ASYMPT
A FORTRAN program is presented which calculates asymptotics of potential curves and adiabatic potentials with an accuracy of O(ρ−2) in the framework of the hyperspherical adiabatic (HSA) approach. Here, ρ is the hyperradius. It is shown that matrix elements of the equivalent operator corresponding to the perturbation ρ−2 have a simple form in the basis of the Coulomb parabolic functions in the body-fixed frame and can be easily computed for high values of total orbital momentum and threshold number. The second-order corrections to the adiabatic curves are obtained as the eigenvalues of the corresponding secular equation. The eigenvectors computed are used to calculate the relevant corrections to matrix elements of potential coupling. The asymptotic potentials obtained can be used for the calculation of the energy levels and radial wave functions of two-electron syste! ms in the adiabatic and coupled-channel approximations of the HSA approach and also in scattering calculations.
(Source: http://cpc.cs.qub.ac.uk/summaries/)
Keywords for this software
References in zbMATH (referenced in 10 articles , 1 standard article )
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Sorted by year (- Gusev, A.A.; Chuluunbaatar, O.; Vinitsky, S.I.; Abrashkevich, A.G.: POTHEA: a program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined 2D elliptic partial differential equation (2014)
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- Srivastava, Muni S.; Solanky, Tumulesh K.S.: Predicting multivariate response in linear regression model (2003)
- Abrashkevich, A.G.; Puzynin, I.V.; Vinitsky, S.I.: ASYMPT: A program for calculating asymptotics of hyperspherical potential curves and adiabatic potentials (2000)
- Zhang, Changgui: On a theorem of Maillet-Malgrange type for $q$-differential-difference equations (1998)
- Čekanavičius, V.: On multivariate Le Cam theorem and compound Poisson measures (1996)
- Goldstein, L.; Khas’minskiĭ, R.Z.: On efficient estimation of smooth functionals (1995)
- Koltchinskii, V.: Nonlinear transformations of empirical processes: Functional inverses and Bahadur-Kiefer representations (1994)
- Field, Christopher; Ronchetti, Elvezio: Small sample asymptotics (1990)