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168 RUGGERO MARIA SANTILLI netic radius of electron, reveal themselves even at low magnetic field intensities, and can be accounted for as very small perturbations. Additional effects are related to the apparent deviation from QED of strongly correlated valence bonds as studied in Chapter 4 [24]. These effects are beyond the scope of the presented study, while being important for high precision studies, such as those on stringent tests of the Lamb shift. It should be noted that locally high-intensity magnetic fields may arise in plasma as the result of nonlinear effects, which can lead to the creation of stable self-confined structures having nontrivial topology with knots [10]. More particularly, Faddeev and Niemi [10] recently argued that the static equilibrium configurations within the plasma are topologically stable solitons describing knotted and linked fluxtubes of helical magnetic fields. In the region close to such fluxtubes, we suppose the magnetic field intensity may be as high as B 0 . In view of this, a study of the action of strong magnetic field and the fluxtubes of magnetic fields on atoms and molecules becomes of great interest in theoretical and applicational plasmachemistry. Possible applications are conceivable for the new chemical species of magnecules. As a result of the action of a very strong magnetic field, atoms attain a great binding energy as compared to the case of zero magnetic field. Even at intermediate B ≃ B 0 , the binding energy of atoms greatly deviates from that of the zero-field case, and even lower field intensities may essentially affect chemical properties of molecules of heavy atoms. This occurrence permits the creation of various other bound states in molecules, clusters and bulk matter [9, 11, 12]. The paper by Lai [12] is focused on very strong magnetic fields, B ≫ B 0 , motivated by astrophysical applications, and provides a good survey of the early and recent studies in the field, including studies on the intermediate range, B ≃ B 0 , multi-electron atoms, and H 2 molecule. Several papers using variational/numerical and/or analytical approaches to the problem of light and heavy atoms, ions, and H 2 molecule in strong magnetic field, have been published within the last years (see, e.g., references in [12]). However, highly magnetized molecules of heavy atoms have not been systematically investigated until Santilli’s proposal for the new species of magnecules [1]. One of the surprising implications is that for some diatomic molecules of heavy atoms, the molecular binding energy is predicted to be several times bigger than the ground state energy of individual atom [13].
THE NEW FUELS WITH MAGNECULAR STRUCTURE 169 To estimate the intensity of the magnetic field which causes considerable deformation of the ground state electron orbit of the H atom, one can formally compare Bohr radius of the H atom in the ground state, in zero external magnetic field, a 0 = 2 /me 2 ≃ 0.53 · 10 −8 cm = 1 a.u., with the radius of orbit of a single electron moving in the external static uniform magnetic field B. ⃗ The mean radius of the orbital of a single electron moving in a static uniform magnetic field can be calculated exactly by using Schrödinger’s equation, and it is given by R n = √ n + 1/2 , (A.1) γ where γ = eB/2c, B is intensity of the magnetic field pointed along the z axis, ⃗B = (0, 0, B), ⃗r = (r, ϕ, z) in cylindrical coordinates, and n = 0, 1, . . . is the principal quantum number. Thus, the radius of the orbit takes discrete set of values (A.1), and is referred to as Landau radius. This is in contrast to well known classical motion of electrons in an external magnetic field, with the radius of the orbit being of a continuous set of values. The energy levels E n of a single electron moving in said external magnetic field are referred to as Landau energy levels, E n = E ⊥ n + E ‖ k z = Ω(n + 1 2 ) + 2 k 2 z 2m , (A.2) where Ω = eB/mc is so called cyclotron frequency, and k z is a projection of the electron momentum ⃗ k on the direction of the magnetic field, −∞ < k z < ∞, m is mass of electron, and −e is charge of electron. Landau’s energy levels En ⊥ correspond to a discrete set of round orbits of the electron which are projected to the transverse plane. The energy E ‖ k z corresponds to a free motion of the electron in parallel to the magnetic field (continuous spectrum), with a conserved momentum k z along the magnetic field. In regard to the above review of Landau’s results, we recall that in the general case of a uniform external magnetic field the coordinate and spin components of the total wave function of the electron can always be separated. The corresponding coordinate component of the total wave function of the electron, obtained as an exact solution of Schrödinger equation for a single electron moving in the external magnetic field with vector-potential chosen as
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Contents Preface 1 THE INCREASINGLY
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HADRONIC MATHEMATICS, MECHANICS AND
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