Single Quantum Transitions Research Articles

Ring-Puckering Vibration of 2,5-Dihydrothiophene

The infrared spectrum of 2,5-dihydrothiophene has been measured from 80 to 4000 cm−1. The far-infrared region contained sharp Q branches at 87.0, 95.5, 102.0, 107.0, 111.2, 114.8, 118.1, 120.7, 123.2, 125.2, and 127.0 cm−1 which have been assigned to single quantum transitions between the first 12 levels of the ring-puckering vibration. A mixed harmonic–quartic potential-energy function has been fitted to the observed frequencies and is described by the following relation in reduced coordinates: V(cm−1) = 16.86 (x4 + 5.93x2). Such a potential function can be rationalized only in terms of a planar ring skeleton with no barrier to inversion. Two combination and one difference band series of the ring-puckering transitions with fundamentals centered near 3064, 670, and 2865 cm−1, respectively, have also been studied. The ring-puckering transitions obtained from the 670-cm−1 band series agree favorably with the far-infrared frequencies; however, those in reference to the two carbon–hydrogen stretching fundamentals exhibit significant deviations which are corrected by an anharmonicity cross term. Ring-puckering transitions calculated for the molecule in the upper state of the three combining mid-infrared modes compare favorably with the far-infrared frequencies; therefore, a similar structure in the upper and ground vibrational states is suggested.

Spin tickling in nuclear magnetic resonance involving single and double quantum transitions

(1968). Spin tickling in nuclear magnetic resonance involving single and double quantum transitions. Molecular Physics: Vol. 15, No. 4, pp. 423-424.

Evaluation of Approximations Used in the Calculation of Excitation by Collision. I. Vibrational Excitation of Molecules

Approximate procedures for calculating transition probabilities for excitation by molecular collision have been examined in terms of a simplified model, vibrational excitation of a harmonic vibrator by collinear collision with an atom. Digital-computer solutions were obtained for the coupled differential equations resulting from time-dependent perturbation theory with an expansion of the total wavefunction in terms of eigenfunctions of the target molecule. Calculations with the expansion truncated at 2, 3, ..., 10 states show that, as the collision velocity is increased, more states must be included to obtain an ``exact'' solution. For single quantum transitions j→j+1 at low velocities, the first-order perturbation approximation results are reliable up to probabilities of about 0.1; at higher velocities, they greatly exceed the ``exact'' results. The two-state approximation always yields drastic underestimates. For multiple quantum transitions at all velocities, the first-order perturbation calculation greatly underestimates the transition probability because it includes only the direct transition j→k and excludes the stepwise transitions during a single collision j→j+1→...→k−1→k. To evaluate this dominant process, a multiple-step perturbation theory was developed. The resulting equation for a harmonic oscillator, P0→n = (P0→1)n/n!, gives excellent predictions in the low velocity range. For higher collision velocities, a computer calculation employing many eigenfunctions is required. The relationship of these results to calculation of other inelastic collision processes is discussed briefly.

Shock-Tube Study of Vibrational Relaxation in Carbon Monoxide for the Fundamental and First Overtone

The rate of vibrational excitation in rapidly heated CO has been determined for the temperature range 1100°—2500°K by observation of infrared emission behind incident shocks. Great care was taken to eliminate impurity effects. The data agree to within 15% with those of Matthews. Separate observations of fundamental and overtone emission demonstrated that excitation occurs in a stepwise fashion. Collisional population of the v=2 level by successive single quantum transition is at least ten times faster than the direct 0→2 excitation process. Vibrational relaxation times of CO were determined for the pure gas and for the mixtures; 5% CO—95% Ar, 5% CO—95% N2, and 99% CO—1% H2. At 2000°K, τ(CO–CO) = 60 μsec, τ(CO–Ar) = 350 μsec, τ(CO–N2) = 640 μsec, τ(CO–H2) = 0.7 μsec, all for one atmosphere total pressure with the CO infinitely dilute in the second-named gas. The differences found between CO–CO collisions and CO–N2 collisions with respect to vibrational excitation are not explained by current theories.

Scattering of Slow Neutrons from Propane Gas

Measurements of the partial differential neutron scattering cross sections for room-temperature propane gas are reported. These measurements were made at incident energies of 0.0101, 0.0254, 0.0736, and 0.102 ev at seven scattering angles between 16.3\ifmmode^\circ\else\textdegree\fi{} and 84.7\ifmmode^\circ\else\textdegree\fi{} using the Materials Testing Reactor phased chopper velocity selector. The data are converted to the scattering-law presentation and compared with three theoretical calculations: (a) The ideal gas, using an effective mass obtained from an average of the mass tensors for the three types of H atoms in propane, gives poor agreement. (b) The Krieger-Nelkin approximation, which includes the effect of zero-point vibrations, gives limited agreement for energy transfer less than $0.5{k}_{B}T$ at intermediate momentum transfers. At large momentum transfers where vibrational effects become important it underestimates the cross section. (c) A modification of the Krieger-Nelkin theory that includes the effects of single-quantum transitions from the three lowest vibrational states gives better agreement. The discrepancies still present at large momentum and energy transfers are attributed to an uncertainty in the methyl-group barrier height for the three lowest energy modes, to the harmonic oscillator approximation for these modes, and to the approximate molecular orientation averaging used in the calculation.

Zweiquanten-�berg�nge in isomeren Kernen

Two quantum emission in nuclei proceeds with such a small probability that it can hardly be detected unless all competing processes are strongly suppressed. Most favourable would be an excited level that can decay only by a 0+-0− transition but, unfortunately, such a case is not yet known. Another possibility for detecting two quantum transitions might be provided by nuclear isomerism. An isomeric single quantum transition of a high multipolarity may be replaced by the emission of two quanta of lower multipolarities. The calculated angular correlation is generally not symmetric about 90°. The total transition probability and the distribution of energy between the two quanta have been evaluated using the single particle model. The experimental possibility of observing two quantum processes is discussed.

Further Observations of Multiple-Quantum Transitions. Saturation Effects in Radio-Frequency Transitions

Multiple-quantum as well as the single-quantum transitions, $\ensuremath{\Delta}F=0$, $\ensuremath{\Delta}m=\ifmmode\pm\else\textpm\fi{}1, 2, 3, 4$, have been observed in ${\mathrm{K}}^{39}$. In the neighborhood of the rf amplitude, required to give a maximum transition probability, the lines have the behavior predicted for transitions induced by a rectangular rf pulse. For higher rf amplitudes, the line width becomes constant or else decreases after having reached a maximum width, the line frequency is modified less rapidly than predicted and anomalous transition probabilities occur. All these effects are markedly dependent on the details of construction of the rf circuit in which transitions are induced. It is suggested that these effects may arise from the end regions of the circuit through an adiabatic traverse of the circuit by the atom.