Knowledge Bank

$Bernstein1$ pointed out in 1966 that the centrifugal barriers of the effective potentials governing rotational predissociation were simply obtainable if the ordinary potential could be expressed as $$ V = D_{0} - C/r^{n}. \eqno{(1)}$$. He (and $others2$) then used these formulas with predissociation data to obtain the constants $D0$ and C for several diatomic molecules, with known long-range values of n. Unfortunately, it now appears that the centrifugal barriers considered in these cases were not at sufficiently large distances for (1) to hold. A search of the rotational predissociation literature produced a $case3$ clearly in the long-range region: v = 2 of B $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Pi$ LiH. Since we have long-range predissociation in only a single vibrational level, we have chosen to calculate the long-range forces accurately and then use the predissociation data to obtain a precise dissociation limit (with respect to v = 0, J = 0 in the ground state). The effect of higher inverse power terms and tunnelling has also been considered. Our value for the dissociation limit (34 $492.8\pm 0.5cm-1$) may be compared with the value given by $Velasco3$ (34 $495\pm 2cm-1)$. If the width of either J = 2 or 3 of v = 2 were known even roughly, the dissociation limit uncertainty could be reduced to $ \mathop {<}\kern -8pt {\vphantom {1 \over 2}}^{\sim} 0.2 cm^{-1}$.