Four-body calculation ofHe6breakup with the Coulomb-corrected eikonal method

Abstract

The elastic breakup of a three-body projectile on a target is studied within the eikonal approximation with full account of final-state interactions. Bound and scattering states are calculated in hyperspherical coordinates on a Lagrange mesh. A correction is introduced to avoid the divergence of breakup cross sections due to the Coulomb interaction. The eikonal approximation allows the direct calculation of various cross sections, and in particular multidifferential cross sections can be obtained. The model is applied to the breakup of 6 He on 208 Pb. The 6 He halo nucleus is described within a three-body α+n+n model involving effective αn and nn interactions. The eikonal phase is obtained from optical potentials between α and n, and the target. Around 0.8 MeV, the total breakup cross sections exhibit a narrow 2 + resonant peak superimposed over a broad bump corresponding to a 1 − resonance. These results suffer from a disagreement with experimental data at 240 MeV/nucleon, where cross sections are much smaller at low energies. The obtained E1 strength distribution resembles other theoretical results and reopens a long-standing problem about the existence of a 1 − low-energy resonance in the 6 He continuum.

Extracting nuclear sizes of medium to heavy nuclei from total reaction cross sections

“…This idea called the Coulomb-corrected eikonal approximation works well and still makes it possible to employ the eikonal approximation [46][47][48]. However, it is only applicable to some special cases, for example, two-or three-body models for a halo nucleus [48][49][50], and it will not give us a convenient formula for a more general case because the knowledge of the photoabsorption cross section of each many-body final state is required.…”

Comparative Study of Three-Body Models for Continuum States

“…The use of Lagrange functions makes the radial integrals very simple. 33) As mentioned in §3.1, treating three-body continuum states with appropriate boundary conditions represents rather long and difficult calculations. A specificity of three-body scattering states is that the number of entrance channels (or, in other words, the number of γ ω K ω values in (4 .…”

Microscopic description ofLi7inLi7 + Pinilla1, Descouvemont2 2014Phys. Rev. CSelf Cite

“…As usual, to compute the cross sections we separate the Coulomb projectile-target eikonal scattering amplitudes to get faster convergence [11]. Figure 5 shows the single channel (GS) and multichannel calculations.…”

“…Even though they are easier to interpret and to integrate in reaction models (see for instance [10][11][12]), they present some drawbacks as: i) the required nucleus-nucleus potentials are generally poorly known or not known at all. ii) Inaccuracy introduced by considering the Pauli principle approximately [13].…”

“…This method relies on some simplifying assumptions at the high energy regime. Different versions and generalizations have been implemented [11,[17][18][19][20][21][22] since the original Glauber's publication [23]. In particular, the eikonal-CDCC method allows to study the influence of continuum states in reactions at high energies [20].…”