arXiv subjects

B. Mohammed-Azizi

Publications and source records attributed to B. Mohammed-Azizi.

9 recordsLinked to original sources

arXiv2021

Derivation of the Strutinsky method from the least squares principle

The main purpose of this paper is to rigorously establish the Strutinsky method from the least squares principle. Thus, it is the mathematical basis of this method (aspect often neglected) which is revisited in an extensive way. Some formulas previously given without demonstration or in a simplified way are set out here with all the details. In this respect, the most important mathematical properties of the averaging functions are also established in this paper. When some conditions are met, it turns out that Strutinsky's method is nothing more than a polynomial moving average of the semi-classical level density.

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arXiv2019

Better insight into the Strutinsky method (published version)

Strutinsky's method is reviewed through a new understanding. This method depends on two free parameters: The smoothing parameter and the order of the curvature correction. It turns out that this method is nothing but a compromise between two fundamental conditions which are the so-called asymptotic limit which comes from the so-called remainder which imposes a small as possible smoothing parameter and the smoothing condition which forces that parameter to be, at least, slightly larger than the inter shell spacing. In this paper, to find the best value of the smoothing parameter, a new criterion is proposed instead of the plateau condition . This new criterion is much more clear and free from ambiguities of the usual plateau condition. It is also found, that the second free parameter, i.e., the order of the curvature correction, plays an accessory role since, it is connected intimately to the smoothing parameter, when the smoothing is realized. This paper provides a new and definitive insight into Strutinsky's method and its relationship with semi-classical methods.

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arXiv2015

Shape transition in the even-even Cerium isotopes

The deformation energy of the even-even nuclei of the Cerium isotopic chain is investigated by means of the Macroscopic-Microscopic method with a semi-classical shell correction. We consider axially symmetric shapes. Binding energy and two neutron separation energy are also evaluated. For the sake of clarity several important details of the calculations are also given. It turns out that all these nuclei have prolate equilibrium shape. The regions of maximum deformation are obtained around N=64 and N=102. There is no critical-point of quantum phase transition in this isotopic chain.

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arXiv2012

Low-lying quadrupole collective states of the light and medium Xenon isotopes

Collective low lying levels of light and medium Xenon isotopes are deduced from the Generalized Bohr Hamiltonian (GBH). The microscopic seven functions entering into the GBH are built from a deformed mean field of the Woods-Saxon type. Theoretical spectra are found to be close to the ones of the experimental data taking into account that the calculations are completely microscopic, that is to say, without any fitting of parameters.

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arXiv2012

The Inglis-Belyaev formula and the hypothesis of the two-quasiparticle excitations (version 2012)

The goal of the present work is to revisit the cranking formula of the vibrational parameters, especially its well known drawbacks. The latter can be summarized as spurious resonances or singularities in the behavior of the mass parameters in the limit of unpaired systems. It is found that these problems are simply induced by the presence of two derivatives in the formula. In effect, this formula is based on the hypothesis of contributions of excited states due only to two quasiparticles. But it turns out that this is not the case for the derivatives. We deduce therefore that the derivatives are not well founded in the formula. We propose then simply to suppress these terms from the formula. Although this solution seems to be simplistic, it solves definitively all its inherent problems.

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arXiv2010

Numerical approach to the nuclear deformation energy

A numerical method close to the Strutinsky procedure (but better) is proposed to calculate the deformation energy of nuclei. Quadrupole (triaxial) deformations are considered. Theoretical as well as practical aspects of the method are reviewed in this paper. A complete fortran program illustrates the feasibility of the method.

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arXiv2010

The cranking formula and the spurious behaviour of the mass parameters

We discuss some aspects of the approach of the mass parameters by means of the simple cranking model. In particular, it is well known that the numerical application of this formula is often subject to ambiguities or contradictions. It is found that these problems are induced by the presence of two derivatives in the formula. To overcome these problems, we state a useful ansatz and we develop a number of simple arguments which tend to justify the removal of these terms. As soon as this is done, the formula becomes simpler and easier to interpret. In this respect, it is shown how the shell effects affect the mass parameters. A number of numerical tests help us in our conclusions.

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arXiv2007

Connection between the "Strutinsky level density" and the semiclassical level density (published version)

We establish an analytical link between the level density obtained by means of the Strutinsky averaging method, and the semiclassical level density. This link occurs only in the so-called "asymptotic limit". It turns out that the Strutinsky method amounts to an approximation to the semiclassical method. This approximation contains an unavoidable remainder which constitutes an intrinsic noise in comparison to the semiclassical method. Thus, the "old" problem of the dependency of the Strutinsky procedure on the two free smoothing parameters of the averaging is intimately connected to this noise. On the other hand, we demonstrate that the noise of the method is small in the average density of states and in the average energy, whereas it might be non-negligible in the shell correction itself. In order to improve this method, we give a "rule" which consists simply of minimizing the relative error made on the average energy.

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arXiv2005

Single particle calculations for a Woods-Saxon potential with triaxial deformations, and large Cartesian oscillator basis

We present a computer program which solves the Schrodinger equation of the stationary states for an average nuclear potential of Woods-Saxon type. In this work, we take specifically into account triaxial (i.e. ellipsoidal) nuclear surfaces. The deformation is specified by the usual Bohr parameters. The calculations are carried out in two stages. In the first, one calculates the representative matrix of the Hamiltonian in the cartesian oscillator basis. In the second stage one diagonalizes this matrix with the help of subroutines of the EISPACK library. If it is wished, one can calculate all eigenvalues, or only the part of the eigenvalues that are contained in a fixed interval defined in advance. In this latter case the eigenvectors are given conjointly. The program is very rapid, and the run-time is mainly used for the diagonalization. Thus, it is possible to use a significant number of the basis states in order to insure a best convergence of the results.

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