Inclusive Breakup Theory of Three-Body Halos

Abstract

Abstract. We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model [1], for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in A (a, b) X / a = x 1 + x 2 + b collisions. The four-body theory is an extension of the three-body approaches developed in the 80's by Ichimura, Autern and Vincent (IAV) [2], Udagawa and Tamura (UT) [3] and Hussein and McVoy (HM) [4]. We expect that experimentalists shall be encouraged to search for more information about the x 1 + x 2 system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the b spectrum.

$${}^{5}$$He($${}^{3}$$He,$${}^{4}$$He)$${}^{4}$$He as a three-body reaction via a continuum resonance in the n+$${}^{4}$$He system

“…In general, exact solutions are not known and approximations have to be used. The reaction 5 He( 3 He, 4 He) 4 He is actually treated as a process n + 4 He + 3 He → 5 He * + 3 He → 4 He + 4 He (30) where the transition proceeds via the 3/2 − resonance in 5 He with a resonance energy E res nα = 0.735 MeV above the n + 4 He threshold. The symbols α, t and n will be used to identify 4 He, 3 He and the neutron.…”

“…The study of nuclear reactions was one of the most prominent topics in the work of Mahir S. Hussein where he made seminal contributions to the theoretical description of various processes. In recent years, he was interested in particular in three-and four-body systems, partly connected to applications in astrophysics or to halo nuclei, see, e.g., [1][2][3][4][5][6][7][8].…”

“…Only during Big Bang nucleosynthis within the first few minutes of the Universe, a considerable amount of neutrons was available, see, e.g., [16,17]. Under these conditions they can form unstable 5 He nuclei with the already synthesized 4 He nuclei. The 5 He ground state is a 3/2 − resonance of 0.648 MeV width at 0.735 MeV excitation energy above the n − α threshold [18].…”

“…Under these conditions they can form unstable 5 He nuclei with the already synthesized 4 He nuclei. The 5 He ground state is a 3/2 − resonance of 0.648 MeV width at 0.735 MeV excitation energy above the n − α threshold [18]. Then the 5 He( 3 He, 4 He) 4 He reaction could be a possible path to synthesize 4 He in Big Bang nucleosynthesis via a neutron transfer reaction.…”

“…Considering the above issues, a simple attempt is made in this work to calculate the rate of the 5 He( 3 He, 4 He) 4 He reaction treating the 5 He system as a resonance in the n+ 4 He continuum. A post-form distorted-wave Born approximation (DWBA) is used to find the relevant T-matrix element that enters in the calculation of the transition rate of this neutrontransfer reaction.…”