Engineering topics

Drachman, Richard J.

Publications and source records attributed to Drachman, Richard J..

At least 19 records

NASA NTRS2012

Further Examination of a Simplified Model for Positronium-Helium Scattering

While carrying out investigations on Ps-He scattering we realized that it would be possible to improve the results of a previous work on zero-energy scattering of ortho-positronium by helium atoms. The previous work used a model to account for exchange and also attempted to include the effect of short-range Coulomb interactions in the close-coupling approximation. The 3 terms that were then included did not produce a well-converged result but served to give some justification to the model. Now we improve the calculation by using a simple variational wave function, and derive a much better value of the scattering length. The new result is compared with other computed values, and when an approximate correction due to the van der Waals potential is included the total is consistent with an earlier conjecture.

DiRienzi, J.↗

NASA NTRS2010

Polarizabilites and Rydberg States in the Presence of a Debye Potential

Polarizabilities and hyperpolarizabilities, alpha(1), beta(1),gamma(1), alpha(2), beta(2),gamma(2), alpha(3), beta(3),gamma(3), delta and epsilon of hydrogenic systems have been calculated by Drachman. We have now calculated these quantities by using pseudostates for the S. P. D and F states. All of them converge very fast as the number of terms in the pseudostates is increased, and are essentially independent of the nonlinear parameters. All the results are in good agreement with the results obtained by Drachman. except for delta, which is of the third-order in perturbation formalism. We have calculated Rydberg states of He for high N and L. The effective potential is -alpha(sub 1)/x(exp 4)+{6 * Beta(sub 1) -alpha(sub 2)/x(exp6), where x is the distance of the outer electron from the nucleus. The exchange and electron-electron correlations are unimportant because the outer electron is far away from the nucleus. This implies that the conventional variational calculations are not necessary. The results agree well with the results of Drachman. We have generalized this approach in the presence of a Debye potential.

Bhatia, A. K.↗

NASA NTRS2007

Polarizabilities of the Ps Negative Ion

We have calculated polarizabilities (alpha(sub l), beta(sub 1), gamma(sub l), alpha(sub 2), beta(sub 2), and gamma(sub 2)) of Ps(sup -) by the pseudostate method. These parameters can be used to calculate Rydberg states of Ps(sup -) in the presence of an external electron with high quantum numbers N and L. They are also of importance in a system containing Ps(sup -) bound to a proton [PsH], and also Rydberg states of Ps(sub 2).

Bhatia, A. K.↗

NASA NTRS2006

Formation of Triplet Positron-helium Bound State by Stripping of Positronium Atoms in Collision with Ground State Helium

Formation of triplet positron-helium bound state by stripping of positronium atoms in collision with ground state helium JOSEPH DI RlENZI, College of Notre Dame of Maryland, RICHARD J. DRACHMAN, NASA/Goddard Space Flight Center - The system consisting of a positron and a helium atom in the triplet state e(+)He(S-3)(sup e) was conjectured long ago to be stable [1]. Its stability has recently been established rigorously [2], and the values of the energies of dissociation into the ground states of Ps and He(+) have also been reported [3] and [4]. We have evaluated the cross-section for this system formed by radiative attachment of a positron in triplet He state and found it to be small [5]. The mechanism of production suggested here should result in a larger cross-section (of atomic size) which we are determining using the Born approximation with simplified initial and final wave functions.

Drachman, Richard J.↗

NASA NTRS2006

Stability of the Helium-Antiproton System

In the course of their Born-Oppenheimer calculations of this system Todd and Armour noted that the lowest-lying state closely resembles the hydrogen negative ion, since the antiproton lies very close to the helium nucleus and shields one unit of nuclear charge. In the present paper this observation will be taken seriously to produce a variationally correct estimate of the total energy of this system, along with a similar estimate of the energy of the once-ionized system. The nonadiabatic effect of exactly treating the reduced masses improves the results.

Drachman, Richard J.↗

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

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

Positron Physics

I will give a review of the history of low-energy positron physics, experimental and theoretical, concentrating on the type of work pioneered by John Humberston and the positronics group at University College. This subject became a legitimate subfield of atomic physics under the enthusiastic direction of the late Sir Harrie Massey, and it attracted a diverse following throughout the world. At first purely theoretical, the subject has now expanded to include high brightness beams of low-energy positrons, positronium beams, and, lately, experiments involving anti-hydrogen atoms. The theory requires a certain type of persistence in its practitioners, as well as an eagerness to try new mathematical and numerical techniques. I will conclude with a short summary of some of the most interesting recent advances.

Drachman, Richard J.↗

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

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

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

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 NTRS1999

Energy Levels of C IV: The Polarization Method

In a previous publication [Can. J. Phys. 75, 11 (1997)] we calculated the generalized polarizabilities up to multipole order 3 as well as certain higher-order hyperpolarizabilities for two-electron atoms and ions of Z=2-6 and 10. In this paper we apply some of these results to calculate excited-state energies in three times ionized (lithium-like) carbon. For states with angular momentum L greater than or equal to 3 accurate results are obtained using an asymptotic polarizability expansion that includes nonadiabatic effects. Comparison is made with recent optical measurements, and a critical discussion of the correct form of the expansion is given. In addition, the possibility of very accurate measurements of the fine-structure splitting encourages us to present a table of such splittings to very high accuracy. An appendix contains similar results for lithium-like oxygen and neon ions.

Bhatia, A. K.↗

NASA NTRS1999

Static Properties and Stark Effect of the Ground State of the HD Molecular Ion

We have calculated static properties of the ground state of the HD(+) ion and its lowest-lying P-state without making use of the Born-Oppenheimer approximation, as was done in the case of H2(+) and D2(+) [Phys. Rev. A 58, 2787 (1998)]. The ion is treated as a three-body system whose ground state is spherically symmetric. The wavefunction is of generalized Hylleraas type, but it is necessary to include high powers of the internuclear distance to localize the nuclear motion. We obtain good values of the energies of the ground S-state and lowest P-state and compare them with 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 was then calculated using second-order perturbation theory with intermediate P pseudostates. Since the nuclei in HD(+) are not of equal mass there is dipole coupling between the lowest two rotational states, which are almost degenerate. This situation is carefully analyzed, and the Stark shift is calculated variationally as a function of the applied electric field.

Bhatia, A. K.↗