Elastic Scattering of Halo Nuclei

Abstract

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...

Four-body continuum-discretized coupled-channels calculations

“…For the reaction at 229.8 MeV we conclude that the effect of coupling to the continuum is a reduction of the cross section for angles beyond 5 • . This effect has also been observed in the scattering of 11 Be+ 12 C at E 49 MeV per nucleon [37], and is probably present in other reactions induced by weakly bound projectiles at energies of a few tens of MeV per nucleon. That the no-continuum coupling calculation reproduces the data reasonably well at the larger angles is probably fortuitous, and cannot be attributed to the adequacy of this approximation.…”

“…The theoretical understanding of reactions involving a three-body projectile, such as 6 He, is a complicated task because it requires the solution of a four-body scattering problem. At high energies, a variety of approximations have been used such as semiclassical approximations [34][35][36], frozen halo or adiabatic approximations [37,38], multiple scattering expansions [39][40][41], fourbody DWBA [42,43], among others. However, at energies of a few MeV per nucleon, some of these approximations are not justified.…”

Optical potentials of halo and weakly bound nuclei

“…There are in the literature a number of papers discussing the breakup potential for a 11 Li projectile, among others [22,15,18,19]. 11 Be breakup from the 2s has been discussed in [20,21]. However the potential due to breakup of the 1p 1/2 bound excited state has never been discussed before.…”

Current Status of Nuclear Physics Research

“…The adiabatic model, i.e., the neglect of the breakup Q-value, is generally used at higher energies, as done in [154], and [155]. In [154] the Glauber approximation while in [155] the usual adiabatic Schrdinger model are used for the radial wave function.…”

“…In [154] the Glauber approximation while in [155] the usual adiabatic Schrdinger model are used for the radial wave function. The result of the analysis of the total reaction cross section in [154] of 11 Li,11 Be, and 8 B and a 12 C target, demonstrated that the breakup channel coupling necessarily increases the reaction cross section and accordingly requires a larger rms radius of the halo nucleus, as seemed to be required by the data on the interaction cross section (the total reaction cross section without the projectile inelastic or breakup contributions) at the time, which were analyzed using the optical, eikonal, approximation [156,157].…”