Structure of the Excited States in 12C. I

Abstract

Structure of both positive- and nCc:gative-parily slates in 12C is studied with a microscopic :l u-parlicle model. The c.m. motions of 3 a-clusters are treated by the generator coordinate method. All the levels with T=O below 15 MeV (except the 1:0.7 MeV r+ level) are suc­ cessfully reproclucecl, including the famous o,+ level and the next positive-parity level which is regarded as :o,+. Another 2', :l1+ and two 4+ stales which have a structure quite similar to that of the O, ,_ and :0, + stales are preclictecl with large K-rnixings. Furthermore the pre­ sent investigation predicts an existence of O, + state. The structure of all the above excited positive-parity slates is quite diiferenl from that expected in the shell model, hut rather should he considered that· o£ a finite a-boson ga,. The negative-parity leveis are quite well de:ribecl ' memhcrs of the K=:l- and I bands in the present model. § 1. Introduetion The nucleus C has been offering a testing field to vanous nuclear models. It is a stable and tight binding system though it is one of the lightest nuclei. On the assumption of a stable average nuclear Jield, shell model \Vas applied in se\·eral \·ersions to explain low energy properties of 12C.'' Unfortunately, all the efforts have resulted in obtaining only partial success. Above all the second 0 t level at 7.7 MeV and the next positive-parity level at 10.3 MeV have been difficult to be reproduced at such low excitation energies. They are also known to have anomalously large a-decay widths.'' Morinaga suggested that they form an excited rotational band with a linear chain structure of 3 a-particles. 11 According to Ikeda's cliagram5l' 61 one can expect appearance of nuclear states with some cluster structure in the neighbourhood o£ decay-threshold energies of a-particles. In 12C, the 0,' le\·el and the next positive-parity level noted aboYe are expected to be such states, that is, to ha\·e distinct cluster structure relevant to the 'Be -1--CY channel al 7.4 MeV. From the \'iewpoint of a-particle mudel this nucleus has been investigated since the early ages of nuclear study. The classical a-particle model was applied to it on the analogy o£ homonuclear tri-atomic mole­ cule. The modeL howeYer, predicts a :3 state at too low an excitation energy compared with experiment. This dr;cm·back is known to disi!ppear in the micro­ scopic model.RJ Recently sc1·eral dynamical calculations' of :3 a-particle system haYe been made by the use of 1·arious a-ct interactions. Fuji\\'ara and Tamagaki 9b 1 11 Preliminary results were