Alignment of the $H_{2}^{+}$ Molecular Ion by Selective Photodissociation. II. Experiments on the Radio-Frequency Spectrum

Magnetic resonance transitions have been observed among several Zeeman sublevels of the hyperfine states of

H_{2}^{+}

in magnetic fields from 50 to 115 mG. The following

g

-factor ratios

\frac{g (K F_{2} F)}{g (K^{'} F_{2}^{'} F^{'})}

have been determined:

\frac{g (1 \frac{1}{2} \frac{3}{2})}{g (1 \frac{3}{2} \frac{5}{2})} = 0.584 (3)

;

\frac{g (1 \frac{3}{2} \frac{3}{2})}{g (1 \frac{3}{2} \frac{5}{2})} = 1.241 (6)

;

\frac{g (1 \frac{1}{2} \frac{3}{2})}{g (3 \frac{3}{2} \frac{9}{2})} = 1.051 (5)

. An analysis using the ratios yields equations relating the hyperfine interaction constants

b

c

, and

d

in the Hamiltonian

H = b I \cdot S + c I_{z} S_{z} + d K \cdot S

, such as

\frac{(\frac{\sqrt{2} c}{6} - \frac{\sqrt{2} d}{3})}{(\frac{3 b}{2} + \frac{23 c}{30 - \frac{d}{6}})} = (\frac{8}{\sqrt{5}}) {[\frac{g (1 \frac{1}{2} \frac{3}{2})}{g (3 \frac{3}{2} \frac{9}{2})}] - 1}

. When nuclear contributions to the

g

factors are included and a weighted average of the measured ratios is used with theoretical values of

b

and

c

from the literature, a value for

d

may be obtained. The result is

d = 32.2 \pm 5.1

MHz. With this it is possible to predict the

H_{2}^{+}

hfs spectrum in the 20-cm region with an error estimate of a few MHz.

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Alignment of theH2+Molecular Ion by Selective Photodissociation. II. Experiments on the Radio-Frequency Spectrum