The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, 6 He+

We show that under certain conditions a simple relationship exists between the elastic scattering of a composite halo nucleus and of its core from a stable target. The coupling of the elastic and projectile excitation channels is crucial to the analysis, which is particularly useful when the ratio of the halo to the core mass is small. In the case of 11 Be elastic scattering the cross section relationship is quite well satisfied. For both 11 Be and 19 C our analysis reveals a significant sensitivity of elastic scattering data to the halo size and structure. [S0031-9007(97)03995-1] PACS numbers: 25.60. Bx, 25.70.Bc The existence of a class of light nuclei with a localized central core surrounded by a dilute "halo" of neutron matter is now well established. Evidence for these novel structures has been gained mainly from measurements of total neutron removal [1] and breakup reaction cross sections [2][3][4], particularly at high energy. We investigate to what extent complementary information can be gained from high quality elastic scattering measurements at lower energies.In this Letter we show that, in certain circumstances, the elastic scattering of a halo nucleus from a stable target can give simple direct evidence for the structure of the halo. The theory makes explicit use of the characteristics of halo nuclei, namely their very small neutron separation energy and the large spatial extension of the halo, which in turn result in strong coupling between the halo ground state and low energy excitations. This coupling of the elastic and projectile excitation channels plays a crucial role in the analysis, the results of which cannot be readily understood in terms of optical or folding model approaches. In elastic scattering, the analysis is expected to be particularly useful in systems where the ratio of the halo particle mass to the core mass is small.We consider the scattering of an assumed two-body projectile nucleus, composed of a core of mass m c and a valence particle of mass m y , by a third (target) nucleus of mass m T . It is assumed that these three bodies are spinless and structureless, although these are not essential assumptions. Two key conditions must be met, however, for the subsequent development to be a useful one:(i) The interaction between the core and target (V cT ) should be effectively much stronger than that between the valence and target particles (V yT ).(ii) The relative motion of the core and valence particles is slow compared to the relative motion of the center of mass of the projectile and target, and so can be treated adiabatically, in the spirit to the work of Johnson and Soper [5].Requirement (i) places limitations on the likely regions of applicability of our model. In strong interactiondominated processes, it is likely to be most valid when the number of nucleons in the core far exceeds that of the valence body. For 11 Be elastic scattering, where this ratio is 10:1, the assumption will be seen to be a good starting point for small scattering angles. Requirement (i) could also...

We have developed an approximate way of dealing with explicit energy dependence of nonlocal nucleon optical potentials as used to predict the (d,p) cross sections within the adiabatic theory. Within this approximation, the nonlocal optical potentials have to be evaluated at an energy shifted from half the incident deuteron energy by the n-p kinetic energy averaged over the range of the n-p interaction and then treated as an energy-independent nonlocal potential. Thus, the evaluation of the distorting potential in the incident channel is reduced to a problem solved in our previous work [N. K. 41 Ca reactions and highlighted the need for a detailed understanding of the energy dependence of nonlocal potentials. We have also suggested a simple way of correcting the d-A effective potentials for nonlocality when the underlying energy-dependent nonlocal nucleon potentials are unknown but energy-dependent local phenomenological nucleon potentials are available.

There is an increasing interest in studying transfer reactions to probe the nuclear structure of exotic nuclei.

We present an alternative theoretical formulation of the Coulomb dissociation process. We apply the formalism to the deuteron as an example of a weakly bound two-body composite nucleus with a charged core and a neutral valence particle and for which exclusive experimental data exist in an appropriate kinematical regime. The theoretical scheme assumes that the projectile excitation is predominantly to states with low internal energy and is expected to be applicable at incident projectile energies of tens of MeV per nucleon and above. A readily calculable expression for the quantum mechanical breakup transition amplitude is obtained without the use of the distorted-wave Born approximation weak channel coupling approximation or of additional approximations for finite-range effects. Calculations are presented, analyzed, and compared with high precision, kinematically complete, measurements of elastic deuteron dissociation into very forward scattering angles. The calculations and data support the importance of the Coulomb breakup mechanism under these kinematical conditions. ͓S0556-2813͑98͒00206-4͔ PACS number͑s͒: 24.10. Eq, 24.50.ϩg, 25.10.ϩs, 25.45.Ϫz

Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g., (d,p) reactions, should be used. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. While there exist several separable representations for the nucleon-nucleon interaction, the optical potential between a neutron (proton) and a nucleus is not readily available in separable form. The purpose of this paper is to introduce a separable representation for complex phenomenological optical potentials of Woods-Saxon type. Results: Starting from a global optical potential, a separable representation thereof is introduced based on the Ernst-Shakin-Thaler (EST) scheme. This scheme is generalized to non-Hermitian potentials. Applications to n + 48 Ca, n + 132 Sn, and n + 208 Pb are investigated for energies from 0 to 50 MeV and the quality of the representation is examined. Conclusions: We find a good description of the on-shell t matrix for all systems with rank up to 5. The required rank depends inversely on the angular momentum. The resulting separable interaction exhibits a different off-shell behavior compared to the original potential, reducing the high-momentum contributions.

This work addresses the question of precisely what features of few body models of halo nuclei are probed by elastic scattering on protons at high centre-of-mass energies. Our treatment is based on a multiple scattering expansion of the proton-projectile transition amplitude in a form which is well adapted to the weakly bound cluster picture of halo nuclei. In the specific case of 11 Li scattering from protons at 800 MeV/u we show that because core recoil effects are significant, scattering crosssections can not, in general, be deduced from knowledge of the total matter density alone.We advocate that the optical potential concept for the scattering of halo nuclei on protons should be avoided and that the multiple scattering series for the full transition amplitude should be used instead.

At medium energies the distorted-wave Born approximation provides a much less reliable description of transfer reactions induced by composite projectiles. shown to reduce the three-body transfer reaction calculation to a very small coupled-channels problem. For the reaction in question, the method introduces significant corrections to the adiabatic method which agree qualitatively with earlier calculations using the quasiadiabatic method. PACS number(s): 24.10. -i, 24. 10. Eq, 24.50. +g, 25.45.Hi