Engineering topics

Bhatia, A. K.

Publications and source records attributed to Bhatia, A. K..

At least 37 records · Page 2

NASA NTRS2004

Electron-Hydrogen Elastic Scattering

Scattering by single-electron systems is always of interest because the wave function of the target is known exactly. Various approximations have been employed to take into account distortion produced in the target. Among them are the method of polarized orbitals and the close coupling approximation. Recently, e-H and e-He+ S-wave scattering in the elastic region has been studied using the Feshbach projection operator formalism. In this approach, the usual Hartree-Fock and exchange potentials are augmented by an optical potential and the resulting phase shifts have rigorous lower bounds. Now this method is being applied to the e-H P-wave scattering in the elastic region. The number of terms in the Hylleraas-type wave function for the 1,3 P phase shifts is 84 and the resulting phase shifts (preliminary) are given. The results have been given up to five digits because to that accuracy they are rigorous lower bounds. They are in general agreement with the variational (VAR) results of Armstead, and those obtained from the intermediate energy R-matrix method (RM) of Scholz et al., and the finite element method (FEM) of Botero and Shertzer. The later two methods do not provide any bounds on phase shifts.

Bhatia, A. K.↗

NASA NTRS2004

Electron-H P-Wave Elastic Scattering

In previous papers [Bhatia and Temkin, Phys. Rev. A 64, 032709-1 (2001), Phys. Rev. A 66, 064702 (2002)], electron-hydrogen and electron-He(+) S-wave scattering phase shifts were calculated using the optical potential approach. This method is now extended to the singlet and triplet electron-H P-wave scattering in the elastic region. Phase shifts are calculated using Hylleraas-type correlation functions with up to 220 terms. Results are rigorous lower bounds to the exact phase shifts and they are compared to phase shifts obtained from previous calculations.

Bhatia, A. K.↗

NASA NTRS2004

Atomic Data and Spectral Line Intensities for Ar XII

Electron impact collision strengths; energy levels; oscillator strengths and spontaneous radiative decay rates are calculated for Ar XII. The configurations used are 2s(exp 2)2p(exp 3), 2s2p(exp4), 2p(exp 5), 2s22p23s, 2s(exp 2)2p(exp 2)3p, and 2s(exp 2)2p(exp 2)3d giving rise to 72 fine-structure levels in intermediate coupling. Collision strengths are calculated at five incident energies: 35,70, 105, 140 and 175 Ry. They are complemented by Coulomb-Born limits towards infinite collision energy for forbidden transitions and line strengths for optically allowed transitions. Excitation rate coefficients are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Using the excitation rate coefficients and the radiative transition rates, statistical equilibrium equations for level populations are solved at electron densities covering the range of 10(exp 8)-101(exp 14) cm(exp -3) at an electron temperature of log T(sub e)/K = 6.4, corresponding to maximum abundance of Ar XII. Relative spectral line intensities are calculated.

Eissner, W.↗

NASA NTRS2004

Atomic Data and Spectral Line Intensities for Ar XII

Electron impact collision strengths, energy levels, oscillator strengths and spontaneous radiative decay rates are calculated for Ar XII. The configurations used are 2s(sup 2)p(sup 3), 2s(sup 2)p(sup 4), 2p(sup 5), 2s(sup 2)2p(sup 2)3s, 2s(sup 2)2p(sup 2)3p, and 2s(sup 2)2p(sup 2)3d giving rise to 72 fine-structure levels in intermediate coupling. Collision strengths are calculated at five incident energies: 35, 70, 105, 140 and 175 Ry. They are complemented by Coulomb-Born limits towards infinite collision energy for forbidden transitions and line strengths for optically allowed transitions. Excitation rate coefficients are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Using the excitation rate coefficients and the radiative transition rates, statistical equilibrium equations for level populations are solved at electron densities covering the range of 10(exp 8)-10(exp 14)/cm(exp 3) at an electron temperature of log T(sub e)/K = 6.4, corresponding to maximum abundance of AR-XII. Relative spectral line intensities are calculated.

Eissner, W.↗

NASA NTRS2004

Development of a Method for Local Electron Temperature and Density Measurements in the Divertor of the JET Tokamak

Plasma volume recombination in the divertor, a process in which charged particles recombine to neutral atoms, contributes to plasma detachment and hence cooling at the divertor target region. Detachment has been observed at JET and other tokamaks and is known to occur at low electron temperatures (T(sub e)<1 eV) and at high electron density (n(sub e)>10(exp 20)/m(exp 3)). The ability to measure such low temperatures is therefore of interest for modelling the divertor. In present work we report development of a new spectroscopic technique for investigation of local electron density (n(sub e)) and temperature (T,) in the outer divertor at JET.

Jupen, C.↗

NASA NTRS2003

Mass Polarization Effect in He-like Ions: First and Second Order

In a paper with a similar title Yamanaka has calculated the mass polarization effect (to first order in mu/M for several low-lying states of the two-electron atoms and ions with atomic number Z from 2 to 10. Here we improve the previous results by using Hylleraas variational wave functions with up to 560 terms and extend the calculation to include some additional states and the Z=1ground state. In addition, we compute the second-order effect using the method of pseudostate summation. In one appendix another method of computation is discussed and used as a check, while the energies of the Z=1 ions are presented and discussed in a second appendix.

Bhatia, A. K.↗

NASA NTRS2003

Calculation of Free-Free Opacities

Free-free absorption is an important contribution to the opacity for radiation transport through hot materials Temperatures can be as high as several keV, such that it becomes a computational challenge to solve the Schrodinger equation efficiently for rapidly oscillating continuum functions for high angular momenta. Several groups\footnots, including ours, have studied the phase amplitude solution (PAS) of the Schrodinger equation, in which one solves equations for the wave function amplitude and phase, which are: smooth functions of the electron energy. It is also important to have an accurate Schroudinger benchmark for the development of the PAS method. We present results for dipole matrix elements, Gaunt factors, and cross sections for the absorption of radiation at various energies for Cs XIX at temperature=100 eV and density=0.187 g/cc for our newly developed PAS and Schrodinger benchmark.

Bhatia, A. K.↗

NASA NTRS2003

Electron-H Elastic Scattering

Precision calculations for e^{-}-H and e^{-}-He^{+} for S-wave scattering in the elastic region have been carried out using the optical potential approach. This formalism is now extended to e^{-}-H P-wave scattering in the elastic region. The scattering equations are solved by the non-iterative method. Phase shifts are calculated using Hylleraas-type correlation functions up to 84 terms. Results are rigorous lower bounds to the exact phase shifts and they are compared to those obtained in previous calculations.

Bhatia, A. K.↗

NASA NTRS2003

Computation of Free-Free Transitions in Atomic Physics: Foundations

The amplitude T for "free-free" processes, such as bremsstrahlung or photo- absorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture, or the photo-effect, this expression contains an unphysical term, proportional to a delta-function and is not really the physical amplitude Tphys. This continues to be true for both the velocity and length form of the dipole approximation to the amplitude T. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude is modified by a long- distance cutoff, the modified form approaches Tphys as the cutoff is removed. The modified form then serves as a basis for the definition of a physical velocity dipole amplitude and this in turn leads to an equivalent length form of the dipole amplitude. This exercise provides a clear theoretical basis for many extant calculations in which cutoff factors are introduces somewhat ad hoc, as needed.

Bhatia, A. K.↗

NASA NTRS2003

Temperature Measurements in the Solar Transition Region Using N III Line Intensity Ratios

UV emission from B-like N and O ions a rather rare opportunity for recording spectral lines in a narrow wavelength range that can potentially be used to derive temperatures relevant to the solar transition region. In these ions, the line intensity ratios of the type (2s2p(sup 2) - 2p(sup 3)) / (2s(sup 2)2p - 2s2p(sup 2)) are very sensitive to the electron temperature. Additionally, the lines involving the ratios fall within a range of only - 12 A; in N III the lines fall in the 980 - 992 A range and in O IV in the 780 - 791 A range. In this work, we explore the use of these atomic systems, primarily in N III, for temperature diagnostics of the transition region by analyzing UV spectra obtained by the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer flown on the Solar and Heliospheric Observatory (SOHO). The N III temperature-sensitive line ratios are measured in more than 60 observations. Most of the measured ratios correspond to temperatures in the range 5.7x10(exp 4) - 6.7x10(exp 4) K. This range is considerably lower than the calculated temperature of maximum abundance of N III, which is approx. 7.6x10(exp 4) K. Detailed analysis of the spectra further indicates that the measured ratios are probably somewhat overestimated due to resonant scattering effects in the 2s(sup 2)2p - 2s2p(sup 2) lines and small blends in the 2s2p(sup 2) - 2p3 lines. Actual lower ratios would only increase the disagreement between the ionization balance calculations and present temperature measurements based on a collisional excitation model. In the case of the O IV spectra, we determined that due to the close proximity in wavelength of the weak line (2s2p(sup 2)-2p3 transitions) to a strong Ne VIII line, sufficiently accurate ratio measurements cannot be obtained. Subject headings: atomic data --- atomic processes --- Sun: transition region --- Sun: U V radiation --- techniques: spectroscopic

Doron, R.↗

NASA NTRS2003

Atomic Data and Emission Line Intensities for CA VII

In the present work we calculate energy levels, transition probabilities and electron-ion collisional excitation rates for the 3s(sup 2)3p(sup 2), 3s3p(sup 3) and 3s(sup 2)3p3d configurations of the silicon-like ion Ca VII. The total number of intermediate coupling levels considered is 27. Collision strengths are calculated at seven incident electron energies: 8, 10, 15, 20, 30,40 and 60 Ry, using the Distorted Wave approximation and a 5-configuration model. Excitation rate coefficients are calculated by assuming a Maxwellian distribution of velocities and are used to calculate level populations and line emissivities under the assumption of statistical equilibrium. Line intensity ratios are calculated and compared with observed values measured from SERTS and SOHO/CDS spectra. The diagnostic potential of Ca VII is demonstrated, with particular emphasis on the possibility to measure the Ne/Ca relative abundance through simultaneous observations of Ca VII and N VI lines. Ca VII proves to be an excellent tool for the study of the FIP effect in the solar transition region.

Landi, E.↗

NASA NTRS2003

Atomic Data and Spectral Line Intensities for S XI

Electron impact collision strengths, energy levels, oscillator strengths and spontaneous radiative decay rates are calculated for S XI. The configurations included are 2s(sup 2)2psup 2), 2s2p(sup 3), 2p(sup 4), 2s(sup 2)2p3l and 2s(sup 2)2p4l (I = s , p , d) giving rise to 72 fine-structure levels in intermediate coupling. Collision strengths are calculated at five incident energies, 32, 60, 90, 120, and 150 Ry. Excitation rate coefficients are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Using the excitation rate coefficients and the radiative transition rates, statistical equilibrium equations for level populations are solved: The effects of resonances, proton rates, photoexcitation and cascades on level populations have been investigate. The predicted S XI line intensities are compared with EUV and UV observations of the quiet and active Sun.

Landi, E.↗

NASA NTRS2002

Atomic Data and Spectral Line Intensities for Ne III

A number of satellites and rockets have been launched to observe radiation from the Sun and other astrophysical objects. Line radiation is emitted when the electron impact excited levels decay to the lower levels by photon emission. From this radiation, the physical parameters such as electron temperature and density of the astrophysical plasma, elemental abundance, and opacity can be inferred. Ne III lines have been observed in H II regions, Ne-rich filaments in supernovae, and planetary nebulae. The allowed line at 489.50 Angstroms due to the transition 2s(sup 2) 2p(sup 5) (sup 3) P2 (goes to) 2s(sup 2)2p(sup 4)(sup 3)P2 has been identified in the solar spectrum by Vernazza and Reeves using Skylab observations. Other Ne III lines in the solar EUV spectrum have been reported by Thomas and Neupert based on observations from the Solar EUV Rocket Telescope and Spectrograph (SERTS) instrument. Atomic data for Ne III have been calculated by using a set of programs developed at, University College, London. The Superstructure and Distorted Wave (DW) programs have been updated over the years. In the Superstructure program, configuration interaction can be taken into account and radial functions are calculated in a modified Thomas-Fermi-Amaldi potential. This is a statistical potential and depends on parameters lambda 1 which are determined by optimizing the weighted sum of term energies. They are found to be lambda(sub 0)=1.2467, lambda(sub 1)=1.1617, and lambda(sub 2)=1.0663. The relativistic corrections are included by using the Breit-Pauli Hamiltonian as a perturbation to the nonrelativistic Hamiltonian. The same potential is used to calculate reactance matrices in the DW approximation in LS coupling. Collision strengths in intermediate coupling are obtained by using term coupling coefficients obtained from the Superstructure program. In this calculation, the configurations used are 2s(sup 2)2p(sup 4), 2s2p(sup 5), 2s(sup 2)2p(sup 3)3s, 2s(sup 2)p(sup 3)3d giving rise to 57 fine-structure levels in intermediate coupling.

Bhatia, A. K.↗

NASA NTRS2002

Mass Polarization Effect in He-like Systems

Eigenvalues for the ground state S and excited S and P states have been calculated for He-like systems, He, Li(+), Be(+2), and Ne(+8), using Hylleraas-type wave functions. These calculations have been carried out for a number of mass ratios R=mu/M=m(sub e)/(m(sub e)+M), where m(sub e) is the mass of the electron and M is the arbitrary mass of the nucleus. The eigenvalues are fitted to a 5th degree polynomial in R giving the mass polarization term (Delta (sub 1) x Delta (sub 2) and higher order corrections. The mass polarization term obtained from the fitting procedure agrees very well with the first-order result obtained directly. For example, in He we find E=E(sub 0)+Sigma(sup 5)(sub n=1)R(sup n)C(sub n), where E(sub 0)=-5.807448754 Ry and C(sub 1)=0.318138927 which agrees very well with the directly obtained first-order value 0.318138966083 and the result 0.318372 obtained by Yamanaka, using wave functions of the configuration-interaction form. We have carried out a similar calculation for the bound state of H(-).

Bhatia, A. K.↗

NASA NTRS2001

Complex Correlation Calculation of e-H Total Cross Sections

Bhatia, A. K.↗

NASA NTRS2001

Complex Correlation Calculation of e-H Total Cross Sections

Calculation of e-H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with projection operators. The number of terms in the Hylleraas-type wave function for the S phase shifts is 95 while for the S it is 56, except for k=0.8 where it is 84. Our results, which are rigorous lower bounds, are given. They are seen to be in general agreement with those of Schwartz, but they are of 0 greater accuracy and outside of his error limits for k=0.3 and 0.4 for S. The main aim of this approach' is the application to higher energy scattering. By virtue of the complex correlation functions, the T matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.

Bhatia, A. K.↗

NASA NTRS2001

Polarizabilities and Other Properties of the td Muons Molecular Ion

Wavefunctions of Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H2+, D2+ and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the Born-Oppenheimer approximation. We try the same approach in a muonic system, td(mu-). Improved convergence is obtained for J = 0 and 1 states for shorter expansions when we use this type of generalized Hylleraas function, but as the expansion length increases the high powers are no longer useful. We obtain good energy values for the two lowest J = 0 and J = 1 states and compare them with the best earlier calculations. Expectation values are obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions are also calculated. The polarizability of the ground state is then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. It should be possible to measure the polarizability by observing Rydberg states of atoms with td(mu-) acting as the nucleus.

Bhatia, A. K.↗

NASA NTRS2001

Complex Correlation Calculation of e(-) - H Total Cross Sections

Calculation of e(-) - H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with 2 projection operators. The number of terms in the Hylleraas-type wave function for the S-1 phase shifts is 95 while for the S-3 it is 56, except for k = 0.8 where it is 84. Our results, which are rigorous lower bounds, are seen to be in general agreement with those of Schwartz, but they are of greater accuracy and outside of his error limits for k = 0.3 and 0.4 for S-1. The main aim of this approach is the application to higher energy scattering. By virtue of the complex correlation functions, the T-matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.

Bhatia, A. K.↗