# Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems

## Abstract

Non-relativistic quantum chemical calculations of the particle mass, m{sub 2}{sup ±}, corresponding to the dissociation threshold in a range of Coulomb three-particle systems of the form (m{sub 1}{sup ±}m{sub 2}{sup ±}m{sub 3}{sup ∓}), are performed variationally using a series solution method with a Laguerre-based wavefunction. These masses are used to calculate an accurate stability boundary, i.e., the line that separates the stability domain from the instability domains, in a reciprocal mass fraction ternary diagram. This result is compared to a lower bound to the stability domain derived from symmetric systems and reveals the importance of the asymmetric (mass-symmetry breaking) terms in the Hamiltonian at dissociation. A functional fit to the stability boundary data provides a simple analytical expression for calculating the minimum mass of a third particle required for stable binding to a two-particle system, i.e., for predicting the bound state stability of any unit-charge three-particle system.

- Authors:

- Department of Chemistry, University of Sussex, Falmer, Brighton BN1 9QJ (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22419922

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; COMPARATIVE EVALUATIONS; DISSOCIATION; HAMILTONIANS; MASS; MOLECULES; PARTICLES; STABILITY; THREE-BODY PROBLEM

### Citation Formats

```
King, Andrew W., Herlihy, Patrick E., and Cox, Hazel, E-mail: h.cox@sussex.ac.uk.
```*Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems*. United States: N. p., 2014.
Web. doi:10.1063/1.4890658.

```
King, Andrew W., Herlihy, Patrick E., & Cox, Hazel, E-mail: h.cox@sussex.ac.uk.
```*Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems*. United States. doi:10.1063/1.4890658.

```
King, Andrew W., Herlihy, Patrick E., and Cox, Hazel, E-mail: h.cox@sussex.ac.uk. Mon .
"Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems". United States.
doi:10.1063/1.4890658.
```

```
@article{osti_22419922,
```

title = {Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems},

author = {King, Andrew W. and Herlihy, Patrick E. and Cox, Hazel, E-mail: h.cox@sussex.ac.uk},

abstractNote = {Non-relativistic quantum chemical calculations of the particle mass, m{sub 2}{sup ±}, corresponding to the dissociation threshold in a range of Coulomb three-particle systems of the form (m{sub 1}{sup ±}m{sub 2}{sup ±}m{sub 3}{sup ∓}), are performed variationally using a series solution method with a Laguerre-based wavefunction. These masses are used to calculate an accurate stability boundary, i.e., the line that separates the stability domain from the instability domains, in a reciprocal mass fraction ternary diagram. This result is compared to a lower bound to the stability domain derived from symmetric systems and reveals the importance of the asymmetric (mass-symmetry breaking) terms in the Hamiltonian at dissociation. A functional fit to the stability boundary data provides a simple analytical expression for calculating the minimum mass of a third particle required for stable binding to a two-particle system, i.e., for predicting the bound state stability of any unit-charge three-particle system.},

doi = {10.1063/1.4890658},

journal = {Journal of Chemical Physics},

number = 4,

volume = 141,

place = {United States},

year = {Mon Jul 28 00:00:00 EDT 2014},

month = {Mon Jul 28 00:00:00 EDT 2014}

}