Two types of proton-electron atoms in a vacuum and an extremely strong magnetic field R. Fedaruk Institute of Physics, University of Szczecin, 70-451, Szczecin, Poland The Rutherford planetary model of a proton-electron atom is modified. Besides the Coulomb interaction of the point elec- tron with the proton, its strong Coulomb interaction with the physical vacuum as well as the magnetic interaction between moving charges are taken into account. The vacuum interaction leads to the motion of the electron with the velocity of light c in the circle with the radius being equal to rthe so-called classical electron radius re. Therefore,r the velocity of the electron consists of two components: the velocity υ of the mechanical motion and the velocity c of the photon-like mo- r v tion. We postulate that υ ⊥ c , and υ < c. Hence, the electron inside the atom moves with the resulting faster-than-light velocity. The existence of two types of proton-electron atoms, the hydrogen atom and the neutron, is interpreted by the different motion and interaction of particles at large ( r >> re) and short ( r < re) distances. In the first atom, the effect of photon-like motion is small, and the electron moves around the proton with the velocity υ << c in an orbit of the radius >> r re . In the second atom, the photon-like motion is the determining factor, and the electron moves around the proton < with the faster-than-light velocity in an orbit of the radius r re . The calculated ground-state properties of the free hy- drogen atom and the free neutron are in good agreement with the experimental data. The properties of these atoms in ex- tremely strong magnetic fields ( B > 10 8 T) are discussed. PACS numbers: 32.10.-f; 14.60.Cd; 03.50.Kk; 14.20.Dh 1. Introduction Difficulties in describing nucleons as the strongly bound three-quark systems are usually related to computational The hydrogen atom is the simplest two-body bound problems. system consisting of a proton and an electron. The hy- Note that two alternative approaches, constructing pothesis of the second allotropic type of proton-electron nucleons either from the stable particles observed in the atom, the strongly bound proton-electron atom called nucleon decay or from quarks nonexistent as free parti- neutron, was suggested by Rutherford in 1920 [1]. The cles, confront with the same problem. That problem is the existence of the neutron was confirmed in 1932 by strong interaction of elementary constituents. Unlike the Chadwick, however the proton-electron model of the quark model, the strongly bound proton-electron model neutron was left because of its contradictions with quan- was definitely rejected. Nevertheless, some new attempts tum mechanics [2]. (a) According to quantum mechanics, to improve of Rutherford’s model of neutron were made the total angular momentum of the proton-electron neu- [6–8]. In these attempts the problem of strong interaction tron must be 0, while the neutron reveals as a particle between the electron and the proton was concealed by with spin 1/2. (b) The binding energy of the proton- assuming the unusual structure of these particles. Re- electron system must be negative, but the measured mass cently, claims that so-called hydrino states exist have of the neutron is 0.782 MeV/c 2 larger than the sum of the been discussed [9–12]. In such states the electron is masses of the proton and the electron. (c) Via the use of strongly bound and is unusually close to the proton. It is the spin magnetic moments of the proton and the electron obvious that, if strongly bound proton-electron states it is impossible to obtain the neutron magnetic moment. really exist as free atoms, their description could not be (d) There is no possibility to reach the small neutron done in the frame of conventional approach. radius (of about 10 –15 m) since the smallest radius of the On the other hand, quantum mechanics predicts proton-electron atom predicted by quantum mechanics strongly bound states of the hydrogen atom in strong and the Schrödinger equation is of 10 –10 m. Although magnetic fields ( B >> 10 5 T). Such states have been thor- these contradictions are based on the theory describing oughly studied theoretically using the Schrödinger and only weakly bound atomic systems, they are generally Dirac equations (see, e.g. Refs. [13–18]). In this case the accepted arguments against the possibility of existence of Coulomb force is treated as a small perturbation com- a strongly bound proton-electron atom. pared to the magnetic force. Because of the strong mag- Today, there are no experimental data related to the netic confinement of the electron, the hydrogen atom hydrogen atom which could give trouble to quantum attains a cylindrical structure elongated along the mag- electrodynamics (QED) [3]. At the same time, the preci- netic field and a much greater binding energy compared sion of the measured proton and neutron properties, in to the zero-field case. For example, in a field of about 1.2 particular their magnetic moments and the mass differ- × 10 10 T, the hydrogen atom becomes a long cylinder 200 ence, is appreciably higher than the precision of their times narrower than its normal diameter [17]. The highest quantum chromodynamics (QCD) calculations [4,5]. magnetic fields (of about 10 2 T) produced in laboratories 1 are too small for the verification of theoretical results. electron has no any additional motion, its average posi- The appropriate magnetic fields (up to 10 13 T) can exist tion does not change and it is observed as the resting on the surfaces of neutron stars [18]. However, adequate electron. experimental data confirmed the predicted properties of It is obvious that in our model the radius re of the cir- the hydrogen atom in such strong-field conditions were cular motion of a point electron is not related to its struc- not found until now. ture. Historically, the term “classical electron radius” for In the present paper, we discuss an opportunity of ex- the value re was introduced in classical electrodynamics istence of strongly bound proton-electron states based on of an extended electron using the idea of its electromag- the modification of the Rutherford planetary model. netic momentum and its electromagnetic mass [20–22]. Apart from the Coulomb interaction between the electron The photon-like motion of an electron differs from the and the proton, an additional strong Coulomb interaction Zitterbewegung. According to the Dirac equation [23], a of charged particles with the physical vacuum as well as point electron, besides its slow motion, also possesses the the magnetic interaction between moving charges should oscillatory motion with the velocity of light (the Zitter- be taken into account. The atomic model presented pre- bewegung [24]). This oscillatory motion occurs with the dicts existence of two allotropic types of proton-electron ω = 2 doubled Compton frequency C e cm / h and the bound states, the hydrogen atom and the neutron. The amplitude of the order of the Compton wavelength ground-state properties of the hydrogen atom and the r = h / cm , where h is the reduced Planck constant. neutron in a vacuum and in extremely strong magnetic C e fields are analyzed. It is important to point out that, in quantum theory, the radius of the Zitterbewegung is determined by the quantization of mechanical properties of an electron by 2. Allotropy of a proton-electron atom means of the Planck constant. In our model, the radius re of the photon-like motion of an electron is due to the In an attempt to search the origin of possible exis- quantization of an electrical charge and is much smaller tence of two types of proton-electron atoms we accent the than the Compton wavelength. fact of duality of radiation and matter. It was experimen- We now consider the motion of two point charged tally proved that photons having energies equal or larger particles in the proton-electron atom. In general, the elec- 2 tromagnetic forces between two moving charged particles than 2 ecm can create electron-positron pairs or these satisfy neither the condition that the forces are along the pairs could annihilate into photons. Here, me is the elec- line joining them nor that these forces are equal in magni- tron rest mass, and с is the speed of light in vacuum. The tude and oppositely directed [20–22]. There is a problem duality of radiation and matter testifies that an electron in the relation between Newton’s third law and electro- and a photon are different manifestations of the same magnetism. However, the ground state of the proton- entity. Therefore, we postulate that, like a photon, a point electron atom represents the extraordinary case of this electron possesses not only the rest energy E = cm 2 , relation. Due to the atom’s stability, the atom is an isolate r e r and closed system, and the emission of any electromag- = = but also a corresponding momentum p E / c ecm netic radiation by the atom is absent. Therefore, we sup- resulting from the electron motion with the velocity of pose that there is the full validity of Newton’s third law light (photon-like motion). for the interaction of moving charges inside the atom. As Let us assume that the photon-like motion of the elec- a result, at any instant, the forces of action and reaction tron is caused by its strong interaction with the environ- between the electron and the proton are equal in magni- ment (physical vacuum).