Internal clusterization in the Coulomb few-body systems and stability of the five- and six-body systems with unit charges

TL;DR

This paper investigates the stability and internal structure of specific five- and six-body Coulomb systems with unit charges, demonstrating their stability and structural similarities to known simpler systems through variational computations.

Contribution

It provides the first detailed analysis of the stability of five- and six-body Coulomb systems with unit charges, revealing their structural similarities to H- ions and H2 molecules.

Findings

All studied systems are stable in their ground states.

Five-body ions have structures similar to H- ions.

Six-body quasi-molecules resemble H2 molecules.

Abstract

Stability of the bound ground states in the six five-body muonic $a b \mu e_2$ ions (or $(a b \mu e_2)^{-}$) and ten six-body $a b c \mu e_2$ quasi-molecules is investigated. The notations $a, b, c$ stand for the bare nuclei of three hydrogen isotopes - protium ($p$), deuterium ($d$) and tritium ($t$). All these systems are the Coulomb five- and six-body systems with unit charges. It is found that the ground bound $S(L = 0)-$states are stable in all six five-body $a b \mu e_2$ ions and in ten six-body $a b c \mu e_2$ quasi-molecules. As follows from accurate variational computations of the five-body $a b \mu e_2$ ions their internal structure is similar to the internal structure of the negatively charged hydrogen ion H$^{-}$. Analogously, we show that the internal structures of the six-body neutral $a b c \mu e_2$ quasi-molecules are similar to the structure of the two-center H$_{2}$ molecule which contains two heavy hydrogen nuclei and two bound electrons.