Pierre Capel

Influence of low-energy scattering on loosely bound states

Compact algebraic equations are derived that connect the binding energy and the asymptotic normalization constant (ANC) of a subthreshold bound state with the effective-range expansion of the corresponding partial wave. These relations are established for positively charged and neutral particles, using the analytic continuation of the scattering (S) matrix in the complex wave-number plane. Their accuracy is checked on simple local potential models for the {sup 16}O+n, {sup 16}O+p, and {sup 12}C+alpha nuclear systems, with exotic nuclei and nuclear astrophysics applications in mind.

Probing the weakly-bound neutron orbit of 31Ne with total reaction and one-neutron removal cross sections

A candidate of a neutron-halo nucleus, {sup 31}Ne, contains a single neutron in the pf shell. Within the Glauber and eikonal models, we analyze reactions used to study {sup 31}Ne. We show in a {sup 30}Ne+n model that the magnitudes of the total reaction and above all of the one-neutron removal cross sections of {sup 31}Ne on {sup 12}C and {sup 208}Pb targets strongly depend on the orbital angular momentum of the neutron, thereby providing us with efficient ways to determine both the spin-parity and structure of the ground state of {sup 31}Ne. Besides these inclusive observables, we also calculate energy and parallel-momentum distributions for the breakup of {sup 31}Ne and show their strong dependence on the orbital of the valence neutron in the bound state of {sup 31}Ne.

Comparing nonperturbative models of the breakup of neutron-halo nuclei

Breakup reactions of loosely bound nuclei are often used to extract structure and/or astrophysical information. Here we compare three nonperturbative reaction theories often used when analyzing breakup experiments, namely the continuum discretized coupled channel model, the time-dependent approach relying on a semiclassical approximation, and the dynamical eikonal approximation. Our test case consists of the breakup of {sup 15}C on Pb at 68 MeV/nucleon and 20 MeV/nucleon.

Coulomb-corrected eikonal description of the breakup of halo nuclei

The eikonal description of breakup reactions diverges because of the Coulomb interaction between the projectile and the target. This divergence is due to the adiabatic, or sudden, approximation usually made, which is incompatible with the infinite range of the Coulomb interaction. A correction for this divergence is analyzed by comparison with the dynamical eikonal approximation, which is derived without the adiabatic approximation. The correction consists in replacing the first-order term of the eikonal Coulomb phase by the first-order of the perturbation theory. This allows taking into account both nuclear and Coulomb interactions on the same footing within the computationally efficient eikonal model. Excellent results are found for the dissociation of

Analysis of Coulomb breakup experiments of 8B with a dynamical eikonal approximation

^{11}\mathrm{Be}

Peripherality of breakup reactions

on lead at 69 MeV/nucleon. This Coulomb-corrected eikonal approximation provides a competitive alternative to more elaborate reaction models for investigating breakup of three-body projectiles at intermediate and high energies.

Analysis of a low-energy correction to the eikonal approximation

Various measurements of the Coulomb breakup of {sup 8}B are analyzed within the dynamical eikonal approximation using a single description of {sup 8}B. We obtain a good agreement with experiment for different observables measured between 40 and 80 MeV/nucleon. A simple {sup 7}Be-p potential model description of {sup 8}B seems sufficient to describe all observables. In particular, the asymmetry in parallel-momentum distributions due to E1-E2 interferences is well reproduced without any scaling. The projectile-target nuclear interactions seem negligible if data are selected at forward angles. On the contrary, like in previous analyses we observe a significant influence of higher-order effects. The accuracy of astrophysical S factors for the {sup 7}Be(p,{gamma}){sup 8}B reaction at stellar energies extracted from breakup measurements therefore seems difficult to evaluate.

Influence of the projectile description on breakup calculations

The sensitivity of elastic breakup to the interior of the projectile wave function is analyzed. Breakup calculations of loosely bound nuclei (B8 and Be11) are performed with two different descriptions of the projectile. The descriptions differ strongly in the interior of the wave function, but exhibit identical asymptotic properties, namely the same asymptotic normalisation coefficient, and phase shifts. Breakup calculations are performed at intermediate energies (40-70 MeV/nucleon) on lead and carbon targets as well as at low energy (26 MeV) on a nickel target. No dependence on the projectile description is observed. This result confirms that breakup reactions are peripheral in the sense that they probe only the external part of the wave function. These measurements are thus not directly sensitive to the total normalization of the wave function, i.e., spectroscopic factor.

Supersymmetric elimination of forbidden states in the Coulomb breakup of the 11Be halo nucleus

Extensions of the eikonal approximation to low energy (20 MeV/nucleon typically) are studied. The relation between the dynamical eikonal approximation (DEA) and the continuum-discretized coupled-channels method with the eikonal approximation (E-CDCC) is discussed. When Coulomb interaction is artificially turned off, DEA and E-CDCC are shown to give the same breakup cross section, within 3% error, of C15 on Pb208 at 20 MeV/nucleon. When the Coulomb interaction is included, the difference is appreciable and none of these models agrees with full CDCC calculations. An empirical correction significantly reduces this difference. In addition, E-CDCC has a convergence problem. By including a quantum-mechanical correction to E-CDCC for lower partial waves between C15 and Pb208, this problem is resolved and the result perfectly reproduces full CDCC calculations at a lower computational cost.

Breakup Reaction Models for Two- and Three-Cluster Projectiles

Calculations of the breakup of {sup 8}B and {sup 11}Be are performed with the aim of analyzing their sensitivity to the projectile description. Several potentials adjusted on the same experimental data are used for each projectile. The results vary significantly with the potential choice, and this sensitivity differs from one projectile to the other. In the {sup 8}B case, the breakup cross section is approximately scaled by the asymptotic normalization coefficient (ANC) of the initial bound state. For {sup 11}Be, the overall normalization of the breakup cross section is no longer solely determined by the ANC. The partial waves describing the continuum are found to play a significant role in this variation, as the sensitivity of the phase shifts to the projectile description changes with the physical constraints imposed to the potential.