A Note on Polarization Vectors in Quantum Electrodynamics

A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence free in the Coulomb gauge. These facts are normally taken into account in QED by introducing two polarization vectors epsilon_\lambda(k) with lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must be very discontinuous functions of k and, consequently, their Fourier transforms have bad decay properties. Since these vectors have no physical significance there must be a way to eliminate them and their bad decay properties from the theory. We propose such a way here.Comment: 6 pages late

There are No Unfilled Shells in Hartree-Fock Theory

Hartree-Fock theory is supposed to yield a picture of atomic shells which may or may not be filled according to the atom's position in the periodic table. We prove that shells are always completely filled in an exact Hartree-Fock calculation. Our theorem generalizes to any system having a two-body interaction that, like the Coulomb potential, is repulsive.Comment: 5 pages, VBEHLMLJPS--16/July/9

Stability of Matter in Magnetic Fields

In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if $\alpha$ or $Z$ is too large. Here we prove that matter {\it is stable\/} if $\alpha<0.06$ and $Z\alpha^2<0.04$.Comment: 10 pages, LaTe

High-Pressure Phase Transition of the Oxonitridosilicate Chloride Ce4[Si4O3+xN7-x]Cl1-xOx with x = 0.12 and 0.18

The high-pressure behaviour of the oxonitridosilicate chlorides Ce4[Si4O3þxN7-x]Cl1-xOx, x = 0.12 and 0.18, is investigated by in situ powder synchrotron X-ray diffraction. Pressures up to 28 GPa are generated using the diamond-anvil cell technique. A reversible phase transition of first order occurs at pressures between 8 and 10 GPa. Within this pressure range the high- and the low-pressure phases are observed concomitantly. At the phase transition the unit cell volume is reduced by about 5%, and the cubic symmetry (space group P213) is reduced to orthorhombic (space group P212121) following a translationengleiche group-subgroup relationship of index 3. A fit of a third-order Birch-Murnaghan equation of state to the p-V data results in a bulk modulus B0 = 124(5) GPa with its pressure derivative B0 = 5(1) at V0 = 1134.3(4) Å3 for the low-pressure phase and in B0 = 153(10) GPa with B0 = 3.0(6) at V0 = 1071(3) Å3 for the high-pressure phase. The orthorhombic phase shows an anisotropic axial compression with the a axis (which is the shortest axis) being more compressible (k(a) = 0.0143(4) 1/GPa) than the b and c axes (k(b) = 0.0045(2), k(c) = 0.0058(2) 1/GPa). The experimental results confirm an earlier prediction of the pressureinduced instability of isotypic Ce4[Si4O4N6]O, and also show that the bulk modulus was predicted reasonably well

Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsaecker model

We consider the zero mass limit of a relativistic Thomas-Fermi-Weizsaecker model of atoms and molecules. We find bounds for the critical nuclear charges that ensure stability.Comment: 8 pages, LaTe