Engineering topics

DiRienzi, Joseph

Publications and source records attributed to DiRienzi, Joseph.

9 records

NASA NTRS2011

Positronium and Electron Scattering on Helium

A recent work [1] establishes experimentally that Positronium scattering by atoms of various elements is surprisingly close in total cross-section to that of an isolated electron of the same velocity. In this work we will look at the scattering of Ps on Helium and compare it to a determination of the scattering of an e- with the same element. For both the Ps scattering and the e- scattering on He, we assume the symmetrization of the e- with the closed shell He electrons is the dominant interaction. A local effective potential employed in [2] and [3] is used to model the electron exchange and cross- sections are determined for a set of partial waves. For the Ps scattering we include as a secondary effect the Van der Waals interaction. For single e- scattering of He, we also employ a short range Coulomb potential and dispersion as contributing effects. Results of the cross-sections determined in each case are then compared

DiRienzi, Joseph↗

NASA NTRS2003

Re-examination of a Simplified Model for Positronium-Helium Scattering

Using a local effective potential to account for electron exchange, R J Drachman and S K Houston analyzed the zero-energy scattering of ortho-positronium by helium atoms in 1970. The idea was to use the existing static-exchange results to fit the parameters of the local potential and then to use the potential in a variational target-elastic calculation. The results were remarkably good, both for the scattering length and the annihilation parameter. Recently, however, a rigorous target-elastic calculation by Blackwood et al disagreed so strongly with these old results that we have undertaken a re-examination. We find that one of the apparently trivial assumptions of the local potential method is much more important than previously believed.

DiRienzi, Joseph↗

NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗

NASA NTRS2003

Re-Examination of a Simplified Model for Positronium-Helium Scattering

Using a local effective potential to account for electron exchange, R J Drachman and S K Houston analyzed the zero-energy scattering of ortho-positronium by helium atoms in 1970. The idea was to use the existing static-exchange results to fit the parameters of the local potential and then to use the potential in a variational target-elastic calculation. The results were remarkably good, both for the scattering length and the annihilation parameter. Recently, however, a rigorous target-elastic calculation by Blackwood et al disagreed so strongly with these old results that we have undertaken a re-examination. We find that the assumption made in the earlier work, that the direct potential is negligible compared with the exchange potential, is not quantitatively correct. But the original idea that omission of the direct potential might compensate approximately for the omission of the van der Waals potential still seems reasonable.

Drachman, Richard J.↗

NASA NTRS2002

D-Wave Resonances in Positronium Hydride

The problem of calculating the position and width of the lowest-lying (L = 0, 1) resonances in the Ps + H scattering system has recently been re-examined by the authors [1]. In the model used, resonances axe assumed generated by bound Rydberg states in the closed re-arranged channel [e(+) + H(-)]. This infinite series of Coulomb bound states are shifted somewhat by the coupling with the open scattering channel [Ps + H]. Estimates using this approach, first carried out by one of the authors [2] using a simple form of scattering wavefunction, indicated an anticipated small shift of resonance away from the Rydberg energy in the S-wave (L = 0). More recent results by Ho and Yan [3] using the complex-rotation method showed unexpected significant shifting in the P (L = 1) and D (L = 2)-wave resonance energies from their respective unperturbed values. Our re-calculation of the resonances [I I for L = 0 and I indicates that, in each case, reasonably consistent resonance energies are obtained by coupling the two lowest lying states (IS and 2S for L = 0 and 2P and 3P for L = 1). For each L it is the higher state (2S and 3P, respectively) that produces the resonance. The lower state (1S and 2P, respectively) is effective only in increasing the non-resonant phase shift. In this work we extend the model to L = 2 (D-waves). Our results show that, unlike the S and P-waves, the 313-state alone produces a resonant energy that is very close to the result of Yan and Ho [3]. Inclusion of the 4D-state produces a second resonance in the scattering system shifted up slightly from its unperturbed Rydberg energy.

Drachman, Richard J.↗

NASA NTRS2002

D-wave Resonances in Positronium Hydride

We have recently reexamined the problem of calculating the positions and widths of the lowest-lying S- and P-state resonances in the Ps+H scattering system. The resonances are generated by bound Rydberg states in the closed rearranged channel (e(+)+H(-)), shifted somewhat by coupling with the open scattering channel. This picture had been successfully applied for S-waves, but more recent results showed unexpectedly large shifts in both P- and D-wave resonances. Our recalculation for the S- and P-waves showed that the series of resonances begins with the second Rydberg state, giving rise to an apparent large shift. Now we have extended the calculations to D states. Here we find the expected results: The 3D Rydberg state produces a resonance very close to the result of Yan and Ho, and inclusion of the 4D state gives a second resonance only slightly shifted.

Drachman, Richard J.↗

NASA NTRS2002

D-wave Resonances in Positronium Hydride

In a previous paper [Phys. Rev. A 65, 032721 (2002)] we re-examined a model describing the structure of the low-energy Ps-H resonances as being due to quasi-bound states of the positron in the perturbed Coulomb potential of the H-ion appearing in the closed, rearranged channel. In particular, we wished to understand why the lowest p-state resonance was so far away from the lowest quasi-bound (2p) state. We found that the lowest resonance actually corresponds to the first excited [3p] state, while the lowest state is not recognizable as a resonance. In the present work we repeat our analysis, but this time for the lowest d state. We find that the lowest [3d] state does correspond to a resonance shifted moderately.

DiRienzi, Joseph↗

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 NTRS1998

Re-examination of a Classic Experiment to Measure the Positronium-Helium Cross Section

In 1975, before the advent of positronium beams, a clever experiment was carried out in an attempt to measure low-energy Ps-atom scattering cross-sections, especially that of Ps-He. A series of parallel thin plates was placed in the vessel containing the sample of gas, and positrons were allowed to enter the chamber from a radioactive source. The time spectrum of annihilation radiation was observed in the traditional way, and the pickoff annihilation due to thermalized Ps striking one of the plates was to be the special feature of the experiment. Using a diffusion analysis the authors derived cross- sections for several gases, and for helium the value obtained was sigma = 0.0166 pi(alpha)(sub o, sup 2). Even then this value was thought to be very much too small, while recent measurements and some calculations suggest a more reasonable value would be sigma = 3 to 13 pi(alpha)(sub o,sup 2). It has always been puzzling that an apparently well-designed experiment should give such an unsatisfactory result. We have now re-examined the analysis of the data with some interesting consequences which may explain the discrepancy. Two main observations support our re-analysis. First, we note that the mean free path for Ps-He scattering would be quite long if the cross-section were as small as that quoted above; the diffusion method itself would seem to be questionable. For the larger values, however, there would be no such problem. Second, it was assumed that when the annihilation rate had settled down and was following an exponential decay curve the asymptotic solution of the diffusion equation had been reached. We find, instead, that a superposition of exponentials can accurately represent the decay curve, consistent with the higher cross-section value.

Drachman, Richard J.↗