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.     

Semiclassical description of the <Superscript>6</Superscript>He+<Superscript>12</Superscript>C elastic scattering

The results of the elastic scattering of ⁶He+¹²C systemat E _Lab = 18 MeV by using the barrier and internal wave decomposition of the S-matrix element within the framework of the WKB method are presented. This is the first detailed study for the interaction of the exotic ⁶He nucleus on different stable nuclei by using a semiclassicalmethod. In this paper, we show that in order to obtain the elastic scattering cross section of the ⁶He+¹²C systemat energies close to the Coulomb barrier, it is vitally important to take into account the inner complex turning points in the calculations and the tunneling effects play a crucial role to explain the experimental data. The semiclassical results are compared with the experimental data as well as the quantum-mechanical one.     

Effect of the structure of neutron-rich <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li isotopes on the characteristics of proton elastic scattering

The differential cross sections of proton elastic scattering from ⁸Li and ⁹Li nuclei in inverse kinematics have been calculated. The cross sections were determined within the Glauber diffraction theory with the wave functions of nuclei in the three-particle α-t-n, α-t-2n, and ⁷Li-n-n models. Comparison with the existing experimental data for E = 700 and 60 MeV/nucleon made it possible to draw a conclusion about the quality of the wave functions and the adequacy of the potentials used for their calculations.     

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.     

Structure of low-lying <Superscript>12</Superscript>C resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of ¹²C in the 3α model. We use Ali-Bodmer potentials and compare results for other potentials α-α with similar ⁸Be properties. A three-body potential is used to adjust the ¹²C resonance positions to desired values extending the applicability of the method to many-body systems decaying into three α-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two 0⁺, three 2⁺, two 4⁺, one of each of 1^±, 2^-, 3^±, 4^-, and 6⁺. The partial-wave decomposition of each resonance is calculated as a function of the hyperradius. Strong variation is found from small to large distance. The connection to previous experimental and theoretical results is discussed and agreements as well as disagreements are emphasized.     

Phase analysis of elastic <Emphasis Type="Italic">p</Emphasis><Superscript>6</Superscript>Li scattering at astrophysical energies

Based on new experimental investigations of elastic p ⁶Li scattering at energies 500–1150 keV and angles 30–170°, a phase analysis is performed and interaction potentials for p ⁶Li-system in ^2,4S- and ²P-states are constructed.     

Reaction mechanism of <Superscript>6</Superscript>Li scattering at 600 MeV

Elastic scattering and inclusive breakup of ⁶Li particles on ¹²C, ⁵⁸Ni, ⁹⁰Zr, and ²⁰⁸Pb targets are measured at 100A MeV. The elastic scattering data are compared with single channel and Coupled Discretized Continuum Channels calculations. The coupling-effect between the elastic and the breakup channels is important even at an incident energy of 100A MeV and cannot be neglected. The inclusive breakup data are investigated for orbital dispersion effects which are found to be less significant at 100A MeV. The longitudinal momentum distributions are broader than predicted by theoretical expectations. Received: 17 December 1999 / Revised version: 9 February 2000     

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.     

Heavy lithium isotope <Superscript>11,12</Superscript>Li production in pion absorption reactions on a <Superscript>14</Superscript>C radioactive target

The results from an experimental search for the production of heavy lithium isotopes ^11,12Li in stopped π⁻-meson absorption reactions on a ¹⁴C radioactive target are presented. A pronounced peak is observed in the missing mass spectrum of the ¹⁴C(π⁻, pp)X reaction, which is associated with the formation of a nucleon-unstable ¹²Li state with the following resonance parameters: E _R = 4.0 ± 0.2 MeV and Γ = 1.1 ± 0.2 MeV. Resonance parameters of three low-lying ¹¹Li excited states were determined in the ¹⁴C(π⁻, pd)X, reaction.     

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.     

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.     

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     

Excitation functions of <Superscript>6</Superscript>Li incomplete fusion reactions with Pt nuclei

Experimentally determined excitation functions of the transfer reactions producing ^194–199Au and ^197m Hg isotopes during the interaction of ⁶Li with Pt nuclei are presented. An analysis of the experimental data as compared to EMPIRE-2.18 model calculations and experimental results on the d + ^natPt and α + ^natPt reactions allow determination of the interaction channels of d- and α-clusters in ⁶Li with the target nucleus. The results from model calculations of the reaction cross sections appear considerably lower than the experimental data. This discrepancy in describing the reactions with weakly bound nuclei is probably associated with the incomplete consideration of various interaction channels in the EMPERE-2.18 software. It is clear that a complete understanding of the interaction pattern in these processes requires consideration of the direct channels of ⁶Li nucleus cluster transfer during ⁶Li breakup near the Coulomb barrier.     

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.     

Spectroscopy of <Superscript>17</Superscript>C and (sd )<Superscript>3</Superscript> structures in heavy carbon isotopes

The structure of ¹⁷C has been investigated using the three-neutron transfer reaction (¹²C,⁹C) on a ¹⁴C target at 231MeV incident energy, the reaction Q-value is Q ₀ = - 46.930MeV. Eleven new states up to 16.3MeV excitation energy were identified. The same reaction has also been used on a ¹²C target ( Q ₀ = - 38.787MeV), and excited states in ¹⁵C up to 19MeV were observed. In ¹⁷C the three transferred neutrons populate (sd )³ configurations on the ¹⁴C core. The comparison of levels populated by the (¹²C,⁹C) reaction in ¹⁷C, ¹⁶C and ¹⁵C reveals a strong similarity of their properties. This concerns especially nine states in each of the three carbon isotopes, which show practically the same excitation energies except a constant mean shift of +5.82MeV for ¹⁶C and +6.65MeV for ¹⁵C with respect to ¹⁷C. The triples of states from the three isotopes, which correspond to each other, have also similar widths and cross-section ratios. It is concluded that the same (sd )³ structures are populated in the three carbon isotopes. The observed levels of ¹⁷C are also compared to the levels of ¹⁹O with known assignments and to shell model calculations, and their decay properties are discussed.     

Structure of the spatial periphery of the <Superscript>11</Superscript>Li and <Superscript>11</Superscript>Be isobars

On the basis of the shell model with an extended basis, the structure of ⁹Li-⁹Be to ¹¹Li-¹¹Be nuclei is examined with allowance for the competition of ^jj coupling and Majorana exchange forces via considering the sequential addition of neutrons, and the respective wave functions are determined. A formalism for calculating the spectroscopic factor for a dineutron and for individual neutrons in nuclei whose wave functions incorporate the mixing of shell configurations is developed. The reactions ⁹Li(t, p)¹¹Li and ⁹Be(t, p)¹¹Be treated with allowance for the mechanisms of dineutron stripping and a sequential transfer of two neutrons are considered as an indicator of the proposed structure of lithium and berylliumisotopes. The parameters of the optical potentials, the wave functions for the bound states of transferred particles, and the interaction potentials corresponding to them are determined from a comparison of the theoretical angular distribution of protons from the reaction ⁹Be(t, p)¹¹Be with its experimental counterpart. It is shown that a dineutron periphery of size about 6.4 fm is present in the ¹¹Li nucleus and that a single-neutron periphery of size about 8 fm is present in the ¹¹Be nucleus.     

Unexpected transparency in the scattering of fragile <Superscript>6</Superscript>Li and <Superscript>6</Superscript>He Nuclei

It is found that the scattering of the fragile nucleus ⁶Li from ¹²C and ¹⁶O is unexpectedly transparent. It is shown that the internal-wave contribution is significantly large in the scattering, which suggests that some transparency could persist in the scattering involving the fragile nucleus ⁶He.     

Analysis of <Superscript>4</Superscript>He+<Superscript>40</Superscript>Ca and <Superscript>4</Superscript>He+<Superscript>44</Superscript>Ti scattering using different optical model potentials

Elastic scattering of ⁴He+⁴⁰Ca and ⁴He+⁴⁴Ti reactions at backward angles has been analyzed using two differentmodels, microscopic and semimicroscopic folding potentials. The derived real potentials supplemented with phenomenological Woods–Saxon imaginary potentials, provide good agreement with the experimental data at energy E_c.m. = 21.8 MeV without need to renormalize the potentials. Coupledchannels calculations are used to extract the inelastic scattering cross section to the low-lying state 2+ (1.083 MeV) of ⁴⁴Ti. The deformation length is obtained and compared with the electromagnetic measurement values as well as those obtained from previous studies.