Proton emission systematics along proton drip line

TL;DR

This paper systematically analyzes proton emission processes along the proton drip line, comparing decay width estimation methods, and demonstrates the universal decay law's applicability to beta-delayed proton emission, unifying experimental data interpretation.

Contribution

It introduces a comprehensive analysis of proton emission systematics, compares decay width estimation methods, and confirms the universal decay law's validity for beta-delayed proton emission.

Findings

Decay width estimation methods yield similar results for Gamow states.

The universal decay law applies to beta-delayed proton emission.

Experimental data follow a linear relation between decay width and penetrability.

Abstract

We analyze the chart containing both spontaneous and beta-delayed proton emission processes in terms of the Coulomb parameter, reduced radius and angular momentum ($\chi$, $\rho$, $l$). We then compare the methods to estimate decay width $\Gamma$ of a resonant state in a proton mean field, namely the continuity equation for outgoing Gamow states, phase shift analysis of real scattering states and numerical integration of the Schr\"odinger equation in the complex plane. We show that they provide similar results in the region where it is possible to evaluate the imaginary part of the energy for a resonant (Gamow) state. We then investigate the role of the centrifugal barrier induced by Coulomb interaction and also by proton single particle orbitals. We show that the so-called universal decay law, connecting the logarithm of the monopole reduced width to the fragmentation potential, remains also valid for beta-delayed proton emission processes. This fact allows us to describe experimental data for all proton emission processes in terms of a linear dependence connecting the logarithm of the monopole Coulomb-reduced decay width to the logarithm of the monopole Coulomb penetrability and fragmentation potential within a factor of three for absolute values.