**Nikiforov**

Vladimir O.

D.Sc., Prof.

Vladimir O.

D.Sc., Prof.

doi: 10.17586/2226-1494-2017-17-1-159-171

doi: 10.17586/2226-1494-2017-17-1-159-171

# A CALCULATION OF SEMI-EMPIRICAL ONE-ELECTRON WAVE FUNCTIONS FOR MULTI-ELECTRON ATOMS USED FOR ELEMENTARY PROCESS SIMULATION IN NONLOCAL PLASMA

**Read the full article**';

**Article in**Russian

**For citation:**Tchernycheva M.V., Sychov S.V., Chirtsov A.S. A calculation of semi-empirical one-electron wave functions for multi-electron atoms used for elementary process simulation in nonlocal plasma.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2017, vol. 17, no. 1, pp. 159–171. doi: 10.17586/2226-1494-2017-17-1-159-171

**Abstract**

**Subject of Research. **The paper deals with development outcomes for creation method of one-electron wave functions of complex atoms, relatively simple, symmetrical for all atom electrons and free from hard computations. The accuracy and resource intensity of the approach are focused on systematic calculations of cross sections and rate constants of elementary processes of inelastic collisions of atoms or molecules with electrons (ionization, excitation, excitation transfer, and others). **Method. **The method is based on a set of two iterative processes. At the first iteration step the Schrödinger equation was solved numerically for the radial parts of the electron wave functions in the potential of the atomic core self-consistent field. At the second iteration step the new approximationfor the atomic core field is created that uses found solutions for all one-electron wave functions. The solution optimization for described multiparameter problem is achieved by the use of genetic algorithm. The suitability of the developed method was verified by comparing the calculation results with numerous data on the energies of atoms in the ground and excited states. **Main Results**. We have created the run-time version of the program for creation of sets of one-electron wave functions and calculation of the cross sections and constants of collisional transition rates in the first Born approximation. The priori available information about binding energies of the electrons for any many-particle system for creation of semi-empirical refined solutions for the one-electron wave functions can be considered at any step of this procedure. **Practical Relevance**. The proposed solution enables a simple and rapid preparation of input data for the numerical simulation of nonlocal gas discharge plasma. The approach is focused on the calculation of discharges in complex gas mixtures requiring inclusion in the model of a large number of elementary collisional and radiation processes involving heavy particles in different quantum states.

**Keywords:**multi-electron atoms, one-electron wave functions, self-consistent field, atomic core polarization, Born method, electron impact ionization, electron impact excitation, optimization, genetic algorithms

**References**

*Proceedings of the National Academy of Sciences*, 1928, vol. 14, no. 8, pp. 627–637. doi: 10.1073/pnas.14.8.627

*Elektricheskii Tok v Gaze. Ustanovivshiisya Tok*[Electric Current in the Gas. Sustained Current]. Moscow, Nauka Publ., 1971, 490 p.

*Fizika Gazovogo Razryada*[Gas Discharge Physics]. Dolgoprudnyi, Intellekt Publ., 2009, 736 p.

*Fizika Tleyushchego Razryada*[Physics of Glow Discharge]. St. Petersburg, Lan' Publ., 2010, 512 p.

*Physics of Plasmas*, 2013, vol. 20, no. 10, art. 101605. doi: 10.1063/1.4823464

*Journal of Plasma Physics*,2013, vol. 79, no. 6, pp. 1099–1105. doi: 10.1017/S0022377813001128

*Vestnik St. Petersburg State University. Ser. 4. Phys. Chem*, 2013, no. 4, pp. 139–142. (In Russian)

*IEEE Transactions on Plasma Science*, 2013, vol. 41, no. 12, pp. 3254–3267. doi: 10.1109/TPS.2013.2278839

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2016, vol. 16, no. 5, pp. 903–916. (In Russian) doi: 10.17586/2226-1494-2016-16-5-903-916

*Plasma Physics and Controlled Fusion*, 2009, vol. 51, no. 12, art. 124003. doi: 10.1088/0741-3335/51/12/124003

*Plasma Sources Science and Technology*, 1995, vol. 4, no. 2, pp. 200–211. doi: 10.1088/0963-0252/4/2/004

*Physics of Plasmas*, 2007, vol. 14, no. 5, art. 057101. doi: 10.1063/1.2436470

*Journal of Plasma Physics*, 2014, vol. 80, no. 3, pp. 395–404. doi: 10.1017/S0022377813001359

*Morgan (Kinema Research & Software)*

**. Available at:www.lxcat.net/Morgan (accessed 22.04.2016).**

*Database**Acta Naturae*, 2012, vol. 4, no. 3, pp. 82–87.

*Elektronnaya Obrabotka Materialov*, 2002, vol. 38, no. 6, pp. 43–49. (In Russian)

*Vestnik Optometrii*, 2010, no. 3, pp. 54–58. (In Russian)

*Biophysics*, 2005, vol. 50, no. 2, pp. 334–337.

*Technical Physics. The Russian Journal of Applied Physics*, 2012, vol. 57, no. 10, pp. 1325–1330. doi: 10.1134/S1063784212100106

*IEEE Transactions on Plasma Science*, 2016, vol. 44, no. 11, pp. 2536–2544. doi: 10.1109/tps.2016.2557587

*Physics of Plasmas*, 2016, vol. 23, no. 10, pp. 109901. doi: 10.1063/1.4941259

*Introduction to the Theory of Atomic Spectra*. Moscow, Fizmatlit Publ., 1963, 641 p.

*Atomic Physics*. Moscow, Mir Publ., 1967, 493 p. (In Russian)

*Secheniya Vozbuzhdeniya Atomov i Ionov Elektronami*[Excitation Cross Sections of Atoms and Ions by Electrons]. Moscow, Nauka Publ., 1973, 142 p.

*Soviet Physics*, 1963, vol. 45, pp. 753–756. (In Russian)

*Trudy Fizicheskogo Instituta AN SSSR*, 1970, vol. 51, pp. 90–123.

*Theorems, Proofs, and Derivations in Quantum Chemistry*. NY, 2003.

*The Calculation of Atomic Structures*. NY: John Wiley and Sons, 1957.

*Nachala Kvantovoi Mekhaniki*[Principles of Quantum Mechanics]. Moscow, Nauka Publ., 1976, 376 p.

*Mécanique Quantique*. Dunod, Paris, 1965.

*Trudy Fizicheskogo Instituta AN SSSR*, 1961, vol. 15, p. 3.

*Quantum Mechanics (Nonrelativistic Theory)*. 6

^{th}ed. Moscow, Fizmatlit Publ., 2004, vol. 3, 800 p.

*Density-Functional Theory of Atoms and Molecules*. NY, Oxford University Press, 1989.

*Vestnik SPbSU. Seriya 4. Fizika. Khimiya*, 1991, no. 1, pp. 146–149. (In Russian)

*Proc. 19*. St. Petersburg, 2016, pp. 265–267

^{th}Int. Conf. on Soft Computing and Measurements