Quantum mechanical models for the Fermi shuttle

Although the Fermi shuttle was originally proposed as an explanation for highly energetic cosmic rays, it is also a mechanism for the production of high energy electrons in atomic collisions [1]. The Fermi shuttle is usually thought of as a classical effect and most models of this process rely on classical or semi-classical approximations. In this work we explore several quantum mechanical models for ion-atom collisions and examine the evidence for the Fermi shuttle in these models. \\[4pt] [1] B. Sulik, Cs. Koncz, K. Tok\'esi, A. Orb\'an, and D. Ber\'enyi, Phys Rev. Lett. {\bf 88} 073201 (2002)