Many-body modified Lippmann--Schwinger equations for Coulomb-like potentials

Journal Article · Mon Jan 01 00:00:00 EST 1973 · Nucl. Phys., A, v. A213, no. 3, pp. 541-569

DOI:https://doi.org/10.1016/0375-9474(73)90752-5· OSTI ID:4413447

Prugovecki, E; Zorbas, J

It is shown that when long-range potentials are present the wave functions for each channel are the solutions of certain homogenous integral equations. These equations imply that the wave functions do not satisfy the Lippmann-Schwinger equations. However, the same wave functions also satisfy inhomogeneous integral equations involving an operator Z(/sup (a)/. This operator guarantees the existence of channel wave operators as strong limits of modified time evolution operators. An explicit integral representation for this operator is presented and it is shown that it displays ultraviolet divergencies at large relative velocities of the fragments whenever these fragments interact via Coulomb-like potentials. In case that long-range forces are absent Z/sup (a)/ = 1 and the inhomogeneous integral equations reduce to the Lippmann-Schwinger equations for the wave function. Also a general method for relating the wave functions for Coulomb-like potentials to the solutions of the Lippmann-Schwinger equations for screened Coulomblike potentials is presented. (auth)

• Research Organization: Univ. of Toronto
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-004079
• OSTI ID: 4413447
• Journal Information: Nucl. Phys., A, v. A213, no. 3, pp. 541-569, Other Information: Orig. Receipt Date: 30-JUN-74
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

N69230* -Physics (Nuclear)-Nuclear Theory-Nuclear Reactions & Scattering
*LIPPMANN-SCHWINGER EQUATION- POTENTIAL SCATTERING
*NUCLEAR REACTIONS- POTENTIAL SCATTERING
MANY-BODY PROBLEM