Abstract
The recently developed dilation (coordinate rotation) theory of the Coulomb Hamiltonian allows the calculation of energies and widths of nonstationary atomic and molecular states using square-integrable basis sets only. In the pioneering applications of this theory to two electron atomic autoionizing states, it was found necessary to employ large basis sets in brute force CI calculations, an expensive approach which has significant limitations when it comes to larger systems. In this paper we present a many-body theory of autoionizing and autodissociating states which implements the dilatation theory in an efficient and consistent way. In the case of autodissociating states it is not required to invoke the Born-Oppenheimer approximation. The present approach first isolates in the ϑ-plane (ϑ is the rotation angle) the “localized” correlation effects from the “asymptotic” ones by rotating the coordinates of the localized function, ψ0, which, in the time dependent theory, represents the initially localized state before it decays. The coordinate rotation leaves the real energy of ψ0 invariant and allows the inclusion of “asymptotic” correlation vectors, in terms of “Gamow orbitals”, which perturb ψ0 and E0 and yield the decay energy shift and width. Our theory is supported by numerical examples on H and He.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P.L. Altick, in this volume.
CA. Nicolaides, Phys. Rev. A6, 2078 (1972)
CA. Nicolaides, Nucl. Inst. Methods 110, 231, (1973).
CA. Nicolaides and D.R. Beck, “Time Dependence, Complex Scaling and the Calculation of Resonances in Many-Electron Systems”, to be published in Int. J. Qu. Chem. 14 (1978).
G.D. Doolen, J. Phys. B8, 525 (1975).
G.D. Doolen, J. Nuttall and R.W. Stagat, Phys. Rev. A10, 1612, (1974).
W.P. Reinhardt, Int. J. Qu. Chem. S10, 359, (1976).
P. Winkler, Z. Physik A283, 149, (1977)
P. Winkler and R. Yaris, J. Phys. B11, 1481, (1978).
J. Aquilar and J.M. Combes, Comm. Math. Phys. 22, 69, (1971).
E. Balslev and J.M. Combes, Comm. Math. Phys. 22, 280, (1971).
B. Simon, Comm. Math. Phys. 27, 1, (1972)
B. Simon, Ann. Math. 97, 247, (1973).
Y.K. Ho, A.K. Bhatia and A. Temkin, Phys. Rev. A15, 1423, (1977).
D.R. Beck and C.A. Nicolaides, Phys. Rev. Letts, submitted May 1978; paper 13, 9th EGAS Conference, Krakow, Poland, July 1977.
We bring to attention the recent excellent work of D.M. Bishop and coworkers, D.M. Bishop, Phys. Rev. Letts. 37, 484, (1976)
D.M. Bishop and L.M. Cheung, Phys. Rev. A16, 640, (1977), where accurate calculations of the ground state of H2 are performed without invoking the B-O approximation. Of course, there is considerable difference between ground state and autodissociating state calculations, including the type of variational procedures which are applicable.
G. Gamow, Z. Phys. 51, 204, (1928).
A.F.J. Siegert, Phys. Rev. 56, 750, (1939).
J.N. Bardsley, A. Herzenberg and F. Mandl, Proc. Phys. Soc. 89, 305, (1966).
Ya. B. Zel’dovich, JETP (Sov. Phys.) 12, 542, (1961).
T. Berggren, Nucl. Phys. A109, 265, (1968).
Gy. I. Szasz, Phys. Letts. 55A, 327, (1976).
CA. Nicolaides and D.R. Beck, Phys. Letts. 65A, 11, (1978).
J. Nuttall, Bull. Am. Phys. Soc. 17, 598, (1972).
J.N. Bardsley and B.R. Junker, J. Phys. B5, 2178, (1972).
A.B. Migdal and V.P. Krainov, “Approximation Methods in Quantum Mechanics”, Chapter 2, Benjamin Press (1969).
C.A. Nicolaides and D.R. Beck, Phys. Rev. Letts. 38, 683 (1977)
C.A. Nicolaides and D.R. Beck, Phys. Rev. Letts. 38 1037, (1977).
Solutions of this type for molecules have not been used before. We do not know whether they exist. We see little difference between them and an in principle numerical integration of the resulting H-F integro-differential equations occuring in nuclei where both protons and neutrons are treated simultaneously. Within the Born-Oppenheimer approximation, ΦHF (r,R) ΦHF (r;R), i.e. one obtains the diabatic states discussed by T.F. O’Malley, Adv. At. Mol. Phys. 7, 223, (1971)
and W.L. Lichten, Phys. Rev. 139, 27, (1965). This approximation essentially omits the nuclear coupling term, ∂/∂R, which then must be included perturbâtively at this stage and not after electron and nuclear correlation is taken into account.
D.R. Beck and C.A. Nicolaides, this volume.
C.A. Nicolaides and D.R. Beck, Chem. Phys. Letts. 36, 79, (1975).
C.A. Nicolaides and D.R. Beck, this volume.
C.A. Nicolaides and D.R. Beck, J. Chem. Phys. 66, 1982, (1977).
E. Brandas and P. Froelich, Phys. Rev. A16, 2207, (1977).
R. Yaris and P. Winkler, J. Phys. B11, 1475, (1978).
C.A. Nicolaides and D.R. Beck, Phys. Letts. 60A, 92, (1977).
A.K. Bhatia and A. Temkin, Phys. Rev. A11, 2018, (1975).
P.K. Mukherjee, S. Sengupta and A. Mukherji, Int. J. Qu. Chem. 4, 139, (1970).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Nicolaides, C.A., Beck, D.R. (1978). Theory of Atomic and Molecular Non-Stationary States Within the Coordinate Rotation Method. In: Nicolaides, C.A., Beck, D.R. (eds) Excited States in Quantum Chemistry. NATO Advanced Study Institutes Series, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9902-2_14
Download citation
DOI: https://doi.org/10.1007/978-94-009-9902-2_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-9904-6
Online ISBN: 978-94-009-9902-2
eBook Packages: Springer Book Archive