On the Mechanism Broadening of Optical Spectrum of a Solvated Electron in Ammonia
The solvated electron is self-trapped (polaron) owing
to strong interaction with the quantum polarization field. If the
electron and quantum field are strongly coupled then the collective
localized state of the field and quasi-particle is formed. In such a
formation the electron motion is rather intricate. On the one hand the
electron oscillated within a rather deep polarization potential well
and undergoes the optical transitions, and on the other, it moves
together with the center of inertia of the system and participates in
the thermal random walk. The problem is to separate these motions
correctly, rigorously taking into account the conservation laws. This
can be conveniently done using Bogolyubov-Tyablikov method of
canonical transformation to the collective coordinates. This
transformation removes the translational degeneracy and allows one
to develop the successive approximation algorithm for the energy and
wave function while simultaneously fulfilling the law of conservation
of total momentum of the system. The resulting equations determine
the electron transitions and depend explicitly on the translational
velocity of the quasi-particle as whole. The frequency of optical
transition is calculated for the solvated electron in ammonia, and an
estimate is made for the thermal-induced spectral bandwidth.
[1] J. C. Thompson. Electron in Liquid Ammonia, Oxford: Claredon, 1976.
ch.2.
[2] N. N Bogolyubov."Ob odnoi novoi forme adiabaticheskoi teorii
vozmuschenii v zadache o vzaimideistvii chastizi c kvantivim polem (About one new form of an adiabatic perturbation theory in a problem
about interaction particles with a quantum field)" Ukr. Matem. Zh.
(Russ. Ed)., vol..2, no..2, pp.3-24, 1950.
[3] S. V Tyablikov. "Adiabaticheskai teoria vozmushenii v zadache o
vzaimodeistvii chastizi c kvantovim polem (The adiabatic form of a
perturbation theory in a problem about interaction particles with a
quantum field)" Zh. Eksp. Teor. Fiz. (Russ. Ed.), vol. 21, no. 3, pp.377-
387, 1951.
[4] V. K Mukhomorov."O spektre sviazannih sostoianii polarona v predele
adiabaticheskoi i silnoi sviasi (On a spectrum of bound states of a
polaron within the limit of adiabatic and strong coupling)" Opt. Spektr.,
(Russ. Ed)., v.71. no..6, pp. 958-965, 1991.
[5] V. K Mukhomorov. "Criterion for formation of the first band of an
optical polaron" Phys. Solid State, vol.42, no..9, pp. 1602-1605, 2000.
[6] V .K Mukhomorov. "Ground and excited states of a three-dimensional
continual bipolaron" Phys. Stat. Sol (b). Vol..231, no..2, pp..462-476,
2002.
[7] V. K. Mukhomorov, Yu. T Mazurenko. "Analiz formi i temperaturnai
zavisimost opticheskogo spectra pogloschenia gidratirovannogo
elektrona (The analysis of the form and temperature dependence of
optical absorption spectrum of a hydrated electron)"Opt. Spektr., (Russ.
Ed), vol..41, no.6, pp. 930-935, 1976.
[8] E.J. Hart, M.Anbar, The Hydrated Electron, New York: Wiley, 1970,
ch.1.
[9] Yu. T Mazurenko, V. K. Mukhomorov."O mehanizme ushirenia
opticheskogo spectra solvatirovannogo elektrona (About the mechanism
of a broadening of an optical spectrum of a solvated electron)" Opt.
Spectr. (Russ. Ed)., vol..41, no.1, pp. 51-56, 1976.
[10] R.C. Dauthit, J. L Dye., "Absorption spectra of sodium and potassium in
liquid ammonia", J. Am. Chem. Soc., vol. .82, no. 17, pp. 4472-4478,
1960.
[11] S. Arai, M. G. Sayer "Absorption spectra of the solvated electron in
polar liquids: Dependence on temperature and composition of mixture"
J. Chem. Phys., vol..44, no. 6, pp.2297-2305, 1966.
[1] J. C. Thompson. Electron in Liquid Ammonia, Oxford: Claredon, 1976.
ch.2.
[2] N. N Bogolyubov."Ob odnoi novoi forme adiabaticheskoi teorii
vozmuschenii v zadache o vzaimideistvii chastizi c kvantivim polem (About one new form of an adiabatic perturbation theory in a problem
about interaction particles with a quantum field)" Ukr. Matem. Zh.
(Russ. Ed)., vol..2, no..2, pp.3-24, 1950.
[3] S. V Tyablikov. "Adiabaticheskai teoria vozmushenii v zadache o
vzaimodeistvii chastizi c kvantovim polem (The adiabatic form of a
perturbation theory in a problem about interaction particles with a
quantum field)" Zh. Eksp. Teor. Fiz. (Russ. Ed.), vol. 21, no. 3, pp.377-
387, 1951.
[4] V. K Mukhomorov."O spektre sviazannih sostoianii polarona v predele
adiabaticheskoi i silnoi sviasi (On a spectrum of bound states of a
polaron within the limit of adiabatic and strong coupling)" Opt. Spektr.,
(Russ. Ed)., v.71. no..6, pp. 958-965, 1991.
[5] V. K Mukhomorov. "Criterion for formation of the first band of an
optical polaron" Phys. Solid State, vol.42, no..9, pp. 1602-1605, 2000.
[6] V .K Mukhomorov. "Ground and excited states of a three-dimensional
continual bipolaron" Phys. Stat. Sol (b). Vol..231, no..2, pp..462-476,
2002.
[7] V. K. Mukhomorov, Yu. T Mazurenko. "Analiz formi i temperaturnai
zavisimost opticheskogo spectra pogloschenia gidratirovannogo
elektrona (The analysis of the form and temperature dependence of
optical absorption spectrum of a hydrated electron)"Opt. Spektr., (Russ.
Ed), vol..41, no.6, pp. 930-935, 1976.
[8] E.J. Hart, M.Anbar, The Hydrated Electron, New York: Wiley, 1970,
ch.1.
[9] Yu. T Mazurenko, V. K. Mukhomorov."O mehanizme ushirenia
opticheskogo spectra solvatirovannogo elektrona (About the mechanism
of a broadening of an optical spectrum of a solvated electron)" Opt.
Spectr. (Russ. Ed)., vol..41, no.1, pp. 51-56, 1976.
[10] R.C. Dauthit, J. L Dye., "Absorption spectra of sodium and potassium in
liquid ammonia", J. Am. Chem. Soc., vol. .82, no. 17, pp. 4472-4478,
1960.
[11] S. Arai, M. G. Sayer "Absorption spectra of the solvated electron in
polar liquids: Dependence on temperature and composition of mixture"
J. Chem. Phys., vol..44, no. 6, pp.2297-2305, 1966.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51401", author = "V.K. Mukhomorov", title = "On the Mechanism Broadening of Optical Spectrum of a Solvated Electron in Ammonia", abstract = "The solvated electron is self-trapped (polaron) owing
to strong interaction with the quantum polarization field. If the
electron and quantum field are strongly coupled then the collective
localized state of the field and quasi-particle is formed. In such a
formation the electron motion is rather intricate. On the one hand the
electron oscillated within a rather deep polarization potential well
and undergoes the optical transitions, and on the other, it moves
together with the center of inertia of the system and participates in
the thermal random walk. The problem is to separate these motions
correctly, rigorously taking into account the conservation laws. This
can be conveniently done using Bogolyubov-Tyablikov method of
canonical transformation to the collective coordinates. This
transformation removes the translational degeneracy and allows one
to develop the successive approximation algorithm for the energy and
wave function while simultaneously fulfilling the law of conservation
of total momentum of the system. The resulting equations determine
the electron transitions and depend explicitly on the translational
velocity of the quasi-particle as whole. The frequency of optical
transition is calculated for the solvated electron in ammonia, and an
estimate is made for the thermal-induced spectral bandwidth.", keywords = "Canonical transformations, solvated electron, width
of the optical spectrum.", volume = "3", number = "7", pages = "471-7", }