Borromean Feshbach resonance in $^{11}$Li studied via $^{11}$Li($p$,$p'$)

Abstract

A dipole resonance of $^{11}$Li is found by a $^9$Li + $n$ + $n$ three-body model analysis with the complex-scaling method. The resonance can be interpreted as a bound state in the $^{10}$Li + $n$ system, i.e., a Feshbach resonance in the $^9$Li + $n$ + $n$ system. As a characteristic feature of the Feshbach resonance of $^{11}$Li, the $^{10}$Li + $n$ threshold is open above the $^{9}$Li + $n$ + $n$ one, which reflects a distinctive property of the Borromean system. A microscopic four-body reaction calculation for the $^{11}$Li($p$,$p'$) reaction at 6 MeV/nucleon is performed by taking into account the resonant and nonresonant continuum states of the three-body system. The calculation of angular distributions of the elastic and inelastic scattering as well as the energy spectrum reproduced a recent experimental result. Furthermore, the $E1$ strength distribution from a Coulomb dissociation experiment was also reproduced in this framework. This means that the existence of the Borromean Feshbach resonance may consistently answer a long-standing open question of an excited state of $^{11}$Li.

Low-energy 11Li + p and 11Li + d scattering in a multicluster model

“…More recently, it was extended to three-body projectiles [7], and even to two-body projectile and target [8]. The present works addresses the 11 Li + p and 11 Li + d reactions, which have been experimentally investigated recently [9,10]. One of the main conclusions drawn in Refs.…”

“…This effect was first shown in d+ nucleus data, owing to the low binding energy of the deuteron [4]. The CDCC formalism was then successfully applied to reactions involving weakly bound nuclei such as 11 Be [6] or 6 He [7].…”

“…One of the main conclusions drawn in Refs. [9,10] is the presence of a dipole resonance in 11 Li. The authors measured the elastic cross section, * pdesc@ulb.ac.be together with an inelastic cross section to a broad 1 − resonance of 11 Li.…”

“…The main goal of the present work is to analyze both systems in a common framework, i.e. with the same 11 Li wave functions, and with the same 9 Li+nucleon interaction. For this purpose, I use a three-body 9 Li + n + n model to describe 11 Li, and apply the CDCC theory for the scattering cross sections.…”

“…I obtain a fair agreement with experiment, and show that breakup effects are maximal at large angles. The breakup cross section is shown to be dominated by the 1 − dipole state in 11 Li, but the role of this resonance is minor in elastic scattering. From CDCC equivalent 11 Li + p and 11 Li + n potentials, I explore the 11 Li + d cross section within a standard three-body 11 Li + (p + n) model.…”