Separation of Variables and Coupling between Rotational and Intrinsic Motion in Deformed Nuclei

Abstract

The separation of variables in the total nuclear Hamiltonian neglecting the rotation of the nucleus as a whole (but not the "core rotation") is carried out. By frame transformation the operator of the interaction between rotational and, intrinsic motions is derived for axial and non-axial nuclei. By using this operator the rotational spectra of deformed nuclei are examined.

Semiphenomenological Model of the Nucleus and its Application to Description of the Rotational Spectra. I

“…This question was briefly discussed in our paper [3], but there we did not pay sufficient attention to the problem of the exact description of the rotational bands with high values of the rotational angular momentum (Irot). This question was briefly discussed in our paper [3], but there we did not pay sufficient attention to the problem of the exact description of the rotational bands with high values of the rotational angular momentum (Irot).…”

“…Certainly all the nuclear states, the collective states including, are the states of a system of strongly interacting particles, the quantum mechanical distribution of density being stationary in the stationary states. [3,71). What is the most economical and simple (but a t the same time adequate) way of describing the nuclear states?…”

“…3 are utilized, the "isospin pairing" corresponding to the np correlations is much stronger than the "spin pairing" corresponding to the nn and pp correlations. 3 are utilized, the "isospin pairing" corresponding to the np correlations is much stronger than the "spin pairing" corresponding to the nn and pp correlations.…”

“…where J,, = MAR^ is the moment of inertia of a rigid sphere possessing the nucleus mass and radius; b1,?, 3 are the numbers which are determined by the nuclear shape (the subscripts 1, 2, 3 in this case have nothing to do with the notations of the axes v = 1, 2, 3). Assuming that a nucleus has the shape of a prolate ellipsoid of revolution, we have [24]:…”

Rotational Motion of Deformed Nuclei

“…I n the present paper the rotational Hamiltonian of the nucleus (H,,t) is obtained and investigated. The problem of the interaction between the rotation and the intrinsic motion in our approach (the operator H (rotlin)) is examined in the next paper [6] (further on referred t o as 11).…”