V.6 No 1 
1 
On excited state of orbital electron 

On excited state of orbital electron S. B. Karavashkin and O.N. Karavashkina Special Laboratory for Fundamental Elaboration SELF 187 apt., 38 bldg., Prospect Gagarina, Kharkov, 61140, Ukraine phone +38 (057) 7370624 email: selftrans@yandex.ru, selflab@mail.ru We will study the linear dynamic model of an orbital electron excited by an external timevariable electric field. Basing on the full solution of the system of differential equations, we will analyse the typical resonance trajectories of the excited motion of electron. We will show the phenomenology of excitation basically different from the conventional idea of discrete orbital levels. In particular, when modelling the external excitation, Kepler’s laws for stationary orbits become invalid. The resonances are caused by the matched frequencies of external excitation and natural frequency of the electron’s orbit at rest. With equal frequencies, the orbital diameter is not quantified, as conventional, but depends on the strength of external field, and strongly retains the resonance condition. If changed ratio in the natural frequency of an orbital electron and the external field frequency, the type of trajectory changes, not the size of orbit. The yielded results will be extended for the case of interaction of stellar shells with the external field and field of excited nucleus of the star. Keywords: atomic physics, quantum mechanics, astrophysics, Kepler laws, Schroedinger equation, Compton effect, Planck law, Bohr atomic theory, excitation of orbital electron, excitation of stellar shell by external field Classification by MSC 2000: 70G60, 70J35, 70J40, 70J50, 81V10, 81V45, 81V70, 85A05, 85A15 Classification by PASC 2001: 31.25.Jf, 32.00.00, 32.30.r, 32.70.Cs, 32.80.Lg, 45.30.+s, 45.40.f, 98.10.+z, 98.35.Df 1. Introduction In [1] we showed how the stable orbits of oscillators form because of spiralshaped dynamic field excitation in the system. In particular, we showed that just the tangential component of electric field compensates the loss of electron’s energy, which, as the researchers thought, in absence of this field had to cause the electron falling onto the nucleus. In this way we in [1] lifted the limitation imposed by the Bohr postulate that electron does not radiate in its orbit; by force of contradictive theory of electromagnetic fields, this postulate was rather a paradox than the postulate as such. As R.W. Pohl expressed, “Bohr forces it (the orbit  Authors) to be stable. He says, the radiationcaused attenuation follows from the classical electrodynamics, i.e. from the Maxwell equations. These last stop to be true within the atom” [2, p. 367]. When we have the difficulties of this postulate got over, it appeared that the ban to radiate is not only excessive but the very fact of permanent nonquantified energy radiation/absorption by the orbital electron in the stationary orbit becomes a basically necessary part of general process of energy redistribution in the material continuum. Actually, if we have some countable set of atoms in isothermic equilibrium, it is impossible to average the temperature in such volume, if between atoms there does not exist a permanent reciprocal energy exchange. Should the Bohr postulate be actually true, the energy exchange could take place exceptionally on those quantified frequencies that follow from Bohr’s solutions. The quantummechanical energy exchange gives the same discrete solutions. But these frequencies are well higher than the infrared range; this means, if the postulate or, alike, the quantification principle was true, we would not register the heat conduction in the substance that takes place on the infrared frequencies  in the range where all line spectra merge into those continuous. But if the orbital electrons of each atom radiated and absorbed the nonquantified energy, the phenomenology of thermal conductivity takes its natural appearance that we see in the experimental practice, when without the quantified excitation of substance, the EM energy propagates from the hotter parts of substance to the cooler parts. Each atom of the considered system consists of mutually moving charges that automatically arrange a dynamic dipole. With it, the atomtoatom energy transfer occurs mutually. If the radiating atom’s frequency was higher than that receiving, the energy absorption causes the higher energetic state of the lowerenergetic atom. And the way, the lowerenergetic atom to affect that higherenergetic, will be such: in the rotation frequency of higherenergetic electron there will appear the harmonics introduced by the lowerenergetic atom. As a result of longterm affection (from the view of inertial processes in the atom) it will lessen the rotation frequency of the highenergetic electron. And if the frequencies of radiating and receiving atoms are same, they will only synchronise their radiation and exchange the energy  this means, they will coordinate the atomic orbits. Due to this, the permanent energetic relations form within the continuum and the elementary dipoles, through the nonquantified radiation/absorption, quickly average the general energy of the system and form the conditions of energetic balance of the system. Thus, we see that since we reveal the spiralshaped dynamic field, the issue of electron orbit stabilisation came to another point of consideration. Now the orbit stability is provided not only by the balance of centrifugal and attractive forces, but also by the measure of inertia of the atomic nucleus that stabilises the rotation frequency of spiral field. As we showed in [1], the stabilisation can work in a continuous spectrum of spin frequency of electron – and this is the main distinction of our model from that Bohr’s. 
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