A comparative analysis of the density distributions and the structure models of <Superscript>9</Superscript>Li

In the present study, we have analysed the elastic scattering cross-section data of ⁹Li + ¹²C system at E _lab = 540 MeV and ⁹Li + ²⁰⁸Pb system at E _c.m. = 28.3 MeV for some cluster models and various density distributions of the ⁹Li nucleus. First, we have obtained five different density distributions of the ⁹Li nucleus to generate real potentials with the help of double-folding model. For these densities, we have calculated the elastic scattering angular distributions. Secondly, using a simple approach, we have investigated some cluster models of the ⁹Li nucleus consisting of ⁶He + ³H and ⁸Li + n systems. We have presented the comparison of elastic scattering angular distributions for each system with each other as well as with the experimental data. Finally, we have given the cross-section values obtained from the theoretical calculations for all the systems studied in this paper.     

Study of the <Superscript>12</Superscript>C (<Superscript>8</Superscript>B, <Superscript>7</Superscript>Be)<Emphasis Type="Italic">X</Emphasis> knockout reaction at intermediate energies

The breakup reactions of ⁸B on a ¹²C target at 142, 285, 790, and 936MeV/nucleon have been studied. One-proton-removal cross sections, leading to the production of ⁷Be fragments in the ground and first excited states (at 0.429MeV), and the longitudinal momentum distributions of the ⁷Be fragments are obtained in the Eikonal approximation of the Glauber Model. The results of the calculations including the contribution of the ⁷Be to the ground and first excited states of ⁸B are compared with the available experimental data. One-proton-removal cross section for the ¹²C(⁸B, ⁷Be)X knockout reaction at 142, 285, 790, and 936 MeV/nucleon energy has been calculated. ⁸B and ⁷Be cross sections and momentum distribution are in a good agreement with available data.     

Examination of the <Superscript>16</Superscript>O + <Superscript>28</Superscript>Si system with microscopic and phenomenological potentials

The ¹⁶O + ²⁸Si reaction has been widely studied both experimentally and theoretically and has been claimed to show indications of chaotic scattering. In order to examine this claim and to address whether reaction models such as the optical one could explain the experimental data, we have analyzed the ¹⁶O + ²⁸Si system within the framework of the optical model for ten energies from 29.0 to 45.0 MeV, by using microscopic folded potentials, which are based on M3Y nucleon-nucleon, alpha-alpha effective interactions and a phenomenological shallow potential. All potentials describe the individual angular distributions very well at forward angles. However, they fail to describe the individual angular distributions over the whole angular range up to 180°. Nevertheless, we have been able to explain the experimental data by modifying the surface region of the microscopic real potentials by adding two surface potentials. With these correction potentials, we have obtained very good agreement for the individual angular distributions over the whole angular range for the given energies as well as for the experimental data near the Coulomb barrier. The failure of these optical potentials in explaining the scattering observables of this reaction without corrections puts a question mark on the model and supports the idea of a chaotic behavior. The text was submitted by the authors in English.     

Structure of the <Superscript>6</Superscript>He nucleus in the three-particle model

The properties of the ⁶He nucleus were investigated in a three-particle approximation (a alpha-particle cluster plus two neutrons) on the basis of the variational approach by using a Gaussian basis. For nn and nα interactions, potentials that make it possible to describe S-wave phase shifts for elastic scattering and, simultaneously, to reproduce faithfully the energy and the size of the ⁶He nucleus were proposed. Characteristic structural features of this nucleus that are manifested in the density distributions, elastic form factor, pair correlation functions, and momentum distributions of particles constituting the ⁶He nucleus in the three-particle model were revealed.     

Studies of multi-nucleon transfer reactions in <Superscript>90</Superscript>Zr(<Superscript>18</Superscript>O,X) and <Superscript>90</Superscript>Zr(<Superscript>16</Superscript>O,X)

Multi-nucleon transfer reactions in ¹⁸O + ⁹⁰Zr and ¹⁶O + ⁹⁰Zr have been studied at an incident energy of 90 MeV. The energy spectra and angular distributions are measured. The data have been analyzed to obtain cross-section dependence on the number of nucleons transferred and on the ground-state Q-values. In the ⁹⁰Zr(¹⁸O, X); X = ¹⁶O, ^17,16,15,14N, ^14,13,12C, ^12,11,10B, ^10,9,7Be and ^7,6Li reactions, 2n and 2n-correlated transfer cross-sections are observed to be enhanced as compared to the ¹⁶O + ⁹⁰Zr reaction. A detailed comparison in the multi-particle stripping and elastic-scattering cross-section between these two systems are made in order to investigate the possible influence of the two valence neutrons in ¹⁸O nucleus. Diffractional model DWBA calculations, based on the direct surface transfer model, have been performed to understand the reaction mechanism of multi-nucleon transfer to continuum.Received: 12 September 2002, Revised: 24 September 2003, Published online: 27 January 2004PACS: 25.70.Hi Transfer reactions - 25.70.Bc Elastic and quasielastic scattering     

Microscopic interpretation of the (<Emphasis Type="Italic">t</Emphasis>, <Superscript>3</Superscript>He) reaction at 130 MeV on <Superscript>90</Superscript>Zr and isovector monopole strength

The 130-MeV primary tritium beam of the AGOR facility with an intensity of up to 10⁸ pps and the Big Bite Spectrometer experimental setup have been used to study the (t, ³He) reaction between 0° and 5° lab angles on ¹²C and ⁹⁰Zr targets. The standard ray-tracing procedure has allowed us to obtain excitation-energy spectra up to 30 MeV in six angular bins for each residual nucleus, with an average energy resolution of 350 keV. We have used the DWBA reaction mechanism model to reproduce those spectra and their angular distributions. In this approximation, the form factor was treated as a folding of an effective projectile-nucleon interaction with a transition density. The effective projectile-nucleon interaction has been adjusted to reproduce the 0° cross section of the 1⁺ ground state of ¹²B populated in the ¹²C(t, ³He) reaction. We have employed RPA wave functions of excited states to construct the form factors. This DWBA+RPA analysis is used to compare calculated and experimental cross sections directly and to discuss the giant resonance excitations in the ⁹⁰Y nucleus. In this talk, we give some details on this analysis. We show that there are important contributions of L = 2 transitions in the observed cross sections for the 1⁺ final states that explain the previous difficulties in clearly identifying the monopole strength distributions. We then have a better indication of where the L = 0 part is located with this reaction and its microscopic analysis. The text was submitted by the author in English.     

Study of the Involvement of <Superscript>8</Superscript>Be and <Superscript>9</Superscript>B Nuclei in the Dissociation of Relativistic <Superscript>10</Superscript>C, <Superscript>10</Superscript>B,and <Superscript>12</Superscript>C Nuclei

The results obtained by estimating the contribution of 8Be and 9B nuclei to the coherent dissociation of ¹⁰C, ¹⁰B, and ¹²C relativistic nuclei in nuclear track emulsions (“white” stars) are presented. The selection of white stars accompanied by 9B leads to a distinct peak appearing in the distribution of the excitation energy of 2α2p ensembles and having a maximum at 4.1 ± 0.3 MeV. A 8Be nucleus manifests itself in the coherent-dissociation reaction ¹⁰B → ²He + H with a probability of (25 ± 5)%, (14 ± 3)% of it being due to 9B decays. The ratio of the branching fractions of the ⁹B + n and ⁹Be + p mirror channels is estimated at 6 ± 1. An analysis of the relativistic dissociation of ¹²C nuclei in a nuclear track emulsion revealed nine 3α events corresponding to the Hoyle state.     

Analysis of the normal optical,Michel and molecular potentials on the <Superscript>40</Superscript>Ca(<Superscript>6</Superscript>Li,d)<Superscript>44</Superscript> Ti reaction

Full finite-range (FFR) distorted-wave Born approximation (DWBA) method has been applied to analyse the angular distributions of cross-sections of the ⁴⁰Ca(⁶Li, d) ⁴⁴Ti reaction at 28 MeV incident energy for the 22 transitions involving both the bound and unbound states of ⁴⁴Ti by using the normal optical, Michel and molecular potentials. The extracted spectroscopic factors for the three optical potentials are compared with those of some previous studies of zero-range (ZR) calculations of the ⁴⁰Ca(⁶Li, d) ⁴⁴Ti reaction using the normal optical potential. The χ² values of all the levels are obtained for the three optical potentials to estimate the quality of the fits. Molecular and Michel potentials have been used for the first time to analyse the four-nucleon transfer reaction and it seems that the molecular potential fits the experimental data more satisfactorily for some of the states than the normal optical and Michel potentials.     

Dynamical decay process of <Superscript>219, 220</Superscript>Ra<Superscript>*</Superscript> formed in <Superscript>10, 11</Superscript>B + <Superscript>209</Superscript>Bi reactions

The excitation functions for both the evaporation residue and fission have been calculated for ¹⁰B + ²⁰⁹Bi and ¹¹B + ²⁰⁹Bi reactions forming compound systems ^{219, 220}Ra^* , using the dynamical cluster-decay model (DCM) with effects of deformations and orientations of the nuclei included in it. In addition to this, the excitation functions for complete fusion (CF) are obtained by summing the fission cross-sections, neutron evaporation and charged particle evaporation residue cross-sections produced through the axn\ensuremath \alpha xn and pxn\ensuremath pxn (x = 2, 3, 4) emission channels for the ²¹⁹Ra system at various incident centre-of-mass energies. Experimentally the CF cross-sections are suppressed and the observed suppression is attributed to the low binding energy of ^{10, 11}B which breaks up into charged fragments. The reported complete fusion (CF) and incomplete fusion (ICF) excitation functions for the ²¹⁹Ra system are found to be nicely fitted by the calculations performed in the framework of DCM, without invoking a significant contribution from quasi-fission. Although DCM has been applied for a number of compound nucleus decay studies in the recent past, the same is being used here in reference to ICF and subsequent decay processes along with the CF process. Interestingly the main contribution to complete fusion cross-section comes from the fission cross-section at higher incident energies, which in DCM is found to consist of an asymmetric fission window, shown to arise due to the deformation and orientation effects of formation and decay fragments.     

Analyzing the p(<Superscript>6</Superscript>He,n gamma)<Superscript>6</Superscript>Li reaction

The differential cross section of the charge-exchange reaction p(⁶He, n)⁶Li(0⁺, 3.56 MeV) is calculated within the context of direct mechanisms: the stripping of a heavy ⁵He cluster, replacing a virtual neutron with a proton in the 5He cluster field, and the mechanism of consecutive transfer of a neutron and an α particle. The spatial structure of initial and final nucleus is determined from the dependence of various direct mechanisms contributions from spatial configurations.     

Instabilities of the Conventional Nucleus-Nucleus Interactions for (<Superscript>3</Superscript>H<Superscript>4</Superscript>He) Proton Pickup Cross-Sections

The angular distributions of the ²⁶Mg, ²⁸Si, ³⁰Si(³H, ⁴He) reactions have been analyzed using the exact finite-range DWBA calculations. The optical model potential is assumed to have the conventional spin-orbit potential. The obtained cross-sections with the spin-orbit potential are not significantly different from those calculated using the phenomenological Woods–Saxon form factors in the forward angle regions. The inclusion of the spin-orbit potential gives the best fit to the data and greatly improves the large angle cross-sections. Different reasonable spectroscopic factors are found to account well for the cross-section magnitudes.     

Electric dipolarizability of <Superscript>7</Superscript>Li

We calculate the electric dipolarizability of ⁷Li nucleus within the cluster model and estimate a value of about 0.0188 fm³. We also discuss the possibility of observing this in the scattering of ⁷Li from a ²⁰⁸Pb target at energies about 30 MeV.      

<Superscript>4</Superscript>He<Superscript>3</Superscript>H<Superscript>2</Superscript>H three-body model of the <Superscript>9</Superscript>Be nucleus

Within the framework of the single-channel approximation, an {αtd} model of the ⁹ Be nucleus is presented. A comparative analysis of the t ⁶ Li wave functions describing relative motion of bound states constructed in {ααn} and {αtd} cluster representations is carried out on the example of calculations of the ⁹ Be(γ,t₀)⁶ Li process characteristics. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 85–89, January, 2008.     

A three-body model of the <Superscript>11</Superscript>B nucleus

The binding energy and the rms charge and mass radii have been calculated in terms of the single-channel three-body ⁴He⁴He³H model of the ¹¹B nucleus with an expansion of the three-body wave function in a nonorthogonal Gaussian basis. Parameters of the wave function are presented and convergence of the three-body energy depending on the number of expansion terms is demonstrated.     

Effect of cluster polarization on the spectrum of the <Superscript>7</Superscript>Li nucleus and on the reaction <Superscript>6</Superscript>Li(<Emphasis Type="Italic">n</Emphasis>, <Superscript>3</Superscript>H)<Superscript>4</Superscript>He

The effect of polarization of the ⁶Li and ³H clusters on the parameters of states of the ⁷Li nucleus and on the cross section for the reaction ⁶Li(n,³H)⁴He was studied. The ⁴He + d + n three-cluster configuration was invoked for this purpose, and cluster dynamics was determined within a microscopic model where the relative motion of the clusters was described in terms of Faddeev amplitudes. The ⁴He + d + n three-cluster configuration made it possible to consider the ⁴He + ³H and ⁶Li + n binary channels, which are dominant in ⁷Li, and to take simultaneously into account the cluster polarization of ⁶Li as a two-cluster subsystemin the ⁴He + d representation and the cluster polarization of ³Has a two-cluster subsystem in the d + n representation.     

Theoretical LSP detection rates for <Superscript>71</Superscript>Ga, <Superscript>73</Superscript>Ge,and <Superscript>127</Superscript>I dark-matter detectors

The low-energy structure of the dark-matter detector nuclei ⁷¹Ga, ⁷³Ge, and ¹²⁷I has been studied by using the microscopic quasiparticle-phonon model. The resulting ground states have been used to calculate theoretical predictions for detection rates of the lightest supersymmetric particle (LSP) in experiments studying elastic scattering of an LSP from an atomic nucleus. The highest rate, approximately 0.27 yr^?1kg^?1, among all the adopted SUSY parameters and renormalization schemes was provided by ¹²⁷I at the zero limit of the detector energy threshold.     

Deuteron scattering on <Superscript>6</Superscript>Li at an energy of 25 MeV

At an energy of 25 MeV and in the angular range 7°−175° in the laboratory frame, angular distributions were measured for elastic deuteron scattering on ⁶Li nuclei and for the respective inelastic-scattering processes accompanied by the transitions to the ground state (1+) of the ⁶Li nucleus and to its excited state at E _x = 2.186 MeV (J ^π = 3⁺). The resulting data were analyzed on the basis of the optical model of the nucleus and the coupled-reaction-channel method with allowance for the mechanism of alpha-particle-cluster exchange. It is shown that only upon including, in the analysis, channel coupling and the exchange mechanism can the experimental cross sections for elastic and inelastic scattering be reproduced over the entire range of angles.     

Neutron single-particle structure of <Superscript>48</Superscript>Ca, <Superscript>50</Superscript>Ti, <Superscript>52</Superscript>Cr, <Superscript>54</Superscript>Fe,and <Superscript>56</Superscript>Ni nuclei

The change in the neutron single-particle structure of (1f?2p)-shell magic nuclei near the Fermi energy with an increase in the number of protons in the 1f _7/2 subshell from 0 for ⁴⁸Ca to 8 for ⁵⁶Ni has been investigated. Good agreement of the experimental and estimated values of the single-particle energies E _nlj of the bound states of neutrons in these nuclei with the results of calculations within the dispersive optical model is obtained.     

Dissociation of deuteron, <Superscript>6</Superscript>He and <Superscript>11</Superscript>Be from Coulomb dissociation reaction cross-section

The fragmentation of deuteron, ⁶He and ¹¹Be have been studied during interaction with the ²⁰⁸Pb nucleus at various projectile energies. The Coulomb dissociation cross-sections and the momentum distribution of the break-up fragments have been analysed within the framework of the direct fragmentation model. The post-acceleration effect of deuteron during break-up and the halo structures of both the ⁶He and ¹¹Be have been investigated.