On the Numerical Solution of the Time-Dependent Schroedinger Equation

An algorithm for the numerical solution of the Schr\"odinger equation in the case of a time dependent potential is proposed. Our simple modification upgrades the well known method of Koonin while negligibly increasing the computing time. In the presented test the accuracy is enhanced by up to an order of magnitude.Comment: 4 pages, Revtex, Published in J. Comp. Physics 119, (1995) p. 206-20

Cluster formation probability in the trans-tin and trans-lead nuclei

Within our fission model, the Coulomb and proximity potential model (CPPM) cluster formation probabilities are calculated for different clusters ranging from carbon to silicon for the parents in the trans-tin and trans- lead regions. It is found that in trans-tin region the 12^C, 16^O, 20^Ne and 24^Mg clusters have maximum cluster formation probability and lowest half lives as compared to other clusters. In trans-lead region the 14^C, 18, 20^O, 23^F, 24,26^Ne, 28,30^Mg and 34^Si clusters have the maximum cluster formation probability and minimum half life, which show that alpha like clusters are most probable for emission from trans-tin region while non-alpha clusters are probable from trans-lead region. These results stress the role of neutron proton symmetry and asymmetry of daughter nuclei in these two cases.Comment: 20 pages, 6 figure

Alpha-nucleus potential for alpha-decay and sub-barrier fusion

The set of parameters for alpha-nucleus potential is derived by using the data for both the alpha-decay half-lives and the fusion cross-sections around the barrier for reactions alpha+40Ca, alpha+59Co, alpha+208Pb. The alpha-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated alpha-decay half-lives and the fusion cross-sections agreed well with the data. Fusion reactions between alpha-particle and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.Comment: 10 pages, 5 figure

Cluster radioactivity in very heavy nuclei: a new perspective

Exotic cluster decay of very heavy nuclei is studied using the microscopic nuclear potentials obtained by folding density dependent M3Y effective interaction with the densities of the cluster and the daughter nuclei. The microscopic nuclear potential, Coulomb interaction and the centrifugal barrier arising out of spin-parity conservation are used to obtain the potential between the cluster and the daughter nuclei. Half life values are calculated in the WKB framework and the preformation factors are extracted. The latter values are seen to have only a very weak dependence on the mass of the emitted cluster.Comment: 4 pages including 2 table

Measurement of ocular aberrations in downward gaze using a modified clinical aberrometer

Changes in corneal optics have been measured after downward gaze. However, ocular aberrations during downward gaze have not been previously measured. A commercial Shack-Hartmann aberrometer (COAS-HD) was modified by adding a relay lens system and a rotatable beam splitter to allow on-axis aberration measurements in primary gaze and downward gaze with binocular fixation. Measurements with the modified aberrometer (COAS-HD relay system) in primary and downward gaze were validated against a conventional aberrometer. In human eyes, there were significant changes (p<0.05) in defocus C(2,0), primary astigmatism C(2,2) and vertical coma C(3,−1) in downward gaze (25 degrees) compared to primary gaze, indicating the potential influence of biomechanical forces on the optics of the eye in downward gaze. To demonstrate a further clinical application of this modified aberrometer, we measured ocular aberrations when wearing a progressive addition lens (PAL) in primary gaze (0 degree), 15 degrees downward gaze and 25 degrees downward gaze

Blendowske R. Paraxial Propagation of Astigmatic Wavefronts in Optical Systems by an Augmented Stepalong Method for Vergences, Optom Vis Sci 2005;82:923–32

ABSTRACT: Purpose. The propagation of astigmatic wavefronts through astigmatic optical systems is reconsidered in the wavefront perspective. Methods. The stepalong method for vergences, described by 2 ؋ 2 matrices, is applied and augmented to produce off-axis information like the magnification. This so-called augmented stepalong method (ASAM) is derived by applying the paraxial propagation of astigmatic wavefronts to tilted wavefronts as well. Results. The features of the ASAM are discussed for a single surface, a thick lens, and a general system. Conclusions. The ASAM provides all necessary information to describe a centered astigmatic optical system in paraxial approximation. 5 He started from the ray optics concept and derived by integration of differential relations the very concept of an astigmatic wavefronts and their properties. Our starting point is the description of electromagnetic scalar waves. We apply what is known as Fresnel propagation to rederive well-known results. Some, as we believe interesting, aspects show up along this way. The second purpose is to provide a method for including off-axis information into the well known stepalong procedure for vergences. In the simplest case of paraxial optics of rotationally symmetric systems, which is called Gaussian optics in the following section, the knowledge of 2 quantities determines the properties of the imagery: position and size of the image. When it comes to a general optical system, like the optics of the eye, we have to switch from Gaussian optics to the linear optics of an astigmatic system, which still works in the paraxial domain. Excluding decentered or tilted systems, everything that can happen to a ray is described by a 4 ϫ 4 system matrix, also called the transference. This matrix is generated by the repeated multiplication of 4 ϫ 4 matrices related to the 2 events in the life of a light ray: transfer (free propagation) and refraction. If the transference is known the linear mapping, which connects all possible ray heights and ray angles in 2 reference planes is completely characterized