Quantum Mechanical Tunneling Effect Research Articles

A classical/semiclassical theory for the interaction of infrared radiation with molecular systems

A classical model for the interaction of molecular systems with infrared radiation is presented. It differs from the usual ’’semiclassical theory of radiation and matter’’ in that the molecular system is treated by classical rather than quantum mechanics, and the radiation field is described, as in Jaynes’ neoclassical theory, as classical (mechanical) harmonic oscillators rather than as a classical field (i.e., via Maxwell’s equations). The classical Hamiltonian for the composite system—molecules, radiation, and their interaction—is thus that of a completely mechanical system, and its classical dynamics is determined by computing the classical trajectories of the system. Quantum mechanical interference and tunneling effects can be built into the description within the framework of the classical S-matrix theory. Even within the strictly classical limit of the model, it is shown that all dynamical effects in the interaction of radiation and matter are obtained; in the perturbative limit, for example, it is shown that absorption and induced emission, and even spontaneous emission, which is often difficult to obtain in other classical or semiclassical models, appear in a completely straightforward manner.

The temperature dependence of quantum mechanical tunneling effects in the nmr spectrum of a methyl group

NMR line shapes have been obtained for CH 3CD 2I in CD 3CD 2I from 4.2 to 127°K. At 4.2°K tunneling is evident, at 87°K neither tunneling nor classical rotation can be detected, and at 127°K there is rapid, thermally activated rotation. The apparent tunneling frequency is found to decrease with increasing temperature.

Observation of Quantum Mechanical Tunneling Effects in the NMR Line Shape for a Methyl Group

Observation of Quantum Mechanical Tunneling Effects in the NMR Line Shape for a Methyl Group

Nonrigid Molecule Effects on the Rovibronic Energy Levels and Spectra of Phosphorous Pentafluoride

Although phosphorous pentafluoride is known from electron diffraction, infrared, and Raman data to have a D3h trigonal bipyramid equilibrium configuration, NMR data shows only one fluorine resonance. Although this is almost certainly due to a fast intramolecular rearrangement process occurring via a Berry pseudo rotation, the detailed mechanism (e.g., classical thermal rearrangement or quantum mechanical tunneling in low vibrational levels) is unknown. A theoretical study has been made of the effects of quantum mechanical tunneling on the rovibronic levels, i.e., treating phosphorous pentafluoride as a nonrigid molecule. The levels are shown to be split in a very characteristic manner. Simple results for the relative intensities of the resultant fine structure to the original rovibronic transitions have also been obtained. This predicted, characteristic fine structure could be searched for experimentally in order to further our understanding of the intramolecular rearrangement process occurring in phosphorous pentafluoride. A theoretical study on a suitable millimeter wave spectroscopic experiment shows that such an experiment is at present on the border line of accessibility. A new general method of treating nonrigid molecule energy levels is illustrated by this application to the specific case of phosphorous pentafluoride.

Dissociation Mechanism of Hydrogen Metastable Ions

The dissociation of the hydrogen metastable ions was studied using a pulsed ion source mass spectrometer. The pressure dependence of the hydrogen metastable ions from H2, HD and D2 indicates that they are all produced by the collision process in the ion source between the respective parent ion and neutral species. The appearance potential of each hydrogen metastable ion has an intermediate value between the ionization potential of the parent molecule and the appearance potential of the fragment ion, and this hydrogen metastable ion may be in a vibronic excited electronic ground state of the parent ion. The kinetic energy(K. E.)released during dissociation from each hydrogen metastable ion has an approximate relation, K. E. ≈ A. P.(m*)-I. P.(m0)+E0, where A. P.(m*)is the appearance potential of the hydrogen metastable ion, I. P.(m 0)is the ionization potential of the hydrogen molecule and E0 is the zero-point energy of the respective parent ion of the electronic ground state. The observed dissociation rate constants of the hydrogen metastable ions well agree with those of the approximate theoretical calculation provided that the dissociation is caused by the quantum mechanical tunnel effect.

Theoretical Treatment of Unimolecular Dissociation Reaction of Diatomic Metastable Ions

The theoretical treatment of the unimolecular dissociation reactions of diatomic molecules and diatomic metastable ions has been given in this paper. It is assumed in this theory that the spontaneous dissociation of diatomic molecules or diatomic metastable ions is caused by the process in which an atom or an atomic ion penetrates through the potential barrier formed by the bound potential and the repulsive potential. The rate constant of the spontaneous dissociation reactions due to the quantum mechanical tunnel effect has been calculated in accordance with the WKB method. It has been shown that the plural rate constants for the same unimolecular dissociation can be contributed from discrete virtual energy levels of diatomic molecules or diatomic metastable ions. The application of this theory will give a good explanation for the experimental results of the appearance potentials for diatomic metastable ions.

Mechanism of Proton Transfer in Acid—Base Reactions

It is proposed that proton transfer in acid—base reactions goes by a quantum-mechanical tunnel effect. The predominance of the tunnel effect in these reactions is attributed to the recognition that the proton transfer can proceed alonga hydrogen bond between the two reactants and the distance which the proton has to travel is only 0.4 to 0.6 Å. On this basis some calculations have been carried out with a one-dimensional Eckart potential barrier, the (apparent) activation energy of the proton transfer being identified with the endothermicity (Q) of the proton-transfer reaction: AH+B→A+HB−Q. For the primary isotope effect for proton and deuteron transfer, it can be shown that increase of the (apparent) activation energy for the deuteron transfer (due to the difference in the zero-point energies) necessarily also affects the magnitude of the transmission coefficient and that this effect can compensate, to a greater or lesser extent, for the increased mass of the deuteron. The Bro/nsted relation in acid—base catalysis can also be derived, as a first approximation, from such a model and without any further a prioriassumptions between activation energies and free energies.

Circuit Model of the Quantum-Mechanical Tunnel Effect

Circuit Model of the Quantum-Mechanical Tunnel Effect

On the creep of metals at very low temperatures

Abstract In 1956 Glen described a rapidly decaying type of creep occurring in cadmium crystals at 1–5°k. His analysis of the process, based on Mott's (1953) theory of low-temperature logarithmic creep, indicates that the energy barrier to the flow is of the order of 0·1 ev. Mott (1956) advanced the hypothesis that the barrier may be surmountable at such low temperatures because of the quantum mechanical tunnel effect; Täubert (1959) believes however that the temperatures are still too high for quantum effects to assume significance in creep. The object of the present note is to show that a plausible explanation of the observations is possible also on the basis of classical dislocation theory.

Study of Superconductors by Electron Tunneling

If a small potential difference is applied between two metals separated by a thin insulating film, a current will flow due to the quantum mechanical tunnel effect. For both metals in the normal state the current-voltage characteristic is linear, for one of the metals in the superconducting state the current voltage characteristic becomes nonlinear, and for both metals in the superconductive state even a negative-resistance region is obtained. From these changes in the current voltage characteristics, the change in the electron density of states when a metal goes from its normal to its superconductive state can be inferred. By using this technique we have found the energy gap in metal films 1000-3000 A thick at 1\ifmmode^\circ\else\textdegree\fi{}K to be $2{\ensuremath{\epsilon}}_{\mathrm{Pb}}=(2.68\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ev, $2{\ensuremath{\epsilon}}_{\mathrm{Sn}}=(1.11\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ev, $2{\ensuremath{\epsilon}}_{\mathrm{In}}=(1.05\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ev, and $2{\ensuremath{\epsilon}}_{\mathrm{Al}}=(0.32\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ev.The variation of the gap width with temperature is found to agree closely with the Bardeen-Cooper-Schrieffer theory. Furthermore, the energy gap in these films has been found to depend upon the applied magnetic field, decreasing with increasing field.

LVII. Creep in metal crystals at very low temperatures

Abstract A theory is given of creep in metallic single crystals at very low temperatures, which is based on the hypothesis that dislocations can pass through barriers, such as those provided by dislocations crossing the slip plane, owing to the quantum-mechanical tunnel effect. A detailed theory would depend on a knowledge of the atomic arrangements at the centre of a dislocation, which in this case does not exist, but a rough calculation shows that creep should be independent of temperature below about 10°K in cadmium.

XXXIX. The creep of cadmium crystals at liquid helium temperatures

Abstract Experiments on single crystals of cadmium at temperatures between 1·2° and 4·2° k have shown that measurable transient creep occurs, and that the amount of such creep does not fall off rapidly with decreasing temperature. It is suggested that this creep is due to the quantum mechanical tunnel effect, which allows dislocations to penetrate barriers to their motion that cannot be overcome by the action of the applied stress alone.

Proton Magnetic Resonance of the CH3 Group. III. Reorientation Mechanism in Solids

The proton magnetic resonance absorption has been reported to change with temperature in a manner suggesting hindred C3 rotational motions of the CH3 groups in several solid compounds. In this paper, the reorientation mechanism is considered more closely. The second moments of the absorption lines are calculated as a function of temperature for three types of motion. Similar predictions are obtained for two classical models, a Brownian type rotation by random angles and a random jumping between fixed positions 2π/3 apart. The results are different for the third model, a quantum-mechanical tunnel effect, for which approximate calculations are given. The experimental data for methyl chloroform, 2,2-dinitropropane, and 2-chloro-2-nitropropane can be fitted either to a classical model or to the tunnel effect by adjusting the potential barrier to the reorientations. However, the activation energies for classical rotation are low, about 2.2 kcal mole—1 and the observed frequency factors of 107 are unexplained. The tunnel effect gives larger barriers, about 5 kcal, and the predicted frequency factors agree well with experiment. In the case of 2,2-dichloropropane a classical motion is indicated by the large frequency factor of 1012.

Carbon-brush contact phenomena in electrical machinery

Attention is drawn to the fact that the change in the contact resistance when sliding occurs has not so far been satisfactorily explained, nor has any mathematical analysis based on physical principles, giving the contact drop in terms of the current density, yet been applied successfully to sliding contacts.The transfer of current across the contact without arcing must be due to either thermionic or field emission, or to a combination of these phenomena, and it can be shown that the mechanism of thermionic emission can play only a very minor role in practical brush contacts.The principles of wave mechanics applied to the problem of field emission give for the true current density:Since this can be written in the formi′ = A0E2e−k/E amp/cm2it appears reasonable to suppose that the generalized contact equation with a true emission area Ae iswhere A0 and k are constants for given materials and x is the effective contact spacing. It is shown that the properties of the contact, such as effects due to pressure, temperature, materials and surface condition alter the values of Ae and x, thus determining the value of the contact drop with a given current density.Conclusions drawn from the experimental results show that the generalized contact equation is not inconsistent with the postulated theoretical process, and some information has been gained about the emitting area and the effective contact spacing of practical brush contacts comprising a carbon brush sliding on a copper or cast-iron slip-ring.The transfer of relatively small currents across the contact is believed to be due to the quantum mechanical tunnel effect and is not discussed in the present paper.