Precision measurements of forbidden transition frequencies using stimulated Raman scattering

The possibility of precision measurements of frequencies of forbidden transitions of cold atoms in a trap using stimulated Raman scattering is shown. Transition $1S$ – $2S$ in a hydrogen atom, in which the atom passes from level $1S$ to level $2S$ via intermediate level $3P$ is considered in detail. In this case, the frequency of the pump field ($103$ nm) is close to the frequency of the $3P$–$1S$ transition, while the stimulated scattering frequency ($656$ nm) is close to the frequency of the $3P$ – $2S$ transition.