Foundation of Deformed Potential Model for Nuclear Rotation

Abstract

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.

Molecular Theory of Relaxation Phenomena in Polymers

“…Young's modulus E of the rubber-like elasticity is expressed by E=3k TpNA/Mc. (6) Here Pis density, NA is the Avogadro number, and Me is the average molecular weight between two adjacent junction points. Eq.…”