The 4-particle hydrogen-antihydrogen system revisited: twofold Hamiltonian symmetry and natural atom antihydrogen

Modern ab initio treatments of H-Hbar systems are inconsistent with the logic behind algebraic Hamiltonians H(+-)=H(0)+/-deltaH for charge-symmetrical and charge-asymmetrical 4 unit charge systems like H(2) and HHbar. Since these 2 Hamiltonians are mutually exclusive, only the attractive one can apply for stable natural molecular H(2). A wrong choice leads to problems with antiatom Hbar. In line with earlier results on band and line spectra, we now prove that HL chose the wrong Hamiltonian for H(2). Their theory explains the stability of attractive system H(2) with a repulsive Hamiltonian instead of with the attractive one, representative for charge-asymmetrical system HHbar. A new second order symmetry effect is detected. Repulsive HL Hamiltonian H(+) applies at long range but at the critical distance, attractive charge-inverted Hamiltonian H(-)takes over and leads to bond H(2) but in reality, HHbar, for which we give an analytical proof. Another wrong asymptote choice in the past also applies for atomic antihydrogen Hbar, which has hidden the Mexican hat potential for natural hydrogen. This generic solution removes most problems, physicists and chemists experience with atomic Hbar and molecular HHbar, including the problem with antimatter in the Universe.