Complex scaling of polynomial potentials

✍ Scribed by H. Lehr; C.A. Chatzidimitriou-Dreismann

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 442 KB
• Volume: 201
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(93)85071-u

✦ Synopsis

Potentials of polynomial type are of common use in physics. For the determination of lifetimes the complex scaling method has proven to be useful. Polynomial potentials do not fulfdl the necessary requirements for the application of complex scaling, because of the lack of dilatation analyticity. In this Letter, we justify the complex scaling treatment of polynomial potentials. We use a window function, which is mostly a square barrier, tending to zero like eexz for large values of 1 xl. Upon multiplication with the polynomial potential one gets a new potential that is dilatation analytic. We show that the "windowed" and the non-windowed potentials have the same resonances and conclude that complex scaling can be successfully applied to the numerical determination of resonance energies of polynomial potentials, despite the fact that the conditions of the Aguilar-Balslev-Combes theorem are not fulfilled.