Long-range behavior of the optical potential for the elastic scattering of charged composite particles

Abstract

The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle α off a bound state of two charged, or one charged and one neutral, particles at small momentum transfer ∆ α or equivalently at large intercluster distance ρ α , is investigated within the framework of the exact three-body theory. For the three-charged-particle Green function that occurs in the exact expression for the optical potential, a recently derived expression, which is appropriate for the asymptotic region under consideration, is used. We find that for arbitrary values of the energy parameter the non-static part of the optical potential behaves for ∆ α → 0 as. From this we derive for the Fourier transform of its onshell restriction for ρ α → ∞ the behavior −a/2ρ 4 α + o (1/ρ 4 α ), i.e., dipole or quadrupole terms do not occur in the coordinate-space asymptotics. This result corroborates the standard one, which is obtained by perturbative methods. The general, energy-dependent expression for the dynamic polarisability C 1 is derived; on the energy shell it reduces to the conventional polarisability a which is independent of the energy. We emphasize that the present derivation is non-perturbative, i.e., it does not make use of adiabatic or similar approximations, and is valid for energies below as well as above 1 the three-body dissociation threshold.

The Few-Body Coulombian Problem

“…Let me just state the result without giving any details. For the latter I refer to [21]. Off the energy shell one finds Ṽopt (as) αm,αm (q ′ α , q α ; E + i0)…”

Three-body theory of the penetration of a charged particle through Coulomb field of a two-fragment nucleus

“…and taking into account the relations ( 25), ( 27) (18), we obtain the formula expressing the transition operator Xeff (ǫ) through the operators X( ǫ) and W (ǫ),…”

“…As a result of the analytical study of the effective interaction between a charged particle and two-particle complex on the basis of the Faddeev integral equations, it has been established that the full concellation of the long-range terms proportional to (e 1 e 2 ) 2 | p − p ′ | −1 , (e 1 e 2 ) 3 ln(| p − p ′ | ρ 0 ) and (e 1 e 2 ) 4 | p − p ′ | occur when the transfer momentum tends to zero (| p − p ′ |→ 0) and the behaviour of the polarization potential at asymptotically large [15][16][17][18] and intermediate [19][20] distances has been determined in an explicit form.…”

Penetration Through the Gamow Barrier of a Two-Fragment Nucleus in the Three-Body Approach

“…2 | p − p ′ | −1 , (e 1 e 2 ) 3 ln(| p − p ′ | ρ 0 ) and (e 1 e 2 ) 4 | p − p ′ | occur when the transfer momentum tends to zero (| p − p ′ |→ 0) and the behaviour of the polarization potential at asymptotically large [15][16][17][18] and intermediate [19][20] distances has been determined in an explicit form.…”