Adiabatic Calculations Research Articles

H+2 —A full three-body variational treatment

The eigenstates of the hydrogen molecule ion have been determined by a variational calculation without resorting to the Born–Oppenheimer or adiabatic approximations. A Slater-type orbital basis in terms of perimetric coordinates was used and the eigenvalues were obtained by diagonalizing a 300×300 matrix. Computational techniques and numerical stability tests are described. Because of the relatively small basis and the large number of bound states, most of the eigenvalues were sensitive to the basis set. With a basis which favored the upper states, 18 bound states were obtained in a single diagonalization vs 20 bound states in the adiabatic approximation. With the best basis for the ground state, the eigenvalues of the six lowest levels were 1 to 3×10−6 a.u. lower than adiabatic calculations and the differences appear to increase with increasing vibrational quantum number.

Adiabatic calculation of the three-nucleon force

A preliminary estimate of the three-nucleon force within the adiabatic framework has already been done. In this work we try to improve the first calculation by using relativistic kinematics for the pion and including theP 11 absorption channel, as well as theP 33 and the less importantS 13,S 11,P 13,P 31 channels, in theπN interaction.

Adiabatic flash calculations for continuous or semicontinuous mixtures using an equation of state

This work presents a thermodynamic framework for adiabatic flash calculations for continuous or semicontinuous mixtures using an equation of state. A Gaussian quadrature method is used to solve phase-equilibrium and enthalpy-balance equations containing integrals of continuous distribution functions. First, comparisons between the quadrature method and pseudocomponent method are presented for a single-stage calculation using an assumed mixture. Second, a multistage gas absorber using a continuous solvent is considered. The results using the quadrature method compare favorably with those using the exact method where all components are considered in the calculation. By contrast, the pseudocomponent method gives different results which depend on the selection of pseudocomponents.

11B(d,n)12C reaction and the adiabatic approximation.

Differential cross sections were measured for the $^{11}\mathrm{B}$(d,n)$^{12}\mathrm{C}$ reaction at 79 MeV. Three different adiabatic model calculations as well as conventional distorted-wave Born approximation calculations were performed for transitions to the 0.0, 4.44, 9.64, 12.71, and 15.11 MeV states in $^{12}\mathrm{C}$. One of the adiabatic optical model parameter sets gave consistently better agreement than the rest with the experimental data. The spectroscopic factors obtained for the above states were compared with theory and with previous measurements.

The skyrmion-skyrmion interaction

Using the Skyrme effective lagrangian, baryons emerge as topological solitons. This effective lagrangian is used in adiabatic calculations aimed at providing an essentially parameter-free model of the interaction between such solitons. The resulting skyrmion-skyrmion interaction can be understood as terms simulating the exchange of π-, ρ-, and ω-mesons between the solitons. It is readily transformed (by essentially projective techniques) into a low-energy nucleon-nucleon potential. Comparisons of this potential with the best available semiphenomenological nucleon-nucleon interactions are found to be successful at the 30% level. Similarities between the Skyrme model and the quark chiral-bag model are discussed.

Resonances in positron-hydrogen-atom scattering

Adiabatic close-coupling calculations were used to compute the interaction potential between a positron and an excited (n = 2) hydrogen atom. The potential was approximated with a Morse-type curve. Two quasi-bound states atE1 = 5.671 eV,G = 10.699.10-3 eV andE2 = 9.914 eV,G = 1.709.10-3 eV were found and were interpreted as Feshbach resonances associated with then = 2 level. A shape resonance of the core-excited type also associated with then = 2 level, was found withEs = 10.675 eV,Gs = 0.224 eV.

Examples of vacuum polarization by solitons

Adiabatic calculations of vacuum polarization of fermion fields by solitons are reviewed and extended, and their proper interpretation elucidated. Possible solitons in the strong and weak interactions are discussed as examples. It is emphasized that the ground-state charge can depend on the scale of the soliton, with the adiabatic result holding for fermions with large mass. The very different physical implications of vacuum polarization effects for scalar fields are mentioned. The dual phenomenon, whereby heavy particles carrying conserved quantum numbers induce solitons, is briefly discussed and contrasted.

Rates of reaction of propyl radicals with molecular oxygen

The rates of reaction of 1-propyl and 2-propyl radicals with O/sub 2/ have been measured in the gas phase at room temperature. The rate constants are k/sub 1/(1-C/sub 3/H/sub 7/+O/sub 2/) = (5.5 +/- 0.9) x 10/sup -12/ cm/sup 3/ molecule/sup -1/ s/sup -1/ and k/sub 2/(2-C/sub 3/H/sub 7/+O/sub 2/) = (14.1 +/- 2.4) x 10/sup -12/ cm/sup 3/ molecule/sup -1/ s/sup -1/. Limited pressure studies suggest that both of these reactions are at or near their high-pressure limits at pressures of a few torr. The logarithms of these and previously measured rate constants show an excellent correlation with the ionization potential of the alkyl radical. Adiabatic channel model calculations have been carried out for these reactions with various long-range potential functions. It is concluded that some mixing of the charge-transfer surface (R/sup +/ + O/sub 2//sup -/) into the neutral surface (R + O/sub 2/) is responsible for the correlation of log (k) with ionization potential.

Rates of reaction of alkyl radicals with ozone

The rate constants for a series of alkyl radicals reacting with ozone have been measured at 298 K and 2 torr by using a photoionization mass spectrometer. The radical (R) + ozone rate constants (in units of 10/sup -12/ cm/sup 3/ molecule/sup -1/ s/sup -1/) are 2.53 +/- 0.54 for CH/sub 3/, 25.3 +/- 5.8 for C/sub 2/H/sub 5/, 24.4 +/- 5.9 for 1-C/sub 3/H/sub 7/, 46.5 +/- 10.6 for 2-C/sub 3/H/sub 7/, and 54.5 +/- 11.4 for t-C/sub 4/H/sub 9/. As was observed for the R + O/sub 2/ reactions the R + O/sub 3/ reactions show a trend of increasing rate constant k/sub 1/ with decreasing ionization potential (IP) of the radical. When log (k/sub 1/) vs. IP(R) - EA(O/sub 2/ or O/sub 3/) is plotted, where EA represents electron affinity, the two families of rate constants are brought into close proximity. In addition, rate constants for fluorescence quenching of substituted benzenes by O/sub 2/ are cited which extend the log (k) vs. IP-EA plot to lower ionization potential. Adiabatic channel model calculations have been done by using a long-range potential resulting from the perturbation between the R/sup +/ + O/sub 3//sup -/ and R + O/sub 3/more » surfaces. These calculations give good agreement with the experimental cross sections and they predict rate constants faster than those derived from the classical harpoon model at low IP-EA.« less

Systematic study of the (d, p) reaction with 56 MeV polarized deuterons

Differential cross sections and vector analyzing powers were measured for the (d, p) reaction with 56 MeV polarized deuterons. The investigation covered the transitions to the single-particle states of the 1p. 2s, 1d. 2p, 1f, 3s, 2d and 1g shells. The analyzing powers showed a j-dependence which depended on the number of nodes in the radial wave function of the transferred neutron. DWBA and adiabatic model calculations were carried out. The DWBA calculations reproduced the experimental cross sections and analyzing powers for the stripping to the j > states. The adiabatic model did not necessarily improve the fits to the data for these transitions. As for the j < transitions, on the other hand, the DWBA calculations could not reproduce the experimental angular distributions, while the adiabatic model calculations improved the agreement with the experimental data.

Coulomb and nuclear contribution to the excitation of 7Li incident on heavy nuclei

Measurements are reported for the elastic and inelastic (478 keV excited state) scattering of 68 MeV 7Li from a 208Pb target. These are compared with coupled-channels and high-energy adiabatic model calculations, using an alpha-triton cluster structure description of 7Li. In contrast to the results of fitting to the breakup cross sections, the purely nuclear contributions to the inelastic processes are too small in both models. Inclusion of a Coulomb amplitude in the coupled-channel calculation helps to fit the cross section at angles down to the grazing angle, but is too large at smaller angles. A DWBA Coulomb correction to the adiabatic model improves its ability to fit the data at angles except near grazing.

Importance of dissociation equilibrium and variable transport properties on estimation of flame temperature and droplet burning rate

By using droplet combustion in oxidizer-rich environments as a model problem, the present investigation demonstrates both experimentally and theoretically that variable transport properties and flame dissociation are important factors which influence the bulk combustion charateristics, such as the fuel consumption rate and the flame temperature and location. A simplified, internally consistent methodology is proposed for the evaluation of these properties by analyzing the transport aspects of the problem and separately determining the characteristics of the flame in dissociation equilibrium through adiabatic flame temperature calculation, with allowance for the falsification of the oxidizer concentration due to diffusional stratification.

A Study on the Formation of Fumed Silica

A study has been made on properties of fumed silica prepared from silicon tetrachloride in hydrogen combustion flames ranging from 1000 to 2200°C, while flame temperature in this study is determined by adiabatic calculation based on equilibrium conditions.A marked change in properties occurred at temperatures around 1500-1700°C as evidenced by surface area, apparent refractive index, number of hydroxyl groups, and size of the primary particles.The particular temperature of 1500-1700°C is considered to correspond to the melting point of silicon dioxide materials. At flame temperatures lower than 1500-1700°C numerous various size pores existed in the silica produced, then these silica particles were assumed to have grown in a non-melted phase. On the other hand, at higher temperature few pores existed and silica particles were assumed to have been grown in a melted phase.

Adiabatic time-dependent Hartree-Fock calculation of fusion cross sections: Application to 40Ca- 40Ca

Using the adiabatic time-dependent Hartree-Fock method we calculate the interaction and inertial mass parameter relevant for a heavy-ion collision. In this work, which extends an earlier study for lighter systems, we investigate the case of 40Ca- 40Ca for which detailed experimental information is available. As already found for lighter colliding ions, the mass parameter exhibits a large peak for interdistances slightly smaller than the barrier radius. We use our results to evaluate the fusion cross section and we find that the structure in the inertial mass brings the theoretical cross section in close agreement with data.

Potential model representation of 6Li break-up through a simple inversion procedure

We introduce a practical, iterative, perturbative phase-shift-to-potential inversion procedure and give a specific example of how it can be used to relate breakup effects to a potential model of 6Li scattering. We do this by exhibiting a local potential equivalent to the adiabatic breakup calculation of Thompson and Nagarajan.

Quasistatic, adiabatic, and impact calculations for the ion broadening and shift of neutral-helium lines in a hot plasma

We calculate in this paper the widths and shifts of many neutral-helium lines in a hot plasma. To evaluate the broadening and shift produced by electronic impacts, a convergent method is applied. The effects of the ions are taken into account by using the quasistatic, adiabatic, and impact approximations. Our theoretical predictions are compared with the experimental results of Wulff, Berg et al., Kelleher, and Diatta.

Modified method of perturbed stationary states. IV. Electron-capture cross sections for the reactionC6++H(1s)→C5+(n,l)+H+

Previously reported ten-state perturbed stationary-state calculations for ${\mathrm{C}}^{6+}\ensuremath{-}\mathrm{H}(1s)$ collisions are extended by increasing the basis to include all molecular states correlating to the principal levels $n=3,4, \mathrm{and} 5$ of the final ${\mathrm{C}}^{5+}(\mathrm{nlm})$ atomic ion. This allows cross sections to be computed for the angular momentum sublevels, $l$, of each of the above $n$. The H-atom energy range extends from 13 eV to 27 keV. Adiabatic calculations are done for energies below 1.3 keV, and partially diabatic calculations are done at higher energies. The inclusion of states with magnetic quantum number $m\ensuremath{\ge}2$ in the new basis leads to significant increases in the $n=5$ capture cross section even at rather low energies. Two translational factors, which depend on the internuclear separation, are employed in the construction of the scattering basis. One is used for the state which correlates to $\mathrm{H}(1s)$; the other is used for all states correlating to states of ${\mathrm{C}}^{5+}$. For purposes of comparison, cross sections are also computed for the same scattering basis, with the use of the method of Bates and McCarroll and the method of Piacentini and Salin. The heavy-particle motion is treated semiclassically, with the use of Riley's average approximation at energies below 1.3 keV and the straight-line impact-parameter method at higher energies. As in the ten-state calculations, it is shown that adiabatic and diabatic formulations lead to rather different values for the cross sections at the higher energies. The results are compared with the experimental and theoretical cross sections obtained by other researchers.

Adiabatic calculation of quench temperature--A simple method for dimensioning the protection circuit of a superconducting magnet

The quenching of superconducting coils is one of the operating conditions to be considered. It determines the design of the protection circuit and, possibly, the cryostat. It is however extremely difficult to calculate the complete quench event. A theory is presented here where the conductor heating by resistive power is calculated assuming adiabatic conditions. The differential equation resulting is integrated to form a function from which the final temperature of the hot spot and the final energy balance can easily be obtained for an individual magnet configuration. Because heat conduction, heat transition to the helium and the effect of eddy currents have been ignored, this result only allows a worst-case-design where a magnet dimensioned in accordance with this simple method must always be on the safe side.

The [formula omitted] state of hydrogen: Adiabatic calculation of vibronic states in H 2, HD, and D 2

The nuclear-mass-dependent diagonal corrections to the electronic energies of the H H 1 Σ g + state of hydrogen are computed in the range 1.25 ≤ R ≤ 11 a.u. The correction energy goes through a pronounced peak near R = 3 a.u., which is discussed in terms of the character of the electronic wavefunction. The rovibrational structures of H 2, HD, and D 2 in the adiabatically corrected double-minimum potential curves of these isotopes in the H H state are presented. Comparison with experimental data indicates the presence of appreciable nonadiabatic perturbations.

Measurements of temperature and concentration fluctuations in turbulent diffusion flames using pulsed raman spectroscopy

Instantaneous values of temperature and major component concentrations have been measured simultaneously using pulsed Raman spectroscopy in hydrogen-air diffusion flames of low turbulence produced in a well-controlled co-flowing fan-induced combustion tunnel. Results are presented in the form of probability density functions for each of these scalar variables as a function of flame position. Simultaneously measured values of temperature and concentration (nitrogen or hydrogen) are compared with adiabatic equilibrium flame calculations of these variables. Close agreement with this simplified escription is obtained in the lean regions of the flame; in the fuel-rich regions, the concentrations of N2 are higher than theoretically predicted and those of H2 are lower. Analysis strongly suggests that these systematic deviations arise from differential diffusion of H2. Initial conditioned sampling measurements are reported for hydrogen-propane-air turbulent diffusion flames and for premixed laminar propane-air flames.