the new fuels with magnecular structure - Institute for Basic Research

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30 RUGGERO MARIA SANTILLI the figures with standing waves, in semiclassical approximation. By contrasts, orbitals are purely mathematical notions given by probability density. As a result, magnetic fields can be more clearly associated with orbits rather than with orbitals. Despite the above differences, it should be stressed that, magnetic polarizations can also be derived via the orbitals of conventional use in chemistry. For example, consider the description of an isolated atom via the conventional Schrödinger equation ( ) p 2 H|ψ〉 = 2m + V |ψ〉 = E|ψ〉, (2.12) where |ψ〉 is a state in a Hilbert space. Orbitals are expressed in terms of the probability density |〈ψ| × |ψ〉|. The probability density of the electron of a hydrogen atom has a spherical distribution, namely, the electron of an isolated hydrogen atom can be found at a given distance from the nucleus with the same probability in any direction in space. Assume now that the same hydrogen atom is exposed to a strong external homogeneous and static magnetic field B. This case requires the new Schrödinger equation, ( (p − e ) c A)2 /2m + V |ψ ′ 〉 = E ′ |ψ ′ 〉, (2.13) where A is vector-potential of the magnetic field B. It is easy to prove that, in this case, the new probability density |〈ψ ′ | × |ψ ′ 〉| possesses a cylindrical symmetry precisely of the type indicated above, thus confirming the results obtained on physical grounds. A similar confirmation can be obtained via the use of Dirac’s equation or other chemical methods. An accurate recent review of the Schrödinger equation for the hydrogen atom under external magnetic fields is that by A. K. Aringazin [8], which study confirms the toroidal configuration of the electron orbits which is at the foundation of the new chemical species of magnecules. A review of Aringazin studies is presented in Appendix A. As one can see, under an external, strong, homogeneous, and constant magnetic fields of the order of 10 13 Gauss = 10 7 Tesla, the solutions of Schrödinger equation of type (2.13) imply the restriction of the electron orbits within a single, small-size toroidal configuration, while the excited states are represented by the double-splitted toroidal configuration due to parity. Intriguingly, the binding energy of the ground state of the H atom is much higher than that in the absence of an external magnetic field, by therefore con-
THE NEW FUELS WITH MAGNECULAR STRUCTURE 31 firming another important feature of the new chemical species of magnecules, that of permitting new means of storing energy within conventional molecules and atoms, as discussed later on in this book. For magnetic fields of the order of 10 9 Gauss, spherical symmetry begins to compete with the toroidal symmetry, and for magnetic fields of the order of 10 5 Gauss or less, spherical symmetry is almost completely restored by leaving only ordinary Zeeman effects. This latter result confirms that the creation of the new chemical species of magnecules in gases as per Definition requires very strong magnetic fields. The situation for liquids is different, as shown later on also in this book. The magnetic polarization of atoms larger than hydrogen is easily derived from the above calculations. Consider, for example, the magnetic polarization of an isolated atom of oxygen. For simplicity, assume that an external magnetic field of 10 Tesla polarizes only the two peripheral valence electrons of the oxygen. Accordingly, its total polarized magnetic field of orbital type is of the order of twice value (2.9), i.e., about 6,000 µ. However, when the same oxygen atom is bonded into the water or other molecules, the maximal polarized magnetic moment is about half the preceding value. Note the dominance of the magnetic fields due to polarized electron orbits over the intrinsic nuclear magnetic fields. This is due not only to the fact that the former are 1,316 times the latter, but also to the fact that nuclei are at a relative great distance from peripheral electrons, thus providing a contribution to the bond even smaller than that indicated. This feature explains the essential novelty of magnecules with respect to established magnetic technologies, such as that based on nuclear magnetic resonances. Note also that a main mechanism of polarization is dependent on an external magnetic field and the force actually providing the bond is of magnetic type. Nevertheless, the ultimate origin is that of charges rotating in an atomic orbit. This illustrates that, as indicated in Sect. 2.1, the name “magnecules” was suggested on the basis of the predominant magnetic origin, as well as for the pragmatic differentiation with molecules without using a long sentence, although a technically more appropriate name would be “electromagnecules.” Needless to say, the polarization of the orbits is not necessarily restricted to valence electrons because the polarization does not affect the quantum numbers of any given orbit, thus applying for all atomic electrons, including those of complete inner shells, of course, under a sufficiently strong external field. As a
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