Three-body Recombination Processes Research Articles

Quantum theory of hydrogen recombination

A fully quantum mechanical treatment is presented of the three-body recombination process H + H + 4He → H2 + 4He for T = 1 K where measurements have recently been performed. The calculation employs accurate interatomic potentials and thermal averaging. An impulse approximation is used to obtain the most important contributions to the rate constant. Off-shell effects are found to be important and are included in the final results which are in reasonable agreement with experiment. We find that the rate of formation of ortho-H2 is substantially larger than that of para-H2. The magnetic field dependence of the recombination rate is also discussed.

Rates of three-body ionic recombination processes in the rare-gas-halides

Employing the method of Flannery (1978), rates for the recombination processes X++H-+M to (XH)*+M and X2++H-+M to (XH)*+X+M are calculated for buffer gas pressures of up to 50 atm and in the temperature range 100-500K. Rates of (3-5)*10-6 cm3s-1 are obtained for pressures 14-23 atm of He buffer gas. At low temperature an increase of the recombination rates is observed.

Investigation of the conditions for efficient initiation of HF chemical lasers by a relativistic electron beam

An investigation was made of the feasibility of achieving a high specific output energy and a high electrical efficiency in an H2?F2 chemical laser excited by a relativistic electron beam. Using an H2:F2:O2:He = 6:15:1.2:50 mixture at a pressure of 1.3 atm, a specific output energy of 100 J/liter was achieved with an efficiency of ~ 900% with respect to the energy deposited in the active volume of the laser and a chemical efficiency of ~ 4%. The degree of initiation and the efficiency were estimated using the experimentally measured electron beam energy absorbed by the active volume of the laser. A high efficiency of utilization of the electron beam energy, ~ 200%, was obtained. It was found that the H(F)+O2+M?H(F)O2+M three-body recombination process was very undesirable in active mixtures at pressures of ~ 1 atm. The rate constants of this reaction for M = He, Xe, and SF6 were determined experimentally.

Laserspektroskopische Untersuchungen an nicht-stabilisierten N2(B3IIg, ν; = 13)-Molekülen / Laser Spectroscopic Studies on Non-stabilized N2(B3IIg, ν; = 13) molecules

Unstabilized N2(B3IIg, ν = 13) quasi-molecules were analysed by excitation with a tunable dye-laser into the N2(C3IIu) state and observation of the following fluorescence to N2(B3IIg, ν) levels. The quasi-molecules are in equilibrium with the free nitrogen atoms. The detection limit of this technique is 105 molecules/cm3. By the same method, a rotational analysis of molecules stabilized into (B3IIg, ν ≦ 12) levels by three-body recombination processes was achieved with a resolution better than that reached by emission spectroscopy of the Lewis-Rayleigh afterglow

Possibility of utilization of three-body recombination processes in generation of high-power continuous-wave visible laser radiation

Consideration is given to two possible laser systems which can be used to generate high-power visible radiation as a result of three-body recombination processes: one of them is a gasdynamic recombination laser and the other a hybrid laser employing additionally an electron-beam-controlled electric discharge. The characteristics of media suitable for such lasers are given and the results are reported of preliminary experiments which suggest that such lasers can be built in the near future.

Plume Separated Region as a Flameholder

The luminous flames in the Apollo first stage exhaust flow are considered in terms of the requirements for stabilizing hydrocarbon flames in low pressure, high speed flowfields. Above 12-15 km alt, flame stabilization depends upon a series of recirculation flows about the base of the first stage. Above 30 km alt, the flames are stabilized by the separated body flow (plume separated) region upstream of the expanding exhaust plume flowfield. The hot, fuel rich separated region is bounded by a combustible outer shear layer which contains the luminous flames. As altitude increases, the length I of the nonluminous gap, from the point of separation to the leading edge of the luminous flame-front, increases. At these altitudes heterogeneous heat release processes, involving direct attack on carbon particles by O and O2, appear to replace homogeneous two and three-body recombination processes. As a result the chemical relaxation lengths for radical formation and heat release are always smaller than the nonluminous gap length, I. Thus the Apollo body separated region flames are in the same region of rapid chemistry as the flame stabilization studies of Zukoski and Marble. After introducing a pressure factor to account for changing heating rates, their blowoff criterion is adapted to the variable pressure flame holder in the Apollo flowfield giving: /tf/w~0.5-1.5x!0' atm-sec, where/? is the separated region pressure, and u is the exterior stream speed. The flames blow off the Apollo exhaust flow when £ attains the length of the plume separated region outer shear layer.

Excitation of the Herzberg bands of O2in laboratory afterglow and night airglow

Relative vibrational populations of the metastable O2 A³Σu+ molecule were calculated from a statistical equilibrium model and compared with vibrational populations determined spectroscopically in an oxygen-argon afterglow at pressures of 5–120 torrs and with the nightglow populations obtained previously. The model assumes the three-body recombination process to be the principal excitation mechanism and vibrational relaxation to be the principal collisional deactivation mechanism. A close fit is obtained with both sets of data when the excited molecule is treated as an anharmonic oscillator during the relaxation process ; thus the peculiar distributions of band intensities observed in the Herzberg band spectra (A³Σu+ − X³Σg−) are the consequence of the strongly anharmonic character of the O2A³Σu+ molecule rather than of some other processes. Although the formulation provides for collisional quenching, the data are not as yet sufficiently complete to make a firm estimate.

Experimental study of the Relaxation Phenomena in Non-Equilibrium MHD Generator Duct

The non-equilibrium electrical conductivity and the relaxation of electron density in seeded plasma for MHD power generators were studied experimentally. The experiments were performed with use made of potassium seeded argon plasma (A+0.14%K) at 1,800°2,000°K, flowing in a rectangular duct at constant velocity (about 240m/sec) under atmospheric pressure. The dependence of the electrical conductivity on the electric current density was found to agree well with theoretical prediction based on the two-temperature model, if a value of 40 was chosen for the collision loss parameter. The effect of the radiative energy loss of potassium atoms was not significant in the present experiments. Furthermore, it was found that the relaxation of the electron density can be well expressed by the recombination coefficient for the electronic three-body recombination processes, and that the relaxation time is about 4 × 104 sec for the present experimental conditions.

Experimental Study of the Relaxation Phenomena in Non-Equilibrium MHD Generator Duct

The non-equilibrium electrical conductivity and the relaxation of electron density in seeded plasma for MHD power generators were studied experimentally. The experiments were performed with use made of potassium seeded argon plasma (A+0.14%K) at 1,800°2,000°K, flowing in a rectangular duct at constant velocity (about 240m/sec) under atmospheric pressure. The dependence of the electrical conductivity on the electric current density was found to agree well with theoretical prediction based on the two-temperature model, if a value of 40 was chosen for the collision loss parameter. The effect of the radiative energy loss of potassium atoms was not significant in the present experiments. Furthermore, it was found that the relaxation of the electron density can be well expressed by the recombination coefficient for the electronic three-body recombination processes, and that the relaxation time is about 4 × 104 sec for the present experimental conditions.

Recombination processes during the expansion of a laser-produced plasma

The decay of a spherical LiH plasma, produced by laser radiation, is considered; three-body and radiative recombinations have been taken into account. Freezing of the degree of ionization is possible, if the energy transferred to the plasma in the three-body recombination processes is considered. Numerical computations are compared with previously published experimental results.

Transition from the Three-Body to the Dissociative Electron-Ion Recombination in an Argon Plasma

An experimental study is presented which is concerned with the transition from the three-body to the dissociative electron-ion recombination in an argon plasma. The measurements are performed, by using the propagation technique of the 8 mm wave, in decaying plasmas produced behind reflected shock waves in a T -type tube. It is filled with argon at initial pressures from 5 to 18 Torr. The electron densities and temperatures are respectively in the ranges from 10 13 to 10 10 cm -3 and from 10 3 to 3×10 2 °K. The recombination coefficients determined from the measured density decays are explained by the three-body recombination process for the electron densities above 10 12 cm -3 . The coefficients, on the other hand, are interpreted by the dissociative process for the electron densities below 10 11 cm -3 with the electron temperatures close to 3×10 2 °K. The transition between these two processes is discussed.

A discussion on advanced methods of energy conversion- Magnetohydrodynamic power generation - Equilibrium and non-equilibrium electrical conductivity of seeded combustion products

From measurements by four electrode and microwave techniques and from theoretical calculations, the conclusions are drawn that the equilibrium electrical conductivity varies with fuel/air ratio, being higher in fuel rich conditions, and that the chlorine and sulphur impurities in power station fuels will not significantly affect the conductivity under m.h.d. generator conditions. Experiments on non-equilibrium conductivity in seeded combustion products at 1500 °K are described. The form of the current-field curve at high values of the ratio of electrical field to molecule density was investigated. At a certain value of the field the current was found to increase many times above the equilibrium value, with little increase in field. To describe these results, a theory is presented in which ionization by electrons having energies greater than the ionization potential is balanced by a three-body recombination process involving electrons, positive potassium ions, and neutral molecules. This gives a current-field curve of the same shape as that experimentally observed but the experimental value of the field at which the current rises differs from the theoretical value by about 25%. The use of this non-equilibrium conductivity in generators is discussed.

Reactions of Metal Carbonyls with Active Nitrogen

Ni(CO)4, Fe(CO)5, Cr(CO)6, W(CO)6, Mn2(CO)10, and Co(NO) (CO)3 were found to react very rapidly with active nitrogen, forming metal atoms. The reaction is accompanied by intense flames due to neutral metal atom emission spectra. The mechanism of the reaction is interpreted as a stepwise degradation: Me(CO)n+N→Me(CO)n−1+NCO. The excitation of emission spectra is shown to be most likely due to collisions of metal atoms (as they diffuse to the walls) with metastable A 3Σ nitrogen molecules. These are formed in the three-body atomic recombination reaction and have only short lifetimes due to destruction on the walls of the tubular flow reactor. Quantitative intensity measurements of Fe(I) and Ni(I) flame spectra yielded rates of excitation of numerous levels of these atoms. The relative rates are found to depend only on the excitation energy, decreasing monotonously as the energy increases. Atomic mercury emission in active nitrogen was also observed and measured, as well as its quenching by ammonia. The dependence of the excitation rates on energy is experimentally the same for nickel, iron and mercury, except that the excitation of the 7s1S0 mercury state, which conflicts with the spin conservation rule if the nitrogen molecules undergo the A 3Σ→X 1Σ transition, occurs about 10−2 as frequently as the energy relationship would predict. It is inferred that this relationship is largely determined by the relative populations of the successive vibrational levels of the A 3Σ nitrogen molecules as these cascade down due to inelastic collisions from the highest levels resulting from the three-body recombination processes.

The ionospheric model of the Venus microwave emission: An obituary

In the ionospheric model of Venus, the observed microwave radiation is attributed to free-free emission of electrons in a dense Cytherean ionosphere. The present paper discusses the mechanisms for formation of such a dense ionosphere, both in the original formulation of Jones and in later formulations which introduce holes in the ionosphere to achieve consistency with the observed radar reflectiveness. Ionization by solar ultra-violet radiation and by the solar proton wind, as measured near Venus by Mariner 2, are considered, assuming that the Cytherean surface magnetic field strength is ≤10 −3 gauss. Both sources of ionization are primarily effective at the level where the neutral particle density is ∼10 11 cm −3, somewhat above the level at which diffusive equilibrium is established. Three-body electron-ion recombination processes are ineffective at these densities. Radiative recombination is plausible only if all the N 2 at this level is converted to N by the Herzberg-Herzberg photodissociation mechanism. But the times for N to diffuse to dense levels where recombination to N 2 occurs are so much shorter than the time for Herzberg-Herzberg photodissociation on Venus, that N 2 must be a predominant atmospheric constituent at the level of the Cytherean ionosphere. If dissociative recombination therefore prevails, characteristics values of the electron density are n e ∼ 10 6 cm −3 over a region of 50-km thickness. If radiative recombination prevailed, n e ∼ 10 8 cm −3 would result, but even this is too small for the ionospheric model to be a valid explanation of the Venus microwave emission. The ionospheric model is accordingly rejected. We conclude that the observed microwave emission arises from the Cytherean surface.

Structure of gaseous detonation. IV. Induction zone studies in H 2-O 2 and CO-O 2 mixtures

The density structure of the flow behind shock waves in H 2 −O 2 and in CO−O 2 mixtures has been examined interferometrically. In the former case it is shown that the oxygen is vibrationally excited before observable exothermic reaction. At least for very rich mixtures and probably for all mixtures, the hydrogen is also, since the vibrational relaxation time for H 2 (as well as for D 2 ) is found to be less than 2×10 −6 atm sec at 1400°K. The induction time for exothermic reaction has been measured for 0.0075≤[H 2 ]/[O 2 ]≤100 and the data may be fit to better than a factor of two for 2200> T >1100°K by log 10 ([O 2 ][H 2 ]) 1/2 ti =3100/ T —9.8, where concentrations are in moles/liter and time in seconds. Induction times in 2 H 2 +5 Air are also found to be represented by this equation. The observed density profiles in the region of rapid exothermic reaction have been analyzed for a number of very rich and very lean mixtures, assuming heat evolution to be due to three-body recombination processes, and termolecular rate constants of reasonable magnitude have been deduced. In 8 CO+O 2 , it is shown that both reactants become vibrationally equilibrated prior to reaction, and that the vibrational relaxation time is significantly less than for pure CO implying that vibrational exchange with excited O 2 is an important process in excitation of the CO. Addition of up to 1% H 2 is shown to reduce the relaxation time and accelerate the reaction, but not to affect the maximum density. With the thinner reaction zone due to added H 2 , the detonation is observed to develop spin and to acquire the characteristic “turbulent” appearance due to the transversely propagating shocks behind the main shock front and the consequent shear layers in the flow.

Electron-Ion Recombination by Collisional and Radiative Processes

Physical principles domlnating the electron-ion threebody recombination process and forming the basis of a general method for calculating the electron temperature and the net rate of three-body recombination are discussed. Calculations and data are presented in graphical and tabular forms. (L.N.N.)

Electron-Ion Recombination in Dense Plasmas

The rate of recombination and the characteristics of the afterglow line emission have been measured in magnetically confined plasmas of helium and hydrogen, with electron densities of the order of ${10}^{13}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and degree of ionization initially of the order of 50%. Electron densities and temperatures are deduced from absolute intensity measurements of spectrum line intensities originating from highly excited states, in good agreement with those obtained from microwave phase shift and plasma conductivity measurements. The results are explained in terms of an electron-electron-ion three-body recombination process. The recombination coefficient for this process is calculated as a function of electron temperature and density.

A Self-Consistent Treatment of the Oxygen Dissociation Region in the Upper Atmosphere

A self-consistent theory is suggested for the determination of the distribution of atomic and molecular oxygen and the temperature in the region 100-140 km of the atmosphere. It is assumed that solar radiation is responsible for the photodissociation of the oxygen molecules, and that the recombination of the atoms by two-body radiative processes is more important than that by three-body collisions (as justified from theoretical considerations). From the postulated conditions for the steady state, namely, for any given volume, (a) the average time rate of dissociations equals that of recombinations, and (b) the average time rate at which radiation energy is absorbed in dissociation processes equals that at which radiation energy is emitted in recombination processes, together with an appropriate form of the barometric equation, it is possible to obtain the concentrations of the molecular and the atomic oxygen and the temperature, all as functions of height, provided the temperature and its gradient are given at one height. Calculations have been carried out for three sets of these boundary values at 100 km, namely, (i) $T=300$\ifmmode^\circ\else\textdegree\fi{}K, $\frac{\mathrm{dT}}{\mathrm{dx}}=10\ifmmode^\circ\else\textdegree\fi{}$/km, (ii) $T=300$\ifmmode^\circ\else\textdegree\fi{}K, $\frac{\mathrm{dT}}{\mathrm{dx}}=5\ifmmode^\circ\else\textdegree\fi{}$/km, and (iii) $T=270$\ifmmode^\circ\else\textdegree\fi{}K, $\frac{\mathrm{dT}}{\mathrm{dx}}=5\ifmmode^\circ\else\textdegree\fi{}$/km. In all these cases, dissociation begins between the heights 90 and 100 km and is not complete until around 150 km. The total gas pressure for various heights above 100 km calculated for case (iii) above agrees quite well with the data obtained from V-2 rocket flights.In the appendices, three-body recombinations are discussed. The cross section for a three-body recombination process is defined, and its relation with the cross section of its inverse two-body excitation process is obtained on statistical mechanical arguments. Also, the relation between the absorption coefficient for a photodissociation process and the cross section of its inverse radiative recombination process is obtained.