Theory of Isotope Effects on He + Trapping in Solid Hydrogen

Abstract

We are currently investigating the influence of vibrational effects on the strength of trapping of He+ in solid hydrogen. Such effects can lead to an isotope dependence of the trapping energy associated with the hydrogen molecules and He+ ion. At the present time, our focus is on the isotope effect for 3He+ and 4He+, which we are studying through the vibrational motions of the trapped He+ ions in the potential they experience as they move about their equilibrium positions. The potential governing the vibrations has been obtained from Hartree–Fock cluster calculations of the total energy of the cluster composed of the He+ ion and up to the third nearest neighbor hydrogen molecules as a function of the displacement of the He+ ion from its trapped position. The energy eigenvalues for the ground vibrational states of 3He+ and 4He+ in this potential come out as 1.29 and 0.96 meV, respectively, leading to corresponding reductions by these amounts in the binding energy of 8.6 eV for both ions without vibrational effects. The difference of these reductions can be considered as an isotope shift, its value for this case being 0.33 meV. From the analysis for these results, it is suggested that isotope shift effects for deuteron and triton in solid D–T would have the same order of magnitude. A procedure for more accurate investigations of the isotope shifts is discussed.