Alignment of theH2+Molecular Ion by Selective Photodissociation. I

On the basis of experimental results obtained by Linlor et al., Fischer, and in this laboratory, demonstrating photodissociation time constants as short as 0.1 sec and trapping times as long as several seconds as practical for the ${\mathrm{H}}_2^{+}$ molecular ion, the feasibility is discussed theoretically of a novel technique to align trapped molecular ions and also monitor the alignment by selective photodissociation. First the limiting case of no electronic and nuclear spins and very large rotational quantum numbers is treated, based on the concept that the photodissociation rate $R$ is proportional to the average squared component of the electric light vector perpendicular to the axis of molecular rotation. This angular dependence of $R$ when a bunch of ions created by a short electron bombardment pulse is subsequently irradiated causes the ions in certain magnetic sublevels to decay much more slowly than others. Consequently when conditions for the preservation of alignment are favorable, the sample becomes increasingly aligned. Furthermore, since a partially aligned sample photodissociates more slowly than an unaligned one, more molecular ions $\overline{N}$ will remain when alignment is allowed to develop than when it is continuously destroyed, resulting in only $N$ ions. Next the nuclear and electronic spins are taken into account and numerical values for the dissociation rates of the 30 magnetic sublevels for the first three rotational states of the ${\mathrm{H}}_2^{+}$ ion are evaluated for linear light polarization. One sees that on the basis of a sample of ${10}^9$ ${\mathrm{H}}_2^{+}$ ions decaying due to photodissociation to 2×${10}^7$ ions, one might expect an optimum signal $\frac{(\overline{N}-N)}{N}\approx 0.25$ compared to a statistical uncertainty of about 0.0003 for two consecutive pulses. The possibilities inherent in the scheme to observe the rf spectrum of ${\mathrm{H}}_2^{+}$ are pointed out.