arXiv subjects

Parviz Gulshani

Publications and source records attributed to Parviz Gulshani.

10 recordsLinked to original sources

arXiv2026

Algebraic Nilsson cranking model and its prediction for 20Ne

Previously, Nilsson-Ragnarsson solved numerically the conventional cranking model (CCRM3) with deformed oscillator potential and spin-orbit interaction (refer to as Nilsson CCRM3) and predicted the 20Ne ground-state rotational-band yrast energies at the angular momenta I=2,4,6, and 8. However, CCRM3 is semi-classical and phenomenological and breaks a number of nuclear symmetries. Recently, we developed, starting from the nuclear Schrodinger equation, a microscopic, quantal, self-consistent cranking model (MSCRM3), where, among other features, the angular velocity is microscopic derived. We solved algebraically the MSCRM3 equations for the pure oscillator potential and used the model to predict energies and rotation types in 20Ne. Some interesting results were obtained, such as the quenching or the transition of planar rotation to a uniaxial rotation thereby reducing the excitation energy at I=8 in 20Ne. In this article, we use the algebraic method developed in our MSCRM3 analysis to solve iteratively the self-consistent Nilsson-CCRM3 Schrodinger equation. The application of this algebraic Nilsson-CCRM3 model to the 20Ne nucleus predicts ground-state rotational-band excitation energies at the angular momenta I=2,4,6, and 8 that are in a much better agreement with the measured energies than those predicted earlier by Nilsson-Ragnarsson using a numerical solution method. This agreement and the predicted excited-state energies at I =4 and 8 that vary periodically with the iteration steps (because of single-particle level crossings) provide a possible explanation for the measured lower yrast-state energies at I =4 and 8 relative to those at the I =2 and 6, somewhat resembling the quenching of planar rotation at I =8 mentioned above. This better agreement may also provide a further indication of the weakness of the pairing correlations in 20Ne.

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arXiv2023

Microscopic triaxial cranking model: preliminary predictions for oscillator potential and light nuclei

The conventional cranking model for uniaxial and triaxial rotation (CCRM3) is frequently used to study rotational features in deformed nuclei. However, CCRM3 is semi-classical and phenomenological because it uses a constant angular velocity, resulting in a number of Hamiltonian symmetry breakings. To investigate the effect of a dynamic angular velocity, a quantal, microscopic, D2, signature, and time-reversal invariant cranking model for triaxial rotation (MSCRM3) is derived exactly from a unitary rigid-flow-velocity-field rotation transformation of the nuclear Schrodinger equation and Hartree-Fock method. Except for a microscopically-determined angular velocity and normally-small residual terms, the MSCRM3 and CCRM3 Schrodinger equations are identical in form. The microscopic angular velocity emerges from the HF variation, and the residual terms may become significant for triaxial rotation at high spins and in back-bending regions where and undergo large changes. A preliminary application of MSCRM3 and CCRM3 to the light nuclei 20Ne, 24Mg, and 28Si using the simple self-consistent deformed harmonic oscillator potential predicts some interesting differences between the rotational features and phenomena predicted by the two models. These differences are attributable to the impact of the dynamic angular velocity. It is important to investigate and understand these differences for the simple and realistic nuclear interactions.

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arXiv2023

Predictions of conventional and microscopic triaxial cranking models for light nuclei

The conventional cranking model for uniaxial rotation is frequently used to study rotational features in deformed nuclei. However, the model uses a constant angular velocity. To investigate the effect of a dynamic angular velocity, a quantal microscopic time-reversal and D2 invariant cranking model for triaxial rotation (MSCRM3) including residual correction terms is derived from a unitary transformation of the nuclear Schrodinger equation and using Hartree-Fock approach. Except for the angular velocity and residual terms, MSCRM3 and the conventional cranking model for triaxial rotation (CCRM3) Schrodinger equations are identical in form, and are solved iteratively in a similar manner. The article identifies the differences in the rotational features predicted by CCRM3 and MSCRM3 for 20Ne, 24Mg, and 28Si using a self-consistent deformed harmonic-oscillator potential. The rotational features studied are: rotational relaxation of the intrinsic system, stability of the rotational states, various rotation modes, nuclear shapes, their transitions, and band termination. MSCRM3 predicts the observed reduced energy-level spacing in 20Ne between J=6 and 8 and attributes its occurrence to quenching of a wobbly rotation. The remaining discrepancy between the observed and MSCRM3-predicted excitation energies for 20Ne is removed by including the spin-orbit interaction and the residuals of the square of the angular momentum and interaction. CCRM3 does not predict the three dimensional phenomena predicted by MSCRM3 (such as the reduced energy-level spacing in 20Ne and the rotational-band termination at J=12 in prolate 28Si and triaxial 24Mg, etc. arising from the angular velocity). We, therefore, conclude that CCRM3 is effectively a uniaxial rotation model. Therefore, using CCRM3 or its uniaxial version, one would miss capturing three-dimensional rotation phenomena.

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arXiv2020

Microscopic quantum ideal rotor model and related self-consistent cranking model, I: uni-axial rotation case

A microscopic quantum ideal rotor-model Hamiltonian (distinct from that of Bohr's rotational model) is derived for a rotation about a single axis by applying a dynamic rotation operator to the deformed nuclear ground-state wavefunction. It is shown that the microscopic ideal rotor Hamiltonian is obtained only for a rigid-flow prescription for the rotation angle, with the attendant rigid-flow kinematic moment of inertia. (For the center-of-mass motion, the method predicts the correct mass.) Using Hartree-Fock variational and second quantization methods, the ideal rotor-model Hamiltonian is reduced to that of a self-consistent cranking model plus residual terms associated with the square of the angular momentum operator and a two-body interaction. The approximations and assumptions underlying the conventional cranking model are revealed. The resulting nuclear Schrodinger equation, including a residual two-body interaction and the residual part of the square of the angular momentum, is then solved in the Tamm-Dancoff approximation using he eigenstates of the self-consistent cranking model, with a self-consistent deformed harmonic oscillator potential, as the particle-hole basis states. Good agreement is obtained between the predicted and measured ground-state rotational-band excitation energies, including the lowering of the excitation energy with increasing angular momentum, in Ne-20 when the effects of a 3-D rotation are simulated in the model.

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arXiv2019

Microscopic quantum ideal triaxial rotor model and related self-consistent cranking model: slow-wobbling rotation in Ne-20

A microscopic quantum ideal rotor-model intrinsic Hamiltonian for triaxial rotation is derived from the nuclear Schrodinger equation by applying a rotation operator to a deformed nuclear ground state. This Hamiltonian is obtained only when a rigid-flow prescription is used for the three rotation angles in the rotation operator. Using Hartree-Fock variational and second quantization methods, the rotor Hamiltonian is transformed into that of a self-consistent triaxial cranking model (MSCRM-3) with a self-consistent angular-velocity vector, plus residual terms associated with the square of the angular momentum operator and with a two-body interaction. The approximations underlying the conventional cranking model are revealed. For a self-consistent deformed harmonic oscillator potential, the MSCRM-3 Schrodinger equation is transformed into that of a uniaxial cranking model plus local potential-energy cross terms using a rotation of the co-ordinate system. It is shown that uniform rotation is not generally possible. However, for a slow-wobbling rotation, an approximate uniform rotation becomes possible. In this limiting wobbly motion, the potential-energy cross terms are negligibly small, and the uni-axial cranking-model equation is solved analytically using a generalization of the isotropic-velocity-distribution condition of Bohr-Mottelson and Ripka-Blaizot-Kassis. The ground-state rotational-band excitation energy and quadrupole moment are calculated and compared with the measured data in Ne-20 . The results explain the mysterious decrease in the excitation-energy level spacing with increasing angular momentum. The impact of the residual of the square of the angular momentum and a separable quadrupole-quadrupole two-body interaction is studied in the Tamm-Dancoff approximation.

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arXiv2017

A microscopic cranking model for uni-axial rotation with vanishing collective angular momentum

The rigid-irrotational flow transformation in the previous microscopic cranking model (MCRM) for nuclear collective rotation about a single axis and its coupling to intrinsic motion is generalized. This generalization allow us to consider the limit of vanishingly small collective angular velocity and hence collective angular momentum while the collective moment of inertia remains finite. In this limit, the collective flow become large and oppose one another collaborating the vanishing of the collective angular momentum. In this limit, the MCRM equation for the angular-momentum constraint on the intrinsic wavefunction becomes identical to that of the conventional cranking model (CCRM). In this limit, the MCRM Schrodinger equation also becomes identical to that of the CCRM with an added irrotational-flow kinetic energy component. In this limit, the time-reversal invariance of the MCRM Schrodinger equation is destroyed. The two MCRM equations (with no free parameters) are solved for the ground-state rotational band in the nucleus for a simple deformed harmonic oscillator potential. The predicted excitation energy and quadrupole moment are close to those observed empirically, with the differences seemingly attributable to the absence, in the model, of pairing correlations at low angular momenta and Coriolis-force induced quasi-particle rotation alignment at higher angular momenta. The ground-state terminal (cut-off) angular momentum is predicted to be 10 instead of 8 observed empirically and predicted by the CCRM. It is assumed that pairing correlations would reduce the cut-off angular momentum.

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arXiv2016

A microscopic cranking model for nuclear collective rotation I: rigid-plus-irrotational-flow rotating frame

We derive in a simple manner and from first principles the Inglis semi-classical phenomenological cranking model for nuclear collective rotation. The derivation transforms the nuclear Schrodinger equation (instead of the Hamiltonian) to a rotating frame using a product wavefunction and imposing no constraints on either the wavefunction or the nucleon motion. The difference from Inglis model is that the frame rotation is driven by the motions of the nucleons and not externally. Consequently, the transformed Schrodinger equation is time-reversal invariant, and the total angular momentum is the sum of those of the intrinsic system and rotating frame. In this article, we choose the rotation of the frame to be given by a combination of rigid and irrotational flows. The dynamic angular velocity of the rotating frame is determined by the angular momentum of the frame and by a moment of inertia that is determined by the nature of the flow combination. The intrinsic-system and rotating-frame angular momenta emerge to have opposite signs. The angular momentum of the rotating frame is determined from requiring the expectation of the total angular momentum to have a given value. The transformed Schrodinger equation has, in addition to the Coriolis energy term, a rigid-flow type kinetic energy term that is absent from the conventional cranking model Schrodinger equation. Ignoring the relatively small effect of the fluctuations in the angular velocity and for a self-consistent deformed harmonic oscillator mean-field potential, the resulting Schrodinger equation is solved for the ground-state rotational band excitation energy and quadrupole moment in different configurations of Ne-20 and the results are compared with those of the conventional cranking model and empirical data.

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arXiv2016

A microscopic nuclear collective rotation-vibration model: 2D submodel

We develop in this article a microscopic version of the successful phenomenological hydrodynamic Bohr-Davydov-Faessler-Greiner (BDFG) model for the collective rotation-vibration motion of a deformed nucleus. The model derivation is not limited to small oscillation amplitudes. The model generalizes the author's previous model to include interaction between collective oscillations in each pair of spatial directions, and to remove many of the previous-model approximations. To derive the model, the nuclear Schrodinger equation is canonically transformed to collective coordinates and then linearized using a constrained variational method. The associated transformation constraints are imposed on the wavefunction and not on the particle co-ordinates. This approach yields four self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. To facilitate comparison with the BDFG model, simplify the solution of the equations, and gain physical insight, we restrict in this article the collective oscillations to only two space dimensions. For harmonic oscillator mean-field potentials, the equations are then solved in closed forms and applied to the ground-state rotational bands in some even-even light and rare-earth nuclei. The computed ground-state rotational band excitation energy, quadrupole moment and electric quadrupole transition probabilities are found to agree favourably with measured data and the results from mean-field, Sp(3,R), and SU(3) models.

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arXiv2015

A microscopic derivation of nuclear collective rotation-vibration model, axially symmetric case

We derive a microscopic version of the successful phenomenological hydrodynamic model of Bohr-Davydov-Faessler-Greiner for collective rotation-vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitude. The nuclear Schrodinger equation is canonically transformed the to collective co-ordinates, which is then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger equations for the rotation-vibration and intrinsic motions, and a self-consistency equation. For harmonic oscillator mean-field potentials, these equations are solved in closed forms and applied to the ground-state rotational bands in some axially-symmetric nuclei. The results are compared with the measured data.

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arXiv2014

A microscopic quantal self-consistent cranking model for oscillations in spherical nuclei

In this article, we transform the previously-derived microscopic rotational-model Schrodinger equation into a form suitable for describing oscillations-coupled-to-intrinsic motion in spherical nuclei. The resulting equation is decomposed into two coupled cranking-type equations, one for the oscillation and another for the intrinsic motion, using a product wavefunction and a constrained variational method. The energy and cranking parameters in the coupled equations are self-consistently determined as functions of the system parameters by the solutions of the equations themselves. This self-consistency makes the two equations time-reversal invariant, unlike the conventional phenomenological cranking models. The self-consistency and time-reversal invariance accept only real solutions to the equations. For the harmonic oscillator mean-field potential, we explicitly determine these solutions and the corresponding eigenvalues, and derive the set of equations that determine self-consistently the parameters. To explore the relative importance of the various model features and approximations, we perform a preliminary scoping calculation of the excitation energy of the first excited states in the light nuclei using a sum rule to determine the oscillation frequency. The preliminary results indicate that, except in the lightest nuclei, the excitation energies are significantly overpredicted in the light nuclei due to the neglect, among other factors, of the deformation degree of freedom. The model derivation presented here serves as guide for eventually developing a corresponding model for the vibrational-rotational motion in deformed nuclei.

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