Spherical Woods-Saxon Potential Research Articles

Uniform descriptions of pseudospin symmetries in bound and resonant states

As a continuation of our previous work on the conservation and breaking of the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847, 138320 (2023)], in this work, the PSS in nuclear single-particle bound and resonant states are investigated uniformly within a relativistic framework by exploring the poles of the Green's function in spherical Woods-Saxon potentials. As the potential depths increase from zero to finite depths, the PS partners evolve from resonant states to bound states. In this progress, the PSS is broken gradually with energy, width, and density splittings. Specially, the energy and width splittings for the resonant and bound states are directly determined by the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious threshold effect is observed for the energy splitting at a critical potential depth, with which one PS partner has become a quasi-bound state inside the centrifugal barrier while the other one is still a high-energy resonant state outside the centrifugal barrier. The differences in the density distributions of the lower component between the PS partners are manifested in the phase shift for the resonant states and amplitudes for bound states.

Theoretical calculations of the alpha decay half-lives of 166−190Pt

Calculations of the α-decay half-lives of Pt isotopes have been carried out using the modified Gamow-like model (MGLM) and deformed Woods-Saxon potential model. In order to see the effect of using deformed nuclear potential on the α-decay half-lives of the Platinum isotopes, the spherical Woods-Saxon potential has also been employed in the computation. When compared with experimental data, all the modelsgive very good descriptions of the experimental half-lives. The comparison also suggests that the calculated half-lives considering deformation give better agreement with the experimental data than the results using spherical configuration. New parameter values were obtained for the MGLM model (termed MGLM2). The MGLM2 model gives better descriptions of the half-lives than the MGLM1 model.

Radial overlap correction to superallowed 0+→0+ β decay reexamined

Within the nuclear shell model, we investigate the correction $\delta_{RO}$ to the Fermi matrix element due to a mismatch between proton and neutron single-particle radial wave functions. Eight superallowed $0^+ \to 0^+$ $\beta$ decays in the $sd$-shell, comprised of $^{22}$Mg, $^{26m}$Al, $^{26}$Si, $^{30}$S, $^{34}$Cl, $^{34}$Ar, $^{38m}$K and $^{38}$Ca are re-examined. The radial wave functions are obtained from a spherical Woods-Saxon potential whose parametrizations are optimized in a consistent adjustment of the depth and the length parameter to relevant experimental observables, such as nucleon separation energies and charge radii, respectively. The chosen fit strategy eliminates the strong dependence of the radial mismatch correction to a specific parametrization, except for calculations with an additional surface-peaked term. As an improvement, our model proposes a new way to calculate the charge radii, based on a parentage expansion which accounts for correlations beyond the extreme independent-particle model. Apart from the calculations with a surface-peak term and the cases where we used a different model space, the new sets of $\delta_{RO}$ are in general agreement with the earlier result of Towner and Hardy [1]. Small differences of the corrected average $\overline{\mathcal{F}t}$ value are observed.

OWL: A code for the two-center shell model with spherical Woods–Saxon potentials

A Fortran-90 code for solving the two-center nuclear shell model problem is presented. The model is based on two spherical Woods–Saxon potentials and the potential separable expansion method. It describes the single-particle motion in low-energy nuclear collisions, and is useful for characterizing a broad range of phenomena from fusion to nuclear molecular structures. Program summaryProgram Title: OWLProgram Files doi:http://dx.doi.org/10.17632/s5pcd54dys.1Licensing provisions: GPLv3Programming language: Fortran-90Nature of problem: The two-center shell model (TCSM) is a basic microscopic model to describe the single-particle (sp) motion during a heavy ion collision near the Coulomb barrier. The sp energies and wave-functions are obtained by solving the Schrödinger equation with a phenomenological two-center mean field based on two spherical Woods–Saxon (WS) potentials [1].Solution method: The potential separable expansion (PSE) method using two basis sets of harmonic oscillator functions is employed [2,3]. A method to ensure the volume conservation of the fusing system is used [1].Additional comments including Restrictions and Unusual features: The program is suited for two spherical WS potentials and provides bound sp states only. [1]A. Diaz-Torres, W. Scheid, Nucl. Phys. A 757 (2005) 373–389.[2]F.A. Gareev, M.Ch. Gizzatkulov, J. Revai, Nucl. Phys. A 326 (1977) 512–522.[3]B. Gyarmati, A.T. Kruppa, J. Revai, Nucl. Phys. A 326 (1979) 119–128.

Resonant and weakly-bound one-particle levels in quadrupole-deformed potentials

Both positive-energy and weakly-bound one-particle levels for neutrons in Y20 deformed Woods-Saxon potentials are examined in comparison with those in spherical Woods-Saxon potentials. While s1/2 levels play a unique role in spherical drip-line nuclei, the Ωπ = 1/2+ levels in Y20 deformed potentials, which always contain some amount of s1/2 component, exhibit an important role in deformed drip-line nuclei. As the potential strength becomes weaker, some weakly-bound Ωπ = 1/2+ levels continue to the positive-energy region as one-particle resonant levels, while others have no such continuation. Among an infinite number of one-particle levels at a given positive-energy and in a given deformed potential, only some selected levels expressed in terms of eigenphase are found to be important in the pair-correlated ground state of neutron-drip-line nuclei.

Two center shell model with Woods–Saxon potentials: Adiabatic and diabatic states in fusion

A realistic two-center shell model for fusion is proposed, which is based on two spherical Woods–Saxon potentials and the potential separable expansion method. This model describes the single-particle motion in a fusing system. A technique for calculating stationary diabatic states is suggested which makes use of the formal definition of those states, i.e., they minimize the radial nonadiabatic coupling between the adiabatic states. As an example the system 16O + 40Ca → 56Ni is discussed.

Hybrid version of the tilted axis cranking model and its application to128Ba

A hybrid version the deformed nuclear potential is suggested, which combines a spherical Woods-Saxon potential with a deformed Nilsson potential. It removes the problems of the conventional Nilsson potential in the mass 130 region. Based on the hybrid potential, tilted axis cranking calculations are carried out for the magnetic dipole band in ${}^{128}\mathrm{Ba}.$

Scattering of 0.8 GeV protons fromN14

Angular distributions are reported for 0.8 GeV proton elastic and inelastic scattering from /sup 14/N. The data are analyzed with the optical model using a spherical Woods-Saxon potential and the distorted wave Born approximation with collective form factors.

Energy systematics of the 1g [formula omitted], neutron hole state and isospin dependence of the nuclear potential

Energies of 1g 9 2 neutron hole states in several nuclei with neutron numbers between 50 and 82 were measured by means of (p, d) reactions at a proton energy of 52 MeV. These data, together with available data from other studies, are used to obtain the systematics of the single-neutron binding energy of the 1g 3 2 neutron state as a function of neutron and proton number. The depths of a spherical Woods-Saxon potential which reproduce the experimental binding energies are obtained. An expression for the potential depth, which includes an isospin-dependent term, is assumed and the depth of the isospin potential is determined by a least-squares fitting procedure. The results are consistent with those for lighter nuclei obtained by Millener and Hodgson in a similar way.