Structure and Decay at Rapid Proton Capture Waiting Points

Abstract

We investigate the region of the nuclear chart around A 70 from a three-body perspective, where we compute reaction rates for the radiative capture of two protons. One key quantity is here the photon dissociation cross section for the inverse process where two protons are liberated from the borromean nucleus by photon bombardment. We find a number of peaks at low photon energy in this cross section where each peak is located at the energy corresponding to population of a three-body resonance. Thus, for these energies the decay or capture processes proceed through these resonances. However, the next step in the dissociation process still has the option of following several paths, that is either sequential decay by emission of one proton at a time with an intermediate two-body resonance as stepping stone, or direct decay into the continuum of both protons simultaneously. The astrophysical reaction rate is obtained by folding of the cross section as function of energy with the occupation probability for a Maxwell-Boltzmann temperature distribution. The reaction rate is then a function of temperature, and of course depending on the underlying three-body bound state and resonance structures. We show that a very simple formula at low temperature reproduces the elaborate numerically computed reaction rate.

Validity of Quasi-classical Approaches to True Three-Body Decays

“…Finally, we conclude that quasiclassical approximation for single channel is quite precise, but the reduction to one-channel approximation leads to significant overestimation of the three-body width. We think that in the view of our results all the three-body width calculations in the papers [3,4,5,6,7,8,9,10] should be questioned and applicability of the quasiclassical formalism in this case reexamined in general.…”

“…For width calculations the lowest-energy branch of the adiabatic potential is taken. Although this procedure was used in numerous works [3,4,5,6,7,8,9,10], it has never been justified theoretically and was just accepted as a reasonable approach.…”

“…Although this procedure was used in numerous works [3,4,5,6,7,8,9,10], it has never been justified theoretically and was just accepted as a reasonable approach.…”

“…The formalism of the Gamow type has been repeatedly used in recent years for the determination of three-body decay widths [3,4,5,6,7,8,9,10]. In this work, we examine the validity of the Gamow-type approximation by the example of the width of the first excited 3/2 − state of 17 Ne [3,6].…”

Combined few-body and mean-field model for nuclei

“…A potential problem with a traditional three-body investigation of the systems that we are considering is the phenomenological character of the approach, which makes it difficult to present concrete predictions [149,152]. However, very little arbitrariness is left in the method we use here, and therefore the prediction capability increases.…”