HREPHAH 0H3HKA, 2004, moM 67, № 10, c. 1877-1884
_ Proceedings of the International Conference _
"Nuclear Structure and Related Topics"
BREAKUP REACTIONS OF HALO NUCLEI
© 2004 S. N. Ershov*
Bogoliubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research, Dubna, Russia
Received January 21, 2004
Different reaction mechanisms of breakup reactions are discussed and the microscopic reaction model for two-neutron halo dissociation is presented. Some examples of halo breakup in reactions with electrons, nucleons, and nuclei are given.
1. INTRODUCTION
In recent years the significant progress was achieved in investigations of the radioactive ion beam physics. Many new and exciting issues were explored: exact locations of the neutron and proton driplines, productions of the heaviest bound nuclei, evolution of shell structure (vanishing of magic numbers, new magic numbers), resonances beyond driplines — just to name few of them. In particular, the discovery of neutron halo has been made [1]. Halo is a new type of structure which appears in weakly bound nuclei at the limits of stability. It can be characterized by clustering into an ordinary core nucleus and veil of halo neutrons forming dilute neutron matter. One-neutron halo nuclei (nBe, 14B, 19C, ...) break into two fragments and their locations on nuclear map are shifted on a few neutrons to stability region away from a limit of nuclear existence. Two-neutron halo nuclei (6He, 11 Li, 14Be, 17B, ...) break into three fragments and appear at the very end of nuclear stability. Thus, one-neutron halo gradually transforms to two-neutron halo in process of the nuclear structure evolution on the way to the edges of the nuclear landscape. Also all two-neutron halo nuclei have the "Borromean" properties [2]. This means that any pair of fragments (two neutrons, neutron and core) can not create a bound system while the bound state of three fragments exists. Therefore, three-body correlations are the most important for two-neutron halo since their existence itself as a bound system is due to such correlations. In general, two-neutron halo structure is a typical dripline phenomenon in light nuclei.
Breakup reactions with fast beams of exotic nuclei are a powerful tool for investigations of halo nuclei (see the recent review [3] and references therein). In particular, measurements of fragments in coincidence are providing basic information about the structure of a number of neutron-rich nuclei. We present a
E-mail: ershov@thsun1.jinr.ru
reaction model which allows calculations of a variety of observables in fragmentation processes leading to the low-energy excitations of two-neutron halo nuclei. Some calculations of halo breakup in collisions with different probes are given. We start with electron scattering when reaction mechanism is the most simple and transparent and continue the discussion of more complicated reaction mechanisms going from fragmentation on nucleons to nuclei.
2. BASIC STRUCTURE OF HALO NUCLEI
Halo nuclei, in most cases, have only one bound state (the ground state), in which the valence nucleons are in low relative angular-momentum states with respect to the rest of the nucleons that make the more bound core. Due to the very weak binding of the last neutrons, the wave function describing their relative motion has a spatial distribution that extends far beyond the range of binding potential. In addition to the specific structure of the bound state, halo nuclei have peculiarities in the low-energy continuum: concentration of a transition strength near the breakup threshold. This follows from experimental cross sections on electromagnetic dissociation what are larger by two orders of magnitude for halo nuclei [4]. Since we understand the reaction mechanism of electromagnetic dissociation, at least qualitatively, the only possibility to describe such huge enhancement is an accumulation of transition strength near the breakup threshold. It is interesting to compare a magnitude of this effect with other indications of halo structure. The interaction cross sections of halo nuclei are larger by tens per cent [5]. The width of fragment momentum distributions is a few times narrower than for stable nuclei [6]. However, for electromagnetic dissociation a difference with stable nuclei increases up to two orders of magnitude. It means that nuclear processes and observables, where a transition from the ground state to the low-energy continuum plays a dominant
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role, are the most sensitive to the presence of halo structure.
Basic dynamics of halo nuclei can be characterized as a coexistence of two subsystems: one which consists of core nucleons and other of halo neutrons moving around the core center of mass. Some arguments support such decoupling of core and halo degrees of freedom. Fact, that a weakly bound system breaks into fragments, evidences that the fragment components must dominate in the ground state wave function. The interaction cross section of high-energy halo nuclei on light targets, which is approximately equal to the sum of interaction cross section of core nucleus and two-neutron removal cross section [5], indicates that the reaction process is going separately on the core and halo subsystems. The large changes in the total cross sections are accompanied by essentially constant charge-changing cross sections [7]. The core and halo nucleus both have similar magnetic dipole and quadrupole moments. These arguments support the assumption that the core is not significantly perturbed by the valence neutrons located far away from it. It means that with good accuracy the wave function of halo nucleus can be written as a product of two functions:
= \^core)\^halo)-
One, |^>core), describes the internal structure of the core and the other, \^haio), describes the relative motion of halo neutrons around the core center of mass. Such factorization is a starting point for application of three-body models to description of the halo structure [2, 8—10]. Few-body models avoid the complicated and still open questions on developing of nuclear clustering and concentrate attention on the halo wave function \^halo). Within such models it is possible to give a consistent description of main properties both the ground state and the low-energy continuum wave functions. Few-body models of halo structure will be used in our analysis of breakup reactions below. The bound and continuum three-body wave functions are calculated by the method of
where is the full scattering solution with ingoing wave boundary condition, and $A are ground state wave functions of the halo and the target, respectively. The distorted wave x(+) describing the relative motion of nuclei in the initial channel is a solution of the Schrodinger equation with optical potential UaA. Vpt is NN interaction between the projectile and
hyperspherical harmonics and detailed description of the applied formalism can be found in [9].
3. BREAKUP REACTIONS OF HALO NUCLEI 3.1. Breakup Reaction Mechanism
Fragmentation reactions have complicated dynamics, where nuclear structure and reaction mechanism are tightly intertwined. The focus of current discussion is on investigations of halo structure in breakup reactions. Hence, the processes that are the most sensitive to halo are singled out from variety of breakup phenomena. It means, our discussion is confined by dissociation reactions with undestroyed core and the low-energy halo excitations. Thus, only peripheral reactions are considered since in the central collisions a core can be destroyed with a big probability. Two breakup scenarios are possible at such conditions. The first is the elastic fragmentation if a target is left in the ground state after collision with halo nucleus. The second is the inelastic breakup if target is excited. The cross section of the breakup reaction a + A ^ 1 + 2 + C + A*, involving collision of projectile a (two-neutron halo nucleus that breaks up into three fragments 1, 2, and C) with target A, is given by
(2n)4 r
<t = ———^ / dkidk2dkcdka* x (1)
HVi a J
x 6(Ei - Ef )S(Pi - Pf) \Tfi\2,
where Vi is the relative velocity of colliding systems in the initial channel, k1)2)c are the wave numbers of neutrons and core, k^» is the target wave number in the final channel. The sum on a is done on all quantum numbers that are necessary to characterize reaction and includes, if particles have spin, the averaging on initial spin projections and sum on final spin projections. The 5 functions ensure the conservation of energy and momentum. The exact transition matrix Tfi in the prior form can be written as
(2)
target nucleons. Due to the translational invariance only relative wave numbers can characterize reaction dynamics. kx, ky, and kj j are relative wave numbers between a pair of fragments, between the center of mass of a pair and the third fragment, and between the center of masses of halo and target nuclei in the initial and final channels, respectively. In the halo rest frame hky corresponds to the momentum of the third
Tfl = U'-Xkx, ky, kf) £
p,t
Vpt — UaA
(ki)
fragment. We know the translational invariance or the recoil effects are very important in light nuclei. In halo nuclei a correct treatment of the translational invariance is even more significant due to larger spatial extension of these systems. The exact T matrix (2) can not be calculated without approximations. Our main goal is a study of halo structure, therefore the reactions will be considered at conditions which allow the simplified treatment of the reaction mechanisms making them both tractable and transparent. Hence, we study the collisions at high enough energy (large momentum hk^ when one-step processes dominate. The excitation energy of halo nucleus1),
Ex =
hy kX
+
h ky
where fix,y are reduced masses, can be used for further classification of reaction mechanisms. The reason is that for large relative momentum h
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