Experimental studies of thev=15hierarchy in the fractional quantum Hall effect

We present an experimental study of the $v=\frac{1}{5}$ ground state of the fractional quantum Hall effect. Weak ${\rho }_{\mathrm{xx}}$ minima at 2/9 and 2/11 are observed, consistent with the predicted "daughter" states of a 1/5 hierarchical "parent" state. The 1/5 activation energy ${\Delta }_{\frac{1}{5}}$ is shown to be significantly smaller than ${\Delta }_{\frac{2}{5}}$. Empirical fits for Coulomb constants $C\left(v\right)\mathrm{}$ confirm that $C\left(\frac{1}{3}\right)>C\left(\frac{2}{5}\right)>C\left(\frac{3}{7}\right)>C\left(\frac{1}{5}\right)$. The data are consistent with a separate hierarchy emanating from $v=\frac{1}{5}$.