Translational Motion of a Free Large Polaron and Broadening of Absorption Spectra

Author(s)
Vladimir Mukhomorov

ABSTRACT

The translational motion of a large polaron as whole is analyzed in the context of its effect on the broadening of an absorption optical spectrum. It was open question how important the role of translational degrees of freedom and the corresponding velocities are on the broadening. The Bogolyubov method of canonical transformation of coordinates is formulated for a system of an electron and field, taking into account rigorous fulfillment of the conservation laws. Separation of variables is carried out for the coordinates describing the translational degrees of freedom and the electron oscillations in a polarization well. The equations obtained for the electronic states explicitly depend on the velocity of the free polaron as a whole. An estimate is made for free polaron in ammonia.

The translational motion of a large polaron as whole is analyzed in the context of its effect on the broadening of an absorption optical spectrum. It was open question how important the role of translational degrees of freedom and the corresponding velocities are on the broadening. The Bogolyubov method of canonical transformation of coordinates is formulated for a system of an electron and field, taking into account rigorous fulfillment of the conservation laws. Separation of variables is carried out for the coordinates describing the translational degrees of freedom and the electron oscillations in a polarization well. The equations obtained for the electronic states explicitly depend on the velocity of the free polaron as a whole. An estimate is made for free polaron in ammonia.

KEYWORDS

Large Polaron, Translational Motion, Canonical Transformation, Broadening, Absorption Spectra, Ammonia

Large Polaron, Translational Motion, Canonical Transformation, Broadening, Absorption Spectra, Ammonia

Cite this paper

nullV. Mukhomorov, "Translational Motion of a Free Large Polaron and Broadening of Absorption Spectra,"*Journal of Modern Physics*, Vol. 1 No. 1, 2010, pp. 9-16. doi: 10.4236/jmp.2010.11002.

nullV. Mukhomorov, "Translational Motion of a Free Large Polaron and Broadening of Absorption Spectra,"

References

[1] S. I. Pekar, “Research in Electron Theory of Crystals,” US AEC Report, 1960.

[2] M. J. Goovaerts, J. M. De Sitter and J. T. Devreese, “Nu-merical Study of Two-Phonon Sidebands in the Optical Ab-sorption of Free Polarons in the Strong-Coupling Limit,” Physical Review B, Vol. 7, No. 6, 1973, pp. 2639-2644.

[3] D. Emin, “Optical Properties of Large and Small Pola-rons,” Physical Review B, Vol. 48, 1993, pp. 13691- 13696.

[4] Y. T. Mazurenko and V. K. Mukhomorov, “On the Mechanism of Optical Spectra Broadening of Polarons,” Optics and Spectroscopy (USSR), Vol. 41, 1976, pp. 51-56.

[5] N. N. Bogolyubov, “About One New Form of an Adia-batic Perturbation Theory in a Problem about Interaction Particles with a Quantum Field,” Ukrainskii Matemati- cheskii Zhurnal (Russian Edtion), Vol. 2, 1950, pp. 3-24.

[6] V. K. Mukhomorov, “On a Spectra of the Coupled States of Polaron in a Limit of Adiabatic and Strong Coupling,” Optics and Spectroscopy (USSR), Vol. 71, 1991, pp. 958-965.

[7] V. K. Mukhomorov, “Singlet and Triplet States of a Con-tinuum Bipolaron for Adiabatic and Strong Coupling Limit,” Optics and Spectroscopy (USSR), Vol. 74, 1993, pp. 544-655.

[8] V. K. Mukhomorov, “Bipolaron States of Electrons and Magnetic Properties of Metal-Ammonia Systems,” Phy- sica Status Solidi B, Vol. 219, 2000, pp. 71-89.

[9] V. K. Mukhomorov, “Ground and Excited States of a Three-Dimensional Continual Bipolaron,” Physica Status Solidi B, Vol. 231, 2002, pp. 462-476.

[10] J. Jortner, “Energy Levels of Bound Electrons in Liquid Ammonia,” Journal of Chemical Physics, Vol. 30, 1959, pp. 839-846.

[11] J. C. Thompson, “Electrons in Liquid Ammonia,” Clare-don, Oxford, 1976.

[12] N. F. Mott, “Metal-Insulator Transitions,” Taylor and Francis, London, 1974.

[13] V. K. Mukhomorov, “Stability of Bipolarons, Elec-tron-Electron Correlations, the Variational Principle, and the Virial Theorem,” Physics of the Solid State, Vol. 48, 2006, pp. 864-870.

[14] V. K. Mukhomorov, “About the Problem of the Existence of a Three-Dimensional Bipolaron,” Physica Scripta, Vol. 69, 2004, pp. 139-145.

[15] V. K. Mukhomorov, “Bipolaron Formations and Interpo-laron Interactions in Dielectric Layers,” Physica Scripta, Vol. 79, No. 6, 2009, pp. 065704-065709.

[16] I. Z. Fisher, “Statistical Theory of Liquids,” University of Chicago Press, Chicago, 1965.

[17] A. I. Gubanov, “Quantum Electron Theory of Amorphous Conductors,” Consultants Bureau, New York, 1965.

[18] E. J. Hart and M. Anbar, “The Hydrated Electron,” Wiley, New York, 1970.

[19] R. C. Dauthit and J. L. Dye, “Absorption Spectra of So-dium and Potassium in Liquid Ammonia,” Journal of the American Chemical Society, Vol. 82, 1960, pp. 4472- 4478.

[20] S. Arai and M. G. Sayer, “Absorption Spectra of the Sol-vated Electron in Polar Liquids: Dependence on Tem-perature and Composition of Mixture,” Journal of Chemi- cal Physics, Vol. 44, 1966, pp. 2297-2301.

[1] S. I. Pekar, “Research in Electron Theory of Crystals,” US AEC Report, 1960.

[2] M. J. Goovaerts, J. M. De Sitter and J. T. Devreese, “Nu-merical Study of Two-Phonon Sidebands in the Optical Ab-sorption of Free Polarons in the Strong-Coupling Limit,” Physical Review B, Vol. 7, No. 6, 1973, pp. 2639-2644.

[3] D. Emin, “Optical Properties of Large and Small Pola-rons,” Physical Review B, Vol. 48, 1993, pp. 13691- 13696.

[4] Y. T. Mazurenko and V. K. Mukhomorov, “On the Mechanism of Optical Spectra Broadening of Polarons,” Optics and Spectroscopy (USSR), Vol. 41, 1976, pp. 51-56.

[5] N. N. Bogolyubov, “About One New Form of an Adia-batic Perturbation Theory in a Problem about Interaction Particles with a Quantum Field,” Ukrainskii Matemati- cheskii Zhurnal (Russian Edtion), Vol. 2, 1950, pp. 3-24.

[6] V. K. Mukhomorov, “On a Spectra of the Coupled States of Polaron in a Limit of Adiabatic and Strong Coupling,” Optics and Spectroscopy (USSR), Vol. 71, 1991, pp. 958-965.

[7] V. K. Mukhomorov, “Singlet and Triplet States of a Con-tinuum Bipolaron for Adiabatic and Strong Coupling Limit,” Optics and Spectroscopy (USSR), Vol. 74, 1993, pp. 544-655.

[8] V. K. Mukhomorov, “Bipolaron States of Electrons and Magnetic Properties of Metal-Ammonia Systems,” Phy- sica Status Solidi B, Vol. 219, 2000, pp. 71-89.

[9] V. K. Mukhomorov, “Ground and Excited States of a Three-Dimensional Continual Bipolaron,” Physica Status Solidi B, Vol. 231, 2002, pp. 462-476.

[10] J. Jortner, “Energy Levels of Bound Electrons in Liquid Ammonia,” Journal of Chemical Physics, Vol. 30, 1959, pp. 839-846.

[11] J. C. Thompson, “Electrons in Liquid Ammonia,” Clare-don, Oxford, 1976.

[12] N. F. Mott, “Metal-Insulator Transitions,” Taylor and Francis, London, 1974.

[13] V. K. Mukhomorov, “Stability of Bipolarons, Elec-tron-Electron Correlations, the Variational Principle, and the Virial Theorem,” Physics of the Solid State, Vol. 48, 2006, pp. 864-870.

[14] V. K. Mukhomorov, “About the Problem of the Existence of a Three-Dimensional Bipolaron,” Physica Scripta, Vol. 69, 2004, pp. 139-145.

[15] V. K. Mukhomorov, “Bipolaron Formations and Interpo-laron Interactions in Dielectric Layers,” Physica Scripta, Vol. 79, No. 6, 2009, pp. 065704-065709.

[16] I. Z. Fisher, “Statistical Theory of Liquids,” University of Chicago Press, Chicago, 1965.

[17] A. I. Gubanov, “Quantum Electron Theory of Amorphous Conductors,” Consultants Bureau, New York, 1965.

[18] E. J. Hart and M. Anbar, “The Hydrated Electron,” Wiley, New York, 1970.

[19] R. C. Dauthit and J. L. Dye, “Absorption Spectra of So-dium and Potassium in Liquid Ammonia,” Journal of the American Chemical Society, Vol. 82, 1960, pp. 4472- 4478.

[20] S. Arai and M. G. Sayer, “Absorption Spectra of the Sol-vated Electron in Polar Liquids: Dependence on Tem-perature and Composition of Mixture,” Journal of Chemi- cal Physics, Vol. 44, 1966, pp. 2297-2301.