Interplay of collective and single-particle properties of excited states of deformable odd nuclei 155 Eu and 161 Tm
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CLEI Theory
Interplay of Collective and Single-Particle Properties of Excited States of Deformable Odd Nuclei 155Eu and 161 Tm Sh. Sharipov, M. J. Ermamatov*, and J. K. Bayimbetova Institute of Nuclear Physics, Uzbek Academy of Sciences, pos. Ulughbek, Tashkent, 702132 Republic of Uzbekistan Received November 2, 2006; in final form, April 3, 2007
Abstract—The properties of excited states of two deformable odd nuclei are investigated within the nonadiabatic model previously developed by the present authors. The results of relevant calculations are compared with available experimental data. PACS numbers: 21.60.-n; 21.60.Ev DOI: 10.1134/S1063778808020026
1. INTRODUCTION Some regularities observed in the spectra of excited states of even–even nuclei were explained in the adiabatic approximation [1–4], where the interaction between single-particle and collective excited states is disregarded. However, this approximation is inapplicable to odd nuclei since the energies of singleparticle excitations in such nuclei are on the same order of magnitude as the energies of rotations and vibrations of the nuclear surface, so that the isolation of single-particle excitations is hardly legitimate. The classification of excited states depends on the choice of phenomenological potential for surface vibrations. Deformable even–even nuclei were investigated in [4], the potential for longitudinal surface vibrations being chosen there in such a way that the β-vibration quantum numbers appeared to be integral. As a result, their determination does not require solving transcendental equations. A simple form of the resulting equations facilitates a physical interpretation of excited states. This choice of potential was also very useful for studying complex excited states of deformable odd nuclei [5, 6]. In view of this, our group developed a model [5– 8] of deformed odd nuclei, taking into account the interaction of collective and single-particle degrees of freedom for various potentials of longitudinal surface vibrations and considering individually nuclei whose nonaxiality is small [6, 8] and those whose nonaxiality is arbitrary [5, 7]. In the present study, we explore the properties of excited states of two deformable odd nuclei 155 Eu and 161 Tm in the approximation of small nonaxiality, *
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relying on the model developed in [8], where we employed an exponential potential for longitudinal surface vibrations, which, in determining β vibrations, also admits integral quantum numbers in the region of deformed nuclei [7, 8]. 2. ENERGIES OF LEVELS AND WAVE FUNCTIONS Suppose that an odd nucleus executes small β and γ vibrations about the equilibrium values β0 = 0 and γ0 ≈ 0. In this case, the respective excited state of deformable odd nuclei characterized by a small non¨ axiality can be determined by using the Schrodinger equation [1, 2, 6, 8] ˆ rot + H ˆ p (x) + H(x) ˆ int Ψ = EΨ, ˆv + H (1) H ˆ int is the Hamiltonian of the outer nuˆp + H where H ˆ p takes into cleon in the field of the nuclear core; H account the
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