Effects of four-body breakup on6Li elastic scattering near the Coulomb barrier

Abstract

We investigate projectile breakup effects on 6 Li+ 209 Bi elastic scattering near the Coulomb barrier with the four-body version of the continuum-discretized coupled-channels method (four-body CDCC). This is the first application of four-body CDCC to 6 Li elastic scattering. The elastic scattering is well described by the p+n+ 4 He+ 209 Bi four-body model. We propose a reasonable three-body model for describing the four-body scattering, clarifying four-body dynamics of the elastic scattering.PACS numbers: 24.10. Eq, 25.60.Gc, 25.70.De Introduction. Plenty of nuclei are considered to have twocluster or three-cluster configurations as their main components. Three-cluster dynamics is, however, nontrivial compared with two-cluster dynamics. Systematic understanding of three-cluster dynamics is hence important. There are many nuclei that can be described by three-cluster models. For example, low-lying states of 6 He and 6 Li are explained by N + N + 4 He three-body models [1][2][3][4][5][6], where N stands for a nucleon. The comparison of the two nuclei is important to see the difference between dineutron and proton-neutron correlations. Two-neutron halo nuclei such as 11 Li, 14 Be, and 22 C are reasonably described by an n + n + X three-cluster model, where X is a core nucleus. Properties of these threecluster configurations should be confirmed by measuring scattering of the nuclei and analyzing the measured cross sections with accurate reaction theories. The reactions are essentially four-body scattering composed of three constituents of projectile and a target nucleus. Accurate theoretical description of four-body scattering is thus an important subject in nuclear physics.The continuum-discretized coupled-channels method (CDCC) is a fully quantum-mechanical method of describing not only three-body scattering but also four-body scattering [7][8][9]. CDCC has succeeded in reproducing experimental data on both three-and four-body scattering. The theoretical foundation of CDCC is shown with the distorted Faddeev equation [10][11][12]. CDCC for four-body (three-body) scattering is often called four-body (three-body) CDCC; see Refs [13][14][15][16][17][18][19][20][21][22][23][24][25] and references therein for four-body CDCC. So far four-body CDCC was applied to only 6 He scattering.

Four- and three-body channel coupling effects on6Li elastic scattering with CDCC

“…[7] for the analysis of 6 Li+ 209 Bi scattering and the detail of model setting. As for U n , we take the potential of Koning and Delaroche [9] determined from the measured elastic cross section of n + 209 Bi.…”

“…where K R stands for the kinetic energy operator with respect to the relative coordinate R between 6 Li and T, and U x (x = n, p, α) represents the optical potential between x and T. Since Coulomb-breakup effects are negligibly small for the present elastic scattering [6,7], the Coulomb part of U p and U α is then approximated into e 2 Z Li Z T /R, where Z A is the atomic number of nucleus A. h npα denotes the internal Hamiltonian of 6 Li in the three-cluster model. In CDCC, Eq.…”

“…[3,7] for the detail. The scattering state Ψ with the total energy E is governed by the four-body Schrödinger equation with the model Hamiltonian H 4 :…”

“…However, the calculation could not reproduce the measured elastic cross section without a normalization factor 0.8 to d-209 Bi and α-209 Bi optical potentials. This problem was solved by four-body CDCC based on the n + p + α + 209 Bi fourbody model [7]. The calculation well describes the experimental data with no adjustable parameter.…”

Eikonal reaction theory for two-neutron removal reactions

“…Four-body CDCC [9][10][11][12][13] is a method of treating projectile breakup in the four-body scattering. Four-body CDCC was applied so far to elastic scattering and exclusive breakup reactions of 6 He from 12 C and 208 Pb targets [9][10][11][12][13], 6 Li elastic scattering from a 209 Bi target [14], 11 Li elastic scattering from a 209 Bi target [15] and 16 C elastic scattering from a 12 C target [16] with success in reproducing the experimental data, and importance of projectile breakup was shown for the three-body projectiles.…”