Semiclassical Features of Wobbling and Chiral Properties in Nuclei

Abstract

A semiclassical approach is used to describe the wobbling and chiral motion in even-even and odd-even nuclei The trial function involved in the variational equation for the quantal action is a coherent state for the SU(2 ) group associated to a triaxial rotor for the case of an even-even system and a coherent state for the group SU(2)$\otimes$ SU(2) describing the particle-core system. Application is made for $^{158}$Er and $^{161, 163, 165,167}$Lu, ${135}$Pr. Th parameters involved in the coherent state expression are complex numbers depending on time and play the role of the phase space generalized conjugate coordinates whose equation of motion may be brought to the Hamilton canonical form.Within a harmonic approximation one analytically obtains the wobbling frequencies which are further used to calculate the excitation energies for the states forming a band. A new procedure to quantize the classical orbitals is proposed. In the new picture the electromagnetic transition probabilities are calculated both for the in-band and the intraband transitions. Additionally, for odd systems, some other observable like aligned angular momentum, excitation energies relative to a reference spectrum, dynamic moment of energies are calculated and compared with the corresponding experimental data.In the parameter space one identified several nuclear phases with specific properties. An example is given where the wobbling and chiral motions coexist. The existence of a transversal wobbling is widely commented. A new boson representation for the angular momenta is proposed. The approach was successfully applied to $^{135}$Pr. One concludes that semiclassical description is an efficient tool to account quantitatively for the wobbling and chiral properties in nuclei.