Classical-Path Calculation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>Matrices for Stark Broadening of the Lyman-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>Line

Bacon, Michael; Shen, K. Y.; Cooper, J.

doi:10.1103/physrev.188.50

Cited by 29 publications

(5 citation statements)

References 15 publications

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“…There are essentially two such known NP approaches. The first one is an analytic solution under the approximation of neglecting time-ordering effects, while the second [23] is a fully numerical solution of the Schrödinger equation. To avoid ambiguities, we have chosen the second approach here.…”

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Problems with the Standard Semiclassical Impact Line-Broadening Theory

Alexiou¹

1995

Phys. Rev. Lett.

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In this work we study in detail the Ne VII 2s3p-2s3s singlet line, which was also the object of a recent experiment.The standard perturbative impact theory predictions are tested against a fully nonperturbative semiclassical impact calculation, taking into account dipole and quadrupole interactions. Potentially very significant problems with the standard perturbative theory are encountered and discussed, and a simple remedy is proposed. PACS numbers: 32.70.Jz, 32.30.Jc, 32.60.+i, 52.70.Kz The calculation of plasma-broadened line spectra provides a very useful diagnostic tool and additionally is a necessary ingredient for large-scale computations in astrophysics and plasma physics. A major cornerstone, reducing the many-body problem of line broadening to the computation of one-body quantities, is the impact approximation [1,2]. For practical calculations, the impact theory is usually employed in its perturbative version, and even then simplified formulas are often used. Isolated lines [2], by being relatively simple and usually unaffected by ion microfield effects, whether static or dynamic [3] are an excellent testing ground for the theories of electron collisional broadening. Such tests require reliable experimental profiles, and much progress has been made in this direction in recent years mainly by the Bochum group [4 -10]. These studies have revealed significant discrepancies with simplified expressions that are often used for the electron collisional broadening [2,11 -14]. Furthermore, serious discrepancies with close-coupling (CC) calculations [15] were found in [5]. Even more impressive is a recently obtained factor of 2 discrepancy between CC calculations [15] and experiment [10], for a line and parameter range where CC should be at its best. In both cases, much better agreement (roughly by a factor of 2) is obtained by semiclassical (SC) calculations. This means that SC calculations are in fact the best available today, in the sense of giving agreement with experiment. At the foundation of any sophisticated [3,16 -20] SC perturbative calculation is the requirement that unitarity is not violated. This is important, of course, since unitarity violation can lead to a serious overestimation of the width [17,21]. Unitarity is preserved for over 30 years by using a criterion, thought to be both necessary and sufhcient. This "fact" has gone unchallenged over this period of time. Hence, a minimum impact parameter p;"(v) is determined, such that unitarity is satisfied for larger impact parameters, by numerically solving the equation t'ai f~V~~((ri) dr) f '~d ry V~(~(rp) + +bi f~Vbbi(ri) dri f '~d t2 Vblb(tp) hw here f. J denotes an angular average, V' denotes the SC [1] emitter-perturber interaction in the interaction picture, a and b denote upper and lower level states, respectively, a' and b' denote a complete set of states that perturb a and b, respectively, and d is a number less than or equal to 1.The condition d = 1 is sufficient to preserve unitarity, but to keep the expansion parameter small, frequentl...

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confidence: 99%

Problems with the Standard Semiclassical Impact Line-Broadening Theory

Alexiou¹

1995

Phys. Rev. Lett.

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“…3 cision diagnostic tool for determination of chargedparticle densities in plasmas. Preliminary examinations of the several approximations which might significantly affect the central structure -neglect of time ordering, 8 The plasma-broadened R a and Hg spectral-line profiles of hydrogen were calculated retaining the time ordering in the S matrices of the width-shift operator by diagonalizing with the 0(4) group. Significant changes occur: The H a peak is decreased 15%, the halfwidth is increased 25%, and the H 0 relative dip is decreased 23% without significant alteration of the maximum intensity of half-width.…”

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confidence: 99%

“…Agreement with experiment is improved appreciably. While previous efforts to retain the time ordering relied upon the analytical or numerical solution of large sets of coupled differential equations, 8 " 11 one can automatically account for the time ordering by analytically diagonalizing the time development operator within an appropriate irreducible representation of 0(4), the internal symmetry group of the nonrelativistic hydrogen atom. 13 * 20 " 25 The subject of this Letter is the significant changes obtained for the plasma-broadened Balmer a and 0 profiles of hydrogen when time ordering is not neglected.…”

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Effects of Time Ordering on Plasma-Broadened Hydrogen Profiles

Roszman

1975

Phys. Rev. Lett.

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bound electrons equal in theory and experiment. The same practice is used for x-ray and y-ray Compton-profile normalization but not in the highenergy electron-impact method. For the other two theories the theoretical curves have been arbitrarily placed on the logarithmic scale in the best way to emphasize shape discrepancies 0The discrepancy between theory and experiment in the earlier (e, 2e) measurements 5 can be explained in part. Firstly, the theory used was slightly in error, since the sum over vibrational states was not carried out although these states were summed over in the experiment. Secondly^, there was a systematic error of 6% in the calibration of q.The small discrepancy between theory and experiment in the Compton-profile measurements gives rise to a more serious disagreement between the calculated and experimentally derived momentum distributions. This discrepancy could quite possibly be due to failure to satisfy binaryencounter conditions in the experiments. If this is indeed the case then, as in (e,2e), the measured Compton profiles will depend on the overlap of the initial target and final ion wave functions rather than the single-particle momentum densities. Of course at sufficiently high energy, closure over final states reduces the theory to dependence only on initial states.We would like to acknowledge very helpful conversations with Dr. R. A" Bonham, Dr c W. A.The plasma-(Stark-) broadened Balmer-line profiles of hydrogen measured during recent experiments 1 * 2 exhibit much less structure in their central regions than predicted by the most comprehensive theories. 3 " 7 This difference is quite serious since the plasma-broadened Balmer lines have found many applications as a convenient pre-The plasma-broadened R a and Hg spectral-line profiles of hydrogen were calculated retaining the time ordering in the S matrices of the width-shift operator by diagonalizing with the 0(4) group. Significant changes occur: The H a peak is decreased 15%, the halfwidth is increased 25%, and the H 0 relative dip is decreased 23% without significant alteration of the maximum intensity of half-width. Agreement with experiment is improved appreciably. 785

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“…The main aggravation is that the unitary transformation which diagonalizes the time development operator after the spherical average is no longer a simple rotation. In the impact limit this will affect primarily the constant B as noted above and cause only negligible asymmetries like in case of the time ordered solutions [21,22].…”

Section: Discussionmentioning

confidence: 96%

“…In the S-matrix hmit the effect of time ordering has been investigated within the classical path theory for Lya (Bacon, Shen, and J. Cooper [21]) and for Ha (Bacon [22]) by solving the complete set of coupled differential equations, which define all the matrix elements of the time development…”

Section: Discussionmentioning

confidence: 99%