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Gerjuoy, E.

Publications and source records attributed to Gerjuoy, E..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Useful extremum principle for the variational calculation of matrix elements. II

Recent work (Gerjuoy et al., 1974) on variational principles for diagonal bound state matrix elements of arbitrary Hermitian operators is extended. In particular, it is shown that the previously derived minimum principle for the trial auxiliary function appearing in such variational principles can be constructed using a modified Hamiltonian possessing not heretofore recognized positive definite properties. Thus there is at least one alternative to the particular modified Hamiltonian on which the results of Gerjuoy et al. (1974) originally were based.

Gerjuoy, E.↗
NASA NTRS1975

Langevin equation with stochastic damping - Possible application to critical binary fluid

We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.

Jasnow, D.↗
NASA NTRS1974

Cross section calculations of astrophysical interest

Cross sections are discussed for rotational excitation associated with theories of absorption and emission lines from molecules in space with emphasis on H2CO, CO, and OH by collisions with neutral particles such H, H2, and He. The sensitivity of the Thaddeus equation for the H2CO calculation is examined.

Gerjuoy, E.↗
NASA NTRS1974

Useful extremum principle for the variational calculation of matrix elements

Variational principles are considered for the approximate evaluation of the diagonal matrix elements of an arbitrary known linear Hermitian operator. A method is derived that is immediately applicable to the variational determination of both the off-diagonal and diagonal matrix elements of normal and modified Green's functions.

Gerjuoy, E.↗
NASA NTRS1974

Applications of the Glauber approximation to atomic collisions

Applications of the Glauber approximation to elastic and inelastic collisions of charged particles with neutral atoms are critically reviewed in an attempt to assess the utility of the Glauber approximation in the atomic collisions domain. Various alternative derivations of the Glauber amplitude formula, both for potential scattering and for composite collisions, also are described and compared. A number of possible problems for future research are listed.

Gerjuoy, E.↗
NASA NTRS1973

Detailed balance as a check on impact parameter calculations.

It is demonstrated numerically that detailed balance indeed is well satisfied in the multi-state impact parameter formulation of proton-hydrogen atom collisions. It is also demonstrated numerically that detailed balance is a much more sensitive test of computational accuracy than is the charge conservation test usually employed in such impact parameter calculations. It is suggested that detailed balance be used as a check on all impact parameter calculations. That even agreement with detailed balance may not be a sufficient test for accuracy of the results is pointed out.

Tai, H.↗
NASA NTRS1973

Properties of resonance wave functions.

Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities.

More, R. M.↗
NASA NTRS1972

Glauber calculations of polarization of Lyman-alpha resulting from e/-/-H/1s/ collisions.

We have calculated the polarization fraction of the Lyman-alpha radiation emitted in e/-/-H/1s/ collisions using the Glauber, Born, and various Vainshtein approximations, and have compared these predictions with observation. We find that the Born, Glauber and all forms of the Vainshtein yield results which are very close to each other and to the data in the energy range from 30 to 700 eV. The comparatively small differences between the various approximations are detailed in the text; also, the reason for the close agreement of the predicted polarization fractions - although the computed 1s-2p total and differential cross sections are not so close - is explained. With respect to the Glauber approximation, the importance of computing the phase integral along a direction perpendicular to the momentum transfer q at each value of q, is stressed.

Gerjuoy, E.↗
NASA NTRS1972

Use of the Glauber approximation in atomic collisions - A progress report.

Recent progress in the use of the Glauber (1970) theory for estimating atomic collision cross sections is reviewed. It appears that the Glauber approximation is reliable for electron-hydrogen elastic scattering and excitation at incident energies exceeding 30 eV. For more complicated atomic collisions, the usefulness of the Glauber approximation has not yet been significantly tested.

Gerjuoy, E.↗