# Rovibrational states of Wigner molecules in spherically symmetric confining potentials

## Abstract

The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the “anomalous” weak-confinement behavior of the {sup 1}S{sub +} state of the four-electron species that is absent in its {sup 1}D{sub +} companion of the strong-confinement regime.

- Authors:

- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden (Germany)

- Publication Date:

- OSTI Identifier:
- 22678966

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CALCULATION METHODS; ELECTRIC POTENTIAL; MOLECULES; SYMMETRY; THREE-DIMENSIONAL LATTICES; WAVE FUNCTIONS

### Citation Formats

```
Cioslowski, Jerzy.
```*Rovibrational states of Wigner molecules in spherically symmetric confining potentials*. United States: N. p., 2016.
Web. doi:10.1063/1.4959899.

```
Cioslowski, Jerzy.
```*Rovibrational states of Wigner molecules in spherically symmetric confining potentials*. United States. doi:10.1063/1.4959899.

```
Cioslowski, Jerzy. Sun .
"Rovibrational states of Wigner molecules in spherically symmetric confining potentials". United States.
doi:10.1063/1.4959899.
```

```
@article{osti_22678966,
```

title = {Rovibrational states of Wigner molecules in spherically symmetric confining potentials},

author = {Cioslowski, Jerzy},

abstractNote = {The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the “anomalous” weak-confinement behavior of the {sup 1}S{sub +} state of the four-electron species that is absent in its {sup 1}D{sub +} companion of the strong-confinement regime.},

doi = {10.1063/1.4959899},

journal = {Journal of Chemical Physics},

number = 5,

volume = 145,

place = {United States},

year = {Sun Aug 07 00:00:00 EDT 2016},

month = {Sun Aug 07 00:00:00 EDT 2016}

}