# Resonance positions and lifetimes for flexible complex absorbing potentials

## Abstract

By adding any complex absorbing potential (CAP) -i{lambda}V(r-vector) to a system Hamiltonian, the corresponding complex eigenvalues are analytical functions of {lambda},E{sub j}({lambda}). It is shown here that for a quite general flexible class of CAP's the real part of lim{sub {lambda}}{sub /0}E{sub j}({lambda}) provides the resonance energy. The imaginary part of that limit is the resonance width (i.e., inverse lifetime) in spite of the fact that Im E{sub j}(0)=0. The need for the Pade approximation within this approach is explained. Application to an illustrative numerical test case model Hamiltonian is given. This method could open a gate for studying systems that could not be studied until now due to the complexity of the numerical computations. In particular, one may in this way obtain resonance energies by a modification, in a straightforward simple manner, of the widely used conventional methods that were developed for the calculations of bound states.

- Authors:

- Department of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems, Technion--Israel Institute of Technology, Haifa 32000 (Israel)

- Publication Date:

- OSTI Identifier:
- 20786507

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052704; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; EIGENFUNCTIONS; EIGENVALUES; HAMILTONIANS; LIFETIME; PADE APPROXIMATION; POTENTIALS; RESONANCE; SCHROEDINGER EQUATION; VECTORS

### Citation Formats

```
Lefebvre, Roland, Sindelka, Milan, and Moiseyev, Nimrod.
```*Resonance positions and lifetimes for flexible complex absorbing potentials*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Lefebvre, Roland, Sindelka, Milan, & Moiseyev, Nimrod.
```*Resonance positions and lifetimes for flexible complex absorbing potentials*. United States. doi:10.1103/PHYSREVA.72.0.

```
Lefebvre, Roland, Sindelka, Milan, and Moiseyev, Nimrod. Tue .
"Resonance positions and lifetimes for flexible complex absorbing potentials". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786507,
```

title = {Resonance positions and lifetimes for flexible complex absorbing potentials},

author = {Lefebvre, Roland and Sindelka, Milan and Moiseyev, Nimrod},

abstractNote = {By adding any complex absorbing potential (CAP) -i{lambda}V(r-vector) to a system Hamiltonian, the corresponding complex eigenvalues are analytical functions of {lambda},E{sub j}({lambda}). It is shown here that for a quite general flexible class of CAP's the real part of lim{sub {lambda}}{sub /0}E{sub j}({lambda}) provides the resonance energy. The imaginary part of that limit is the resonance width (i.e., inverse lifetime) in spite of the fact that Im E{sub j}(0)=0. The need for the Pade approximation within this approach is explained. Application to an illustrative numerical test case model Hamiltonian is given. This method could open a gate for studying systems that could not be studied until now due to the complexity of the numerical computations. In particular, one may in this way obtain resonance energies by a modification, in a straightforward simple manner, of the widely used conventional methods that were developed for the calculations of bound states.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}