Isotope effects for molecules in a cavity

Abstract

A model problem of the motion of a particle in an impenetrable cavity is considered in order to establish how the energy levels and transition energies between them depend on the linear size, R, of the cavity and on the particle mass. In the case of one particle problem with a uniform potential inside the cavity there exists a simple qualitative solution that describes the effect of the cavity size and shows that a decrease in R can cause the isotopic frequency shift to increase as compared to the free system. The estimates obtained were used to interpret the results of numerical calculations of low lying energy states of hydrogen molecule and its isotopomers confined within impenetrable spherical cavity. The effect of the cavity radius on the structure of the low lying part of the energy spectra of H2, D2, and HD molecules and on the reliability of adiabatic separation of nuclear variables are considered. The approach provides a qualitatively correct description of the changes in the energy level positions but the behavior of the isotopic frequency ratio is too smooth compared with results of more accurate calculations.