Deformed Oscillator Model Research Articles

Weak quadrupole moments

We introduce the weak quadrupole moment (WQM) of nuclei, related to the quadrupole distribution of the weak charge in the nucleus. The WQM produces a tensor weak interaction between the nucleus and electrons and can be observed in atomic and molecular experiments measuring parity nonconservation. The dominating contribution to the weak quadrupole is given by the quadrupole moment of the neutron distribution, therefore, corresponding experiments should allow one to measure the neutron quadrupoles. Using the deformed oscillator model and the Schmidt model we calculate the quadrupole distributions of neutrons, Qn, the WQMs, , and the Lorentz invariance violating energy shifts in 9Be, 21Ne, 27Al, 131Xe, 133Cs, 151Eu, 153Eu, 163Dy, 167Er, 173Yb, 177Hf, 179Hf, 181Ta, 201Hg and 229Th.

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

The so-called \mu-deformed oscillator (or \mu-oscillator) introduced by A.Jannussis, though possesses rather exotic properties with respect to other better known deformed oscillator models, also has good potential for diverse physical applications. In this paper, the corresponding \mu-Bose gas model based on \mu-oscillators is explored. Within this model, the intercepts \lambda^(2)(K) and \lambda^(3)(K) of two- and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose type behavior of the intercepts of two- and three-pion correlations, observed in the experiments on relativistic heavy ion collisions. In derivation of intercepts, different orders of approximation in the deformation parameter \mu are considered. Our analysis also yields asymptotical behavior of the intercepts \lambda^(2)(K) and \lambda^(3)(K). The results for \lambda^(2)(K) are compared with experimental data, and with earlier known results drawn using other deformed Bose gas models.

Effect of nuclear deformation on the electric-dipole strength in the particle-emission threshold region

The role of nuclear deformation in the photoabsorption cross section in the tail region of the electric giant dipole resonance (GDR) is studied in terms of a deformed oscillator model and a Nilsson-plus-random-phase-approximation model. It is found within the framework of these approaches that extra electric dipole strength is generated at energies below the GDR maximum if the nuclear system is spatially deformed. This is important in the prediction of stellar photodisintegration rates, knowing that an extra strength can affect these rates even below the particle separation energies through the so-called \ensuremath{\gamma} process. Because the nuclear deformation is governed by shell effects, this extra strength does not directly correlate with the neutron excess.

SU(3) model description of Be isotopes

Experimental data on light nuclei close to dripline suggests that as the nucleon number asymmetry increases, the shell structure from stability line is not preserved. In contrast with spherical shell model, Elliott's SU(3) model, uses a deformed multi-nucleon basis to describe nuclear states. The SU(3) symmetry is a strong feature of 1p shell nuclei, where symmetry breaking spin-orbit force is rather weak. We have calculated the binding energies and low-lying energy spectra of Be isotopes (A=6 to A=14), within the framework of Elliott's SU(3) model, with special emphasis on effects due to the presence of intruder orbit 1S1/2 in the region. The model space includes SU(3) basis states that maximize the quadrupole-quadrupole interaction (-chiQ.Q). An extended model space includes, in addition, a set of 2p-2h excitations, with excited nucleons occupying lowest energy SU(3) states in harmonic oscillator shell N=2. Group theoretical methods have been used to classify the states and calculate the nuclear interaction matrix elements. Good angular momentum states are projected out from intrinsic deformed SU(3) states by using standard angular momentum projection techniques. The interaction used contains the monopole-monopole, quadrupole-quadrupole and isospin dependent terms. Interaction parameters are fixed so as to reproduce the binding of 4 nucleons in N=1 orbit for the N=Z isotope-8Be in ground state and first excited 2+ state, along with the known systematics of single neutron separation energies for Be isotopes. The calculated energy espectra are compared with available experimental data. The calculated excitation energies of intruder states in 8Be and 10Be, are discussed in the light of available experimental evidence and theoretical results from shell model as well as deformed oscillator model calculations of Fayache et al..

Question of low-lying intruder states in8Beand neighboring nuclei

The presence of not yet detected intruder states in ${}^{8}\mathrm{Be},$ e.g., a ${J=2}^{+}$ intruder at 9 MeV excitation would affect the shape of the ${\ensuremath{\beta}}^{\ensuremath{\mp}}$-delayed $\ensuremath{\alpha}$ spectra of ${}^{8}\mathrm{Li}$ and ${}^{8}\mathrm{B}.$ In order to test the plausibility of this assumption, shell-model calculations with up to $4\ensuremath{\Elzxh}\ensuremath{\omega}$ excitations in ${}^{8}\mathrm{Be}$ (and up to $2\ensuremath{\Elzxh}\ensuremath{\omega}$ excitations in ${}^{10}\mathrm{Be}$) were performed. With the above restrictions on the model spaces, the calculations did not yield any low-lying intruder state in ${}^{8}\mathrm{Be}.$ Another approach---the simple deformed oscillator model with self-consistent frequencies and volume conservation---gives an intruder state in ${}^{8}\mathrm{Be}$ which is lower in energy than the above shell-model results, but its energy is still considerably higher than 9 MeV.

Classical bifurcation and enhancement of quantum shells: Systematic analysis of reflection-asymmetric deformed oscillator

Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory reveals several aspects of quantum level structure for this non-integrable system. Good classical- quantum correspondence is obtained in the Fourier transform of the quantum level density, and importance of periodic orbit bifurcation is demonstrated. Systematic survey of the local minima of shell energies in the two-dimensional deformation parameter space shows that prominent shell structures do emerge at finite values of the octupole parameter. Correspondences between the regions exhibiting strong shell effects and the classical bifurcation lines are investigated, and significance of these bifurcations is indicated.

Comment on "Orbitial M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule"

It is pointed out that the inclusion of residual interactions in the deformed oscillator model modifies the linear energy-weighted sum rule for orbital [ital l][sup +] excitations in even-even deformed nuclei and increases the ratio of the high-frequency to the low-frequency contribution to the sum rule.

Deformation dependence of magnetic dipole strength below 4 MeV in doubly even rare earth nuclei

We show: (1) In the presence of the pair correlation the M1 transition strength calculated in the deformed oscillator model has a dependence on the quadrupole deformation parameter δ which is considerably stronger than linear and, in fact, it varies quadratically with δ in the limit of small deformation; (2) The deformation dependence in samarium isotopes calculated using the quasiparticle random phase approximation (QRPA) reproduces the qualitative behaviour of the recent experimental data of Ziegler, Rangacharyulu, Richter and Spieler.

Quantization of non-separable isoscalar vibrations in the time-dependent deformed oscillator model

Quantization of non-separable isoscalar vibrations in the time-dependent deformed oscillator model

Quantization of non-separable isoscalar vibrations in the time-dependent deformed oscillator model

Abstract We propose a new method for determining the least-coupled Hamilton system. This method is applied to describe coupled isoscalar vibrational excitations in the quantized time-dependent deformed oscillator model. Results for both least-coupled variables and excitation energies in light deformed nuclei are given and compared with those obtained in the generator coordinate method.

Isoscalar giant vibrations in the quantized time-dependent deformed oscillator model

The gauge-invariant quantization prescription is applied to the solutions of the time-dependent deformed-oscillator model (TDDOM) for the isoscalar giant multipole resonances in light atomic nuclei. The quantized TDDOM results are in good agreement with those obtained in the generator-coordinate method. The problems found in the application of the gauge-invariant quantization method to the non-separable Hamilton systems are presented.

Algebraic approach to the projected deformed oscillator model

Abstract A new method of calculation in terms of the projected deformed oscillator model is proposed. The method involves expansion of its wave functions in terms of the wave functions of an isotropic oscillator potential. Only overlap integrals between projected wave functions and reduced probabilities B (E2) of E2 transitions are examined. B (E2) values are expressed as a series containing the corresponding values of the Elliott SU(3) scheme. The convergence of these expansions is shown to be fairly good. The expectation values of operators ( QQ ) and ( QQQ ), which characterize the effective internal non-sphericity and non-axiality of the nucleus, are also calculated and discussed.

Analysis of Alpha-Decay Widths for Molecular Viewpoints in Light Nuclei

Alpha-decay widths of SU/sub 3/, deformed oscillator and cluster model wave functions are calculated quantitatively for the ground band levels of /sup 8/ Be and the first K = 0- band levels of /sup 20/Ne. Tails of the reduced width amplitudes of these model wave functions are amended by two methods, of which one is to connect smoothly the inner original reduced width amplitude with the resonance tail given by the release energy of alpha particle, and the other is to apply the Green's-function method developed by Kawai and Yazaki for the calculation of the radial form factor for the stripping or pick up reactions. From comparisons of the calculated results with experiments It is concluded that the SU/sub 3/ model is insufficient to reproduce large alpha -decay widths. It is further shown that the deformed oscillator model is also considered to be inappropriate for the general explanation of the (rotational) levels with large cluster widths. From these consequences on SU/sub 3/ and deformed oscillator models and by the numerical confirmation that the cluster model wave functions can naturally reproduce the experiments consistently With the variational energy calculations, the importance of the molecular viewpoint in light nuclei is emphasized. (auth)

Generalised quartet model for particle-hole excitations across major shells

The schematic quartet model of Arima et al. is generalised to include any number of particle-hole excitations. The assumption of constancy of particle-hole matrix elements with mass number is examined in the deformed-oscillator model and shown to be poor in certain cases. A revised picture for particle-hole excitations shows smoother trends than with the schematic model. Comparison with the Zamick model yields greater insight into the structure of two-particle excited states.

Dependence of the r.m.s. nuclear radius on the deformation parameters

The concept of "nuclear compressibility under deformation", introduced by Fradkin and others in their experimental studies of isotope shifts, is analyzed. It is shown that in the harmonic-oscillator model Fradkin's compressibility parameter ξ can occur in a natural way. Theoretical estimates of ξ are obtained, using spherical and deformed oscillator models, as ξ = −5/4π and −5/16π respectively. They bracket the experimental value [Formula: see text]. Possible improvements of these estimates are discussed.