the new fuels with magnecular structure - Institute for Basic Research

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182 RUGGERO MARIA SANTILLI Figure A8. A schematic view of the ground and first-excited state of H + 2 ion. The solid line traces |000〉, and the dashed line follows |0 -1 0〉. The triangles give the positions of the protons for the ground state and the squares for the excited state. The magnetic field B = 4.7 · 10 12 Gauss is pointed along the internuclear axis; ζ = 2παz/λ e denotes z in a.u.; 1 a.u. = 0.53 · 10 −8 cm (reproduction of Figure 5 by Heyl and Hernquist [14]). tion, even at the intensities as high as B = 100B 0 . . . 1000B 0 . The outer domain appears to be of specific, highly elongated distribution along the direction of the magnetic field as shown in Fig. A7. The possible interpretation that the inner electrons remain to have a spherical distribution while outer electrons undergo the squeeze seems to be not correct unless the spin state of the iron atom is verified to be partially polarized. So, we can conclude that all the electrons are in the highly magnetically polarized state (Landau state mixed a little by Coulomb interaction), and the electronic structure is a kind of Landau multi-electron cylindrical shell, with the spins of all the electrons being aligned antiparallel to the magnetic field (fully spin polarized configuration). Another remark regarding Fig. A7 is that the contours indicating a nearly spherical distribution will always appear since the Coulomb center (nucleus) is not totally eliminated from the consideration (non-adiabatic approximation), and it forces a spherical distribution to some degree, which evidently depends on the distance from the center (closer to the center, more sphericity). We note that outer contours in Fig. A7 is in qualitative agreement with Fig. A6 in the sense that the predicted charge distribution reveals symmetry under the inversion z → −z, with the characteristic z-elongated Landau-type orbits.
THE NEW FUELS WITH MAGNECULAR STRUCTURE 183 An interesting problem is to study H 2 molecule under the action of a strong external static uniform magnetic field using Schrödinger’s equation. However, prior to that study, it would be useful to investigate the simpler two-center H + 2 ion, since it can give valuable information on the features of the full hydrogen molecule under the action of a strong magnetic field. We refer the interested reader to Refs. [12, 14, 15] for studies on H + 2 ion and H 2 molecule in strong magnetic field. Figure A8 displays the ground and first excited state wave functions of H + 2 [14].
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Contents Preface 1 THE INCREASINGLY
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