Molecular Beam Electric Resonance Method Research Articles

Rotational Spectra of RbCl by the Molecular Beam Electric Resonance Method

Rotational Spectra of RbCl by the Molecular Beam Electric Resonance Method

Molecular Constants of Cesium Chloride by the Molecular Beam Electric Resonance Method

The electric resonance method of molecular beam spectroscopy was used to observe the CsCl spectra arising from transitions of the type J,mJ→J,mJ′, where J is the rotational quantum number and mJ the electric quantum number. The following transitions were identified and studied : 2,0→2,1;3,0→3,1;4,0→4,1;4,1→4,2; and 5,1→5,2. An analysis of the spectra for several values of the electric field intensity gave the following molecular constants for the ground vibrational state of Cs133Cl35: μ0=10.46±0.14 debye; A0=(385±9)×10−40 g cm2; B0=(72.7±1.7)×10−3 cm−1; r0=(2.88±0.03)×10−8 cm. μ0 is the electric dipole moment, A0 is the moment of inertia, B0 is the rotational constant, and r0 is the internuclear distance. If μ is assumed to be proportional to the internuclear distance, and if the potential function is assumed to be a cubic, then the vibration-rotation constant αe is calculated to be (0.53±0.08)×10−3 cm−1. From measurements of line widths it was possible to set upper limits on the quadrupole interaction constants of Cs and Cl; viz, |eqQ/h|Cs⩽4 mc/sec and |eqQ/h|Cl⩽3 mc/sec.

Energy Levels, Selection Rules, and Line Intensities for Molecular Beam Electric Resonance Experiments with Diatomic Molecules

In the molecular beam electric resonance method the energy levels in an electric field of a diatomic molecule which is in the ground electronic state, and a low vibrational and rotational state are studied. Transitions are produced between states with different space quantization of the molecule relative to the electric field and with different couplings of the angular momenta of the nuclei and of the molecular rotation. Thus the interaction of the molecule with the field and the internal molecular interactions (e.g., nuclear electrical quadrupole interactions and nuclear spin---molecular orbit interactions) are measured. In this paper we give the stationary state energy values and eigenfunctions for very weak, and strong field conditions for a diatomic molecule in which one nucleus has a spin of \textonehalf{}. Selection rules for the transitions are developed and some considerations on line intensities are discussed. Finally, there is presented the theory of double quantum transitions, which are predicted to occur at one-half the frequency given by the Bohr condition, $\ensuremath{\Delta}W=h\ensuremath{\nu}$, provided the radiofrequency field is sufficiently intense.

The Radiofrequency Spectrum ofK39F by the Electric Resonance Method

The molecular beam electric resonance method has been used to investigate the rotational Stark spectrum of ${\mathrm{K}}^{39}$F. In this method linear polar diatomic molecules in one, or at most two, rotational states and definite states of space quantization are selected by means of inhomogeneous electric fields. The molecular transitions are not of the $\ensuremath{\Delta}J$ type (transition between different rotational states). Rather, the transitions are between states with the same value of $J$ but different values of ${m}_{J}$, the electric quantum number characterizing the state of space quantization. Lines are observed as a change in intensity of the refocused beam when the frequency of an oscillating field, which is perpendicular to an homogeneous field, times Planck's constant is equal to the energy difference between different states of space quantization. The frequency of the rotational Stark line is determined by the value of the homogeneous static field. The Stark line was observed at low and high fields for $J=1$ and low fields for $J=2$. It is found to be split. The fine structure is due to an interaction of the nuclear electric quadrupole moment of the ${\mathrm{K}}^{39}$ nucleus with the rest of the charges of the molecule as well as a variation of ${\ensuremath{\mu}}^{2}A$ with the vibrational state of the molecule. Here $\ensuremath{\mu}$ is the permanent electric dipole moment, and $A$ is the moment of inertia. In addition, the quadrupole interaction constant is found to vary with the vibrational state. It is measured when the molecule is in the rotational state $J=1$ and the vibrational states $v=0,1,2,3 \mathrm{and} 4$; and $J=2$, $v=0,1\mathrm{and}2$.The frequency dependence of the Stark line at strong fields permits the determination of $\ensuremath{\mu}$ and $A$; they were determined only for the zeroth vibrational state.The results are: For $J=1$, $v=0$, $\frac{\mathrm{eqQ}}{h}=(\ensuremath{-}7.938\ifmmode\pm\else\textpm\fi{}0.040)$ Mc/sec. The absolute value of $\frac{\mathrm{eqQ}}{h}$ decreases about 1.3 percent when the vibrational quantum number increases by unity. Within experimental error the quadrupole interaction and its variation with vibrational state for $J=2$ is the same as for $J=1$. A complete tabulation of the results will be found in Table II. For the zeroth vibrational state $\ensuremath{\mu}=(7.33\ifmmode\pm\else\textpm\fi{}0.24)$ Debye, $A=(138.4\ifmmode\pm\else\textpm\fi{}6.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}$ g-${\mathrm{cm}}^{2}$. From $A$ we find for the internuclear distance for the zeroth vibrational state $r=(2.55\ifmmode\pm\else\textpm\fi{}0.06)$ angstr\oms. From the variation in intensity with vibrational state for a single transition the vibrational constant ${\ensuremath{\omega}}_{0}=(390\ifmmode\pm\else\textpm\fi{}39)$ ${\mathrm{cm}}^{\ensuremath{-}1}$.

The Radiofrequency Spectrum ofRb85F andRb87F by the Electric Resonance Method

The radiofrequency spectrum of the two molecular species ${\mathrm{Rb}}^{85}$F and ${\mathrm{Rb}}^{87}$F was studied by the molecular beam electric resonance method. The electrical quadrupole interaction constant, $\frac{e{q}_{1}{Q}_{1}}{h}$, of Rb in RbF was determined for ${\mathrm{Rb}}^{87}$F in rotational states $J=1$ and $J=2$ for the first few vibrational states, and for ${\mathrm{Rb}}^{85}$F in rotational state $J=1$ for the first few vibrational states. The interaction constants are unusually large for an alkali halide molecule; for the zeroth vibrational state of ${\mathrm{Rb}}^{85}$F, $\frac{e{q}_{1}{Q}_{1}}{h}=\ensuremath{-}70.31\ifmmode\pm\else\textpm\fi{}0.10$ Mc/sec. and for the zeroth vibrational state of ${\mathrm{Rb}}^{87}$F, $\frac{e{q}_{1}{Q}_{1}}{h}=\ensuremath{-}34.00\ifmmode\pm\else\textpm\fi{}0.06$ Mc/sec. The absolute value of the interaction constant decreases about 1.1 percent from one vibrational state to the next higher one; the values of the interaction constants for rotational states $J=1$ and $J=2$ are the same within the limit of error. The ratio of the electric quadrupole moment of ${\mathrm{Rb}}^{85}$ to that of ${\mathrm{Rb}}^{87}$ is +2.07\ifmmode\pm\else\textpm\fi{}0.01. Results are reported on the spin-orbit coupling ${c}_{2}({\mathbf{I}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{J})$, between the spin of the fluorine nucleus and the molecular rotational angular momentum. For the zeroth vibrational state of ${\mathrm{Rb}}^{85}$F, $|\frac{{c}_{2}}{h}|=11\ifmmode\pm\else\textpm\fi{}3$ kc/sec. and for the zeroth vibrational state of ${\mathrm{Rb}}^{87}$F, $|\frac{{c}_{2}}{h}|=14\ifmmode\pm\else\textpm\fi{}4$ kc/sec. No variation in $|\frac{{c}_{2}}{h}|$, with vibrational state was observed. Finally, an unpredicted line group was observed in the spectrum at one-half the frequency of one of the line groups in the ${\mathrm{Rb}}^{85}$F spectrum. Possible origins of this line group are discussed, including that of a double quantum transition. The vibrational frequency, ${\ensuremath{\omega}}_{0}$, of ${\mathrm{Rb}}^{85}$F is 340\ifmmode\pm\else\textpm\fi{}68 ${\mathrm{cm}}^{\ensuremath{-}1}$.