Microscopic three-cluster study of light exotic nuclei

I develop a microscopic three-cluster model for exotic light nuclei. I use the hyperspherical formalism, associated with the Generator Coordinate Method. This model is well adapted to halo nuclei, since the long-range part of the radial wave functions is accurately reproduced. The core wave functions are described in the shell model, including excited states. This technique provides large bases, expressed in terms of projected Slater determinants. Matrix elements involve seven-dimension integrals, and therefore require long calculation times. I apply the model to 11Li, 14Be, 15B, and 17N described by two neutrons surrounding a 9Li, 12Be, 13B and 15N core, respectively. The 17Ne (as 15O+p+p) and 15Ne (as 13O+p+p) mirror nuclei are briefly discussed. I present the spectra and some spectroscopic properties, such as r.m.s. radii or E2 transition probabilities. I also analyze the importance of core excitations.Comment: Accepted for publication in Phys. Rev.

Low-energy 6^{6}He scattering in a microscopic model

A microscopic version of the Continuum Discretized Coupled Channel (CDCC) method is used to investigate $^{6}$He scattering on $^{27}$Al, $^{58}$Ni, $^{120}$Sn, and $^{208}$Pb at energies around the Coulomb barrier. The $^{6}$He nucleus is described by an antisymmetric 6-nucleon wave function, defined in the Resonating Group Method. The $^{6}$He continuum is simulated by square-integrable positive-energy states. The model is based only on well known nucleon-target potentials, and is therefore does not depend on any adjustable parameter. I show that experimental elastic cross sections are fairly well reproduced. The calculation suggests that breakup effects increase for high target masses. For a light system such as $^{6}$He+$^{27}$Al, breakup effects are small, and a single-channel approximation provides fair results. This property is explained by a very simple model, based on the sharp-cut-off approximation for the scattering matrix. I also investigate the $^{6}$He-target optical potentials, which confirm that breakup channels are more and more important when the mass increases. At large distances, polarization effects increase the Coulomb barrier, and provide a long-tail absorption component in the imaginary part of the nucleus-nucleus interaction.Comment: 11 pages, 11 figures, accepted at Phys. Rev.

An R-matrix package for coupled-channel problems in nuclear physics

We present an $R$-matrix Fortran package to solve coupled-channel problems in nuclear physics. The basis functions are chosen as Lagrange functions, which permits simple calculations of the matrix elements. The main input are the coupling potentials at some nucleus-nucleus distances, specified by the program. The program provides the collision matrix and, optionally, the associated wave function. The present method deals with open and closed channels simultaneously, without numerical instability associated with closed channels. It can also solve coupled-channel problems for non-local potentials. Long-range potentials can be treated with propagation techniques, which significantly speed up the calculations. We first present an overview of the $R$-matrix theory, and of the Lagrange-mesh method. A description of the package and its installation on a UNIX machine is then provided. Finally, five typical examples are discussed.Comment: 28 pages, 6 figures, accepted for publication at Computer Physics Communication

Four-body continuum effects in 11Be+d scattering

We present a new reaction model, which permits the description of reactions where both colliding nuclei present a low threshold to breakup. The method corresponds to a four-body extension of the Continuum Discretized Coupled Channel (CDCC) model. We first discuss the theoretical formalism, and then apply the method to 11Be+d scattering at Ecm = 45.5 MeV. The 11Be nucleus and the deuteron are described by 10Be+n and p + n structures, respectively. The model involves very large bases, but we show that an accurate description of elastic-scattering data may be achieved only when continuum states of 11Be and of the deuteron are introduced simultaneously. We also discuss breakup calculations, and show that the cross section is larger for 11Be than for the deuteron. The present theory provides reliable wave functions that may be used in the analysis of (d,p) or (d,n) experiments involving radioactive beams.Comment: 5 pages, 4 figures, accepted for publication at Physics Letters

9Be scattering with microscopic wave functions and the CDCC method

We use microscopic 9Be wave functions defined in a alpha+alpha+n multicluster model to compute 9Be+target scattering cross sections. The parameter sets describing 9Be are generated in the spirit of the Stochastic Variational Method (SVM), and the optimal solution is obtained by superposing Slater determinants and by diagonalizing the Hamiltonian. The 9Be three-body continuum is approximated by square-integral wave functions. The 9Be microscopic wave functions are then used in a Continuum Discretized Coupled Channel (CDCC) calculation of 9Be+208Pb and of 9Be+27Al elastic scattering. Without any parameter fitting, we obtain a fair agreement with experiment. For a heavy target, the influence of 9Be breakup is important, while it is weaker for light targets. This result confirms previous non-microscopic CDCC calculations. One of the main advantages of the microscopic CDCC is that it is based on nucleon-target interactions only; there is no adjustable parameter. The present work represents a first step towards more ambitious calculations involving heavier Be isotopes.Comment: Phys. Rev. C in pres

The R-matrix theory

The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering properties from the Schr\"odinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the $R$-matrix formalism is applied to transfer and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.Comment: 93 pages, 26 figures. Rep. Prog. Phys., in pres

Microscopic description of 7^7Li in the 7Li+12C^{7}\text{Li}+^{12}\text{C} and 7Li+28Si^7\text{Li}+^{28}\text{Si} elastic scattering at high energies

We employ a microscopic continuum-discretized coupled-channels reaction framework (MCDCC) to study the elastic angular distribution of the $^7$Li$=\alpha+t$ nucleus colliding with $^{12}$C and $^{28}$Si targets at $E_{\text{Lab}}$=350 MeV. In this framework, the $^7$Li projectile is described in a microscopic cluster model and impinges on non-composite targets. The diagonal and coupling potentials are constructed from nucleon-target interactions and $^7$Li microscopic wave functions. We obtain a fair description of the experimental data, in the whole angular range studied, when continuum channels are included. The inelastic and breakup angular distributions on the lightest target are also investigated. In addition, we compute $^{7}$Li$+^{12}$C MCDCC elastic cross sections at energies much higher than the Coulomb barrier and we use them as reference calculations to test the validity of multichannel eikonal cross sections.Comment: 9 Pages, 6 Figure

Coulomb breakup of 22C in a four-body model

Breakup cross sections are determined for the Borromean nucleus 22C by using a four-body eikonal model, including Coulomb corrections. Bound and continuum states are constructed within a 20C + n + n three-body model in hyperspherical coordinates. We compute continuum states with the correct asymptotic behavior through the R-matrix method. For the n+ n potential, we use the Minnesota interaction. As there is no precise experimental information on 21C, we define different parameter sets for the 20C + n potentials. These parameter sets provide different scattering lengths, and resonance energies of an expected 3/2+ excited state. Then we analyze the 22C ground-state energy and rms radius, as well as E1 strength distributions and breakup cross sections. The E1 strength distribution presents an enhancement at low energies. Its amplitude is associated with the low binding energy, rather than with a three-body resonance. We show that the shape of the cross section at low energies is sensitive to the ground-state properties. In addition, we suggest the existence of a low-energy 2+ resonance, which should be observable in breakup experiments