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495From the analyses of unsatisfactory points in the usual irrotational collective model, it has been -considered that there should exist a kind of " internal " rotational collective motion to be coupled with the usual irrotational surface motion. Using Watanabe's method, a generalization of the collec· tive description with redundant variables is developed and it is shown that the introduction of the ·rotational collective motion is indispensable in describing the collective motion in a closed form con-.sistendy. It is confirmed that this rotational mode plays an important role in explaining the discrepancy between the experimental and theoretical values of the effective moments of inertia of nuclei. The fundamental assumption of the various models concerning the moments of inertia is discussed. § I. IntroductionThe nuclear collective model proposed by Bohr-Mottelson 1 l and Hill-Wheeler 2 l has :had considerable success in accounting for many features of the nuclear structure. J>articularly the confirmation of the existence of low energy rotational states in nuclei ·with mass numbers between 150 and 190 and above 222 has made the reality of this model decisive. Such a striking success of the model has stimulated the interest of many :researchers in analysing some of the underlying problems.An important problem among those is the one concerning the values of the effective moments of inertia, Jeff• which are deduced from the separations of rotational energy 1evels. Recently it was recognized that the collective model in the original work of Bohr-Mottelson, based on the assumption of incompressible and irrotational collective flow, _gives the values of moments of inertia smaller than the empirical values by a factor 1/3-.1/5, while the latter are found to be smaller than the rigid-body value by a factor 1/3-.1/2. 3 ) A number of attempts 4 J-lSJ has been made to elucidate the above situation ·by 'trying to take into account not only the surface rotation caused by the irrotational collective motion, but also another kind of rotations due to the motion of individual -particles. For example, Tomonaga 10 l assumed the existence of the " internal" rotational -collective motion in addition to the usual irrotational collective motion and considered ;:he effective moments of inertia to be increased by the strong coupling between these 1:wo kinds of collective motions. In order to formulate this physical consideration, how--ever, we need to introduce some hypothetical quantities for the new internal modes of -collective motion, and as long as we use such quantities it is impossible to derive the at East Tennessee State University on June 14, 2015 http://ptp.oxfordjournals.org/ Downloaded from 496S. Nagata, R. Tamagaki, S. Amai and T. Marumori relation ex1stmg necessarily between the new internal -modes and the usual irrotational modes from the formulation itself. Another approach was made by Inglis 4 J using the so-called "cranking model." In this model the moments of inertia are discussed in terms of the motion of nucleon...

807A possible model which discriminates rr-N, K-N and N-N collisions in the cosmic-ray energy region is proposed. The difference in dependence of the mutiplicities on the energy of incident particles in rr-N, K-N and N-N collisions is discussed, which is due to the difference of the kinds of the incident particles. Experimental data obtained with nuclear emulsions are analysed by using our model. If our model is justified, the mean energy of the secondary particles of the rr-primary jets must be greater (about rwice) than that of the N-primary one, both in nucleon target and nucleus target cases.

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