Mean square radii of nuclei calculated with the Woods-Saxon potential

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the antibound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case.

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“…Equations (11) and (12) According to (9), wave functions for purely outgoing states are given, up to a constant factor, by…”

Section: A the Scattering And Transfer Matricesmentioning

confidence: 99%

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

2017

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“…[10], and the parameters for protons were adjusted in order to describe the main sequence of angular momentum and parity of the three lowest-lying single particle states, as well as their binding energy; from these states it was then possible to calculate the quasi-particle states using the LINDEN code [11]. The values obtained were compared to the parameters suggested by Cwiok et al [12], called Universal Parameters (see Table I.…”

Section: B Single Particle Energiesmentioning

confidence: 99%

“…The deformation parameters in equilibrium were obtained by minimizing the total energy calculated by the macroscopic-microscopic method [8]. The single particle energy spectra and wave functions for protons and neutrons were calculated in a deformed Woods-Saxon potential [9], with the potential parameters for neutrons obtained from the literature [10] and the parameters for protons adjusted in order to describe the main sequence of angular momentum and parity of the bandheads, as well as the proton binding energy. The residual pairing interaction was calculated using the BCS prescription with the LipkinNogami approximation [11].…”

Section: Introductionmentioning

confidence: 99%

Low-energy levels calculation for 193Ir

Zahn¹,

Zamboni²,

Genezini³

et al. 2006

Braz. J. Phys.

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In this work, a model based on single particle plus pairing residual interaction was used to study the low-lying excited states of the 193 Ir nucleus. In this model, the deformation parameters in equilibrium were obtained by minimizing the total energy calculated by the Strutinsky prescription; the macroscopic contribution to the potential was taken from the Liquid Droplet Model, with the shell and paring corrections used as as microscopic contributions. The nuclear shape was described using the Cassinian ovoids as base figures; the single particle energy spectra and wave functions for protons and neutrons were calculated in a deformed Woods-Saxon potential, where the parameters for neutrons were obtained from the literature and the parameters for protons were adjusted in order to describe the main sequence of angular momentum and parity of the bandheads, as well as the proton binding energy of 193 Ir. The residual pairing interaction was calculated using the BCS prescription with Lipkin-Nogami approximation. The results obtained for the first three bandheads (the 3/2 + ground state, the 1/2 + excited state at E ≈ 73keV and the the 11/2 − isomeric state at E ≈ 80keV) showed a very good agreement, but the model so far greatly overestimated the energy of the next bandhead, a 7/2 − at E≈ 299keV.

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“…The obtained results have been compared with experimental data. Lojewski [6] has been evaluated the meansquare charge radii of even-even nuclei using the realistic single-particle Woods-Saxon potential and compared the results with experimental data and theoretical values obtained with the single-particle Nilsson potential. Gamba [7] determined the parameters of a Woods-Saxon potential well for ten p-shell nuclei by fitting the electron scattering form factors and single-particle binding energies.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Nuclear Structure for Some p-Shell Nuclei by Harmonic Oscillator and Woods-Saxon Potentials

Abdullah

2017

JNUS

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The single particle radial wave functions of harmonic oscillator potential and Woods-Saxon potential have been used to calculate the charge density distributions, charge form factor and the matter and charge root mean square (rms) radii for some odd-A 1p shell nuclei, namely 9 IntroductionThe charge density distribution has been well studied experimentally over a wide range of nuclei because it is one of the many most important quantities in the nuclear structure [1]. The important information about the nuclear structure is obtained from the high energy electron scattering by the nuclei. At high energy, in the range of 100 MeV and more, the electron represents a best probe to study the nuclear structure because with these energies the de Broglie wavelength will be in the range of the spatial extension of the target nucleus [2]. We can distinguish two different types of the electron scattering: the first type is called elastic electron scattering where the nucleus is left on its ground state. The second is inelastic electron scattering where the nucleus is left in its different excited states [3].Gibson [4] has been study the ground state of the 4 He nucleus using a single-particle phenomenological model. Wave functions were generated from a potential whose parameters are chosen to reproduce the correct neutron separation energy. Ridha [5] has been used the single-particle radial wave functions of Woods-Saxon potential and harmonicoscillator potential to study the nuclear charge density distributions, form factors and corresponding proton, charge, neutron, and

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Mean square radii of nuclei calculated with the Woods-Saxon potential

Cited by 21 publications

References 18 publications

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

Low-energy levels calculation for 193Ir

Investigation of the Nuclear Structure for Some p-Shell Nuclei by Harmonic Oscillator and Woods-Saxon Potentials

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