Microscopic calculation of the coupling between relative motion and quadrupole deformation in heavy-ion collisions

Using a microscopic formalism and taking fully nto account the Pauli principle, we compute the interaction potential between two ⁴⁰Ca nuclei as a function of their interdistance and their deformation. We attempt an analysis of our results within the proximity formalism and we point out some difficulties. We also extract the coupling parameter between the radial motion of the ions and the excitations of their giant quadrupole modes.     

A test of the fish bone optical model onα-16O scattering

The recently proposed fish bone optical model is tested on0α-¹⁶ O scattering. Using a microscopic interaction similar to that of resonating group calculations the characteristic rotational bands in²⁰Ne as well as the gross structure of the elastic differential cross section are reproduced. It is shown that the fish bone optical model can be extended by inclusion of a phenomenological imaginary part. A numerical comparison with the corresponding double folding model and with the Saito model confirms the theoretical prediction that the fish bone optical model is a further step towards inclusion of the effect of the Pauli principle in the optical model.     

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.     

Shallow folding potential for O + C elastic scattering

The ¹⁶O + ¹²C elastic scattering data have been well described, for the first time, with a shallow folded potential obtained from a single folding method. The constituent parameters of the potential, excepting one, for its real part are generated from the nucleon–¹⁶O and α–¹⁶O potentials, and the cluster structure of ¹²C. Only the repulsive part of the α–¹⁶O potential needs some adjustment to fit the data, reflecting the need to include the Pauli exclusion effects among the unclustered nucleons.     

Exchange interaction and elastic 16O + 12C scattering

The effect of core exchange on the potential of interaction between the ¹⁶O and ¹²C nuclei is considered. The amplitudes corresponding to nonlocal exchange interactions are calculated in the Born approximation. It is shown that the inclusion of exchange processes leads to the growth of the elasticscattering amplitude in in the region of large scattering angles. The dependence of amplitudes on the parity of relative motion is analyzed.     

Multichannel neutron scattering on <Superscript>11</Superscript>Be nucleus

The effect of the Pauli exclusion principle on the relative motion of colliding light neutron-rich nuclei is investigated within a microscopic method for the examples of the ¹¹Be + n and ¹⁰Be + ² n reactions. The effective interaction of nuclei that is due to the change in the kinetic energy of their relative motion under the effect of the antisymmetrization operator is analyzed on the basis of a discrete representation of harmonic-oscillator states allowed by the Pauli exclusion principle. It is concluded that the bound state of the ¹²Be nucleus owes its origin to the impact of exchange effects on the operator of the kinetic energy of the relative motion of the neutron and the ¹¹Be nucleus. The structure of the ¹²Be ground state is discussed in the approximation of two coupled cluster configurations. The cross section for the inelastic-scattering reaction ¹¹Be(n, ² n)¹⁰Be is estimated.     

Analysis of deep inelastic collisions between16O and27Al

Deep inelastic collisions in light systems formed with¹²C,¹⁴N and¹⁶O projectiles and different target nuclei have been studied at incident energies between 5 and 7 MeV/u. A detailed analysis is presented for the results of the¹⁶O+²⁷Al reaction at 80.6 MeV incident energy which is based on trajectory calculations and the transport theory. The questions of angular distributions and the interaction time, the energy dissipation and the fragment deformation as well as the element-distribution and the effect of the nuclear structure are discussed.     

Variational definition of the single-particle potential in the Brueckner-Hartree-Fock approach

The consequences of the variational definition of the self-consistent potential in Brueckner-Hartree-Fock theory are explored to higher orders even summing up some classes of diagrams to infinity. The consistency of this definition with a diagrammatic expansion are checked. Overcounting terms in the variational approach are pointed out and their numerical influence on the ground state properties of nuclei is checked at the example of¹⁶O. Ambiguities of the potential defined by the variational procedure stemming from the property of the Pauli-operatorQ ² =Q are studied diagrammatically and numerically. The application to¹⁶O shows that the influence of the Pauli rearrangement term is partially cancelled by the higher order starting energy rearrangement terms discussed in this work.     

IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.     

Hyperfine interactions of 19O in TiO2 and quadrupole moments of 13,19O

The electric quadrupole interaction of ¹⁹O(I^π=(5/2)⁺, T_1/2=27.0 s) in TiO₂ single crystal was studied in detail by means of the β-NQR to determine the electric quadrupole moments Q of short-lived β-emitting nuclei ¹⁹O and ¹³O(I^π=(3/2)^-, T_1/2=8.6 ms). Two implantation sites were found for the implanted O nucleus and the quadrupole coupling constants of ¹⁹O at these sites were determined. We observed FT-NMR of the enriched stable isotope ¹⁷O in TiO₂ and obtained the electric field gradient (EFG) at the oxygen substitutional site. With this knowledge, we have determined Q(¹³O)=11.0 ± 1.3 mb and Q(¹⁹O)=3.7 ± 0.4 mb. The present results are compared with the theoretical values calculated by the shell model code, OXBASH and by the Hartree–Fock calculation with the realistic potential. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multichannel nuclear reactions involving light neutron-rich nuclei: Microscopic approach

The influence of the Pauli exclusion principle on the relative motion of light neutron-rich nuclei in their collision is investigated within the microscopicmethod using as an example ¹¹Be + n and ¹⁰Be + ² n nuclear reactions, as well as ³ n + n and ² n + ² n reactions. Antisymmetrization effects related to the kinetic and potential energy of the relative motion of colliding nuclei are analyzed. The influence of the Pauli exclusion principle on the kinetic energy of the relative motion of the ¹¹Be nucleus and a neutron is shown to result in their attraction. The same phenomenon is observed for the case of the ³ n + n cluster system. The strength of such attraction is high enough to ensure the existence of a bound state in the ¹²Be nucleus and a low-energy resonance in the tetraneutron. The conclusion is drawn that, for a resonance state in the ⁴ n system to exist, the value of the oscillator length must be large enough. It is shown also that increasing the oscillator length results in depression of the cluster-cluster potential. The text was submitted by the authors in English.     

Elastic deuteron scattering on 12C and 16O nuclei in the alpha-cluster model

On the basis of the dispersive alpha-cluster model for target nuclei and the theory of multiple diffractive scattering, differential cross sections and analyzing powers for the elastic scattering of 400 and 700-MeV deuterons on ¹²C and ¹⁶O target nuclei were calculated in the pointlike-deuteron approximation. In these calculations, the amplitude for incident-deuteron scattering on nuclei was constructed with the aid of amplitudes for dα scattering that were obtained from a fit to data on d ¹⁶O scattering. The same features were calculated on the basis of the diffraction approximation with allowance for the internal deuteron structure by using the amplitudes obtained earlier for nucleon scattering on ¹²C and ¹⁶O nuclei within the same dispersive alpha-clustermodel. The latter made it possible to perform calculations without employing adjustable parameters. The observables calculated on the basis of either approach agree with available experimental data.     

Possible mechanisms of fragmentation of 16O nuclei with a momentum of 4.5 GeV/c per nucleon in track emulsions

The angular distributions of doubly charged fragments of ¹⁶O nuclei having a momentum of 4.5 GeV/c per nucleon and interacting with track-emulsion nuclei were studied. The experimental angular distributions of doubly charged fragments of a ¹⁶O nucleus are not described by the statistical model of the fragmentation of nuclei. The possible channels of fragmentation of ¹⁶O nuclei may include ¹⁶O → 2⁸Be → 4α, ¹⁶O → ⁸Be +⁸ Be* → 4α, ¹⁶O → 2⁸Be* → 4α, ¹⁶O → α+¹²C, ¹⁶O → α +¹²C* → α + 3α, ¹⁶O → α +¹²C* → α + pα ⁷Li, ¹⁶O → α +¹²C* → α + 2⁶Li, ¹⁶O → α +¹²C* → α + pt2α, ¹⁶O → Li + B, and ¹⁶O → Li* + B*.     

Effect of the Pauli principle on collective states in transitional Xe,Ba and Ce nuclei

It is shown how the modified harmonic method can be used to correct the quadrupole operator of the interacting boson model for the effect of the Pauli principle on states with several d-bosons. This gives a possible explanation for the observed strange reduction of ground-state band B(E2) values in the xenon-barium region.     

Comparison of the fusion reactions12C+20Ne and16O+16O near the Coulomb barrier

The partial cross sections of heavy residual nuclei produced in the heavy ion fusion of¹²C+²⁰Ne have been measured atE _c.m.=6–15 MeV viaγ-ray spectroscopy with a Ge(Li) detector. Windowless and recirculating gas target systems have been used. The dominant residual nuclei are²⁴Mg,²⁷Al,²⁸Si,³⁰Si,³⁰P and³¹P, which arise from two- and three-body breakups in the exit channels. The observed excitation functions are smooth in their energy dependence and give no indications for the existence of pronounced resonance structures, in contrast to theoretical predictions. The Coulomb excitation of²⁰Ne served as an intrinsic calibration standard in the determination of absolute partial and total fusion cross sections. The same experimental set-up was also used in the reaction studies of¹⁶O+¹⁶O atE _c.m.=7–14 MeV, going through the same compound nucleus³²S at similar excitation energies. The observed energy dependence in the excitation functions is in good agreement with previous work. The total fusion cross section agrees fairly well with two sets of values reported previously, but deviates significantly from other reported absolute cross section values. The relative evaporation distributions of the residual nuclei are similar for both heavy ion reactions. However, the ratio of their total fusion cross sections deviates from model predictions and suggests that compound nucleus formation does depend on the microscopic structure of the colliding nuclei in the entrance channel. From the observed energy dependence of the above ratio, particularly at subcoulomb energies, geometrical effects in the entrance channel (due to deformed and spherical nuclei) appear to be weak. The astrophysical aspects of the data in the context of late stellar nucleosynthesis are discussed.     

The 5v 3 bands of 18O enriched ozone: line positions of 16O16O18O, 16O18O16O, 16O18O18O and 18O16O18O

The four 5v ₃ bands of ¹⁸O enriched ozone have been observed and analysed for the first time. Two species (¹⁶O¹⁸O¹⁶O and ¹⁸O¹⁶O¹⁸O) belong to the C_2v symmetry group and two other (¹⁸O¹⁸O¹⁶O and ¹⁶O¹⁶O¹⁸O) to the C_s symmetry group. They have been recorded at a resolution of 0.008 cm^?1 with a pathlength of 32.16 m. Despite the very weak absorptions observed, almost 250 energy levels have been derived for each of the 4 species, with J ? 35 and K _a ? 13, and suitable sets of Hamiltonian parameters have been determined. For 3 species it has been necessary to account for the resonance between the (005) and (311) states to correctly reproduce the spectra observed. These resonances, anharmonic for C_2v, and hybrid (both anhar-monic and Coriolis) for C_s symmetry confirm the accidentally extremely strong coupling between the (005) and (311) states for ¹⁶O₃, due in that case to the very close distance between unperturbed energy levels. This work also confirms the excellent prediction of band centres of these four species derived from the recently determined isotopically invariant molecular potential function.     

Density expansion of the energy of N close-to-boson excitons

Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na _x ³/)ⁿ with n ≥ 2. An exact procedure to get these density dependent terms is given. Received 11 February 2002 / Received in final form 30 May 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr