Evidence of nonlocality due to a gradient term in the optical model

Jaghoub, M. I.; Rawitscher, George

doi:10.1016/j.nuclphysa.2011.12.004

Cited by 20 publications

(16 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should also be mentioned that the surface form of ρ(r), chosen in refs. [1,2,3], gives a surface-peaked effective nucleon mass m * (r)/m = 1/(1 − ρ(r)), equal to the square of the nucleon Perey factor. Detailed mean-field calculations of variable nucleon mass in finite nuclei suggest that m * (r)/m has a volume form, decreasing from 1 at large r to 0.8 at r = 0 [28].…”

Section: Numerical Calculations For 40 Ca(dp) 41 Ca Reactionmentioning

confidence: 99%

“…On the other hand, it is also known that a nonlocal two-body problem is equivalent to one with a potential that contains an infinite sum of powers of kinetic energy operators arising from the Taylor series expansion of an exponent that contains the nucleon kinetic energy operator [7]. Thus, from a formal point of view, the velocity dependence used in Refs [1,2,3,4,5] is just a particular case of a more general nonlocal problem, truncated to retain linear terms only.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Three-body problem with velocity-dependent optical potentials: a case of (d, p) reactions

Timofeyuk

2019

J. Phys. G: Nucl. Part. Phys.

View full text Add to dashboard Cite

The change in mass of a nucleon, arising from its interactions with other nucleons inside the target, results in velocity-dependent terms in the Schrödinger equation that describes nucleon scattering. It has recently been suggested in a number of publications that introducing and fitting velocity-dependent terms improves the quality of the description of nucleon scattering data for various nuclei. The present paper discusses velocity-dependent optical potentials in a context of a three-body problem used to account for deuteron breakup in the entrance channel of (d, p) reactions. Such potentials form a particular class of nonlocal optical potentials which are a popular object of modern studies. It is shown here that because of a particular structure of the velocity-dependent terms the three-body problem can be formulated in two different ways. Solving this problem within an adiabatic approximation results in a significant difference between the two approaches caused by contributions from the high n-p momenta in deuteron in one of them. Solving the three-body problem beyond the adiabatic approximation may remove such contributions, which is indirectly confirmed by replacing the adiabatic approximation by the folding Watanabe model where such contributions are suppressed. Discussion of numerical results is carried out for the 40 Ca(d, p) 41 Ca reaction where experimental data both on elastic scattering in entrance and exit channels and on nucleon transfer are available.

show abstract

Section: Numerical Calculations For 40 Ca(dp) 41 Ca Reactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three-body problem with velocity-dependent optical potentials: a case of (d, p) reactions

Timofeyuk

2019

J. Phys. G: Nucl. Part. Phys.

View full text Add to dashboard Cite

show abstract

“…The reflection of the mass of the changes in the velocity of an electron moving in a semiconductor crystal environment, and therefore in its position, can be expressed as a position‐dependent mass (PDM). In this manner, if the position dependence of the electron mass is modified and included in the interaction potential, the Schrödinger operator can be written by considering Equation ) to be [ 9 ]

- \nabla . \frac{{normalℏ}^{2}}{2 m^{*} ((), r)} \nabla + V - E = \frac{- ℏ^{2}}{2 m_{0}} \nabla^{2} + \overset{V}{true} ((), r, p) - E,

where m 0 is the mass in free environment, and m *( r ) is the PDM function. In this case, the VDP function is given by

\overset{V}{true} ((), r, p) = V ((), r) + \frac{{normalℏ}^{2}}{2 m_{0}} \nabla . ρ ((), r) \nabla .

…”

Section: Introductionmentioning

confidence: 99%

Optical analysis of quantum dot with velocity‐dependent potential

Bahar

Ungan

Kaya

et al. 2020

Int J of Quantum Chemistry

View full text Add to dashboard Cite

In this study, for the first time, the velocity‐dependent potential (VDP) effects on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of the parabolic quantum dot with spherical confinement, generated by GaAs/GaAlAs heterostructure, are comprehensively investigated. In order to obtain the subband energy spectra and the electronic wave function of the quantum dot system, the wave equation is numerically solved due to the VDP's complexity by using Runge‐Kutta‐Fehlberg method within the effective mass approximation. The nonlinear optical specifications of the quantum dot with velocity‐dependent potential (QDVDP) are analyzed using the compact density matrix formalism within the framework of the iterative method. To investigate the optical specifications of QDVDP, the isotropic form factor of VDP is taken into consideration as the harmonic oscillator type, F(r) = γρ0r2 (being γ and ρ0 are constants). Optical analysis is also executed for parabolic encompassing under the influence of VDP, as well as VDP, analyzing for TRICs and TACs of QDVDP, for which the result is quite a change compared to cases without VDP due to the symmetry‐breaking repercussion on system confinement of VDP. The main motivation of the present study is to clearly distinguish VDP effects on optical properties of the quantum dot, carrying out an analysis on optimal range and alternative parameter for optical properties.

show abstract

“…Hence the shell potential becomes non-local, and it is hoped that the present method may facilitate the formulation of this non-locality. Similarly, the optical model potential describing nucleon-nucleus scattering is also non-local, (but for more reasons) and efforts to determine its nature are in progress [43][44][45].…”

mentioning

confidence: 99%

A Spectral Integral Equation Solution of the Gross-Pitaevskii Equation

Rawitscher¹

2013

View full text Add to dashboard Cite

The Gross-Pitaevskii equation (GPE), that describes the wave function of a number of coherent Bose particles contained in a trap, contains the cube of the normalized wave function, times a factor proportional to the number of coherent atoms. The square of the wave function, times the above mentioned factor, is defined as the Hartree potential. A method implemented here for the numerical solution of the GPE consists in obtaining the Hartree potential iteratively, starting with the Thomas Fermi approximation to this potential. The energy eigenvalues and the corresponding wave functions for each successive potential are obtained by a spectral method described previously. After approximately 35 iterations a stability of eight significant figures for the energy eigenvalues is obtained. This method has the advantage of being physically intuitive, and could be extended to the calculation of a shell-model potential in nuclear physics, once the Pauli exclusion principle is allowed for.

show abstract

Evidence of nonlocality due to a gradient term in the optical model

Cited by 20 publications

References 30 publications

Three-body problem with velocity-dependent optical potentials: a case of (d, p) reactions

Three-body problem with velocity-dependent optical potentials: a case of (d, p) reactions

Optical analysis of quantum dot with velocity‐dependent potential

A Spectral Integral Equation Solution of the Gross-Pitaevskii Equation

Contact Info

Product

Resources

About