Core excitation in ${}^{11}$Be_gs via the p(${}^{11}$Be,${}^{10}$Be)d reaction

Abstract

The p(${}^{11}$Be,${}^{10}$Be)d reaction has been studied using a radioactive ${}^{11}$Be beam of 35.3 MeV/nucleon. Differential cross sections have been compared with Distorted Wave Born Approximation calculations, using bound state form factors determined by solving the particle-vibration coupling equations. Calculated cross sections corresponding to a 16% core excitation admixture in the ${}^{11}$Be_gs wave function are in good agreement with the present data.

Introduction

Much effort has been devoted to the understanding of the light neutron-rich ${}^{11}$Be nucleus, since the observation of a parity inversion between its ground state (J^π=1/2⁺) and its first excited state at 0.32 MeV (J^π=1/2⁻) several decades ago. This interest in ${}^{11}$Be was further enhanced following experimental evidence for a neutron “halo” around the ${}^{10}$Be core 1, 2. Various theoretical calculations 3, 4, 5, 6, 7, 8, 9, 10, 11, 12have attempted to reproduce the level sequence in this benchmark halo nucleus. Most models emphasize the role of coupling between the valence neutron and the first excited 2⁺ state at 3.34 MeV in ${}^{10}$Be core in generating the parity inversion, but they predict very different core excitation admixtures in the ${}^{11}$Be_gs wave function, varying from 7% 6, 10to 75% [3]. In this context, it is important to get experimental information on the relative weights of its [0⁺⊗2s] and [2⁺⊗1d] components, which may be provided by measuring the cross sections of one-neutron pick-up reactions feeding the 0⁺_gs and 2⁺₁ states in ${}^{10}$Be.

This letter reports a study of the structure of ${}^{11}$Be_gs by means of the (p,d) reaction in inverse kinematics. This experiment may be considered as a testing ground for future investigations of exotic nuclei via transfer reactions induced by radioactive beams. Preliminary data have been reported in Refs. 13, 14, together with the first results of a standard DWBA analysis, which used single-particle form factors evaluated according to the usual Separation Energy (SE) prescription. Spectroscopic factors deduced from this preliminary analysis indicate a very large [2⁺⊗1d] admixture in the ${}^{11}$Be_gs wave function, exceeding most theoretical predictions [14]. However, such a comparison between experiment and structure calculation via spectroscopic factors assumes that the radial wave function u_ℓj(r) may be approximated by the product of the single-particle form factor times a spectroscopic amplitude. This assumption is in fact questionable, considering the large deformation parameter of the final nucleus ${}^{10}$Be (β₂=0.74 [15]), which could induce important coupling effects. Under such conditions, correct form factors should be taken as solutions of coupled equations [16]. The present (p,d) transfer reaction data are compared with the results of DWBA calculations, using bound state form factors evaluated in the framework of the particle-vibration coupling model [17], in order to assess the magnitude of this effect.