Unexcited Atoms Research Articles

Quantum statistics of field after double-beam two-photon absorption

Two-photon absorption for a collection of unexcited two-level atoms from two beams of light is considered and the statistical properties of the beams after the interaction are investigated. The dynamical behaviour of the beams is described by assuming the atoms maintained with a nearly fixed population distribution. By applying iteration methods the time development for the paired generating functional of the field is obtained and by means of this generating functional paired modal densities are written. The modal densities are then used for discussing the statistical properties of light after the interaction.

Laser photolysis of perfluoroalkyl iodides

A new method is presented for the simultaneous determination of the quantum yields of excited and unexcited iodine atoms produced by photodissociation of alkyl and fluoroalkyl iodide molecules, and for the determination of the rate constants of the subsequent recombination processes. The method involves taking simultaneous oscillograph traces of the 1313 and 580 nm luminescence signals of the material being studied, produced during molecular photodissociation by neodymium laser harmonics. These constants were determined for CF3I, 1–C3F7I, and (CF3)3CI molecules using the radiation of the fourth harmonic (266 nm) with a pulse energy of 0.4–0.8 J. The results significantly altered the estimate, based on previous investigations, of the possible population inversion in the active medium of a Q-switched iodine laser.

Resonance light pressure

The forces acting on a resonance particle in the fields of laser radiation sources can be large. Acceleration, heating, and cooling of atoms by using these forces are discussed. Since the forces are of a resonance type, one can employ them to separate isotopes and excited atoms from unexcited atoms. Light pressure can play an important role in the spectroscopy of narrow atomic and molecular resonances. The quantum features of the motion of particles in a standing light wave are manifested in a fine structure of the absorption coefficient. This review is concerned with analyzing the resonance light-pressure forces and discussing the application of them in optics and quantum electronics.

Molecule formation and energy transfer processes in a vapor with high density of 3P-excited sodium atoms

A rich fluorescence spectrum extending between 4000 and 8200 Å has been observed whenever sodium vapor is excited by dye laser light tuned to the 3 2S → 3 2P transition. Molecule formation due to collisions between excited and unexcited atoms is manifested by the presence of an emission band of sodium in the spectral range 4160–4570 Å.

Superradiance and energy transfer within a system of atoms

We investigate cooperative effects in energy relaxation and energy transfer for N atoms in a thermal radiation field with superradiance master equations as well as a closed set of coupled moment equations. Both spatially large and spatially small systems are considered. For small systems nonlinear rate equations for the energy are related to the moment equations. Symmetry of the small system to interchanging atoms is used to incorporate off-diagonal solutions of the superradiance master equation in expressions for the probability of the transfer of energy from one group of atoms to another. The long time excitation probability for initially unexcited atoms is large and strongly correlated. Cooperative processes in a large system which fall off with the distance between a cooperating pair of atoms include energy loss and transfer terms in the master equation. The energy transfer is oscillatory in time. Energy relaxation is shown by numerical solution to become cooperative in a very sudden manner as the scale of the atomic system is decreased through the resonant wavelength.

Quantum electrodynamics in the presence of dielectrics and conductors. VI. Theory of Lippmann fringes

A quantum-theoretic treatment of Lippmann fringes is given using the response-function formalism of part I of this series of papers. It is shown that the field emitted by the excited atom in the presence of a dielectric mirror possesses first-order coherence, and the absorption of such a field by the unexcited atom leads to the interference fringes. The nature of the emitted field is also examined from the point of view of excitation of surface modes. The causal character of the absorption process is also briefly commented upon.

On the exchange and overlap corrections in electron capture

Abstract The approximations made in the calculations of the exchange and overlap correction coefficients were investigated. It is shown that the one-electron wave functions of the final state cannot be replaced by those of the unexcited daughter atom, and that the overlap of all inner s, p and d electrons is to be taken into consideration. The new approximation gives a better agreement with the experimental K/β + , L/K and M/L capture ratios than the old approximation.

Theory of excitation transfer in collisions between alkali atoms. II. Dissimilar partners

Possible mechanisms are considered for the transfer of electronic excitation energy in collisions between an excited alkali atom MA*(2Pj) and an unexcited atom MB(2S1/2). It is shown that a dipole–dipole interaction which is responsible for the transfer of electronic excitation energy in collisions between identical partners (MA = MB) is not sufficient to explain the observed magnitudes of the cross sections and that, therefore, the exchange interaction can no longer be neglected. If the exchange interaction is taken into account, it can be shown that there are regions of nonadiabaticity in the energy diagram, which are probably responsible for the change in the electronic energy states of the collision partners. The calculated cross sections are compared with experimental values.

A calculation of repulsive force constants of the Lennard-Jones potential for some excited states of noble gases

Collision diameters and repulsive force constants of the Lennard-Jones potential are calculated for interactions between noble gas atoms, one of which is in an excited state. The excited-state atoms considered are neon (3s2, 2p4, 1s2) and argon (2p2, 1s2) (Paschen notation); the ground-state atoms are helium, neon and argon. It is shown that repulsive interactions between two atoms, one of which is in an excited state, are operative at much larger internuclear separations than those known for interactions between two unexcited atoms; the corresponding collision cross section for ground-state noble gas atom collisions is not at all representative when one of the interacting atoms is in an excited state.

Sensitized fluorescence in vapors of alkali metals. XII. 42P1/2–42P3/2 mixing in potassium, induced in collisions with ground-state rubidium atoms

The total cross sections for collisions between excited potassium and unexcited rubidium atoms, leading to the transfer of excitation between the 42P states in potassium, have been determined in a sensitized fluorescence experiment. The experiments were carried out at partial pressures of potassium vapor lower than 10−5 mm Hg, at which the imprisonment of resonance radiation may be disregarded. The cross sections Q12″ (42P1/2 → 42P3/2) and Q21″ (42P1/2 ← 42P3/2) equal 260 Å2 and 175 Å2, respectively, and are in the ratio predicted by the principle of detailed balancing.

Sensitized fluorescence in vapors of alkali metals. X. Energy transfer in sodium–sodium collisions

The total cross sections for 3 2P1/2–3 2P3/2 mixing collisions between excited and unexcited sodium atoms have been determined in a series of sensitized fluorescence experiments with pure sodium vapor at pressures in the range 0–1.6 × 10−5 mm Hg. The cross section Q2(3 2P1/2 ← 3 2P3/2) was found to be 283 Å2 ± 10%. The cross section Q1(3 2P1/2 → 3 2P3/2) = 532 Å2 was obtained from Q2 through the application of the principle of detailed balancing.

Resonance Broadening of Absorption Lines

A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.

Chemiluminescence and Radical Reactions in Diffusion Flames of Alkali Metals with Organic Halides

Chemiluminescent reactions in diffusion flames of alkali metals with haloforms and carbon tetrahalides appear to provide examples of reactions in which essentially all of the exothermicity appears as vibration in a newly formed bond. A self-consistent account of the intensity distributions in the flame spectra requires that, in CX4—K flames, both excited and unexcited carbon atoms participate in the reactions, C+CX→C2*+X, and that the X atoms be produced both in the ground and first excited states. Excited C atoms appear not to be produced in CHX3—K flames in appreciable concentrations. The excited C2 intensity distributions in emission are compatible with the bond dissociation energies, C–Cl=77 kcal, C–Br=66 kcal, and C–I=50 kcal, with uncertainties of about 4 kcal in each.

SENSITIZED FLUORESCENCE IN VAPORS OF ALKALI METALS: I. ENERGY TRANSFER IN POTASSIUM–POTASSIUM COLLISIONS

Sensitized fluorescence in potassium vapor at pressures between 10−5 mm Hg and 10−1 mm Hg was investigated to determine the cross sections for collisions of the second kind between unexcited and excited potassium atoms. An idealized fluorescence tube was used in the experiment and the fluorescent light was analyzed with a photoelectric recording spectrometer. The collision cross sections at low vapor pressures, where imprisonment of radiation is absent, are identical for both the 42P1/2 → 42P3/2 and 42P1/2 ← 42P3/2 transitions and equal 6.6 × 10−12 cm2 at 2 × 10−4 mm Hg. The experimental results are interpreted on the basis of new selection rules for sensitized fluorescence.

Theory of the positive column in mercury rare-gas discharges

A detailed theory of the uniform positive column is developed for d.c. fluorescent lamp type discharges in mercury and rare-gas mixtures at 0.5 to 5 mmHg pressure, taking into account multi-stage excitation and ionization processes, using available cross section curves, the Ramsauer collision cross sections and imprisonment of the resonance radiation. The distributions of the ions, unexcited and excited atoms and temperature throughout the discharge are calculated and used to evaluate the complete characteristics, using digital computer methods. A substantial degree of agreement with experiment is obtained without the use of adjustable `fitting parameters'. A simplified form assumes constant gas temperature and unexcited mercury atom density, together with simpler boundary conditions, and this is shown to be adequate for most purposes. The general form can be used to investigate temperature distributions, radial cataphoresis (`ionic pumping'), and reflection of ultra-violet light at the walls, etc.

Ionization Transients in Cesium

First Page

Low-Energy 5Σ+g States of the Nitrogen Molecule

The wave functions of the two 5Σ+g states of N2 derivable from configurationally unexcited (s2p3) atoms, one from 4S+4S atomic states, the second from 4S+2D states, are examined. With the help of empirical data on the normal state of F2, to which the valence-bond structure of the lower of the two 5Σ+g states is closely related, estimated potential curves for the two states are constructed. It is shown that for the lower 5Σ+g state, the theoretically expected curve agrees rather well with that deduced from empirical evidence {see Carroll's accompanying paper [J. Chem. Phys. 37, 805 (1962) ]}. The wave function of the 5Σ—g state from 4S+2P atoms is also given.

Theory of Long-Range Interatomic Forces. I. Dispersion Energies between Unexcited Atoms

A general theory of second-order dispersion forces between atoms in nondegenerate ground states is first developed by using an irreducible tensor formalism and the theory of angular momentum. This forms the basis for calculations of forces between excited systems, which are the subject of later publications. Attention is given to the interaction of two noble gas atoms where it is assumed that each electron oscillates with simple harmonic motion, and the interaction between two alkali atoms is calculated by considering the electrons to be moving in a Coulomb field. The dominant terms of the dispersion energy between a number of atoms and molecules are tabulated. The results indicate that the hitherto neglected dipole-octupole contributions are in many cases larger than the quadrupole-quadrupole terms.

Emission and Two-Body Recombination in Bromine

The visible emission from hot, partially dissociated bromine raised to temperatures as high as 2500°K by means of a shock wave has been studied as a function of wavelength and temperature. At total pressures around 1 to 2 atmos in a 1-in. shock tube, the emission is continuous. It is caused by two-body atom recombinations of two types, one involving two unexcited Br atoms and the other involving one excited atom and one unexcited atom. The first type yields excited Br2 molecules in the states 3π1u and 1πu, while the latter type produces excited molecules in the 3π0+u state. Proof of these mechanisms comes through analysis of emission spectra in terms of the potential diagram of bromine and through photomultiplier observations of the emission intensity at specific wavelengths as it varies with temperature and Br atom concentration. Some information is obtained on the shapes of the excited state potentials in the high energy region and an assignment of the transitions responsible for visible absorption in bromine is recommended.

Photometric investigations of alkali metals in hydrogen flame gases - I. A general survey of the use of resonance radiation in the measurement of atomic concentrations

Experiments on the intensity of emitted resonance radiation in various of the first and second doublets of alkali metals have been made in the hot gases a few centimetres above the primary zone of combustion of hydrogen-oxygen flames diluted with nitrogen, using a photoelectric technique. The results confirm that the emission is thermal in origin and lead to several conclusions of interest. ( а ) Very low intensities are always obtained with lithium, on account of removal of the metal by hydroxyl radicals to form the very stable gaseous hydroxide. This effect is decreasingly important with caesium and potassium, and is negligible with sodium. ( b ) This reaction to give the metallic hydroxide appears to be thermodynamically equilibrated in the hotter flames (> 2000° K), but becomes progressively and very markedly incomplete towards lower temperatures. ( c ) In the case of caesium only, the ionization of the metal accounts for a substantial fraction of the total metal present. Estimation of this amount leads to the conclusion that negatively charged OH ¯ ions, as well as free electrons, are present. A value of the electron affinity of OH of 65 ± 5 kcal is deduced. ( d ) Consideration of the results for sodium, which are not complicated either by formation of hydroxide, or by ionization, shows that it is possible to estimate the relative concentration of unexcited atoms by a two-flame technique, and that the absolute concentration of sodium atoms in the flame gases may be measured by observation of the onset of self-absorption. ( e ) The method appears to be useful in the confirmation and determination of the f -values of resonance lines.