Ibraheem Nasser

The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states

This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound-state energy spectrum by diagonalizing the finite-dimensional Hamiltonian matrix of H2, LiH, HCl and CO molecules for arbitrary angular momentum. The calculation was performed using the J-matrix basis that supports a tridiagonal matrix representation for the reference Hamiltonian. Our results for these diatomic molecules have been compared with available numerical data satisfactorily. The proposed method is handy, very efficient, and it enhances accuracy by combining analytic power with a convergent and stable numerical technique.

Measuring the refractive index of crude oil using a capillary tube interferometer

A method for measuring the refractive index of low-transparent crude oils using a capillary tube interferometer is described. The method is based on analyzing the resulting transverse interference fringe patterns in terms of their positions with respect to the lens/capillary tube interferometer. The refractive indices of seven blended crude oils of low transparency were measured with accuracy of up to six decimal digits and were related to the API gravity of the oils. The ray tracing inside the capillary tube is explained and the transverse bell-shaped interference fringes are interpreted.

Analytical treatment of the Yukawa potential

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate exactly the matrix elements of the Yukawa potential in this representation. This enabled us to compute the bound state spectrum as the eigenvalues of the associated analytical matrix representing the full Hamiltonian. We also used the complex scaling method to evaluate the resonance energies and compared our results with those obtained using the Gauss quadrature approach and the corresponding results from the literature.

J-Matrix approach for the exponential-cosine-screened Coulomb potential

The bound state energies for the exponential-cosine-screened Coulomb potential were calculated by using the Gauss quadrature method. The resonance energies were calculated using the complex rotation method and were then used as a seed for our J-matrix approach in order to achieve improved results. The calculated bound and resonance state energies are compared with the available numerical data in this paper. The trajectories of the resonance states in the complex E-plane are also shown. New data, for both bound and resonance state energies close to the crossover region of the transition from bound to resonance, have been reported for guiding future studies.

The Manning–Rosen potential using J-matrix approach

Close to the bound-resonance crossover region, state energies for the Manning–Rosen (MR) potential have been calculated. New data, for both bound and resonance state energies have been reported nearby the crossover region, using the J-matrix approach, for LiH and CO molecules. Furthermore, the average oscillator strength, multipole moments and transition probabilities for certain states have been reported for future comparison.

Hellmann potential in the J-matrix approach: I. Eigenvalues

The trajectories of the poles of the S-matrix for Hellmann potential, in the complex energy plane, have been studied near the critical screening parameter. The calculation has been performed using the J-matrix approach, which uses a suitable L2 basis to tridiagonalize the reference Hamiltonian matrix. The calculated bound and resonance state energies have been compared with available numerical data.

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

Abstract A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.

The rotating Morse potential model for diatomic molecules in the J-matrix representation: II. The S-matrix approach

This is the second article in which we study the rotating Morse potential model for diatomic molecules using the tridiagonal J-matrix approach. Here, we further improve the accuracy of computing the bound states and resonance energies for this potential model from the poles of the S-matrix for arbitrary angular momentum. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian, which is included in the computations analytically without truncation. Our method has been applied to both the regular and inverted Morse potential with favourable results in comparison with available numerical data. We have also shown that the present method adds a few significant digits to the accuracy obtained from the finite dimensional approach (e.g. the complex rotation method). Moreover, it allows us to easily handle both analytic and non-analytic potentials as well as 1/r singular potentials.

A comparative study of spliced optical fibers

A fusion-spliced optical fiber is examined with a laser sheet of light. A CCD camera is used to record the transverse interference pattern from the fiber. The buckling on the fiber material in one direction of the spliced point is distinct inside the transverse interference pattern. The refractive index profile inside the fiber core, obtained at different illumination directions, is calculated using a new method showing the change in the refractive index due to fusion splicing of the fiber. A simple theoretical model is introduced to simulate the anomalous behavior in the transverse interference fringes due to a slight change of the optical parameters.

Scaling behaviour of Fisher and Shannon entropies for the exponential-cosine screened coulomb potential

ABSTRACT The scaling laws are given for the entropies in the information theory, including the Shannons entropy, its power, the Fishers information and the Fisher–Shannon product, using the exponential-cosine screened Coulomb potential. The scaling laws are specified, in the r-space, as a function of |μ − μc, nℓ|, where μ is the screening parameter and μc, nℓ its critical value for the specific quantum numbers n and ℓ. Scaling laws for other physical quantities, such as energy eigenvalues, the moments, static polarisability, transition probabilities, etc. are also given. Some of these are reported for the first time. The outcome is compared with the available literatures’ results.