Schematic coupled-channel calculations for nuclear reactions with unstable beams

Abstract

We study nuclear reactions in collisions of unstable projectiles with heavy targets. For this purpose, we use a simple approximation for the breakup channel and treat two-neutron halos as a single particle. We then evaluate cross sections for collisions of 6 He projectiles with targets of 238 U and 209 Bi. Comparing our results with recently measured fusion cross sections, we conclude that the large enhancement observed in 6 He+ 238 U fusion at sub-barrier energies cannot be explained by the coupling with the breakup channel. The effects of the halo on other reaction channels are also investigated. Coulomb-nuclear interference in the breakup channel is discussed.

Investigation of the Calculation of Coupled Channels for Some Halo Systems

“…The coupling of channels is taken into account to match to bound states of the partners. The expansion of this theory to the fusion of unstable (halo) nuclei, which includes the coupling with the breakup channel was achieved is the past by using deuteron projectiles scattered on various targets in the Continuum Discretized Coupled Channels (CDCC) Method [19]. Involving the breakup channel within coupling is consider very difficult, since an infinite set of three or more nucleons in the continuum state should be described in the breakup channel.…”

“…However, the enforcement of this process is more complex [18]. The representation of a coupled channel in fusion reactions, where the fusion cross-sections can be resulted from the total reaction cross-sections, looks as [19,22].…”

“…where ⟨ | (+) ⟩ is the wave function that describes the elastic scattering, and is the full potential [19,23],…”

Modelling scattering and resonances of weakly-bound radioactive nuclei

“…[5][6][7], particle-unstable scattering bodies are considered in coupled-channel calculations for heavy mass systems at high energies where resonances are not an important feature in cross sections. However, in the lowenergy and low-mass regime where resonances are important, a different method of accounting for particleinstability is more appropriate: modifying the Green's functions of the S -matrix [8].…”