Yrast Band Research Articles

Shape evolution in the neutron-rich osmium isotopes: Promptγ-rayspectroscopy ofOs196

The shape transition in the neutron-rich Os isotopes is studied by investigating the neutron-rich 196Os nucleus through in-beam γ-ray spectroscopy using a two-proton transfer reaction from a 198Pt target to a 82Se beam. The beam-like recoils were detected and identified with the large-acceptance magnetic spectrometer PRISMA, and the coincident γ rays were measured with the advanced gamma tracking array (AGATA) demonstrator. The de-excitation of the low-lying levels of the yrast-band of 196Os were identified for the first time. The results are compared with state-of-the-art beyond-mean-field calculations, performed for the even-even 188−198Os isotopes. The new results suggest a smooth transition in the Os isotopes from a more axial rotational behavior towards predominately vibrational nuclei through triaxial configurations. An almost perfect γ-unstable/triaxial rotor yrast band is predicted for 196Os which is in agreement with the experimentally measured excited states.Received 14 July 2014DOI:https://doi.org/10.1103/PhysRevC.90.021301©2014 American Physical Society

Interpretation of the high spin states inLu161: A paired and unpaired study

A paired cranked Nilsson-Strutinsky-Bogoliubov (CNSB) model is presented, which employs the same method to calculate the liquid-drop energy and moment of inertia as the unpaired cranked Nilsson-Strutinsky (CNS) model. In the CNSB model, the energy minimization is carried out in the mesh of pairing gaps $\ensuremath{\Delta}$ and Fermi levels $\ensuremath{\lambda}$ as well as deformation parameters. The high spin states in $^{161}\mathrm{Lu}$ are then investigated with the CNSB and CNS models. The terminating structure shows a striking similarity with these two models. Combining the CNSB and CNS models, a complete understanding of high spin structures, including the normal deformed (ND) and triaxial strongly deformed (TSD) bands and observed side bands in $^{161}\mathrm{Lu}$, is achieved. It appears that the only important paired crossings are the first ${i}_{13/2}$ neutron crossing and the first ${h}_{11/2}$ proton crossing. For the description of the unpaired high spin crossings, it is important to be able to distinguish between the pseudospin partners in the proton $\mathcal{N}=4$ shell, $({d}_{5/2}$,${g}_{7/2}$) and $({d}_{3/2}$,${s}_{1/2}$). The yrast bands are predicted to terminate, which explains the structure of a TSD-like band X2. A band crossing at $I\ensuremath{\approx}36.5$ for the TSD band in $^{161}\mathrm{Lu}$, unique within the chain of even-$N$ Lu isotopes, is well described by the CNSB model.

Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qps. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the Projected Shell Model is expanded to include 6-qp states for both positive and negative parities. Taking $^{166}$Hf as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I \approx 34\hbar$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in $^{176}$Hf are analyzed as another example.

Study of neutron-rich Mo isotopes by the projected shell model approach

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even 102−110Mo and odd—even 103−109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The g-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for 103−107Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in 103,105Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.

Spectroscopy of 74Ge: From soft to rigid triaxiality

The first heavy ion fusion–evaporation reaction study for 74Ge has been performed through the reaction channel Zn70(Li7,2np)Ge74 at beam energies of 30 and 35 MeV. Previously known yrast band is extended to higher spins and five new collective bands are established. Based on comparison with the neighboring 72,76Ge isotopes, an intermediate pattern of energy staggering S(I) is observed in the γ band of 74Ge. The collective structure of 74Ge, including the excitation energies and transition probabilities of ground-state band and γ band, is reproduced by the state-of-the-art five-dimensional collective Hamiltonian (5DCH) model constructed from the covariant density functional. By including the 72,76,78Ge isotopes, systematical investigation of the structure evolution in Ge isotopes is performed. Based on the systematic comparisons and analysis, the triaxial evolution with spin in 74Ge is revealed and 74Ge is found to be the crucial nucleus marking the triaxial evolution from soft to rigid in Ge isotopes.

Quasiparticle alignments andα-decay fine structure of175Pt

Excited states and decay properties of ${}^{175}$Pt have been investigated using the ${}^{92}$Mo${(}^{86}\mathrm{Sr},2pn)$ fusion-evaporation reaction. The JUROGAM I $\ensuremath{\gamma}$-ray spectrometer and the GREAT spectrometer were used in conjunction with the gas-filled recoil separator RITU for the measurement of the radiation at the target and focal plane positions, respectively. Two new band structures, assigned to be based on the ${I}^{\ensuremath{\pi}}=({{}^{7}{/}_{2}}^{\ensuremath{-}})$ ground state in ${}^{175}$Pt, have been established and the known yrast band has been extended up to ${I}^{\ensuremath{\pi}}=({{}^{49}{/}_{2}}^{+})$. Rotational properties of the excited states in ${}^{175}$Pt have been investigated within the cranked shell-model formalism. The low-frequency changes in the alignments of the positive- and negative-parity bands are interpreted as a sign of proton-pair excitations in the rotating core. Furthermore, the $\ensuremath{\alpha}$-decay measurements reveal a candidate for a fourth $\ensuremath{\alpha}$-decay branch in ${}^{175}$Pt, feeding a non-yrast state in ${}^{171}$Os.

Lifetime measurements and magnetic rotation in107Ag

The excited states in ${}^{107}$Ag were populated through the heavy-ion fusion evaporation reaction ${}^{100}$Mo (${}^{11}$B, 4$n$) ${}^{107}$Ag at a beam energy of 46 MeV. Lifetimes of high-spin states in ${}^{107}$Ag have been measured through the Doppler shift attenuation method. The deduced $B(M1)$ values, gradually decreasing with increasing spin, clearly demonstrate that both the yrast positive-parity band and the yrast negative-parity band in ${}^{107}$Ag are magnetic rotation bands. Furthermore, experimental deduced $B(M1)$ values for the yrast positive-parity band are compared with the predictions of the particle rotor model. The approximate agreement between theoretical calculations and experimental results further confirms the mechanism of magnetic rotation for the yrast positive-parity band. In addition, a systematic investigation shows the evolution of the magnetic rotation mechanism in the $A\ensuremath{\approx}110$ mass region.

Energy splitting of the states in the rotational bands in 40Ca

It is demonstrated that the local-potential alpha-cluster model for 40Ca describes the basic properties of the low-lying positive-parity rotational band and the negative-parity band. The properties of the low-lying negative-parity band are interpreted in the framework of a one-dimensional model with octupole-vibration with axial symmetry. This simple model allows us to describe the spin dependence of the energy-parity splitting for the yrast band in 40Ca. A good agreement with experimental data is observed.

Identification of multi-phononγ-vibrational bands in odd-Z105Nb

Background: The odd-$Z$ ${}^{105}$Nb nucleus is located in the $A=100$ neutron-rich region. The study of multi-phonon vibrational band structures is important for understanding nuclear structure in this region.Purpose: To search for multi-phonon $\ensuremath{\gamma}$-vibrational bands in ${}^{105}$Nb.Methods: The high spin states of ${}^{105}$Nb have been studied by measuring the prompt $\ensuremath{\gamma}$ rays emitted in the spontaneous fission of ${}^{252}$Cf. The data analysis is carried out using triple- and four-fold $\ensuremath{\gamma}$ coincidence methods.Results: A new level scheme of ${}^{105}$Nb is established. The yrast band has been confirmed, and three new collective bands have been identified. Compared with previous results, a total of 14 new levels and 36 new $\ensuremath{\gamma}$ transitions are observed. Two bands built on 625.9 keV and 1231.9 keV levels are proposed as one-phonon- and two-phonon $\ensuremath{\gamma}$-vibrational bands, respectively. The evidences for supporting assignments of the multi-phonon $\ensuremath{\gamma}$-vibrational bands have been discussed. Triaxial projected shell model calculations for the $\ensuremath{\gamma}$-vibrational band structures are found in good agreement with the experimental data, thus further supporting the $\ensuremath{\gamma}$-vibrational interpretations for the experimental results in ${}^{105}$Nb.Conclusions: The one-phonon- and two-phonon $\ensuremath{\gamma}$-vibrational bands have been identified in ${}^{105}$Nb. Our results provide new data to systematically understand the characteristics of the multi-phonon $\ensuremath{\gamma}$-vibrational bands in the $A=100$ neutron-rich region.

Lifetime Measurement of the Low Lying Yrast States in 189Pt

High-spin states in 189Pt are populated through the heavy-ion fusion-evaporation reaction176Yb (18O, 5n)189Pt at 87MeV beam energy. An array consisting of 13 HPGe detectors is used in conjunction with the plunger device in CIAE. The lifetimes of two levels in the yrast band are determined by using the recoil distance Doppler shift method. The transition quadrupole moments Qt are extracted. The results show that the state has a much larger Qt value than that of the ground state, whereas the value deceases quickly with spin increasing. This may contribute to the shape driving effect of the quasi-neutron from the i13/2 orbital.

In search of empirical rule relating E21+ and B(E2; 01+→21+) in asymmetric even–even nuclei of mass region A = 90–120

The quadrupole deformation β are extracted independently from energy and transition rates. The set of asymmetric parameters γ are obtained from energy ratio [Formula: see text]. It is observed that the set of β values evaluated from B(E2) are closer to the values of β extracted from [Formula: see text] on considering the Grodzins empirical rule (Grodzins. Phys. Lett. 2, 88 (1962)) with uncertainty in even Mo, Ru, and Pd nuclei. The moment of inertia [Formula: see text] generating the yrast band in these nuclei is evaluated from [Formula: see text] using the asymmetric rotor model (Davydov and Filippov. Nucl. Phys. 8, 237 (1958)). The β, γ, and I0 values have good correlations with NpNn. In addition, β and I0 are related linearly in general. This systematic relate [Formula: see text] [Formula: see text] and asymmetric deformation γ that enables one to predict [Formula: see text], the static quadrupole moment Q0 and quadrupole deformation β of those nuclei whose only [Formula: see text] is known.

High-Spin States and Level Structure in Stable Nucleus Strontium-84

High-spin states of 84Sr are populated through the reaction 70Zn (18O, 4n) 84Sr at the beam energy of 75 MeV. The measurements of excitation functions, γ-γ coincidences, directional correlations of oriented states (DCO) ratios and γ-transition intensities are performed using eight anticompton HPGe detectors and one planar HPGe detector. Based on the experimental results, we establish a new level scheme of 84Sr, in which 12 new states and nearly 30 new γ-transitions are identified in the present work. The positive-parity yrast band is extended to spin Iπ = 24+, while one negative-parity band is extended to spin Iπ = 19− and it is found that the even-spin and odd-spin members in high-spin states show the nature of signature staggering. The deformation of 84Sr is studied by calculating the total-Routhian-surfaces (TRS) of positive-parity yrast states in the cranked shell model formalism.

Signature splitting and magnetic rotation in86Y

Based on recent experimental data, the band structure of the odd-odd nucleus ${}^{86}$Y has been studied. The positive-parity yrast band built on the configuration $\ensuremath{\pi}{g}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}^{\ensuremath{-}1}$ shows a large signature splitting, and a signature inversion occurs at $I\ensuremath{\sim}13\ensuremath{\hbar}$. The signature inversion is interpreted by the competition between single-particle and collective excitations in this nucleus. The negative-parity dipole band, which is probably connected with magnetic rotation, is assigned to the configurations $\ensuremath{\pi}{g}_{9/2}^{2}{({p}_{3/2}/{f}_{5/2})}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}^{\ensuremath{-}1}$ before and to $\ensuremath{\pi}{g}_{9/2}^{2}{({p}_{3/2}/{f}_{5/2})}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}^{\ensuremath{-}3}$ after the alignment. Self-consistent titled axis cranking calculations based on relativistic mean-field theory are performed to interpret the rotational structure. Characteristic features of magnetic rotation are found for the negative-parity band.

Structure of nearly degenerate dipole bands in 108Ag

The high spin negative parity states of 108Ag have been investigated with the 11B+100Mo reaction at 39 MeV beam energy using the INGA facility at TIFR, Mumbai. From the γ–γ coincidence analysis, an excited negative parity band has been established and found to be nearly degenerate with the ground state band. The spin and parity of the levels are assigned using angular correlation and polarization measurements. This pair of degenerate bands in 108Ag is studied using the recently developed microscopic triaxial projected shell model approach. The observed energy levels and the ratio of the electromagnetic transition probabilities of these bands in this isotope are well reproduced by the present model. Further, it is shown that the partner band has a different quasiparticle structure as compared to the yrast band.

Microscopic study of positive-parity yrast bands of 224−234Th isotopes

The positive-parity bands in 224 − 234Th are studied using the projected shell model (PSM) approach. The energy levels, deformation systematics, B(E2) transition probabilities and nuclear g-factors are calculated and compared with the experimental data. The calculation reproduces the observed positive-parity yrast bands and B(E2) transition probabilities. Measurement of B(E2) transition probabilities for higher spins and g-factors would be a stringent test for our predictions. The results of theoretical calculations indicate that the deformation systematics in 224 − 234Th isotopes depend on the occupation of low k components of high j orbits in the valence space and the deformation producing tendency of the neutron–proton interaction operating between spin orbit partner (SOP) orbits, the [(2g9/2) π –(2g7/2) ν ] and [(1i13/2) π –(1i11/2) ν ] SOP orbits in the present context. In addition, the deformation systematics also depend on the polarization of (1h11/2) π orbit. The low-lying states of yrast spectra are found to arise from 0-quasiparticle (qp) intrinsic states whereas the high-spin states turn out to possess composite structure.

Doublet bands in 128La and systematic features of energy separation of doublet bands observed in the A∼130 mass region

High spin states of 128La have been studied through the fusion-evaporation reaction 118Sn(14N, 4n)128La at a beam energy of 69 MeV. A positive-parity side band with the same configuration as that of the yrast band has been identified. Moreover, it is noted that the energy separation ΔE(I) = E(I)side − E(I)yrast of all doublet bands reported in odd-odd nuclei in the A∼130 mass region exhibit a staggering pattern systematically, and they stagger up at even-spin and stagger down at odd-spin.

Signature splitting inversion and backbending in80Rb

High-spin states of ${}^{80}$Rb are studied via the fusion-evaporation reactions ${}^{65}$Cu+${}^{19}$F, ${}^{66}$Zn+${}^{18}$O, and ${}^{68}$Zn+${}^{16}$O with the beam energies of 75 MeV, 76 MeV, and 80 MeV, respectively. Twenty-three states with twenty-eight \ensuremath{\gamma} transitions are added to the previously proposed level scheme, where the second negative-parity band is significantly pushed up to spins of 22${}^{\ensuremath{-}}$ and 15${}^{\ensuremath{-}}$ and two sidebands are built on the known first negative-parity band. Two successive band crossings with frequencies 0.51 MeV and 0.61 MeV in the \ensuremath{\alpha} $=$ 0 branch as well as another one in the \ensuremath{\alpha} $=$ 1 branch of the second negative-parity band are observed. Signature inversions occur in the positive-parity and first negative-parity bands at the spins of 11$\ensuremath{\hbar}$ and 16$\ensuremath{\hbar}$, respectively. The signature splitting is seen obviously in the second negative-parity band, but the signature inversion is not observed. It is also found that the structure of the two negative-parity bands is similar to that of its isotone ${}^{82}$Y. Signature inversion in the positive-parity yrast band with configuration \ensuremath{\pi}${g}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}$ in this nucleus is discussed using the projected shell model.

Tidal Waves inPd102: A Rotating Condensate of MultipledBosons

Low-lying collective excitations in even-even vibrational and transitional nuclei may be described semiclassically as quadrupole running waves on the surface of the nucleus ("tidal waves"), and the observed vibrational-rotational behavior can be thought of as resulting from a rotating condensate of interacting d bosons. These concepts have been investigated by measuring lifetimes of the levels in the yrast band of the (102)Pd nucleus with the Doppler shift attenuation method. The extracted B(E2) reduced transition probabilities for the yrast band display a monotonic increase with spin, in agreement with the interpretation based on rotation-induced condensation of aligned d bosons.

A semi-microscopic approach to the backbending phenomena in even-even nuclei

The phenomenon of backbending in rare earth nuclei is described by means of the band hybridization mechanism. The hybridization of two rotational bands is performed by treating a model Hamiltonian associated with a set of interacting particles moving in a deformed mean field and coupled to a phenomenological core described in terms of quadrupole boson operators, in a product space of angular momentum projected states. The model states for the ground and S bands are obtained by angular momentum projection of a deformed product state with an axially symmetric coherent boson state standing for the core factor function and a BCS type single-particle factor function defining the nature of the band. The yrast band energies are defined by the lowest eigenvalues of the model Hamiltonian in an orthogonal basis constructed by diagonalizing the overlap matrix of the ground and S band states, which are not mutually orthogonal. The formalism is positively tested on six deformed even-even nuclei known to exhibit a backbending behavior in their moment of inertia.

Emergence of rotational bands in ab initio no-core configuration interaction calculations of light nuclei

The emergence of rotational bands is observed in no-core configuration interaction (NCCI) calculations for the odd-mass Be isotopes (7⩽A⩽13) with the JISP16 nucleon–nucleon interaction, as evidenced by rotational patterns for excitation energies, quadrupole moments, and E2 transitions. Yrast and low-lying excited bands are found. The results demonstrate the possibility of well-developed rotational structure in NCCI calculations using a realistic nucleon–nucleon interaction.