Singlet-Triplet Mixing in then=3States of Helium

Abstract

We have measured the energy-independent ratio of the proton apparent-excitation cross sections between corresponding triplet and singlet states of helium for the $n=3\mathrm{}$ level. In the Russell-Saunders description of the states of helium, proton excitation of triplet states is forbidden; i. e., $\Delta S=1\mathrm{}$ transitions are not allowed (Wigner spin rule). However, the spin-orbit interaction for the two electrons in helium mixes the spin states. Thus, there is a small singlet component in the triplet-state wave function. The square of the small singlet-triplet mixing parameter $\gamma \left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)$ is equal to the ratio of the proton excitation cross sections to corresponding triplet and singlet states, i. e., ${\gamma }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)=\frac{{\sigma }_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)}{{\sigma }_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}X\right)}$. The symbol $X$ refers to the orbital angular momentum states $S$, $P$, or $D$. If we designate the ratio of the proton apparent-excitation cross sections $\frac{Q_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)}{Q_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}X\right)}$ by ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)$, then ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)={\gamma }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)+(\mathrm{cascade}\mathrm{contributions}$. Our results for ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)$ for the $n=3\mathrm{}$ states of helium are as follows: ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)=0\mathrm{}\pm 0.0002$, ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)=0.0028\mathrm{}\pm 0.0007$, and ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)=0.06\mathrm{}\pm 0.014$.