Observations of the $4 \;{}^1\Sigma_u^+$ state of H$_2$

Resonantly-enhanced multiphoton ionization via the $EF\;{}^1\Sigma_g^+$, $v'=6$ double-well state has been used to probe the energy region of the high vibrational levels of the $4\;{}^1\Sigma_u^+$ state of H$_2.$ Theoretical {\it ab initio} potential energy curves\footnote{G. Staszewska and L. Wolniewicz, {\it J. Mol. Spectrosc.} {\bf 212}, 208--212 (2002)} for this state predict a deep inner-well and shallow outer well due to an avoided crossing with the $B''\bar{B} \;^1\Sigma_u^+$ curve. Transitions to the $4\;^1\Sigma_u^+$ state have not been assigned previously because absorption from the $(1s\sigma)^2$ ground state is forbidden due to the $f$ character of the inner well. However, transitions from the $EF\;^1\Sigma_g^+$ state with inner well $s$ character and combined doubly-excited and $d$ character outer well are allowed. The high vibrational levels converging on the third dissociation limit should exhibit rotational constant values dependent on the varying amounts of inner and outer-well character for a given $v$. We report experimental energies for the $v=8-12$ levels and compare favorably to the predicted adiabatic rovibrational energies$^1$. The $v=9$ level is the exception since it lies just above the avoided crossing, which makes predicting its energy difficult.