Problems with the Standard Semiclassical Impact Line-Broadening Theory

Abstract

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...

Quantum-mechanical calculation of Stark widths of Ne VIIn=3, Δn=0transitions

“…The electron density and temperature were measured independently by laser Thomson scattering and turned out to be in the ranges N e = (3 − 3.5) · 10 18 cm −3 and T e = (19 − 20.5) eV. The measured line widths agree well with most semiclassical [1,5,9] or semiempirical [10] calculations but only marginally with other semiempirical results [11].…”

Electron collisional broadening of isolated lines from multiply-ionized atoms

“…In spite of these potentially serious problems, the nonperturbative semiclassical calculations 37,38 give widths, e.g., for the Ne VII 2s3s-2s3p singlet and triplet lines which agree within reasonable errors with gas-liner experiments, 38 whereas previous calculations yielded smaller widths by as much as a factor of 2. A similar discrepancy is found if comparison is made with a fully quantum-mechanical close-coupling (CC) calculation, 39 albeit only for the rather similar 3s-3p transition in Ne VIII.…”

“…The second improvement, 37 by the same author, was to replace the lowest order, dipole interactions, perturbation theory by a numerical solution of the time-dependent equations to all orders, and to include long-range quadrupole interactions. This nonperturbative approach no longer requires the unitarity check, but of course still a minimum impact parameter, etc., to avoid errors from breakdown of the semiclassical approximation and of the long-range approximation to the exact electron-ion Coulomb interactions.…”

Measurement of the Resonance Transition in C IV in a Gas-Liner Pinch Device

“…[1], [2]). Systematic discrepancies between experimental data and semi-classical calculations along isoelectronic sequences [3]- [6] indicate the importance of taking into consideration the contribution of strong collisions and terms of higher order [8], [9]. [3]- [6]).…”

“…Nevertheless, for ions of higher spectroscopic charge number (Z 6) inconsistencies between experiment and theory became recently apparent. Systematic discrepancies between experimental data and semi-classical calculations along isoelectronic sequences [3]- [6] indicate the importance of taking into consideration the contribution of strong collisions and terms of higher order [8], [9]. Recent measurements of the Stark width of the resonance transitions in B iii [10] encouraged new quantum mechanical calculations [11] since the experimental width is in disagreement with former quantum mechanical calculations [12] by a factor of two.…”