**Authors: **A.V. Glushkov

**Year: **2015

**Issue: **19

**Pages: **142-147

**Abstract**

We propose a new serial, single quantum-mechanical approach to the problem of quasi-stationary states, including both the Stark effect and the scattering problem at all. The approach allows the calculation of complex energy resonances and is particularly useful in the study of the spectral region near the boundary of the new continuum. We have developed a method of describing quasi-stationary states, in principle, devoid of all the shortcomings of the existing quantum-mechanical methods for solving the problem based on the Stark and operator formalism of perturbation theory. Its essence – the inclusion of a well-known in the theory of scattering “distorted waves” approach within the formal precision of perturbation theory. The proposed new method can be used to explore the resonances of any nature. Currently it is used by us to the study of resonances of the compound – nucleus formed by the collision of heavy ions. Unlike other approaches, it allows to calculate not only the function of the scattering states, but also to determine the function of the state with complex energy plus a full complement of functions orthogonal scattering.

**Tags: **energy and resonance widths; operator formalism of perturbation theory; the Stark effect

**Bibliography**

- Landau L.D., Difshits E.M. Quantum mechanics. Moscow: Nauka, 1977. 790 p. (In Russian).
- Glushkov A.V. An atom in an electromagnetic field: Numerical mo-Delhi. Kiev: TNT, 2005. 450 p. (In Russian).
- Lisitsa V.S. New in Stark and Zeeman effects in the hydrogen atom. UFN. 1977. T.153, no. 3. pp. 379-422. (In Russian).
- Harmin D.A. Theory of the Non hydrogenic Stark Effect. Phys.Rev.Lett., 1982, vol.49, no. 2. pp. 128-131.
- Kazansky A.I. Diabatic quasi-stationary states and unstable closed trajectories. JETP. 1989, vol.95, №4. pp. 1162-1168. (In Russian).
- Yamabe T., Tashiibana A., Silverstone H.J. Theory of ionization of hydrogen atom by external electric field. Phys.Rev.A, 1977, vol.16, no. 3, pp. 877-890.
- Kazansky A.I., Ostrovsky V.N., Tel’nov D. Above-threshold resonance series associated with unstable classical trajectories in the problem of the hydrogen atom in an electric field. Proc. of the Atomic Spectroscopy Seminar. Rostov Velikiy, 1990. p. 29. (In Russian).
- Maquet A., Chu S-I., Reinhardt V.P. Stark ionization in dc and ac electric field: an L2 complex coordinate approach. Phys.Rev.A., 1983, vol.26, no. 6, pp. 2246-2261.
- Telnov D.A., DC Stark effect in hydrogen atom via sturmian expansion. J.Phys. B: At. Mol. Opt. Phys, 1989, vol.22, no. 4.- pp. L399-404.
- Moore V.D., Popov V.S., Sergeev A.V., Shcheblykin A.V. Stark resonances and scaling Rydberg atoms. JETP, 1989, vol.96, no. 1, pp. 91-106. (In Russian).
- Hehenberger M., McIntosh H.V., Brändas E. Weyl’s theory applied to the Stark effect in the hydrogen atom. Phys. Rev. A., 1974, vol.10, pp. 1494–1506.
- Popov V.S., Mur V.D., Sergeev A.V. 1/n expansion for the Stark effect in Rydberg atoms. Phys.Lett.A., 1990, vol.149, no. 9, pp. 425-433.
- Zimmerman M., Littman M., Kash M., Kleppner D. Stark structure of Rydberg states of alkali-metal atoms. Phys.Rev.A., 1979, vol.20, no. 6, pp. 2251-2275.
- Damburg R.J., Kolosov V.V. Hydrogen atom in uniform electric field. J. Phys. B.: Atom.,Mol.,Opt. Phys, 1979, vol.12, no. 22, pp. 2637-2644.
- Damburg R.Ya., Kolosov V.V. Asymptotic approach to the problem of the Stark. Riga: Zilitis, 1987.-180 p. (In Russian).
- Glushkov A.V., Ivanov L.N. DC Strong-Field Stark-Effect: consistent quantum-mechanical approach. J.Phys. B:At.Mol.Opt. Phys., 1993, vol.26, no. 16, pp. L379-396.
- Glushkov A.V. Operator Perturbation Theory for Atomic Systems in a Strong DC Electric Field. Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology. Series: Progress in Theoretical Physics and Chemistry. Berlin: Springer, 2013, vol.27, pp. 161-188.
- Glushkov A.V., Ambrosov S.V., Ignatenko A.V., Korchevsky D.A. DC Strong Field Stark Effect for Non-hydrogenic Atoms: Consistent Quantum Mechanical Approach. Int.Journ.Quant.Chem, 2004, vol.99, no. 6, pp. 936-939.
- Glushkov A.V., Lepikh Ya.I., Khetselius O.Yu., Fedchuk A.P., Ambrosov S.V , Ignatenko A.V. Wannier-mott excitons and atoms in a DC elecric field: photoionization, Stark effect, resonances in the ionization continuum. Sensor Electr. and Microsyst. Techn., 2008, no. 4, pp. 5-11.
- Glushkov A.V., The atoms and diatomic molecules in external efficient fields of N-component materials. Computer simulation of elementary atomic processes. Kiev, 1992, pp.121-124. (In Russian).
- Glushkov A.V., Khetselius O.Yu., Svinarenko A.A., Lovett L. Energy Approach to Nuclei and Atoms in a Strong Laser Field: Stark Effect and Multi-photon Resonances. Quantum Theory: Reconsideration of Foundations (AIP), 2010, vol.1232, pp. 228-234.