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NASA NTRS1995

The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. The application of the Schwinger variational (SV) method to e-molecule collisions and molecular photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions. Since this is not a review of cross section data, cross sections are presented only to server as illustrative examples. In the SV method, the correct boundary condition is automatically incorporated through the use of Green's function. Thus SV calculations can employ basis functions with arbitrary boundary conditions. The iterative Schwinger method has been used extensively to study molecular photoionization. For e-molecule collisions, it is used at the static exchange level to study elastic scattering and coupled with the distorted wave approximation to study electronically inelastic scattering.

Huo, Winifred M.↗
NASA NTRS1995

The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems they can be grouped into two types: those based on the Schroedinger equation and those based on the Lippmann-Schwinger equation. The application of the Schwinger variational (SV) method to e-molecule collisions and photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions.

Huo, Winifred M.↗
NASA NTRS2001

Resonances in Positronium Hydride

Recently, Ho and his colleagues have calculated the positions and widths of a series of resonances in the Ps+H scattering system, using the complex -rotation method and have compared them with estimates that I made many years ago using a quite different technique. I assumed that the resonance mechanism was the existence in the rearrangement channel [e+ + H-] of an infinite series of perturbed Coulomb bound states. Although these must be broadened and shifted by coupling with the open scattering channel, I expected them to lie very close to the actual resonance positions. To verify this, I did a model calculation for S-waves, including the coupling, and found that the first two resonances were not shifted very far from their unperturbed position. The new, detailed calculation agrees with this result, but when the P-wave was examined it was found, surprisingly, that the lowest resonance indeed moved up in energy by a large amount. With the help of Joseph DiRienzi of the College of Notre Dame of Maryland I am now extending the old calculation to P- and D-waves, in an attempt to understand this unexpected energy shift. Results will be presented at the Workshop.

Drachman, Richard J.↗
NASA NTRS2001

Resonances in Positronium Hydride

We re-examine the problem of calculating the positions and widths of the lowest-lying resonances in the Ps + H scattering system which consists of two electrons, one positron and one proton. The first of these resonances, for L=0, was found by the methods of complex rotation and stabilization, and later described as a Feshbach resonance lying close to a bound state in the closed-channel e (+) + H (-) system. Recently, results for the L=1 and 2 scattering states were published, and it was found, surprisingly, that there is a larae shift in the positions of these resonances. In this work we repeat the analysis for L=1 and find an unexpected explanation for the shift.

DiRienzi, Joseph↗
NASA NTRS1995

The FEM-R-Matrix Approach: Use of Mixed Finite Element and Gaussian Basis Sets for Electron Molecule Collisions

For the calculation of electron molecule collision cross sections R-matrix methods automatically take advantage of the division of configuration space into an inner region (I) bounded by radius tau b, where the scattered electron is within the molecular charge cloud and the system is described by an correlated Configuration Interaction (CI) treatment in close analogy to bound state calculations, and an outer region (II) where the scattered electron moves in the long-range multipole potential of the target and efficient analytic methods can be used for solving the asymptotic Schroedinger equation plus boundary conditions.

Thuemmel, Helmar T.↗
NASA NTRS2007

Application of the Finite Element Method in Atomic and Molecular Physics

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Shertzer, Janine↗
NASA NTRS2007

The Photodetachment of Ps ion and Low-Energy e(+) -H Collisions

Two calculations in the area of positron collisions are presented. The first is the calculation of the photodetachment cross section of the positronium negative ion (Ps-) using accurate variational wave functions for both the initial bound-state and the final P continuum state. The second is the calculation of partial wave cross sections for Ps(1s)-formation in ef -H(ls) collisions using the hyperspherical hidden crossing method. Since the S-wave Stiickelberg phase is close to pi, the very small S-wave Ps(1s) formation cross section can be understood in terms of destructive interference. Other examples in positron collisions are given where it is either known or expected that destructive interference is the cause of the small S-wave Ps(1s) formation cross section. In addition, examples are presented of processes in atomic physics where the Stiickelberg phase is a multiple of pi/2.

Ward, S.J.↗
NASA NTRS2007

Electron-Molecule Col1isions: Quantitative Approaches, and the Legacy of Aaron Temkin

This article, on electron-molecule collisions, is dedicated to the legacy of my good friend and sometime collaborator, Aaron Temkin on his retirement from the NASA-Goddard Space Flight Center after many years of work at the highest intellectual level in the theoretical treatment of electron-atom and electron-molecule scattering. Aaron's contributions to the manner in which we think about electron-molecule collisions is clear to all of us who have worked in this field. I doubt that the great progress that has occurred in the computational treatment of such complex collision problems could have happened without these contributions. For a brief historical account, see the discussion of Temkin's contribution to electron-molecule scattering in the first article of this volume by Dr. A. K. Bhatia. In this article, I will concentrate on the application of the so called, non-adiabatic R-matrix theory, to vibrational excitation and dissociative attachment, although I will also present some results applying the Linear Algebraic and Kohn-Variational methods to vibrational excitation. As a starting point for almost all computationally effective approaches to electron-molecule collisions, is the fixed nuclei approximation. That is, one recognizes, just as one does with molecular bound states, that there is a separation of electronic(fast) and nuclear(s1ow) degrees of freedom. This separation makes it possible to "freeze" the nuclei in space, calculate the collision parameters for the frozen molecule and then, somehow to add back the vibrations and rotations. The manner in which this is done, depends on the details of the collision problem. It is the work of Aaron and a number of other researchers that has provided the guidance necessary to resolve these issues.

Schneider, B.I.↗
NASA NTRS2011

Constraining the Braneworld with Gravitational Wave Observations

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, L, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining L via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain L at the approximately 1 micron level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of L less than or equal to 5 microns.

McWilliams, Sean T.↗
NASA NTRS2012

Positron Interactions with Atoms and Ions

Dirac, in 1928, combining the ideas of quantum mechanics and the ideas of relativity invented the well-known relativistic wave equation. In his formulation, he predicted an antiparticle of the electron of spin n-bar/2. He thought that this particle must be a proton. Dirac published his interpretation in a paper 'A theory of electrons and protons.' It was shown later by the mathematician Hermann Weyl that the Dirac theory was completely symmetric between negative and positive particles and the positive particle must have the same mass as that of the electron. In his J. Robert Oppenheimer Memorial Prize Acceptance Speech, Dirac notes that 'Blackett was really the first person to obtain hard evidence for the existence of a positron but he was afraid to publish it. He wanted confirmation, he was really over cautious.' Positron, produced by the collision of cosmic rays in a cloud chamber, was detected experimentally by Anderson in 1932. His paper was published in Physical Review in 1933. The concept of the positron and its detection were the important discoveries of the 20th century. I have tried to discuss various processes involving interactions of positrons with atoms and ions. This includes scattering, bound states and resonances. It has not been possible to include the enormous work which has been carried out during the last 40 or 50 years in theory and measurements.

Bhatia, Anand K.↗
NASA NTRS2012

Bound-free Spectra for Diatomic Molecules

It is now recognized that prediction of radiative heating of entering space craft requires explicit treatment of the radiation field from the infrared (IR) to the vacuum ultra violet (VUV). While at low temperatures and longer wavelengths, molecular radiation is well described by bound-bound transitions, in the short wavelength, high temperature regime, bound-free transitions can play an important role. In this work we describe first principles calculations we have carried out for bound-bound and bound-free transitions in N2, O2, C2, CO, CN, NO, and N2+. Compared to bound ]bound transitions, bound-free transitions have several particularities that make them different to deal with. These include more complicated line shapes and a dependence of emission intensity on both bound state diatomic and atomic concentrations. These will be discussed in detail below. The general procedure we used was the same for all species. The first step is to generate potential energy curves, transition moments, and coupling matrix elements by carrying out ab initio electronic structure calculations. These calculations are expensive, and thus approximations need to be made in order to make the calculations tractable. The only practical method we have to carry out these calculations is the internally contracted multi-reference configuration interaction (icMRCI) method as implemented in the program suite Molpro. This is a widely used method for these kinds of calculations, and is capable of generating very accurate results. With this method, we must first of choose which electrons to correlate, the one-electron basis to use, and then how to generate the molecular orbitals.

Schwenke, David W.↗
NASA NTRS2012

Application of P-wave Hybrid Theory to the Scattering of Electrons from He+ and Resonances in He and H ion

The P-wave hybrid theory of electron-hydrogen elastic scattering [Phys. Rev. A 85, 052708 (2012)] is applied to the P-wave scattering from He ion. In this method, both short-range and long-range correlations are included in the Schroedinger equation at the same time, by using a combination of a modified method of polarized orbitals and the optical potential formalism. The short-correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia [Phys. Rev. A 69, 032714 (2004)]. This indicates that the correlation function is general enough to include the target distortion (polarization) in the presence of the incident electron. The important fact is that in the present calculation, to obtain similar results only a 20-term correlation function is needed in the wave function compared to the 220- term wave function required in the above-mentioned calculation. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts. The lowest P-wave resonances in He atom and hydrogen ion have been calculated and compared with the results obtained using the Feshbach projection operator formalism [Phys. Rev. A, 11, 2018 (1975)]. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances, bound states and the continuum in which these resonance are embedded.

Bhatia, A. K.↗
NASA NTRS2012

The Possible Interstellar Anion CH2CN-: Spectroscopic Constants, Vibrational Frequencies, and Other Considerations

The A 1B1 <-1A0 excitation into the dipole-bound state of the cyanomethyl anion (CH2CN􀀀) has been hypothesized as the carrier for one di use interstellar band. However, this particular molecular system has not been detected in the interstellar medium even though the related cyanomethyl radical and the isoelectronic ketenimine molecule have been found. In this study we are employing the use of proven quartic force elds and second-order vibrational perturbation theory to compute accurate spectroscopic constants and fundamental vibrational frequencies for ~X 1A0 CH2CN􀀀 in order to assist in laboratory studies and astronomical observations. Keywords: Astrochemistry, ISM: molecular anions, Quartic force elds, Rotational constants, Vibrational frequencies

Astrochemistry↗
NASA NTRS1961

Absolute Definition of Phase Shift in the Elastic Scattering of a Particle from Compound Systems

The projection of the target wave function on the total wave function of a scattered particle interacting with the target system is used to define an absolute phase shift including any multiples of pi. With this definition of the absolute phase shift, one can prove rigorously in the limit of zero energy for s-wave electrons scattered from atomic hydrogen that the triplet phase shift must approach a nonzero multiple of pi. One can further show that at least one pi of this phase shift is not connected with the existence of a bound state of the H- ion.

Temkin, A.↗
NASA NTRS1983

Photodissociation processes in the OH molecule

The potential energy curves of several excited states of OH of 2Sigma(+), 2Sigma(-), 2Pi, and 2Delta symmetries, and the transition moments connecting the excited states with the ground state and with each other, are calculated using two previously published theoretical models. The importance of the excited states in photodissociation is explored. Direct photodissociation by absorption into repulsive electronic states, as well as the contribution of absorption into bound electronic states, are discussed. Because they may participate in the photodissociation processes, several quartet states and one of the sextet spin multiplicity are investigated. The mechanism by which bound states can be dissociated are considered and estimates of the dissociation efficiencies of the mechanisms are made. Absorption into the bound 3 2Pi state may be an important dissociation channel. It is shown that OH is dissociated by the absorption of Lyman alpha radiation, a channel of particular significance in shocked interstellar gas and in cometary atmospheres.

Van Dishoeck, E. F.↗