Bound states of composite particles and the GSI lines

Abstract

Abstract.We calculate the correlated wave functions and the energy eigenvalues of a charged fermion-antifermion pair bound in the Coulomb field of a heavy nucleus, assuming a confining potential between the fermions. This model is motivated by properties of the coincident electron-positron lines observed at GSI. We confirm the resuits of earlier calculations which were based on simplifying assumptions. In addition we find new, very weakly bound states which, however, do not have the decay properties required to explain the experiments.

Two-particle bound states in the field of a heavy nucleus

“…The model is characterized by the Hamiltonian (1) with q'= -q=e, m'=m, Q=Ze and a linearly rising potential V(rl ) = arl. The results of this calculation will be discussed in [8]. Here we only mention some general aspects.…”

“…The developed techniques and formulae can be used for any problem of this kind. In a subsequent publication [8] we will specifically discuss the following scenario, which was inspired by attempts to explain the anomalous electron-positron coincidences measured in heavy-ion collisions at GSI: two hypothetical light particlesf + and f-, bound together by a confinement potential, move in the Coulomb field of a heavy ion. In Sect.…”