Dipole-dipole broadening of \textit{ns-np} Rydberg transitions*

Using a microwave resonance technique we have measured the dipole-dipole broadening of \textit{ns-np} transitions of 300\textit{$\mu $K} Rb Rydberg atoms. The experiment has been done with $n$=28, 29, 34, 39, 44, and 50 states, all of which exhibit a linear increase in the linewidth with atomic density. The broadening rate varies as $n^{4}$, which is to be expected since \textit{$\mu $}$_{sp}\approx n^{2}$. The broadening is not Lorentzian, but results in asymmetric, cusp shaped resonances. To reproduce the observed resonances we have developed a molecular model in which pairs of atoms are driven from the \textit{nsns} to the \textit{nsnp/npns} states, which have a dipole-dipole energy splitting which scale as 1/R$^{3}$. We calculate the dipole-dipole splitting of the \textit{nsnp/npns} states, and the transition strengths from the nsns states with the spins of the two electrons included. The results, averaged over the density of Rydberg atoms, yield asymmetric cusp shaped resonances, which agree very well with the observations.