Two-proton emission systematics

TL;DR

This paper demonstrates that two-proton emission follows similar systematic rules as binary decay processes, with predictable decay widths related to physical variables like Coulomb parameter and pairing gap, aiding experimental predictions.

Contribution

It introduces a simple rule for estimating two-proton decay widths based on physical variables, extending binary decay systematics to this complex three-body process.

Findings

Logarithm of decay width linearly depends on Coulomb parameter.

Linear dependence between reduced width and pairing gap.

Similar formation probability patterns for diproton and alpha-cluster emissions.

Abstract

The simultaneous emission of two protons is an exotic and complex three-body process. It is very important for experimental groups investigating the nuclear stability on the proton drip line to have a simple rule predicting the two-proton decay widths with a reasonable accuracy for transitions between ground as well as excited states in terms of relevant physical variables. In spite of its complexity, we show that the two-proton emission process obeys similar rules as for binary emission processes like proton, alpha and heavy cluster decays. It turns out that the logarithm of the decay width, corrected by the centrifugal barrier, linearly depends upon the Coulomb parameter within one order of magnitude. On the other hand, the universal linear dependence with a negative slope between the logarithm of the reduced width and the fragmentation potential, valid for any kind of binary decay process, is also fulfilled for the two-proton emission with a relative good accuracy. As a consequence of pairing correlations the two protons are simultaneously emitted from a singlet paired state. We evidence that indeed one obtains a linear dependence between the logarithm of the reduced width and pairing gap within a factor of two, giving a good predictive power to this law. It turns out that the diproton and alpha-cluster formation probabilities have similar patterns versus the pairing gap, while in the one-proton case one has a quasi-constant behavior.