Three-body Coulomb interaction effects in the final state of thePb208(B8,Be7p)Pb208Coulomb breakup reaction

Abstract

The photodissociation reaction $^{8}\mathrm{B}+\ensuremath{\gamma}\ensuremath{\rightarrow}^{7}\mathrm{Be}+p$ is used to provide information on the astrophysical ${S}_{17}$ factor of the inverse radiative capture reaction, knowledge of which is crucial for an estimation of the high-energy neutrino flux from the sun. Since, at present, the Coulomb field of a fully stripped nucleus serves as the source of the photons, an adequate analysis requires a genuine three-body treatment of this reaction. Among the uncertainties still affecting present analyses, the possible modification of the dissociation cross section by the post-decay acceleration of the fragments $^{7}\mathrm{Be}$ and p in the target field plays a major role. Working with the prior form of the dissociation amplitude, we first discuss why the standard approximation for the final-state wave function is not appropriate for a proper investigation of this problem; instead, use of a genuine three-particle wave function for the final state proves to be mandatory. Such is provided by a recently proposed wave function for three charged particles in the continuum [A. M. Mukhamedzhanov and M. Lieber, Phys. Rev. A 54, 3078 (1996)] which possesses all the essential features required. It is an exact solution of the three-body Schr\odinger equation, but only asymptotically, i.e., for large distances. Therefore, only qualitative predictions can be made currently, such as predicting the kinematic configurations in which post-decay acceleration effects play a negligible role. Explicit calculations are presented for the single and the double differential cross sections for the $^{208}\mathrm{Pb}(^{8}\mathrm{B},^{7}\mathrm{Be}\phantom{\rule{0.3em}{0ex}}p)^{208}\mathrm{Pb}$ Coulomb breakup reaction. We also investigate the influence of the $E2$ multipole and find its contribution to be small for small scattering angles, but comparable to the one from the $E1$ dipole for large scattering angles.