Molecular Excitation in Beta Decay

Abstract

The theory of molecular excitation in beta decay is developed for the general case of a polyatomic molecule. Calculations of the daughter molecule vibrational excitation are carried through for diatomic molecules, and the results are presented graphically. Finally, the formation of the ${({\mathrm{He}}^{3}{\mathrm{H}}^{3})}^{+}$ molecule ion in the decay of one nucleus of a tritium molecule is studied in detail. It is concluded that the ${({\mathrm{He}}^{3}{\mathrm{H}}^{3})}^{+}$ ground electronic state vibrational spectrum should be observable in the light spontaneously emitted by tritium. For example, neglecting nonradiative transitions, one expects approximately ${10}^{14}$ photons per second to be radiated at wave number \ensuremath{\cong}2.35\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ by every gram of tritium in the 1\ensuremath{\rightarrow}0 vibrational transition.