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Register a new userChanges in rotational characters of one- and two-phonon $gamma$-vibrational bands in $^{105}$Mo
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Authors
Masayuki Matsuzaki
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The $gamma$ vibration is the most typical low-lying collective motion prevailing the nuclear chart. But only few one-phonon rotational bands in odd-$A$ nuclei have been known. Furthermore, two-phonon states, even the band head, have been observed in a very limited number of nuclides not only of odd-$A$ but even-even. Among them, that in $^{105}$Mo is unique in that Coriolis effects are expected to be stronger than in $^{103}$Nb and $^{105}$Nb on which theoretical studies were reported. Then the purpose of the present work is to study $^{105}$Mo paying attention to rotational character change of the one-phonon and two-phonon bands. 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. The present model reproduces the observed yrast zero-phonon and one-phonon bands well. Emerging general features of the rotational character change from low spin to high spin are elucidated. In particular, the reason why the one-phonon band does not exhibit signature splitting is clarified. The calculated collectivity of the two-phonon states, however, is located higher than observed.
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In order to clarify the nature of hypernuclear low-lying states, we carry out a comprehensive study for the structure of $^{144-154}_{~~~~~~~~Lambda}$Sm-hypernuclei, which exhibit a transition from vibrational to rotational characters as the neutron number increases. To this end, we employ a microscopic particle-core coupling scheme based on a covariant density functional theory. We find that the positive-parity ground-state band in the hypernuclei shares a similar structure to that of the corresponding core nucleus. That is, regardless of whether the core nucleus is spherical or deformed, each hypernuclear state is dominated by the single configuration of the $Lambda$ particle in the $s_{1/2}$ state ($Lambda s_{1/2}$) coupled to one core state of the ground band. In contrast, the low-lying negative-parity states mainly consist of $Lambda p_{1/2}$ and $Lambda p_{3/2}$ configurations coupled to plural nuclear core states. We show that, while the mixing amplitude between these configurations is negligibly small in spherical and weakly-deformed nuclei, it strongly increases as the core nucleus undergoes a transition to a well-deformed shape, being consistent with the Nilsson wave functions. We demonstrate that the structure of these negative-parity states with spin $I$ can be well understood based on the $LS$ coupling scheme, with the total orbital angular momentum of $L=[Iotimes 1]$ and the spin angular momentum of $S=1/2$.
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.
We expand the triaxial projected shell model basis to include triaxially-deformed multi-quasiparticle states. This allows us to study the yrast and gamma-vibrational bands up to high spins for both gamma-soft and well-deformed nuclei. As the first application, a systematic study of the high-spin states in Er-isotopes is performed. The calculated yrast and gamma-bands are compared with the known experimental data, and it is shown that the agreement between theory and experiment is quite satisfactory. The calculation leads to predictions for bands based on one- and two-gamma phonon where current data are still sparse. It is observed that gamma-bands for neutron-deficient isotopes of 156Er and 158Er are close to the yrast band, and further these bands are predicted to be nearly degenerate for high-spin states.
Structure of eight superdeformed bands in the nucleus 151Tb is analyzed using the results of the Hartree-Fock and Woods-Saxon cranking approaches. It is demonstrated that far going similarities between the two approaches exist and predictions related to the structure of rotational bands calculated within the two models are nearly parallel. An interpretation scenario for the structure of the superdeformed bands is presented and predictions related to the exit spins are made. Small but systematic discrepancies between experiment and theory, analyzed in terms of the dynamical moments, J(2), are shown to exist. The pairing correlations taken into account by using the particle-number-projection technique are shown to increase the disagreement. Sources of these systematic discrepancies are discussed -- they are most likely related to the yet not optimal parametrization of the nuclear interactions used.
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