Why complex absorbing potentials work: A discrete-variable-representation perspective
- Argonne National Laboratory, Argonne, Illinois 60439 (United States)
The use of a complex absorbing potential (CAP) of the form -i{eta}W to calculate the Siegert energy of a resonance state rests on a solid mathematical foundation [U. V. Riss and H.-D. Meyer, J. Phys. B 26, 4503 (1993)]. In this paper, in order to facilitate a better understanding of the basic principles underlying the CAP method, a radial one-particle Hamiltonian with a model potential supporting resonances is analyzed. Using a purely quadratic CAP [W(r)=r{sup 2}], the eigenstates of H=-(1/2)d{sup 2}/dr{sup 2}-i{eta}W(r) are employed to construct a discrete variable representation. The introduction of this grid method makes it transparent how using a CAP is related to the method of complex scaling, and why, in the limit of an infinite basis set, the exact Siegert energy may emerge in the spectrum as {eta}{yields}0{sup +}.
- OSTI ID:
- 20857779
- Journal Information:
- Physical Review. A, Vol. 74, Issue 3; Other Information: DOI: 10.1103/PhysRevA.74.034701; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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