Two-proton capture on the 68Se nucleus with a new self-consistent cluster model

Abstract

We investigate the two-proton capture reaction of the prominent rapid proton capture waiting point nucleus, 68 Se, that produces the borromean nucleus 70 Kr ( 68 Se+p + p). We apply a recently formulated general model where the core nucleus, 68 Se, is treated in the mean-field approximation and the three-body problem of the two valence protons and the core is solved exactly. The same Skyrme interaction is used to find core-nucleon and core valence-proton interactions. We calculate E2 electromagnetic two-proton dissociation and capture cross sections, and derive the temperature dependent capture rates. We vary the unknown 2 + resonance energy without changing any of the structures computed self-consistently for both core and valence particles. We find rates increasing quickly with temperature below 2 − 4 GK after which we find rates varying by less than a factor of two independent of 2 + resonance energy. The capture mechanism is sequential through the f 5/2 proton-core resonance, but the continuum background contributes significantly.

Combined few-body and mean-field model for nuclei

“…Experimentally, the lowest lying resonance in 69 Br ( 68 Se+p) is known to be a f 5/2 state at 0.6MeV [153]. Using an unaltered SLy4 parameterization the lowest allowed state also turns out to be an f 5/2 state [151], in accordance with experimental findings. To achieve the correct energy the SLy4 parameterization is scaled by a factor of S=0.9515, which has been used in all the results presented in this section.…”

“…Another vital issue, which touches on the most fundamental aspects of the reaction, is to examine the reaction mechanism [149,151]. The two-proton capture process can proceed through a well-defined three-body resonance, or as a non-resonant reaction through a continuum state, while after penetrating the Coulomb barrier the only transition to the 0 + ground state is through γ-decay.…”

“…This is given as a function of hyperradius, ρ, and hyperangle, α, related to the Jacobi coordinate system where 'x' is between core and proton. Reproduced with permission from [151].…”

$^{42}$Ca and $^{50}$Ca with the (Many- and Few-body) Unified Method

“…One of the simplest clusterized systems is a many-body core surrounded by a group of valence nucleons. This structure is particularly suitable to describe nuclei close to the proton and neutron driplines, as shown in the previous works [16,17,18].…”

“…This invariant mass spectrum is basically dictated by the derived core-valence neutron interaction, which, once a nucleon-nucleon interaction has been chosen to describe the core, is obtained without any additional free parameter. In [17] the method is applied in the proton dripline region. In particular, the two-proton capture reaction 68 Se + p + p → 70 Kr + γ is considered, the corresponding reaction rates computed, and the capture mechanism investigated.…”