Low-lying Rotational Bands Research Articles

The first and second crossings in low-lying rotational bands of Er isotopes: A systematic study

Essential understanding about the structure of rotating nuclei has come from the study on the band crossings which are often associated with the alignment of a pair of quasiparticles. In this work, the first and second discontinuities in the low-lying rotational bands of [Formula: see text]Er nuclei have been investigated systematically, for the first time, within the paired cranked Nilsson–Strutinsky–Bogoliubov (CNSB) framework. Our calculations show these irregularities are related to the high-j intruder [Formula: see text] neutron and [Formula: see text] proton alignment, which is consistent with the previous studies within the cranked shell model (CSM) approach. A comparison was made with the experimental data where available, and good agreement is observed.

Magnetic properties of the excited states of <sup>156</sup>Gd

Theoretical calculations within the framework of a phenomenological model with Coriolis mixing of states of low-lying positive-parity rotational bands were performed for 156Gd. The Coriolis interaction allows to explain the observed non-adiabaticity effects in the properties of the excited states. Reduced probabilities of the M1 transitions B(M1) and multipole mixing coefficients \(\delta ({{E{\text{2}}} \mathord{\left/ {\vphantom {{E{\text{2}}} {M{\text{1}}}}} \right.} {M{\text{1}}}})\) for transitions from vibrational states were calculated. The behavior of the probabilities of M1 transitions from the mixing states as a function of the total angular momentum was studied. The agreement of the theoretical results with experimental data is, in the whole, satisfactory.

Proton-neutron symplectic model description of 20Ne

A microscopic description of the low-lying positive-parity rotational bands in 20Ne is given within the framework of the symplectic-based proton-neutron shell-model approach provided by the proton-neutron symplectic model (PNSM). For this purpose, a model Hamiltonian is adopted. This includes an algebraic interaction lying in the enveloping algebra of the dynamical group of the PNSM, which introduces both horizontal and vertical mixings of different irreducible representations within the irreducible collective space of 20Ne. A good overall description is obtained for the excitation energies of the ground and first two excited β bands, including the ground state intraband quadrupole collectivity and the known interband transition probabilities between the low-lying collective states, without utilizing an effective charge.

Triaxial rigidity of Er166 and its Bohr-model realization

The triaxial nature of low-lying rotational bands of $^{166}\mathrm{Er}$ is presented from the viewpoint of the Bohr Hamiltonian and from that of many-fermion calculations by the Monte Carlo shell model and the constrained Hartree-Fock method with projections. A recently proposed novel picture of those bands suggests definite triaxial shapes of those bands, in contrast to the traditional view with the prolate ground-state band and the $\ensuremath{\gamma}$-vibrational excited band. Excitation level energies and $E2$ transitions can be described well by the Bohr Hamiltonian and by the many-fermion approaches, where rather rigid triaxiality plays vital roles, although certain fluctuations occur in shell-model wave functions. Based on the potential energy surfaces with the projections, we show how the triaxial rigidity appears and what the softness of the triaxiality implies. The excitation to the so-called double $\ensuremath{\gamma}$-phonon state is discussed briefly.

Study of excited states and observation of collective level structures in the odd–odd nucleus $${}^{194}$$Bi

High-spin states of the odd–odd $${}^{194}$$ Bi nucleus have been studied by means of nuclear spectroscopy for the first time. Two low-lying rotational bands were observed. The positive-parity band built on a short-lived isomeric state 633 keV above the $$\alpha $$ and $$\beta $$ decaying long-lived (10 $$^-$$ ) state is assigned a $${\pi i_{13/2} \otimes \nu i_{13/2 }^{-1}}$$ configuration, while the other band is attributed to the $${\pi h_{9/2} \otimes \nu i_{13/2 }^{-1}}$$ configuration. Both of these bands are assumed to have oblate shape. Three band-like structures composed predominantly of $$\Delta I = 1$$ transitions were also found. One of the shears band candidates is firmly linked to the lower lying level structures whereas for the other two links to lower-lying structures remain missing.

ALPHA-RESONANCES IN MEDIUM AND HEAVY NUCLEI I. Review of phenomenological models

"The low-lying rotational bands in light nuclei were explained a long time ago by α-clusters orbiting around the remaining core. These quasimolecular states are related to an enhancement of the elastic α-particle cross section at large angles, the so-called Anomalous Large Angle Scattering (ALAS) phenomenon. On the other hand, α-particles were evidenced by the discovery of the α-decay for nuclei with Z > 50. We used a phenomenological model of an α-particle moving in a pocket-like potential, able to explain the ALAS phenomenon, in order to understand the main features of the decay data between ground and excited states. Then we extended the Brink model, explaining giant resonances, and presented a possibility to detect α-like collective resonances."

Phenomenological Analysis of Characteristics of Rotational Bands in $$^{{158,160}}$$Gd Isotopes

Nonadiabatic effects manifested in the energies of states and the probabilities of electromagnetic transitions in $$^{{158,160}}$$Gd nuclei are studied in the context of a phenomenological model that takes into account Coriolis mixing of low-lying rotational bands. The energies of states of the lowest bands built at the internal $${{2}^{ + }}$$, $${{0}^{ + }}$$, and $${{1}^{ + }}$$ levels and the probabilities of $$E2$$-transitions between them are calculated. The mixing effect noticeably affects the wave functions of the band-heads. The calculated energies and probabilities of $$E2$$-transitions are in general satisfactory agreement with experimental data.

Modified particle-rotor model and low-lying rotational bands in odd-A triaxial nuclei

The low-lying rotational bands of triaxially deformed nuclei 137Pr, 137Pm and 139Eu are studied with a modified particle-rotor model following the nonadiabatic quasiparticle approach. The matrix elements of the odd-A nucleus are obtained in terms of a coupling matrix and the rotational energies of the even–even core. The spectra of the cores 136Ce, 136Nd and 138Sm indicate a strong influence of triaxial deformation and vibrational degrees of freedom. These properties are appropriately carried forward to the calculations for the odd-A nucleus. We demonstrate that the ground and side bands of the odd-A nucleus and its core can be explained with the same set of deformation parameters (, γ). We argue that this method could be useful in studying the low-lying states in exotic nuclei also.

Nucleon scattering on actinides using a dispersive optical model with extended couplings

Tamura coupling model has been extended to consider the coupling of additional low-lying rotational bands to the ground state band. Rotational bands are built on vibrational bandheads (even-even targets) or single particle bandheads (odd-$A$ targets) including both axial and non-axial deformations. These additional excitations are introduced as a perturbation to the underlying axially-symmetric rigid rotor structure of the ground state rotational band. Coupling matrix elements of the generalized optical model are derived for extended multi-band transitions in even-even and odd-$A$ nuclei. Isospin symmetric formulation of the optical model is employed. A coupled-channels optical model potential (OMP) containing a dispersive contribution is used to fit simultaneously all available optical experimental databases including neutron strength functions for nucleon scattering on $^{232}$Th, $^{233,235,238}$U and $^{239}$Pu nuclei and quasi-elastic ($p$,$n$) scattering data on $^{232}$Th and $^{238}$U. Lane consistent OMP is derived for all actinides if corresponding multi-band coupling schemes are defined. Calculations using the derived OMP potential reproduce measured total cross-section differences between several actinide pairs within experimental uncertainty for incident neutron energies from 50 keV up to 150MeV. Multi-band coupling is stronger in even-even targets due to the collective nature of the coupling; the impact of extended coupling on predicted compound-nucleus formation cross section reaches 5% below 3 MeV of incident neutron energy. Coupling of ground-state rotational band levels in odd-$A$ nuclei is sufficient for a good description of the compound-nucleus formation cross sections as long as the coupling is saturated (a minimum of 7 coupled levels are typically needed).

Octupole bands and simplex inversion in the neutron-rich nucleusBa145

The issue of the existence of reflection asymmetry in $^{145}\mathrm{Ba}$ has stood for the past 30 years without a common conclusion. The recent experimental data show a number of low-lying rotational bands with alternative parities, providing more strict constraints on the relevant modeling. With a proper octupole deformation, all the observed six rotational bands in $^{145}\mathrm{Ba}$ have been well reproduced by the reflection asymmetric shell model (RASM). The three octupole deformed neutron single-particle orbitals just above the octupole shell gap 88, with $K=1/2,K=3/2$, and $K=5/2$, respectively, dominate the intrinsic configurations of the observed bands. Based on the analysis of the calculated RASM wave functions, the assignments for the observed bands have been given. The experimental yrast band ($\ensuremath{\Delta}I=1$) presents a simplex inversion at around the $11/{2}^{\ensuremath{-}}$ state where the simplex staggering phase changes. This phenomenon may be explained in the framework of the RASM as from the change of the dominate intrinsic configuration, induced by the band mixing. The present results strongly support the appearance of the reflection asymmetry in the ground and low-lying states of $^{145}\mathrm{Ba}$.

Rotational-vibrational Description of Nucleon Scattering on Actinide Nuclei Using a Dispersive Coupled-channel Optical Model

Tamura's coupling formalism has been extended to consider low-lying rotational bands built on vibrational (single-particle) band heads in well-deformed even-even (odd) actinides. These additional excitations are introduced as a perturbation to the underlying rigid rotor structure that is known to describe well the ground state rotational band of major actinides. Coupling matrix elements needed in extended Tamura's formalism are derived for both even-even and odd actinides. Employed dispersive optical model (DCCOMP) replaces the incident proton energy Ep (for proton induced reactions) by the equivalent Coulomb subtracted energy in all potential terms including both the imaginary and real potentials with the corresponding dispersive corrections. Therefore, the optical potential becomes fully symmetric for protons and neutrons. This potential is used to fit simultaneously all the available optical experimental databases (including neutron strength functions) for nucleon scattering on 238U and 232Th (even even) nuclei. Quasi-elastic (p,n) scattering data to the isobaric analogue states of the target nuclei are also used to constrain the isovector part of the optical potential. Derived Lane-consistent DCCOMP is based on coupling of almost all levels below 1 MeV of excitation energy. The ground state, octupole, beta, gamma and non-axial rotational bands are considered for even nuclei, and rotational bands built on single-particle levels – for odd nuclei. Application of derived potential to odd targets based on a new coupling scheme is foreseen.

The low-lying rotational bands of the neutron-rich nucleus 172Tm

The microscopic mechanism of four experimentally observed bands in 172Tm is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions. The experimental results, including the moments of inertia and angular momentum alignments of four bands in 172Tm are reproduced well by the particle-number conserving calculations. The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed. Other unobserved low-lying bands of 2-quansiparticles in 172Tm are predicted.

Systematics of deformed states around doubly-magic 40Ca

The low-lying rotational bands of A = 36-48 nuclei are consistently explained by starting from the recently discovered, superdeformed intrinsic state of 36Ar as the core, filling successively the first three Nilsson orbits above the Fermi border. The critical single-particle energies were obtained from experimental data as were the residual interactions in the parametrization of Brink and Kerman. Implicit are the rearrangement energies due to configuration-dependent equilibrium deformations. The binding energies of 20 experimental bandheads were used to derive the parameters while another 38 bandheads were subsequently predicted and identified almost completely. The Racavy expression reduced by 20% reproduces or predicts the values of the deformation parameter ɛ. The empirical Nilsson model amended by γ-vibrational and rotation-aligned bands accounts completely for the multi-particle excitations from the N = 2 into the N = 3 major shell which are not accessible by shell-model calculations. In the case of 40Ca a spectrum of 42 states below Ex = 8MeV is explained.

Introduction of the deformed base AMD and application to the stable and unstable nuclei

A new theoretical framework named as deformed base antisymmetrized molecular dynamics is presented. The theoretical framework enables us to describe sufficiently well the deforemd mean-field structure, cluster structure and their mixed structure within the same framework. Indeed the coexistence and mixture of the deformed mean-field structure and the cluster structure in the low-lying rotational bands of 20Ne are described well. The possible existence of the cluster core + valance neutron structure in the K π =0 3 + band of 30Ne is shown as well as the reasonable description of the observed properties of the ground bands of 30Ne and 32Mg.

The Interacting Boson Model of Dipole-Octupole Strong Correlations in SU(3) Limit for Positive Parity States**The project supported by the Fundamental Research Foundation of Shanghai Jiao Tong University

Within the framework of the Usdpf(16) interacting boson model (IBM), the effects of strong correlations of the dipole (p−-boson) and the octupole (f−-boson) degree of freedom on the positive-parity states of even-even nuclei in SU(3) limit are discussed. It is shown that configurations of an even number of many p- and f-bosons can not only be incorporated into the usual low-lying collective rotational bands, such as the ground state band, β- and γ-vibrational bands, but also naturally form the rotational bands, etc. These results are similar to that of Usdg(15)-IBM and in good agreement with the experimental data of the nucleus. Besides, several intraband E2 transition probabilities are given, which are consistent with that of Usd(6)-IBM.

Identification of spherical states at low energy in the deformed nucleus185Pt

The nucleus {sup 185}Pt, which has a strongly deformed ground state and numerous low-lying rotational bands, is shown to possess low-lying excited states which are nonrotational. This is demonstrated through the absence of rotational excitations associated with two low-spin (J= (3) /(2) ; (5) /(2) ) states at excitations between 500 and 600 keV. The implications of these observations for shape changes and shape coexistence in this region are discussed. {copyright} {ital 1998} {ital The American Physical Society}

Search for stable octupole deformation in 225Fr

Levels in 225Fr have been studied by γ-ray and conversion-electron spectroscopy following the β-decay of 225Rn, and by the 226Ra(t,α) 225Fr single-proton-pickup reaction. Multipolarities were obtained for ∼50 γ-transitions, and a level scheme was established in which definite spin-parity values were determined for over 20 of the 48 levels. Although low-lying rotational bands of both parities exist for K = 1 2 and K = 3 2 , there is no experimental evidence to claim these are parity doublets. E1 strengths connecting the K π = 3 2 ± bands are intermediate between those for nuclides which are reflection symmetric and those claimed to be octupole deformed. The (t,α) cross sections are in better agreement with those predicted for the reflection-symmetric case than with those from an octupole-deformed description. These observations may be confirming theoretical predictions that octupole correlations are important in 225Fr, but that there is no large stable octupole deformation.

Possible conservation of the K-quantum number in excited rotating nuclei.

The \ensuremath{\gamma} cascades feeding into low-K and high-K bands in ${}^{163}$Er are investigated analyzing variances and covariance of the spectrum fluctuations. From a large data set of 1${0}^{9}$ triple coincidences, \ensuremath{\gamma}-\ensuremath{\gamma} coincidence spectra gated by resolved low-lying rotational bands are analyzed. Low-K bands are found to be fed by a much larger effective number of cascades than high-K bands. The covariance between pairs of gated spectra shows that the cascades feeding low-K bands are different from those feeding the high-K bands. The persistence of the K-selection rules for the excited rotational bands within the angular momentum region $30\ensuremath{\Elzxh}\ensuremath{\le}I\ensuremath{\le}40\ensuremath{\Elzxh}$ is suggested as explanation.

Cooling and diffusion in the γ-decay of rotating nuclei

Abstract A well-deformed nucleus in an excited state at high angular momentum decays towards the yrast line mostly by statistical dipole and rotational quadrupole emission. We study the interplay of these two modes and show that the cooling can be viewed as a drift-diffusion process in the two-dimensional space of energy and angular momentum. The associated master equation is solved numerically and accurate analytic approximations are derived. It is found that within the first quarter of the cascade, the dependence on the initial condition is lost, and from then on the γ-flow follows a generic behavior. The average and the variance of the heat energy then display a quadratic and cubic dependence on the angular momentum, respectively. Moreover, the flow obeys simple scaling laws, which can easily be applied to different regions of mass and deformation. The results are compared to the observed intensities of low-lying rotational bands.

Rotational bands in the u(3)-boson model

It is shown how the u(3)-boson model with a nonscalar su(3) lowest-weight state can generate low-lying rotational bands and that it does so by the addition of vorticity degrees of freedom to the Bohr-Mottelson irrotational flow model. The model is applied to $^{20}\mathrm{Ne}$ with a $(\ensuremath{\lambda},\ensuremath{\mu})=(8,0)$ lowest-weight state and compared both with experiment and with its fully microscopic $\mathrm{sp}(3R)$ counterpart. It is shown that one can easily obtain $B(E2)$ values with the experimentally required enhancements over the simple su(3) model.NUCLEAR STRUCTURE sp(3,R), sp(6,R), su(3), collective theory, boson models.