Elsevier

Physics Letters B

Volume 499, Issues 1–2, 1 February 2001, Pages 109-115
Physics Letters B

Momentum distributions and reaction mechanisms for breakup of two-neutron halos

https://doi.org/10.1016/S0370-2693(00)01384-8Get rights and content

Abstract

A theoretical model able to describe fragmentation reactions of three-body halo nuclei on different targets, from light to heavy, is used to compute neutron and core momentum distributions. Both Coulomb and nuclear interactions are simultaneously included. We specify the different reaction mechanisms related to various processes. The method is applied to fragmentation of 6He and 11Li on C and Pb. We find good agreement with the available experimental results.

Introduction

Fragmentation reactions are one of the most powerful tools to investigate halo nuclei [1], [2], [3], [4]. Not only the large interaction cross sections, but also the narrow momentum distributions of the fragments, are clear evidence of the unusual large spatial extension of such nuclei [5], [6], [7], [8]. Their main properties are successfully described by few-body models, where the halo nucleus is viewed as an inert core surrounded by a few weakly bound nucleons [9], [10]. Models for one-neutron halo breakup reactions and the corresponding momentum distributions have been discussed [11], [12], but two-neutron halos clearly require different methods. Several were developed in order to understand the available experimental cross sections and momentum distributions [5], [6], [7], [8]. These theoretical investigations fall in two independent groups. One discusses nuclear breakup reactions and applies, therefore, only to light targets [10], [13] whereas the other focuses on heavy targets and considers only Coulomb dissociation [14], [15], [16], [17]. At best Coulomb and nuclear breakup are computed in independent models and the cross sections subsequently simply added [18], [19].

A consistent model describing two-neutron halo fragmentation on any target, from very light to very heavy, with simultaneous treatment of nuclear and Coulomb interactions was recently presented [20], [21]. Absolute values are computed of all possible dissociation cross sections distinguished according to the particles left in the final state. The two-neutron removal cross sections, core breakup cross sections and interaction cross sections for different targets are in good agreement with the measurements for energies above 100 MeV/nucleon. This is the only model for breakup of two-neutron halos which uses the same two-body interactions in initial and final states, is applicable for light, intermediate and heavy targets, and provides all possible three-body observables. Even absolute cross sections are calculated successfully [20], [21] considering the difficulties related to the intrinsic structures of core and target. The precision in relative quantities like momentum distributions is much higher.

The breakup reaction mechanism is inevitably different for light and heavy targets and it is therefore surprising that the momentum distributions are rather similar [6]. To understand this almost forgotten problem requires simultaneous inclusion of both Coulomb and nuclear interactions which in itself is a problem of general interest. Differential cross sections, i.e., momentum distributions of the fragments, must be computed. The purpose of this letter is then to extract the reaction mechanism in two-neutron halo breakup processes by providing evidence from model computations. The calculated momentum distributions are especially well suited as test observables as they depend sensitively on reaction assumptions.

The predictions vary substantially from the present participant-spectator model to different models where the reaction proceeds through intermediate two or three-body resonances or continuum states. The invariant neutron–neutron mass spectra after breakup of  6He and 11Li exemplify the large differences between reaction assumptions. Decay through two-body resonances clearly produce the same spectra for both halo nuclei in contrast to our model where the final state wave packet strongly depends on the initial halo wave function [22]. We do not use three-body continuum wave functions as in [17]. We apply in this letter the one-participant model using optical potentials for one halo particle-target interaction while the other interactions are treated by the black disk model.

Section snippets

The model

The breakup reaction is described as a superposition of three independent reactions, each corresponding to the interaction with the target of one of the three constituents in the halo projectile. Thus, in each of these three reactions only one of the constituents (participant) interacts with the target, while the other two are mere spectators. In the center of mass frame of the halo nucleus we obtain for a spinless target that the differential cross sections for absorption and elastic

Reaction geometries

The finite extension of the projectile constituents and the target is partially destroying the simple picture described above. Simultaneous collisions with the target of more than one constituent have to be considered. In Fig. 1 we sketch the geometries needed to describe the reaction. The short-range target–halo interactions only act for the constituents inside the cylinder along the beam axis around the target (Figs. 1(a), (b) and (c)).

When the core is inside the cylinder the core–target

Numerical examples

We apply the method to fragmentation reactions of 6He and 11Li on carbon and lead, for which experimental neutron and core momentum distributions are available. The wave functions of the three-body halo projectiles are obtained by solving the Faddeev equations in coordinate space using the neutron–neutron and neutron–core interactions specified in [10], [17]. The optical potentials for the neutron–target, α–target and 9Li–target interactions are from [24], [25], where range and diffuseness

Summary and conclusions

Fragmentation reactions of two-neutron halo nuclei are described as superposition of all possible reactions where one, two or three halo constituents interact with the target. Nuclear and Coulomb interactions are simultaneously considered allowing light and heavy targets. The two-neutron removal and core breakup cross sections can be described through processes where only one of the halo constituents interact with the target. The appropriate interactions are described by an optical potential

Acknowledgements

We thank K. Riisager for continuous discussions and suggestions.

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