# Classical helium atom with radiation reaction

## Abstract

We study a classical model of helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models, most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero-dipole manifold that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time-evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular withmore »

- Authors:

- Universita degli Studi di Milano, Corso di Laurea in Fisica, Via Celoria 16, I-20133 Milano (Italy)
- Dipartimento di Matematica, Universita degli Studi di Milano, Via Saldini 50, I-20133 Milano (Italy)

- Publication Date:

- OSTI Identifier:
- 22093606

- Resource Type:
- Journal Article

- Journal Name:
- Chaos (Woodbury, N. Y.)

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ATOMS; AUTOIONIZATION; BREAKDOWN; DIPOLES; ELECTRODYNAMICS; EMISSION; EVOLUTION; HELIUM; MATHEMATICAL SOLUTIONS; MODIFICATIONS

### Citation Formats

```
Camelio, G., Carati, A., and Galgani, L.
```*Classical helium atom with radiation reaction*. United States: N. p., 2012.
Web. doi:10.1063/1.4703945.

```
Camelio, G., Carati, A., & Galgani, L.
```*Classical helium atom with radiation reaction*. United States. doi:10.1063/1.4703945.

```
Camelio, G., Carati, A., and Galgani, L. Fri .
"Classical helium atom with radiation reaction". United States. doi:10.1063/1.4703945.
```

```
@article{osti_22093606,
```

title = {Classical helium atom with radiation reaction},

author = {Camelio, G. and Carati, A. and Galgani, L.},

abstractNote = {We study a classical model of helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models, most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero-dipole manifold that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time-evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular with respect to that of Lebesgue.},

doi = {10.1063/1.4703945},

journal = {Chaos (Woodbury, N. Y.)},

issn = {1054-1500},

number = 2,

volume = 22,

place = {United States},

year = {2012},

month = {6}

}