Optimal Intrinsic Frame of Reference for Deformed Nuclei

TL;DR

This paper develops an optimal intrinsic frame-of-reference method for deformed nuclei, improving the description of quasiparticle states by incorporating quantum rotational recoil, and demonstrates its effectiveness with model calculations on $^{163}$Er.

Contribution

It introduces a new variational approach using the optimal intrinsic frame that accounts for quantum rotational recoil, enhancing the modeling of quasiparticle states in deformed nuclei.

Findings

Improved agreement with experimental data for $^{163}$Er rotational bands.

Generalization of the cranking model including quantum recoil effects.

Enhanced theoretical framework for quasiparticle-rotation coupling.

Abstract

Nowaday, in study of effective interactions, more attention is devoted to single-particle properties of near-magic nuclei and bulk properties of deformed ones but quasiparticle states of the latter are rarely used so far because of theoretical difficulties. In particular, the angular momentum projection remains too time-consuming for such calculations and the methods, which are based on the transformation to an intrinsic frame have some unsolved problems such, e. g., as quantum fluctuations of rotational recoil in the description of quasiparticle-rotation coupling. To remove a part of these difficulties, the method of the optimal intrinsic. frame-of-reference is developed. After applying the Mikhajlov transformation to obtain the nuclear Hamiltonian in the intrinsic frame, approximate constraints on nucleon's variables are substantiated, and the quasiparticle structure of the nucleus orientation angle operators is investigated. That gives possibility to use the variational principle to derive equations for matrix elements of these operators. An approximation similar to the cranking model (CM), but with the quantum rotational recoil, is formulated, which may be considered as a generalization of the usual self-consistent CM. Simplified model calculations for rotational bands in $^{163}$Er show that taking into account the recoil operator. considerably improves the agreement with experimental data