A three-center phenomenological model, able to explain qualitatively therecently obtained experimental results concerning the quasimolecular stage of alight-particle accompanied fission process, was developed. A new minimum of ashort-lived molecular state appears in the deformation energy at a separationdistance very close to the touching point. The influence of the shell effectsis discussed. The half-lives of some quasimolecular states which could beformed in the ^{10}Be and ^{12}C accompanied fission of ^{252}Cf are roughlyestimated to be the order of 1ns, and 1 ms, respectively.
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