TITLE

AUTHOR(S)
Ryaboy, Victor; Lefebvre, Roland; Moiseyev, Nimrod
PUB. DATE
September 1993
SOURCE
Journal of Chemical Physics;9/1/1993, Vol. 99 Issue 5, p3509
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
New computational techniques for calculation of cumulative reaction probabilities, N(E), are suggested. They are based on the expression of N(E) through the imaginary part of the Green function G [Seideman and Miller, J. Chem. Phys. 96, 4412 (1992)]. We use three methods to overcome numerical problems arising from branch cuts of G located along the real positive energy axes, addition of constant imaginary part iÎµ to the Hamiltonian, addition of unoptimized optical potentials of the form iÎ»|s| or iÎ»|s|2, and complex rotation of the reaction coordinate sâ†’sÂ·exp(i[variant_greek_theta]). When N(E,u) is calculated on a grid of values of the numerical parameter u (u being Îµ, Î», or [variant_greek_theta]), PadÃ© analytical continuation to their zero values gives correct energy dependence of N(E). The method makes it possible to save computer time by using unoptimized parameters of the optical potential or of the complex scaling when calculating N(E,u). Test calculations on a one dimensional Eckart barrier and a model H+H2(Î½=1) potential which supports a quasibound state have shown high accuracy and convergence of the method with respect to PadÃ© input parameters.
ACCESSION #
7647026

## Related Articles

• Asymptotic Distributions of Zeros of Quadratic Hermite—Pade Polynomials Associated with the Exponential Function. Stahl, Herbert // Constructive Approximation;Jan2006, Vol. 23 Issue 2, p121

The asymptotic distributions of zeros of the quadratic Hermite--Pad\'{e} polynomials $p_{n},q_{n},r_{n}\in{\cal P}_{n}$ associated with the exponential function are studied for $n\rightarrow\infty$. The polynomials are defined by the relation (*)\qquad...

• Rational Polynomial Hazard Functions. Bebbington, M.; Lai, C. D.; Murthy, D. N. P.; Zitikis, R. // International Journal of Performability Engineering;Jan2010, Vol. 6 Issue 1, p35

Lifetime modeling of physical systems and biological organisms involves the use of failure distribution functions. The shape of the hazard rate (HR) function associated with the distribution function characterizes the effect of age (and other factors) on the failure. Examples of failure (and...

• Reducing the theoretical uncertainty in extracting |V[sub ub]| from the inclusive Bâ†’X[sub u]l[sup -]Î½Â¯[sub l] decay rate. Ahmady, M. R.; Chishtie, F. A.; Elias, V.; Steele, T. G. // AIP Conference Proceedings;2000, Vol. 541 Issue 1, p51

Utilizing asymptotic PadÃ©-approximant methods, we estimate the three-loop order &MSmacr; coefficients of Î±Â³[sub s][log(Î¼Â²/mÂ²[sub b](Î¼)][sup k] terms [k = {0, 1,2,3}] within the b â†’ ul-&vmacr;[sub t] decay rate. Except for the coefficient of the k = 0 term, all other...

• Bounds to two- and three-body long-range interaction coefficients for S-state atoms. Standard, J. M.; Certain, P. R. // Journal of Chemical Physics;9/15/1985, Vol. 83 Issue 6, p3002

New upper and lower bounds to the van der Waals C6, C8, and C10 coefficients for hydrogen, noble gas, alkali, and alkaline earth atoms are determined by using PadÃ© approximants to bound the dynamic multipole polarizabilities. Also, the nonadditive, three-body coefficients involving dipole,...

• Infrared Dynamics in vector-like gauge Theories: QCD and beyond. Elias, Victor // AIP Conference Proceedings;2001, Vol. 601 Issue 1, p140

Pade-approximant methods are used to extract information about leading positive zeros or poles of QCD and SQCD Î²-functions from the known terms of their perturbative series. For QCD, such methods are seen to corroborate the flavour-threshold behaviour obtained via lattice approaches for the...

• Two-point quasifractional approximant in physics. Truncation error. Martín, Pablo; Baker, George A. // Journal of Mathematical Physics;Jun91, Vol. 32 Issue 6, p1470

The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with...

• Gorskyâ€“Braggâ€“Williams Theory of Phase Transitions in the Approximants of Icosahedral Quasicrystals. Chizhikov, V. A. // Crystallography Reports;Jan2000, Vol. 45 Issue 1, p122

The Gorskyâ€“Braggâ€“Williams (GBW) theory has been modified to describe phase transitions caused by the ordering of two kinds of atoms in the even and the odd sublattices of the structures of icosahedral quasicrystals with the dodecahedral local order (DLO) and their approximants. The...

• PadÃ© interpolation: Methodology and application to quarkonium. Leung, C. N.; Murakowski, J. A. // Journal of Mathematical Physics;May2000, Vol. 41 Issue 5

A novel application of the PadÃ© approximation is proposed in which the PadÃ© approximant is used as an interpolation for the small and large coupling behaviors of a physical system, resulting in a prediction of the behavior of the system at intermediate couplings. This method is applied to...

• THE NUMERICAL SOLUTION OF MHD BLASIUS FLOW ALONG WITH DIFFERENTIAL TRANSFORMATION METHOD AND PADE APPROXIMANT. MISHRA, S. R.; BAAG, S. // Annals of the Faculty of Engineering Hunedoara - International J;Aug2015, Vol. 13 Issue 3, p201

The Magnetohydrodynamics (MHD) Blasius boundary layer flow over a flat plate in the presence of transverse magnetic field is studied in this paper. The approximate solution and skin friction coefficient of MHD boundary layer flow are obtained by using Runge-Kutta fourth order along with shooting...

Share