# Scattering and bound states of fermions in a mixed vector–scalar smooth step potential

## Abstract

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space–time. - Highlights: • Scattering and bound states of fermions in a kink-like potential. • No pair production despite the high localization. • No bounded solution under exact spin and pseudospin symmetries.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22314840

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 346; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; CHIRALITY; COUPLING; EFFECTIVE MASS; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; PAIR PRODUCTION; POTENTIALS; RELATIVISTIC RANGE; SCALARS; SCATTERING; SPACE-TIME; SPIN; SYMMETRY; TRANSFORMATIONS; VECTORS

### Citation Formats

```
Castilho, W.M., E-mail: castilho.w@gmail.com, and Castro, A.S. de, E-mail: castro@pq.cnpq.br.
```*Scattering and bound states of fermions in a mixed vector–scalar smooth step potential*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.04.011.

```
Castilho, W.M., E-mail: castilho.w@gmail.com, & Castro, A.S. de, E-mail: castro@pq.cnpq.br.
```*Scattering and bound states of fermions in a mixed vector–scalar smooth step potential*. United States. doi:10.1016/J.AOP.2014.04.011.

```
Castilho, W.M., E-mail: castilho.w@gmail.com, and Castro, A.S. de, E-mail: castro@pq.cnpq.br. Tue .
"Scattering and bound states of fermions in a mixed vector–scalar smooth step potential". United States.
doi:10.1016/J.AOP.2014.04.011.
```

```
@article{osti_22314840,
```

title = {Scattering and bound states of fermions in a mixed vector–scalar smooth step potential},

author = {Castilho, W.M., E-mail: castilho.w@gmail.com and Castro, A.S. de, E-mail: castro@pq.cnpq.br},

abstractNote = {The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space–time. - Highlights: • Scattering and bound states of fermions in a kink-like potential. • No pair production despite the high localization. • No bounded solution under exact spin and pseudospin symmetries.},

doi = {10.1016/J.AOP.2014.04.011},

journal = {Annals of Physics (New York)},

number = Complete,

volume = 346,

place = {United States},

year = {Tue Jul 15 00:00:00 EDT 2014},

month = {Tue Jul 15 00:00:00 EDT 2014}

}