Necessary conditions for accurate computations of three-body partial decay widths

TL;DR

This paper investigates the conditions necessary for accurately computing three-body partial decay widths, emphasizing the importance of basis size and wave function accuracy at various distances, using the adiabatic expansion and WKB methods.

Contribution

It introduces minimal basis conditions for three-body decay calculations and compares different interactions and methods to validate the approach.

Findings

Agreement with experimental decay widths for large enough basis

Derived minimal basis conditions for accurate wave functions

Illustrated with alpha and two-proton emission examples

Abstract

The partial width for decay of a resonance into three fragments is largely determined at distances where the energy is smaller than the effective potential producing the corresponding wave function. At short distances the many-body properties are accounted for by preformation or spectroscopic factors. We use the adiabatic expansion method combined with the WKB approximation to obtain the indispensable cluster model wave functions at intermediate and larger distances. We test the concept by deriving conditions for the minimal basis expressed in terms of partial waves and radial nodes. We compare results for different effective interactions and methods. Agreement is found with experimental values for a sufficiently large basis. We illustrate the ideas with realistic examples from $\alpha$-emission of $^{12}$C and two-proton emission of $^{17}$Ne. Basis requirements for accurate momentum distributions are briefly discussed.