Volume 49, Issue 6
December 1997, pages 563-651
pp 563-580 December 1997
Darboux transformation and elementary exact solutions of the Schrödinger equation
Vladislav G Bagrov Boris F Samsonov
Darboux transformation is applied to three classical potentials, namely the harmonic oscillator, effective Coulomb and Morse potentials to generate exactly solvable potentials of elementary form. For every potential, the isospectral families of potentials are constructed. For almost all potentials, a set of normalized discrete spectrum wave functions is given.
pp 581-590 December 1997
The space overlap of an attractor reconstructed from a time series with a similarly reconstructed attractor from a random series is shown to be a sensitive measure of determinism. Results for the time series for Henon, Lorenz and Rössler systems as well as a linear stochastic signal and an experimental ECG signal are reported. The overlap increases with increasing levels of added noise, as shown in the case of Henon attractor. Further, the overlap is shown to decrease as noise is reduced in the case of the ECG signal when subjected to singular value decomposition. The scaling behaviour of the overlap with bin size affords a reliable estimate of the fractal dimension of the attractor even with limited data.
pp 591-601 December 1997
Schrödinger picture formalism of Φ^{6} theory
The static effective potential for a scalar field with Φ^{6} interaction is calculated using the effective action in Schrödinger picture formalism. It is found that the effective potential obtained is same as the Gaussian effective potential as far as static case is concerned. Equivalence with the CJT formalism can also be established. As in CJT formalism after renormalization an unrenormalized mass term persists. Nonzero turning points are obtained both for positive and negativeλ. Results are analysed numerically. Graphical analysis indicates a behaviour similar to that obtained for CJT formalism at zero temperature.
pp 603-607 December 1997
Motion of test particles around domain walls
Subenoy Chakraborty Lalit Biswas
We present a detailed analysis of the motion of test particles around domain walls. The study of the trajectories of the test particles has been done using the Hamilton-Jacobi formalism. In most of the cases we show that the particles can not be trapped by the walls.
pp 609-615 December 1997
Einstein pseudotensor and total energy of the universe
The total energy of the universe has been calculated assuming that it is the sum of the contributions from the matter part and gravitational part. The calculations involve the use of Einstein pseudotensor. Calculations have been carried out in some specific examples of spacetime geometries. In some cases the total energy is indeed zero confirming previous results but in other cases the total energy is nonzero. So Rosen’s idea that the pseudotensorial calculations will lead to the result that the total energy of the universe is zero, is very much model dependent.
pp 617-622 December 1997
Semi-empirical formula for Λ-binding energies in ground states of light hypernuclei
M Z Rahman Khan Nasra Neelofer M A Suhail
Starting with a Λ-nucleus potential, we have obtained a semi-empirical formula, which gives a fairly satisfactory account of the ground state Λ-binding energy of light hypernuclei, if the very light nuclei are ignored.
pp 623-633 December 1997
M Ismail R P Sharma M H Rashid
Excitation function and mean projected recoil ranges of nuclei produced in the^{12}C-induced reactions on^{51}V target were measured by conventional stacked foil and thick-target thick-recoil-catcher technique for bombarding energiesE ≤ 84 MeV for^{12}C ion beam. The measured recoil ranges are converted to momentum transfer. Information on momentum transfer was used to get clues about some aspects of the interaction such as complete fusion which corresponds to full momentum transfer and incomplete fusion reaction mechanism. The measured excitation functions are compared with the calculation based on the statistical model which describes only equilibrium decay of the compound nucleus using the Cascade code and the geometry dependent hybrid model which describes equilibrium as well as pre-equilibrium decay of the compound nucleus using the Alice/91 code. The measured excitation functions and average ranges of the radioisotope products of the reactions^{12}C on^{51}V indicate that the three separate reaction mechanisms could be attributable to complete fusion of^{12}C, incomplete fusion of^{8}Be and incomplete fusion of^{4}He respectively with the target. The^{8}Be and^{4}He are the break-up component of^{12}C into^{8}Be +^{4}He. The predictions of the codes, especially the Cascade, generally agree with the measured cross-sections which could be attributed to complete fusion of^{12}C with the target^{51}V.
pp 635-643 December 1997
Spherical aberration and its correction using Lie algebraic methods
Govindan Rangarajan Minita Sachidanand
We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat’s principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.
pp 645-651 December 1997
Two body non-leptonic Λ_{b} decays in the largeN_{c} limit
The two body non-leptonic Λ_{b} decays are analysed in the HQET with factorization approximation and largeN_{c} limit. In this limit, Λ_{b} and Λ_{c} baryons can be treated as the bound states of chiral soliton and heavy meson, and consequently the Isgur-Wise function comes out in a straight forward manner. The results obtained remain well below their previously predicted upper limit.
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