Knowledge Bank

Quantum defect techniques are applied to calculate vibrational levels and the photoionization cross section of $H2+$. Assuming a Born-Oppenheimer approximation at small electron distances, we calculate the body-frame quantum defect funciton $\mu (c,R)1$ by exactly solving the fixed-nuclei Schr""{o}dinger equation. $\mu (c,R)$ provides sufficient information to describe electron escape to long range, which is treated by standard QDT procedures. While the energy-dependence of $\mu (c,R)$ can be neglected in vibrational level calculations, it must be included to obtain the correct ionization cross $section.2$ Although electronic excitations of $H2+$ always results in its dissociation (in this sense $H2+$ cannot be viewed as a Rydberg molecule), the quantum defect calculation nevertheless gives good results. This prototype calculation shows how MQDT can be applied successfully even to a non-Rydberg molecule such as $H2+$, which is somewhat surprising.