Angular momentum reduction in the four-body problem

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

“…It states that in the asymptotic expansion of the energy-shell restriction of the optical potential for large intercluster separation there occurs as the first nonvanishing term after the center-of-mass Coulomb interaction, which arises from the multipole expansion of the folded Coulomb channel interaction, the local (induced) polarisation potential −a/2ρ 4 α . This result extends the one derived in [18][19][20][21][22][23] for E < 0, to arbitrary energies.…”

“…We emphasize that this compensation was proved here both on and off the energy shell, and for arbitrary total three-body energy E < 0 and E > 0. It generalizes the cancellation proofs, given in [18][19][20][21][22][23] for energies below the dissociation threshold, to positive energies. In addition, at negative three-particle energy our derivation avoids the various inconsistencies existing there.…”

“…For these reasons, there have recently appeared several attempts to provide nonperturbative derivations based on three-body theory, both in coordinate [18] and in momentum [19][20][21][22][23] space. Indeed, it was found that the above mentioned, approximately derived long-range behavior could be recovered.…”

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

“…[24] and [25]) as a coefficient function before the wave function of the bound state of the two-body complex in the expansion of the complete three-particle wave function in the set of the two-particle wave functions of the relative motion of the interacting particles 2 and 3,…”

“…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.…”