QUANTUM DEFECT CALCULATIONS OF $H_{2}^{+}$

Abstract

Quantum defect techniques are applied to calculate vibrational levels and the photoionization cross section of $H_{2}^{+}$. 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 $H_{2}^{+}$ always results in its dissociation (in this sense $H_{2}^{+}$ 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 $H_{2}^{+}$, which is somewhat surprising.