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Register a new userSingle-phonon and multi-phonon excitations of the $gamma$ vibration in rotating odd-$A$ nuclei
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Authors
Masayuki Matsuzaki
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Multi-phonon excitations in atomic nuclei were observed very rarely although collective motions in quantum many-body systems are described as bosonic excitations. In particular, the first two-phonon $gamma$ vibrational ($2gamma$) excitation in odd-$A$ nuclei was reported in 2006 and only a few have been known. Quite recently, conspicuously enhanced $B(E2)$s feeding $2gamma$ states were observed in $^{105}$Nb and conjectured that their parent states are candidates of $3gamma$ states. In the present work, the model space is enlarged from the present authors previous calculation for $^{103}$Nb. The purpose is twofold: One is to see how the description of $2gamma$ states is improved, and the other is to examine the existence of collective $3gamma$ states, and when they exist, study their collectivity through calculating interband $B(E2)$s. The particle-vibration coupling model based on the cranking model and the random-phase approximation is used to calculate the vibrational states in rotating odd-$A$ nuclei. Interband $B(E2)$s are calculated by adopting the method of the generalized intensity relation. The present calculation reproduces the observed spectra of $0gamma$ - $2gamma$ states well and gives collective $3gamma$ states with enhanced $B(E2)$s to $2gamma$ states in $^{103}$Nb and $^{105}$Nb. The most collective $3gamma$ state with the highest $K$ at zero rotation is thought to be the main component of the observed band.
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Distribution of the two phonon $gamma$ vibrational collectivity in the rotating triaxial odd-$A$ nucleus, $^{103}$Nb, that is one of the three nuclides for which experimental data were reported recently, is calculated in the framework of the particle vibration coupling model based on the cranked shell model plus random phase approximation. This framework was previously utilized for analyses of the zero and one phonon bands in other mass region and is applied to the two phonon band for the first time. In the present calculation, three sequences of two phonon bands share collectivity almost equally at finite rotation whereas the $K=Omega+4$ state is the purest at zero rotation.
Inspired by the recent experimental data (Phys. Lett. B {bf 675} (2009) 420), we extend the triaxial projected shell model approach to study the $gamma$-band structure in odd-mass nuclei. As a first application of the new development, the $gamma$-vibrational structure of $^{103}$Nb is investigated. It is demonstrated that the model describes the ground-state band and multi-phonon $gamma$-vibrations quite satisfactorily, supporting the interpretation of the data as one of the few experimentally-known examples of simultaneous occurrence of one- and two-$gamma$-phonon vibrational bands. This generalizes the well-known concept of the surface $gamma$-oscillation in deformed nuclei built on the ground-state in even-even systems to $gamma$-bands based on quasiparticle configurations in odd-mass systems.
Evidence of strong coupling of quasiparticle excitations with gamma-vibration is shown to occur in transitional nuclei. High-spin band structures in [166,168,170,172]Er are studied by employing the recently developed multi-quasiparticle triaxial projected shell model approach. It is demonstrated that a low-lying K=3 band observed in these nuclei, the nature of which has remained unresolved, originates from the angular-momentum projection of triaxially deformed two-quasiparticle (qp) configurations. Further, it is predicted that the structure of this band depends critically on the shell filling: in [166]Er the lowest K=3 2-qp band is formed from proton configuration, in [168]Er the K=3 neutron and proton 2-qp bands are almost degenerate, and for [170]Er and [172]Er the neutron K=3 2-qp band becomes favored and can cross the gamma-vibrational band at high rotational frequencies. We consider that these are few examples in even-even nuclei, where the three basic modes of rotational, vibrational, and quasi-particle excitations co-exist close to the yrast line.
For $N=Z$ odd-odd nuclei, a three-body model assuming two valence particles and an inert core can provide an understanding of pairing correlations in the ground state and spin-isospin excitations. However, since residual core-nucleon interactions can have a significant impact on these quantities, the inclusion of core excitations in the model is essential for useful calculation to be performed. The effect of core excitations must be included in order to gain a detailed understanding of both the ground state and spin-isospin properties of these systems. To this end, we include the vibrational excitation of the core nucleus in our model. We solve the three-body core-nucleon-nucleon problem including core vibrational states to obtain the nuclear ground state as well as spin-isospin excitations. The spin-isospin excitations are examined from the point of view of SU(4) multiplets. By including the effect of core excitation, several experimental quantities of $N=Z$ odd-odd nuclei are better described, and the root mean square distances between proton and neutron and that between the center of mass of proton and neutron and core nucleus increase. Large $B$($M1$) and $B$(GT) observed for $^{18}$F and $^{40}$Ca were explained in terms of the SU(4) symmetry. The core nucleus is meaningfully broken by the residual core-nucleon interactions, and various quantities concerning spin-isospin excitations as well as the ground state become consistent with experimental data. Including the core excitation in the three-body model is thus important for a more detailed understanding of nuclear structure.
After identifying the nuclei in the regions near A =80 and A = 160 for which beta-decay rates have the greatest effect on weak and main r-process abundance patterns, we apply the finite-amplitude method (FAM) with Skyrme energy-density functionals (EDFs) to calculate beta-decay half-lives of those nuclei in the quasiparticle random-phase approximation (QRPA). We use the equal filling approximation to extend our implementation of the charge-changing FAM, which incorporates pairing correlations and allows axially symmetric deformation, to odd-A and odd-odd nuclei. Within this framework we find differences of up to a factor of seven between our calculated beta-decay half-lives and those of previous efforts. Repeated calculations with nuclei near A = 160 and multiple EDFs show a spread of two to four in beta-decay half-lives, with differences in calculated Q values playing an important role. We investigate the implications of these results for r-process simulations.
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