Knowledge Bank

A new method for constructing the outer branch of the potential energy curve has been developed. Classically (or with corrections for tunneling) the rotational predissociation data define a Limiting Curve of Dissociation: $$ E_{LCD}(J(J+1)) =D_{0} + \frac{n^{2}J(J+1)}{2\mu(r_{J}^{\not=})^{2}}.$$ Hence the slope $(dELCD/d(J(J+1)))$ provides a value of $rJ\ne$, the position of the maximum in the effective potential $$ U_{J} (r) = V(r) + \frac{n^{2}J(J+1)}{2\mu r^{2}} $$ However, since each $U_{J}(r_{J}^{\not=}) $ represents a maximum, $$ \left.\frac{dV(r)}{dr} \right|{r=r{j}^{\pm}} =\frac{h^{2}J(J+1)}{\mu(r_{J}^{\not=})^{3}}, $$ and one obtains the slope of the potential at the set of points $rJ\ne$. Interpolation and integration provide the outer branch of the potential. While this method is usually not as precise as the Rydberg-Klein-Rees method, it often provides the potential at larger internuclear distances and uses nearly independent information as input.