Gamma Vibrational Bands Research Articles

Coexistence of octupole deformation and beta and gamma vibrational bands in 148Ce

From γ-γ-γ and γ-γ-γ-γ coincidence studies of spontaneous fission of 252Cf, new high spin states in 148Ce were identified. The octupole bands with s=+1 and s=−1 are expanded with spins with 28+ and 18−, respectively. Importantly, a 1γ vibrational band has been established up to 14+ and a 1β vibrational band up to 6+. The levels in γ and β bands in 148Ce are compared systematically to those in neighboring 150Nd and 152Sm isotones. This comparison informs the role of deformation and shape transition in this mass region. New 3− and 5− members of the s=+1 octupole band were observed.

E2/M1 mixing ratios in transitions from the gamma vibrational bands to the ground state rotational bands of 102, 104, 106, 108Mo, 108, 110, 112Ru, and 112, 114, 116Pd

E2/M1 mixing ratios have been measured for transitions from states in the $\gamma$ vibrational bands ( $ I^{+}_{\gamma}$ ) to states in the ground state bands ( $I^{+}$ or $ [I-1]^{+}$ ) of the neutron rich, even-even, deformed isotopes, 102, 104, 106, 108Mo, 108, 110, 112Ru, and 112, 114, 116Pd, including from states as high as $ 9^{+}_{\gamma}$ . These measurements were done using the GAMMASPHERE detector array, which, at the time of the experiment, had 101 working HPGe detectors, arranged at 64 different angles. A 62 $\mu$ Ci source of 252Cf was placed inside GAMMASPHERE yielding $5.7\times 10^{11}$ $\gamma$ - $\gamma$ - $\gamma$ and higher coincidence events. The angular correlations between the transitions from the $\gamma$ -bands to the ground bands, and the pure E2 transitions within the ground band were then measured. These angular correlations yielded the mixing ratios, demonstrating that these transitions are pure or nearly pure E2, in agreement with theory. In order to correct for possible attenuation due to the lifetime of the intermediate state in these correlations, the g-factors of the intermediate states needed to be known. Therefore, the g-factors of the 2+ states in the ground state band have been measured.

Relativistic Dirac analyses of polarized proton scatterings to the 2+ gamma vibrational band in 24Mg and 26Mg

Relativistic Dirac analyses are performed phenomenologically for the high-lying excited states that belong to the 2+ gamma vibrational band at the 800 MeV polarized proton inelastic scatterings from the s-d shell nuclei, 24Mg and 26Mg. Optical potential model is used and scalar and time-like vector potentials are considered as direct potentials. First-order vibrational collective models are used to obtain the transition optical potentials to accommodate the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically to reproduce the differential cross section and analyzing power data by varying the optical potential and deformation parameters. It is found that the relativistic Dirac coupled channel calculation could describe the high-lying excited states of the 2+ gamma vibrational band at the 800 MeV polarized proton inelastic scatterings from s-d shell nuclei 24Mg and 26Mg reasonably well, showing mostly better agreement with the experimental data compared to the results obtained from the nonrelativistic calculations. Calculated deformation parameters for the excited states are analyzed and compared with those of nonrelativistic calculations.

Infinitesimal cranking for triaxial angular-momentum-projected configuration-mixing calculations and its application to theγvibrational band

Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum from the one obtained without cranking. Employing the Gogny D1S force as an effective interaction, we apply the method to the calculation of the multiple gamma vibrational bands in $^{164}$Er as a typical example, where the angular-momentum-projected configuration-mixing with respect to the triaxial shape degree of freedom is performed. With this method, both the $K=0$ and $K=4$ two-phonon gamma vibrational bands are obtained with considerable anharmonicity. Reasonably good agreement, though not perfect, is obtained for both the spectrum and transition probabilities with rather small average triaxial deformation $\gamma\approx 9^\circ$ for the ground state rotational band. The relation to the wobbling motion at high-spin states is also briefly discussed.

Impact of triaxiality on the rotational structure of neutron-rich rhenium isotopes

A number of 3-quasiparticle isomers have been found and characterised in the odd-mass, neutron-rich, 187Re, 189Re and 191Re nuclei, the latter being four neutrons beyond stability. The decay of the isomers populates states in the rotational bands built upon the 9/2−[514] Nilsson orbital. These bands exhibit a degree of signature splitting that increases with neutron number. This splitting taken together with measurements of the M1/E2 mixing ratios and with the changes observed in the energy of the gamma-vibrational band coupled to the 9/2−[514] state, suggests an increase in triaxiality, with γ values of 5°, 18° and 25° deduced in the framework of a particle-rotor model.

Changes in rotational characters of one- and two-phonon gamma-vibrational bands in 105Mo

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.

Dirac coupled channel analyses of the 2− gamma vibrational band excitation in 20Ne

Dirac coupled channel analyses are performed using optical potential model for the high-lying excited states that belong to the 2$^-$ gamma vibrational band at the 800 MeV unpolarized proton inelastic scatterings from $^{20}$Ne. The first order vibrational collective models are used to obtain the transition optical potentials to describe the high-lying excited vibrational collective states and Lorentz-covariant scalar and time-like vector potentials are used as direct optical potentials. The complicated Dirac coupled channel equations are solved phenomenologically to reproduce the differential cross sections data by varying the optical potential and deformation parameters using minimum chi-square method. It is found that relativistic Dirac coupled channel calculation could describe the excited states of the 2$^-$ gamma vibrational band in $^{20}$Ne much better than the nonrelativistic coupled channel calculation, especially for the 2$^-$ and 3$^-$ states of the band. It is shown that the multistep excitation process via channel coupling with the $3^-$ state is essential to describe the $2^-$ state excitation and pure direct transition from the ground state is dominant for the 3$^-$ state excitation of the 2$^-$ gamma vibrational band in $^{20}$Ne.

Mixing of quasiparticle excitations andγvibrations in transitional nuclei

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.

New multi-phonon gamma vibrational bands in A∼110 neutron-rich nuclei

The high spin states of neutron-rich 103Nb, 107Tc and 109Tc nuclei in A∼110 region have been investigated by measuring prompt γ-γ-γ coincident measurements populated with the spontaneous fission of 252Cf with the Gammasphere detector array. In 103Nb, one-phonon K = 9/2 and two-phonon K = 13/2 γ-vibrational bands have been identified. In 107Tc and 109Tc, one-phonon K = 11/2 and two-phonon K = 15/2 γ-vibrational bands, in which the zero-phonon bands are based on K=7/2 excited states, have also been identified. The two-phonon bands are first observed in odd-Z nuclei. The characteristics for these band structures have been discussed.

清华大学物理系原子核结构实验研究进展

For the centenary celebration of Tsinghua University we give a brief review of the experimental research on nuclear structure by our research group in this article. The main research progress are: the shape driving effect in A≈140 neutron-deficient region, such as the oblate deformed bands, the shape coexistence etc.; the multi-phonon gamma vibrational bands, the new chiral doublet bands, the new quasi-particle bands etc. in A≈110 neutron-rich region; the octupole deformation etc. in A≈150 neutron-rich region. The research results provide new valuable information to understand the nuclear structure.

Electromagnetic properties of vibrational bands in 170Er

Excited states of the nucleus Er-170 have been studied by Coulomb excitation using the GASP gamma-ray detector system at the Laboratori Nazionali di Legnaro. The ground-state band along with a low-lying K-pi = 0(+) band and gamma-vibrational band were populated during the experiment. Based on the measured gamma-ray yields, a set of interband and intraband matrix elements has been extracted using the Coulomb excitation code GOSIA. The resulting E2 matrix elements are compared to collective model predictions.

Gamma Vibrational Bands and Chiral Doublet Bands in A≈100 Neutron-rich Nuclei

The level structures of neutron-rich 105Mo,106Mo,108Mo and 110Ru nuclei in A ≈ 100 region have been carefully investigated by coincidence measurements of the prompt γ-rays populated in the spontaneous fission of 252Cf with the Gammasphere detector array. In 105Mo,one-phonon K=9/2 and two-phonon K=13/2 γ-vibrational bands have been identified. In 108Mo,one-phonon γ-vibrational band is expanded and two-phonon γ-vibrational band has been identified. Two similar sets of bands in 106Mo and 110Ru are observed to high spins,which have been proposed as the soft chiral γ-vibrational bands. The characteristics for these γ-vibrational bands and chiral doublet bands have been discussed.

Excited levels of 148Ce

Available experimental data on excited levels of the 148Ce nucleus are analyzed. With the aid of model concepts and systematics that cover neighboring nuclei, the spectrum of 148Ce is supplemented with a K π = 2− rotational band that has a bandhead at 1368.98 keV, which extends up to the 16− state at 3897.9 keV, and which is new. Three states at E = 1422.85, 1786.57, and 2198.6 keV of spin-parity 5+, 7+, and 9+, respectively, are included in the gamma-vibrational band featuring the known 2+ and 3+ levels at 989.90 and 1116.63 keV, respectively. A significant difference in the behavior of the moments of inertia in positive-and negative-parity bands is highlighted.

Evidence of rigid triaxiality in some xenon nuclei

The present study deals with a topic of current interest, getting clear evidence for triaxiality in the 120–130 Xe nuclei near A = 130. The odd–even staggering in a so-called gamma-vibrational band may be treated using the asymmetric rotor model (ARM) on employing the Lipas parameter. The Hilbert space is too limited to describe the full variation of the moment of inertia and, therefore, the Lipas Ansatz ismade to correct the ARM energies, which conserve the good result for B(E2) values.PACS Nos.: 21.10.Re, 21.60.Ev, 27.60.+j

Evolution of 2+ γ wave functions and gamma-stiffness in well-deformed rare-earth nuclei

The evolution of the structure of the gamma-vibrational band head 2+ γ in well-deformed rare-earth nuclei is studied within the framework of RPA calculations using a quasiboson approximation based on the Nilsson model. The obtained evolution of the quasiparticle structure of the gamma-vibrational band head is shown to correlate well with the evolution of the same nuclei within the IBA symmetry triangle when described in the extended consistent-Q formalism. An empirical relation is presented that links the IBA parameter χ with the quasiparticle structure of the gamma-vibrational band head.

Unexpected rapid variations in odd-even level staggering in gamma-vibrational bands

Triple-γ coincidence data were used to study the γ-vibrational bands to 14+ in 104–106Mo, to 13+ in 108,110Ru and 17+ in 112Ru, and to 13+, 15+ in 112–116Pd. The even-odd spin energy level splittings show rapid variations with spin and neutron number in these nuclides. With one exception, the Sm-Pt nuclei show no such reversal and much smaller staggering.

The many relationships between the IBM and the Bohr model

Relationships between the IBM-1 and the Bohr collective model are explored in which the states of the IBM in its various dynamical symmetry limits are identified with subsets of Bohr model states of corresponding dynamical symmetries. The maps of interest are ones which give the contractions of the IBM in the limit of large boson number. The known map from the IBM into the Bohr model gives a contraction appropriate for the U(5) dynamical symmetry limit. A new map is given consistent with a contraction of the O(6) dynamical symmetry of the IBM. This map gives an explicit identification of IBM states in an O(6) ⊃ O(5) basis with states of the Wilets–Jean model and makes it possible to benefit from the different but complementary perspectives of the two models. For example, it leads to explicit expressions for the matrix elements of an IBM O(6) irrep in terms of the known matrix elements of the corresponding Wilets–Jean model. The relationship also shows how to obtain the familiar rotor plus beta- and gamma-vibrational bands of the Bohr–Mottelson model, in the IBM, by the addition to an O(6) Hamiltonian of a scalar cubic in the quadrupole moment operators of the type considered recently by Van Isacker. The establishment of close relationships between the two models enables one to benefit from the different and complementary perspectives they afford. For example, recent developments of an algebraic version of the collective model has shown that the Bohr model has an SU ( 1 , 1 ) × O ( 5 ) dynamical group with representations ranging from those of a spherical vibrator to a beta-vibrational soft-gamma rotor of the Wilets–Jean limit and, with the addition of an interaction, to a rotor of the standard Bohr–Mottelson type with beta- and gamma-vibrational bands. A parallel range of results can now be obtained in the IBM, albeit with some differences, within the framework of an SU ( 1 , 1 ) × O ( 5 ) dynamical group.

Systematics of theK π = 2 + gamma vibrational bands and odd-even staggering

The structure of theK π = 2+ gamma vibrational bands and the quasi-gamma bands of even-Z-even-N nuclei is investigated on a global scale, vis-a-vis the variation of band head, the moment of inertia of the band and the odd-even spin staggering. The variation withN andZ and with spinJ of the odd-even spin energy staggering index is studied and a unified view of the same is presented.

γ vibrational band and quasiparticle excitations in80Sr

Non-yrast states in ${}^{80}\mathrm{Sr}$ were populated in the ${}^{24}\mathrm{Mg}{(}^{58}\mathrm{Ni}{,2p)}^{80}\mathrm{Sr}$ reaction at 200 MeV and their \ensuremath{\gamma} decays investigated using Gammasphere, in order to investigate shape softness and quasiparticle excitations. A large data set was collected which was A and Z gated, using the Argonne Fragment Mass Analyzer and a focal plane ion chamber. The excellent channel selection enhanced the sensitivity to energetically nonfavored configurations. Several new rotational bands were found, and many conflicts between previous experiments were resolved. In particular, the gamma vibrational band is now clearly delineated, and more than ten quasiparticle bandheads have been identified. At the highest spins, evidence for a long-predicted shape change was found.

Search for two-phonon gamma vibrational states in 164Dy.

Excited states in $^{164}\mathrm{Dy}$ were produced using Coulomb excitation. Rotational properties of the ground-state and gamma-vibrational band were studied. Angular distribution and band-mixing parameters were extracted from the data. No evidence was found for a two-phonon gamma vibration with anharmonicity in the range 1.7\ensuremath{\le}E(${4}_{\ensuremath{\gamma}\ensuremath{\gamma}}^{+}$)/E(${2}_{\ensuremath{\gamma}}^{+}$)\ensuremath{\le}2.7.