Collective States Of Even-even Nuclei Research Articles

Alternating-parity collective states of yrast and nonyrast bands in lanthanide and actinide nuclei

Excited collective states of even-even nuclei featuring quadrupole and octupole deformations are studied within a nonadiabatic collective model with a Gaussian potential energy. Rotational states of the yrast band and vibrational-rotational states of nonyrast bands are considered in detail. The energies of alternating-parity excited states of the yrast band in the 164Er, 220Ra, and 224Th nuclei; the yrast and first nonyrast bands in the 154Sm and 160Gd nuclei; and the yrast, first nonyrast, and second nonyrast bands in the 224Ra and 240Pu nuclei are described well on the basis of the proposed model.

Calculation the Energy Levels and Energy Bands and Energy Ratios for even-even154, 156,158Dy Isotopes

Summary: Interacting boson model (IBM-1) was used in the present work to study some of nuclear structures for selected Dysprosium isotope of even mass number Dy( A=154-158). The energy levels and energy ratios of these isotopes were investigated for there are experimental. The calculated results were compared with the available experimental data, the results were in general good agreement. I. Introduction The Interacting Boson Model (IBM), initially introduced by Arima and Iachello has been rather successful in describing the collective properties of several medium and heavy nuclei .We note that in the interacting boson model-1 (IBM-1)one describes an even-even nucleus as a system of N bosons able to occupy two levels, one with angular momentum re- stricted to zero (s boson) and one with angular momentum 2 (d boson). )1( II. The interacting Boson model In the simplest version of the interacting boson model (IBM-1), its assumed that low-lying collective states in even-even nuclei away from closed shells are dominated by excitation of the valence protons and the valence neutrons (particles outside the major closed shell) while the closed shell core is inert. Furthermore, its assumed that the particle configurations which are most important in shaping the properties of the low-lying states are these in which identical particles are coupled together forming pairs of angular momentum 0 and 2.(1) The interacting Boson model (IBM-1) is used in the present work, this model represents very important step formed in the description of collective nuclear excitations. The underlying U(6) group structure of model basis leads to a simple Hamiltonian which is capable of describing the three specific limits of collective structure vibrational U(5), rotational SU(3) and gamma unstable O(6). (2) The interacting boson model offers a simple Hamiltonian, capable of describing collective nuclear properties across a wide range of nuclei, based on general algebraic group theoretical techniques which have also recently found application in problems in atomic, molecular, and high- energy physics )3,4(.

Microscopic study of low energy collective states in even-even nuclei: A prospective analysis of dynamical corrections to vibrational mass parameters

A systematic study of low energy nuclear structure at normal deformation has been carried out using the Generator Coordinate Method mapped onto a 5-Dimensional Collective quadrupole Hamiltonian (5DCH) by using the Gaussian Overlap Approximation (GCM-GOA). The collective space is spanned by Hartree Fock Bogoliubov (HFB) states under axial and triaxial quadrupole constraints deduced with the D1S Gogny force. In addition, our 5DCH includes the Thouless-Valatin dynamical corrections to its rotational kinetic terms. The work is described in detail elsewhere together with the corresponding comparisons with experimental data when it is available. Many properties show a satisfactory agreement with experiment, but there is an almost systematic overestimation of vibrational band head energies, which is the subject of the present paper. We show here the performance of the theory on related observables, and propose improvements of the theory to address the problem of the vibrational band heads. An important reason for the deficient is the treatment of vibrational inertial parameters. In particular, the theory needs to include the dynamical Thouless-Valatin corrections to the vibrational terms in the 5DCH. In present work, on the aim of a simple formula grounded by known symmetry rules within the 5DCH, these dynamical TV corrections are roughly estimated, allowing us to handle their possible effects in term of spectroscopic properties, to present a guess of the next model improvment, and to isolate some areas in the chart where states Inπ = 0+2, 2+2 or 2+3 seem to have important components out of the scope of a pure collective quadrupole approach.

Q-phonon scheme in the collective nuclear model

The Q-phonon scheme developed on the basis of the algebraic collective nuclear model is discussed. It is shown that, within this scheme, low-lying collective states of even-even nuclei can be described to a precision higher than 90% of the norm by using one or, at maximum, two components of the Q-phonon basis constructed by applying a fixed number of the quadrupole operators Q to the exact ground state of the system. Various applications of this approximate scheme are discussed. It is shown that, by using this scheme, the relations between several E2-transition probabilities or between the energies of the collective states can be derived. It is also shown that the Q-phonon scheme can be used to extract information about the equilibrium shapes of nuclei and their fluctuations from data on the E2-transition probabilities.

Chaos in the low-lying collective states of even-even nuclei: Quantal fluctuations.

We study the fluctuations in the spectrum and the E2 transition intensities of the low-lying collective states in heavy nuclei. Using the interacting boson model we investigate the transition from rotational nuclei to \ensuremath{\gamma}-unstable nuclei. Near those two limits the system exhibits regular behavior but in the transition region we observe the onset of chaos where both the level statistics and the intensities statistics are described by the Gaussian orthogonal ensemble of random matrices. The systematics of the onset of chaos within different spin/parity classes are investigated. The quantal results agree with the classical mean-field analysis.

Chaos in the low-lying collective states of even-even nuclei: Classical limit.

We study the classical dynamical behavior of a family of Hamiltonians in the interacting boson model which describe the low-lying collective states of even-even nuclei. Two measures of classical chaos, the fractional volume of chaotic trajectories and the average largest Lyapunov exponent, are studied as a function of energy, angular momentum, and a parameter which interpolates between rotational and \ensuremath{\gamma}-unstable nuclei. Near these two limits the dynamics is regular but in the transition region it becomes chaotic. The results agree with a previous study of quantum chaos in the corresponding quantal model, where spectral and E(2) intensity fluctuations were analyzed. Contrary to most previous numerical studies which were restricted to unrealistic models in two degrees of freedom, the present model is realistic and has five degrees of freedom. The latter correspond to the five quadrupole nuclear shape degrees of freedom.

Chaos in the low-lying collective states of even-even nuclei.

We study the fluctuation properties of the spectrum and the electromagnetic E2 transitions of low-lying collective states in even-even nuclei. Using the framework of the interacting-boson model we discuss the transition between rotational and \ensuremath{\gamma}-unstable nuclei. Near those two limits the system exhibits regular behavior but in the transition region it shows chaotic behavior, where the fluctuations are characterized by the Gaussian orthogonal ensemble. Analysis of the classical mean-field dynamics of the five nuclear quadrupole shape degrees of freedom confirms the quantal results.

Algebraic description of intrinsic modes in nuclei

We present a procedure for extracting normal modes in algebraic number-conserving systems of interacting bosons relevant for collective states in even-even nuclei. The Hamiltonian is resolved into intrinsic (bandhead related) and collective (in-band related) parts. Shape parameters are introduced through non-spherical boson bases. Intrinsic modes decoupled from the spurious modes are obtained from the intinsic part of the Hamiltonian in the limit of large number of bosons. Intrinsic states are constructed and serve to evaluate electromagnetic transition rates. The method is illustrated for systems with one type of boson as well as with proton-neutron bosons.

Unified description of quadrupole-octupole collective states in nuclei

We present a unified description of quadropole-octupole collective states in even-even nuclei in terms of an s-p-d-f boson model. This model enables us, for the first time, to describe K=0 + and K=0 − bands within a single scheme covering vibrational to rotational situations. The moment of inertia varying within a band and the energy displacement are reproduced well. As examples, Ra and Th isotopes are analyzed.

Relativistic DWBA calculations for proton inelastic scattering

The inelastic scattering of nucleons leading to the excitation of collective states in even-even nuclei is described using a relativistic DWBA approach. The distorted waves are Dirac spinors obtained using complex vector and scalar optical potentials and the transition operators are generated by deforming these potentials. The results are compared with inelastic cross section, analyzing power and polarization transfer data in the energy range 200–800 MeV. The results are generally in good agreement with the data for collective states with small deformation parameters and, in the case of analyzing power, are somewhat superior to equivalent calculations based on the Schroedinger equation. For strongly deformed nuclei the present calculations fail in providing adequate description of the inelastic data. We compare our results with those from earlier calculations.

Relativistic DWBA calculations for polarization transfer in proton inelastic scattering

The matrix element for inelastic scattering of protons leading to the excitation of collective states in even-even nuclei is calculated in the framework of Dirac phenomenology using a DWBA approach. The deformed parts of the Lorentz scalar and four-vector optical potentials serve as the transition operators. The results are compared with the recently measured polarization transfer coefficients on 40Ca and 208Pb at 500 MeV. The agreement with experiment is good.

An extension of the interacting boson model and its application to the even-even Gd isotopes

In order to obtain a more complete description of the low-lying collective states of even-even nuclei, we present an extended version of the interacting boson model. Besides s- and d-bosons we also consider s′-, d′- and g-bosons as elementary building blocks. The model is applied on even-even Gd isotopes ( Z = 64; 90 ⩽ N ⩽ 96). We present the results of calculations of energy spectra, EQ, E2 and E4 transition properties of these nuclei.

A calculation of low-lying collective states in even-even nuclei

We present results of a calculation of the low-lying collective quadrupole states in even-even nuclei within the framework of the proton-neutron interacting boson model.

Shell model description of interacting bosons

The interacting boson model, describing collective states of even-even nuclei, is introduced as a drastic truncation of large scale shell model calculations. The shell model hamiltonian can be diagonalized by using a correspondence, or mapping, of the nucleon states in the truncated space into states obtained by coupling proton and neutron s- and d-bosons. The equivalent boson hamiltonian in a simple case is obtained and diagonalized. Eigenstates with definite proton-neutron symmetry (good F-spin) emerge for certain values of proton and neutron numbers. In general the situation is more complex but the results obtained follow closely the experimental data.

Microscopic approach to coupled modes in nuclei

A microscopic theory of low-lying collective states in even-even nuclei is developed. It treats rotations, vibrations and their coupling on the same footing. It is based on elementary transition operators, which are an extension of the phonon concept, on a density-matrix expansion in terms of these operators, and on equations of motion for the density matrix. The example of ground, beta and gamma rotational bands is treated up to second order of the density-matrix expansion. The cranking-model results for rotations and the random-phase approximation results for vibrations are reproduced, both for energies and E2 transition rates, by the same formalism in first order. For E2 transition rates the effects of rotation-quasiparticle, rotation-vibration and vibration-quasiparticle coupling are described in second order. This covers non-adiabatic corrections to the Alaga rules inside the bands and between the ground, beta and gamma bands, deviations in the intrinsic moments of the beta and gamma bands, and the beta-gamma transitional moment.

Energies of the octupole collective states of even-even nuclei in the region 228 ≤ A ≤ 254

Energies of the octupole collective states of even-even nuclei in the region 228 ≤ A ≤ 254