Far-Infrared Laser Stark Spectroscopy of CH3OD

The high resolution Stark spectra of the singly deuterated methanol isotope, CH₃OD, have been studied using the HCN laser with Stark fields up to approximately 60 000 V/cm. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations, resulting in the following assignments: with the 311 m line – J _K = 18₁ 18₀ E ₂, _t = 1; and with the 337 m line – J _k = 6₄ 5₃ E ₂, _t = 0 and J _K = 14₆ 13₅ A, _t = 1. Zero-field frequencies for the assigned transitions are in agreement with Fourier transform measurements and those calculated from the available molecular constants.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

Laser Stark saturation spectroscopy in methyl alcohol

The method of Lamb dip spectroscopy in Stark tuned molecular gases is discussed and applied to the experimental assignment of methyl alcohol infrared transitions in the ₅ C–O stretch band. Theoretical expressions for Stark Lamb dip patterns are derived for P, Q and R-branch transitions. Stark tuning results and transition quantum number assignments are presented for several 10m transitions, along with measured values of resonant frequencies, absorption coefficients and pressure broadening coefficients.Work supported by the Army Research Office, Durham, and the National Science Foundation.     

Far-infrared laser stark spectroscopy of CH3OH and13CH3OH

The high resolution laser Stark spectra of methanol and¹³C-substituted methanol have been studied up to Stark fields of about 60 000V/cm with the HCN and DCN lasers. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations. For methanol, the transitions J _k =7₅ 6₄ A, _t=0; J _k =11₄ 10₃ E _l , _t=0; and J _k =17₃ 16₂ E₂, _t=0 have been identified while the assignments for¹³C-substituted methanol are J _k =14₈ 15₇ A, _t=0; J _k =15₃ 14₂ A⁺, _t=0; J _k =10₇ 9₆ A, _t=0; and J _k =27₉ 27₈ E₁, _t=0. Zero-field frequencies for the assigned transitions are given with improved accuracy over those calculated from available molecular constants, especially for¹³CH₃OH.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Parity operator and quantization of δ-functions

In the Weyl quantization scheme, the -function at the origin of phase space corresponds to the parity operator. The quantization of a functionf() on phase space is the operator f(/2)W()dM, whereM is the parity andW() the Weyl operator.     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.