663An attempt to investigate the nuclear collective motion from the standpoint of particle excitations is outlined. In our method it is possible to investigate the roles of the effective inter-particle interactions in the nuclear collective motions and clarify the mechanism of the collective excitation. The fundamental idea is illustrated by taking the simplified twodimensional harmonic oscillator shell model with the quadrupole-quadrupole effective interactions between particles.It is shown that this system successfully describes both the surface vibrational and the rotational collective motions consistently, depending upon the assumed configurations of particles in the shells.

It is suggested :from experimental data and theoretical analyses that the charge distribution function of the proton will become negative in the inner region. The analysis of Stanford data on the electron-proton scattering is reexamined, and a lower bound for (,-2)1, JJ is given model-independently from some general assumptions. As examples, two trial proton models are considered which are consistent with the prescnt Stanford data and in which the values of (,-2)1, J) are rather smallcr than the usually accepted ones.

Following the preSCrlptlon suggested by Bohr and Mottelson, we develop a formulation of theseparation of the nuclear Hamiltonian into rotational and intrinsic parts. In the light of this formulation, the foundation of various methods with the deformed potential model for the estimation of the moments of inertia for nuclear rotation is discussed and the interrelation among these methods is clarified., Treatments are restricted to the twO dimensional case for simplicity. § 1. IntroductionThe fact that the existence of rotational spectra had been confirmed in certain region$ of elements brought forward the problem of finding the transformation which leads, at least approximately, to the separation of the nuclear Hamiltonian into intrinsic and rotational parts.The early workersl) in this field succeeded in indicating the existence of rotational states of nuclei qualitatively, but they could say nothing quantitative about the values of the moments of inertia associated with these rotational motions. They gave much smaller values for the moments of inertia than those empirically determined. It has become clear in time this discrepancy originates in the poor separation of the nuclear Hamiltonian. On the other hand, various prescriptions for the calculation of the moment of inertiawithout recourse to the coordinate transformation were also proposed by many authors.2) -8) Among those, the so-called generator coordinates method2)3) and the cranking mode1 4 )-7) are most typical. The common characteristic of these methods is that the wave functions corresponding to the independent particle motions in a deformed Hartree field are used' as the model wave functions to evaluate the moment of inertia. Hence we may call them the methods with the deformed potential model.Many authors derived different expressions2) 4)8) for the moment of inertia of the rotating nucleus by making use of this deformed potential model. But, it was difficult to discuss the relative merits of these results, because the physical foundations of such calculations were not so clear. Further, as was pointed out by Lipkin,9) the question that at what stage of the calculation the model wave function is to be adopted has been left open. Thus, there are two problems in our face: the first problem is to find the compact * The author thanks the Iwanami Fujukai for the financial aid.

No abstract

It seems to be generally believed that the experiments on high-energy electron-proton and electron-deuteron scatterings and low-energy neutron-atom scattering indicatefor the mean square radii of charge and a. m. m, of the nucleon. 1) But from our previous theoretical investigations,2) we feel it rather unlikely that the current meson theory predicts such large mean square radii as shown by (2) . However, before we doubt the validity of meson theory or quantum electrodyna-Plics at short distances, we must of course examine the adequacy of deriving the results (1) and (2) froIp the