TITLE

Cumulative reaction probabilities using Padé analytical continuation procedures

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
Academic Journal
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 iε to the Hamiltonian, addition of unoptimized optical potentials of the form iλ|s| or iλ|s|2, and complex rotation of the reaction coordinate s→s·exp(i[variant_greek_theta]). When N(E,u) is calculated on a grid of values of the numerical parameter u (u being ε, λ, or [variant_greek_theta]), Padé 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(ν=1) potential which supports a quasibound state have shown high accuracy and convergence of the method with respect to Padé 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 B→X[sub u]l[sup -]ν¯[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 Padé-approximant methods, we estimate the three-loop order &MSmacr; coefficients of α³[sub s][log(μ²/m²[sub b](μ)][sup k] terms [k = {0, 1,2,3}] within the b → 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 Padé 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 β-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...

  • Gorsky–Bragg–Williams Theory of Phase Transitions in the Approximants of Icosahedral Quasicrystals. Chizhikov, V. A. // Crystallography Reports;Jan2000, Vol. 45 Issue 1, p122 

    The Gorsky–Bragg–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...

  • Padé 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 Padé approximation is proposed in which the Padé 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

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics