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and Werner Scheid Institut Pir Theoretisclze Physik der 6300 Giessen, West G e r m a n y (Received 22 February 1983) On the basis of the two-center shell m d e l a molecular reaction theory is applied to the reaction l3c(I3c, 1 2~) 1 4~a Prominent structures in the measured differential c r o s s sections can be reproduced by this theory.PACS numbers: 25.70.Cd, 21.60.C~ Molecular single-particle effects in heavy-ion reactions have been considered up to now to be of minor interest in contrast to the molecular collective states which have been thoroughly investigated in experiment and theory because of their prominent sigtiatures in the cross sections (gross and intermediate structures).' On the other hand, the underlying fundamental model for a nuclear molecule is the two-center shell model (TCSM) which describes the binding of the molecule in terms of molecular single-particle states.'v3 Hence, molecular single-particle states should play an important role and a verification of their effects is called for.There exists at present little experimental evidence for molecular single-particle effects. Recently, it was proved that the neutron orbits in the elastic transfer reaction of 12C On 13C a r e of molecular n a t~r e .~ The excitatiori Function for the neutron transf e r reaciion 13C (13C, 12C)14C, measured by Korotky et al. ,"' showed a large resonantlike behavior, which could not be reproduced by finite-range, full-secoil, single-step distorted-wave Born-approximation (D wBA) calc~l a t i o n s .~ This last result was our motivation for applying a molecular particle-core description to the reaction 13C(13C, 12C)14C. It i s the aim of this paper to show that the resonantlike struc-I tures in the experimental differential cross sections can be satisfactorily explained a s the transfer of a neutron occupying a molecular singleparticle state during the reaction.A molecular description of loosely bound nucleons has been worked out earlier on the basis of a molecular particle-core model and the TCSM for heavy-ion r e a c t i~n s .~'~~ These models a r e justified for the reaction considered since the characteristic collision time is considerably longer than the single-particle rearrangement time, namely by a factor 2 -3 a s estimated with the collision and Fermi energies.13The neutron transfer process is described with the molecular particle-core m 0 d e 1 .~~~~ The 13C and 14C nuclei a r e thought t o be constructed of 12C cores and valence neutrons. The valence neutrons move in the mean field of all nucleons and a r e treated in the framework of the two-cent e r shell model. The cores can also be excited, which may be described with collective models for core vibrations and rotations.The Hamiltonian of the particle-core model in laboratory coordinates consists of the kinetic energies T c { of the cores, their interaction Wclc2, the single-particle Bamiltonians h"" (i) of the valence particles described by the TCSM, and the residual interaction V", between the valence particles :In our present calculations w...

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