# Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods

## Abstract

The spectrum of the Dirac equation for hydrogenlike systems with extended nuclei becomes complicated when the nuclear charge exceeds a critical value Z{approx_equal}170, since the lowest bound state becomes a resonance in the negative energy continuum. We address the problem of computing the resonance parameters by extending the mapped Fourier grid method to incorporate either complex scaling of the radial coordinate, or alternatively a complex absorbing potential. The method is tested on the case of quasimolecular collisions in the monopole approximation.

- Authors:

- Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 (Canada)

- Publication Date:

- OSTI Identifier:
- 20982107

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022508; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ATOMIC NUMBER; BOUND STATE; COLLISIONS; COMPUTER CALCULATIONS; DIRAC EQUATION; MONOPOLES; NUMERICAL ANALYSIS; POTENTIALS; RESONANCE; SCALING

### Citation Formats

```
Ackad, Edward, and Horbatsch, Marko.
```*Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022508.

```
Ackad, Edward, & Horbatsch, Marko.
```*Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods*. United States. doi:10.1103/PHYSREVA.75.022508.

```
Ackad, Edward, and Horbatsch, Marko. Thu .
"Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods". United States.
doi:10.1103/PHYSREVA.75.022508.
```

```
@article{osti_20982107,
```

title = {Numerical calculation of supercritical Dirac resonance parameters by analytic continuation methods},

author = {Ackad, Edward and Horbatsch, Marko},

abstractNote = {The spectrum of the Dirac equation for hydrogenlike systems with extended nuclei becomes complicated when the nuclear charge exceeds a critical value Z{approx_equal}170, since the lowest bound state becomes a resonance in the negative energy continuum. We address the problem of computing the resonance parameters by extending the mapped Fourier grid method to incorporate either complex scaling of the radial coordinate, or alternatively a complex absorbing potential. The method is tested on the case of quasimolecular collisions in the monopole approximation.},

doi = {10.1103/PHYSREVA.75.022508},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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