. Calculations are performed for the ¹⁴²(p, γ) reaction in the 5–30 MeV energy region. A detailed analysis provides indications on effects related to the interaction range as regards both the E1 and E2 integrated cross sections and the forward-backward asymmetry of the γ-ray angular distributions. Sensitivity to the interaction range shows connections with the proton final-level spin.     

Two-body photodisintegration of 3He with realistic bound-state wave functions

Total and differential cross sections for two-body photodisintegration of ³He have been recalculated using realistic bound-state wave functions. Contrary to previous calculations we find neither any unusual structure in the energy distributions nor any distinct signature of D-state components in the bound-state wave functions for photon energies ω ≦ 35 MeV. Final-state interactions and, possibly, meson exchange currents increase the total cross section substantially, but decrease the E2 contribution from 1 % to 0.5 %. After subtraction of spurious non-orthogonal components in the wave function, the M1 contribution decreases by about one order of magnitude to a value of 1.5 % in agreement with the experimental data.     

Fusion excitation function measurements for the 16O+58Ni and 16O+62Ni systems

High precision fusion excitation functions have been measured for the ¹⁶O+⁵⁸Ni and ¹⁶O+⁶²Ni systems from which fusion barrier distributions have been evaluated. Coupled-reaction-channels (CRC) calculations, which describe elastic and quasi-elastic scattering, also satisfactorily reproduce the fusion cross sections and barrier distributions. The small value of Z₁Z₂ in this case leads to barrier distributions with relatively little structure. However, in conjunction with the detailed elastic scattering data for these systems, this allows us to elucidate the role of previously ignored states in ¹⁶O in pushing the entire distribution to lower energies. These shifts are consistent with derived magnitudes of polarization potentials for both systems.     

Systematic studies on α-decay half-lives for super heavy nuclei

Radioactive decay of super heavy nuclei via the emission of α-particles has been studied theoretically in the preformed cluster model (PCM). The nucleus-nucleus (NN) potential is obtained by double folding the density distributions of the α-particle and the daughter nucleus with a realistic effective interaction. The M3Y effective interaction, supplemented by a zero-range pseudo-potential for exchange term, is used to calculate the NN potential. The α decay half-lives for 317 nuclei at Z=102–120 are performed in the PCM framework with the theoretical Q values extracted from the Mller-Nix-Kratz and Liran-Marinov-Zeldes mass tables and are compared with the experimental data. The calculated results are also compared with those obtained by using Q values from the Muntian-Hofmann-Patyk-Sobiczewski and Myers-Swiatecki mass estimates.