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

TL;DR

This paper models the two-proton capture process on $^{68}$Se using a self-consistent cluster approach, calculating reaction rates and elucidating the capture mechanism relevant for astrophysical nucleosynthesis.

Contribution

It introduces a novel self-consistent three-body model combining mean-field and exact solutions to study two-proton capture on $^{68}$Se, including resonance effects and reaction rates.

Findings

Reaction rates increase rapidly below 2-4 GK.

Capture mechanism is sequential via $f_{5/2}$ resonance.

Continuum background significantly influences the process.

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.