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the new fuels with magnecular structure - Institute for Basic Research

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182 RUGGERO MARIA SANTILLI<br />

Figure A8. A schematic view of <strong>the</strong> ground and first-excited state of H + 2 ion. The solid line<br />

traces |000〉, and <strong>the</strong> dashed line follows |0 -1 0〉. The triangles give <strong>the</strong> positions of <strong>the</strong> protons<br />

<strong>for</strong> <strong>the</strong> ground state and <strong>the</strong> squares <strong>for</strong> <strong>the</strong> excited state. The magnetic field B = 4.7 · 10 12<br />

Gauss is pointed along <strong>the</strong> internuclear axis; ζ = 2παz/λ e denotes z in a.u.; 1 a.u. = 0.53 · 10 −8<br />

cm (reproduction of Figure 5 by Heyl and Hernquist [14]).<br />

tion, even at <strong>the</strong> intensities as high as B = 100B 0 . . . 1000B 0 . The outer domain<br />

appears to be of specific, highly elongated distribution along <strong>the</strong> direction of <strong>the</strong><br />

magnetic field as shown in Fig. A7. The possible interpretation that <strong>the</strong> inner<br />

electrons remain to have a spherical distribution while outer electrons undergo<br />

<strong>the</strong> squeeze seems to be not correct unless <strong>the</strong> spin state of <strong>the</strong> iron atom is verified<br />

to be partially polarized. So, we can conclude that all <strong>the</strong> electrons are in<br />

<strong>the</strong> highly magnetically polarized state (Landau state mixed a little by Coulomb<br />

interaction), and <strong>the</strong> electronic <strong>structure</strong> is a kind of Landau multi-electron cylindrical<br />

shell, <strong>with</strong> <strong>the</strong> spins of all <strong>the</strong> electrons being aligned antiparallel to <strong>the</strong><br />

magnetic field (fully spin polarized configuration).<br />

Ano<strong>the</strong>r remark regarding Fig. A7 is that <strong>the</strong> contours indicating a nearly<br />

spherical distribution will always appear since <strong>the</strong> Coulomb center (nucleus) is<br />

not totally eliminated from <strong>the</strong> consideration (non-adiabatic approximation), and<br />

it <strong>for</strong>ces a spherical distribution to some degree, which evidently depends on <strong>the</strong><br />

distance from <strong>the</strong> center (closer to <strong>the</strong> center, more sphericity). We note that<br />

outer contours in Fig. A7 is in qualitative agreement <strong>with</strong> Fig. A6 in <strong>the</strong> sense that<br />

<strong>the</strong> predicted charge distribution reveals symmetry under <strong>the</strong> inversion z → −z,<br />

<strong>with</strong> <strong>the</strong> characteristic z-elongated Landau-type orbits.

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