A dipole correlation function which incorporates velocity-changing (motional narrowing) effects and the
effects of speed-dependent Lorentz relaxation rates into otherwise Voigt profile correlation functions is developed,
based partly upon previous work by the author. For the first time simple closed expressions, which lend themselves
to elementary calculation beginning only with the relevant parts of intermolecular interaction energies, are
developed for the cubic time-dependent term within the exponent describing the decay of the correlation function.
This term is of first order in perturber number density, as are the Lorentz parameters, and is complex, thereby
allowing for narrowing, changing in shape and asymmetry in the line profile. &#8220;Soft&#8221; and &#8220;hard&#8221; collisions play no explicit role, though both are variously present for each line. Quartic time dependencies are also discussed,
though they are thought to be negligible in nonhydrogen molecular spectroscopy. Finally, some comments are
added about a relevant technique for hydrogen spectra.

Roger M. Herman

Unified Impact Theory for Velocity-Changing Effects and Speed Dependencies in Neutral Species Lineshapes

Simulations of Shapes and Shifts of Spectral Lines (SSSL) are important as the third powerful research methodology&#8212;in addition to theories and experiments. However, there is a growing tendency in physics in general and in the area of SSSL in particular, to consider the ultimate test of any theory to be the comparison with results of a code based on fully-numerical simulations starting from the &#8220;scratch&#8221; rather than from some analytical advance. In this paper, we show by examples that fully-numerical simulations are often not properly verified and validated, fail to capture emergent principles and phenomena, and lack the physical insight. Physics is the experimental science. So, the ultimate test of any theory&#8212;including theories of SSSL&#8212;should be the comparison with experiments conducted in well-controlled conditions (benchmark experiments).

Eugene Oks

Relation between Theories, Experiments, and Simulations of Spectral Line Shapes

The phenomenon of the acceleration of the (perturbing) electrons by the ion field (AEIF) significantly reduces Stark widths and shifts in plasmas of relatively high densities and/or relatively low temperature. Our previous analytical calculations of the AEIF were based on the <i>dynamical</i> treatment: the starting point was the ion-microfield-caused changes of the trajectories and velocities of individual perturbing electrons. In the current paper, we employ a <i>statistical</i> approach: the starting point is the electron velocity distribution function modified by the ion microfield. The latter had been calculated by Romanovsky and Ebeling in the multiparticle description of the ion microfield. The result shows again the reduction of the electron Stark broadening. Thus two totally different analytical approaches (dynamical and statistical) agree with each other and therefore disprove the corresponding recent fully-numerical simulations by Stambulchik et al. that claimed an increase of the electron Stark broadening.

New Statistical Multiparticle Approach to the Acceleration of Electrons by the Ion Field in Plasmas

The line profile of the <svg style="vertical-align:-4.25601pt;width:55.275002px;" id="M2" height="19.2125" version="1.1" viewBox="0 0 55.275002 19.2125" width="55.275002"  xmlns="http://www.w3.org/2000/svg">
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			</text>

			<text transform="matrix(1,0,0,-1,-58.07,66)">
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			</text>

			<text transform="matrix(1,0,0,-1,-53.57,60.93)">
				<tspan style="font-size: 12.50px; " x="0" y="0">−</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-45,65.93)">
				<tspan style="font-size: 8.75px; " x="0" y="0">5</tspan>
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			<text transform="matrix(1,0,0,-1,-40.13,60.93)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-32.7,57.8)">
				<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
			</text>

		</g>
	</g>
</svg> transition of atomic oxygen was measured by diode laser absorption spectroscopy. As a result, it was found that the absorption line profile had a wing component in the wavelength range detuned from the line center and was not fitted with a Gaussian function. The wing component was considered to be originated from dissociative excitation of
molecular oxygen. We fitted the absorption line profile with the superposition of two Gaussian
functions corresponding to high and low translational temperatures. We propose that the ratio of
the high-temperature to low-temperature components is useful for monitoring the relative degree of
dissociation of molecular oxygen in oxygen-containing plasmas. The ratio of the high-temperature
to low-temperature components was compared with the survival ratio of molecular oxygen, which
was evaluated from the lifetime of <svg style="vertical-align:-4.25601pt;width:44.799999px;" id="M3" height="19.4125" version="1.1" viewBox="0 0 44.799999 19.4125" width="44.799999"  xmlns="http://www.w3.org/2000/svg">
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			<text transform="matrix(1,0,0,-1,-71.95,60.76)">
				<tspan style="font-size: 12.50px; " x="0" y="0">O</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-62.92,60.76)">
				<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
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			<text transform="matrix(1,0,0,-1,-58.76,65.93)">
				<tspan style="font-size: 8.75px; " x="0" y="0">5</tspan>
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			<text transform="matrix(1,0,0,-1,-53.89,60.76)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑆</tspan>
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			<text transform="matrix(1,0,0,-1,-44.88,65.83)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
				<tspan style="font-size: 8.75px; " x="-0.88" y="9.3100004">2</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-40.38,60.76)">
				<tspan style="font-size: 12.50px; " x="0" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg> in the afterglow of pulsed discharges.

K. Sasaki

Y. Okumura

R. Asaoka

Absorption Line Profile of the <svg style="vertical-align:-3.27605pt" height="20.4125" version="1.1" viewBox="0 0 55.362499 20.4125" width="55.362499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.012,-0,0,-.012,.062,8.1)"><path id="x1D7D3" d="M148 676h322l-45 -127h-276l-22 -81q103 -6 151 -20q82 -23 127.5 -79.5t45.5 -134.5q0 -109 -79 -176q-78 -66 -203 -66q-64 0 -105.5 25.5t-41.5 62.5q0 26 17.5 43.5t43.5 17.5q47 0 100 -46q49 -42 90 -42q42 0 71 29.5t29 74.5q0 51 -36.5 90.5t-105.5 61.5&#xA;q-47 14 -180 22z" /></g><g transform="matrix(.017,-0,0,-.017,6.638,16.263)"><path id="x1D446" d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68&#xA;l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" /></g><g transform="matrix(.012,-0,0,-.012,14.8,8.1)"><path id="x1D45C" d="M445 282q0 -64 -27.5 -125t-80.5 -104q-80 -65 -168 -65q-73 0 -109.5 46.5t-36.5 116.5q0 92 46.5 163t119.5 104q66 30 108 30q67 0 107.5 -43.5t40.5 -122.5zM355 280q0 62 -26.5 94.5t-64.5 32.5q-26 0 -44 -8q-39 -18 -74 -82t-35 -163q0 -57 25.5 -90.5t70.5 -33.5&#xA;q22 0 36 6q46 20 79 89t33 155z" /></g><g transform="matrix(.012,-0,0,-.012,14.8,20.35)"><path id="x1D7D0" d="M453 211h25l-46 -211h-415v23q97 102 151 166q42 49 81 110q51 78 51 148q0 56 -31.5 91.5t-87.5 35.5q-77 0 -122 -90h-28q67 204 223 204q82 0 132 -49.5t50 -133.5q0 -110 -114 -218l-162 -154h140q82 0 107 13q27 13 46 65z" /></g><g transform="matrix(.017,-0,0,-.017,21.363,16.263)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.012,-0,0,-.012,31.35,8.1)"><use xlink:href="#x1D7D3"/></g><g transform="matrix(.017,-0,0,-.017,37.912,16.263)"><path id="x1D443" d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5&#xA;t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" /></g><g transform="matrix(.012,-0,0,-.012,48.725,20.35)"><path id="x1D7CF" d="M441 24v-24h-373v24q75 2 96 20q22 19 22 85v378q0 70 -36 70q-26 0 -65 -16l-20 -8v26l251 109h18v-570q0 -57 19 -75q19 -17 88 -19z" /></g></svg> Transition of Atomic Oxygen and Its Application to Plasma Monitoring

Measurements and analysis are reported of Stark-broadened profiles of the H-gamma line emitted from plasma formed by Laser-Induced Optical Breakdown (LIOB) in a pulsed methane flow. Electron densities <svg     style="vertical-align:-3.3907pt;width:20.525px;" id="M1" height="15.4" version="1.1" viewBox="0 0 20.525 15.4" width="20.525"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D441" d="M857 650l-6 -28q-44 -4 -61.5 -16.5t-29.5 -48.5q-11 -32 -37 -166l-78 -399h-29l-351 537h-4l-56 -276q-24 -120 -24 -164q0 -35 17.5 -46t75.5 -15l-6 -28h-245l7 28q41 2 62 14t31 44q10 30 41 171l53 245q8 44 6.5 60.5t-14.5 33.5q-10 15 -27 19.5t-64 6.5l6 28h153&#xA;l350 -516h5l48 257q25 131 25 171q0 34 -17.5 45t-77.5 15l7 28h240z" /></g>

			<g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><path id="x1D452" d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350&#xA;q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" /></g>

		
	
</svg> are deduced for 18 instants of time in the range between 0.4 and 2.1 microseconds after LIOB and for 2 different gas pressures. The obtained values of <svg     style="vertical-align:-3.3907pt;width:20.525px;" id="M2" height="15.4" version="1.1" viewBox="0 0 20.525 15.4" width="20.525"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D441"/></g>

			<g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><use xlink:href="#x1D452"/></g>

		
	
</svg> are in a good agreement with the corresponding values found previously from Stark-broadened profiles of the H-alpha and H-beta lines.

Christian G. Parigger

Laser-Induced Optical Breakdown in Methane: Diagnostic Using H-Gamma Line Broadening

Stark broadening of hydrogen lines is investigated in low-density magnetized plasmas, at typical conditions of magnetic fusion experiments. The role of time ordering is assessed numerically, by using a simulation code accounting for the evolution of the microscopic electric field generated by the charged particles moving at the vicinity of the atom. The Zeeman effect due to the magnetic field is also retained. Lyman lines with a low principal quantum number <svg style="vertical-align:-0.1638pt;width:8.6625004px;" id="M1" height="7.9499998" version="1.1" viewBox="0 0 8.6625004 7.9499998" width="8.6625004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45B" d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2&#xA;q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" /></g></svg> are first investigated, for an application to opacity calculations; next Balmer lines with successively low and high principal quantum numbers are considered for diagnostic purposes. It is shown that neglecting time ordering results in a dramatic underestimation of the Stark effect on the low-<svg style="vertical-align:-0.1638pt;width:8.6625004px;" id="M2" height="7.9499998" version="1.1" viewBox="0 0 8.6625004 7.9499998" width="8.6625004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45B" /></g></svg> lines. Another conclusion is that time ordering becomes negligible only when ion dynamics effects vanish, as shown in the case of high-<svg style="vertical-align:-0.1638pt;width:8.6625004px;" id="M3" height="7.9499998" version="1.1" viewBox="0 0 8.6625004 7.9499998" width="8.6625004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45B" /></g></svg> lines.

J. Rosato

D. Boland

M. Difallah

Y. Marandet

R. Stamm

Time Ordering Effects on Hydrogen Zeeman-Stark Line Profiles in Low-Density Magnetized Plasmas

In a recent paper (Lewis,  2008)  a class of models suitable for application to collision-sequence interference was introduced. In these models velocities are assumed to be completely
randomized in each collision. The distribution of velocities was assumed to be Gaussian. The
integrated induced dipole moment <svg style="vertical-align:-4.15506pt;width:16.1625px;" id="M1" height="12.9125" version="1.1" viewBox="0 0 16.1625 12.9125" width="16.1625" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D707" d="M538 96q-38 -45 -84 -76.5t-71 -31.5q-44 0 -15 117q12 49 18 89h-2q-99 -128 -163 -178q-36 -28 -70 -28q-26 0 -44 38h-2q-16 -69 -16 -129q0 -43 11 -75.5t24 -42.5l1 -6q-7 -12 -24.5 -23t-37.5 -11q-40 0 -40 76q0 52 35 202l94 407l78 24l5 -5q-32 -122 -72 -310&#xA;q-7 -33 0 -55t25 -22q36 0 105.5 75t107.5 145l32 146l75 26h10q-50 -197 -78 -347q-7 -38 6 -38q7 0 31 17t47 39z" /></g><g transform="matrix(.012,-0,0,-.012,9.5,12.713)"><path id="x1D458" d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1&#xA;l5 26q38 4 74 13.5t57 17t25 7.5q12 0 4 -32l-104 -443h2q35 38 97 93q39 35 65.5 56t62 41.5t58.5 20.5q19 0 30.5 -10t11.5 -22z" /></g></svg>, for vector interference, or the scalar modulation <svg style="vertical-align:-4.15506pt;width:16.1625px;" id="M2" height="12.9125" version="1.1" viewBox="0 0 16.1625 12.9125" width="16.1625" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D707" /></g><g transform="matrix(.012,-0,0,-.012,9.5,12.713)"><use xlink:href="#x1D458" /></g></svg>, for scalar
interference, was assumed to be a function of the impulse (integrated force) <svg style="vertical-align:-3.3907pt;width:12.3875px;" id="M3" height="16.0875" version="1.1" viewBox="0 0 12.3875 16.0875" width="12.3875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.813)"><path id="x1D41F" d="M14 417v44h57q0 132 40 179q42 51 135 51q64 0 103.5 -28t39.5 -72q0 -28 -17 -46t-45 -18q-25 0 -42.5 17t-17.5 40q0 12 5.5 25t11 22t5.5 10q0 19 -29 19q-27 0 -38.5 -17.5t-11.5 -61.5v-120h86v-44h-86v-310q0 -49 15 -66q14 -15 67 -17v-24h-278v24q34 4 45.5 16.5&#xA;t11.5 46.5v330h-57z" /></g><g transform="matrix(.012,-0,0,-.012,5.725,15.888)"><use xlink:href="#x1D458" /></g></svg>, or its magnitude
<svg style="vertical-align:-4.15506pt;width:17.65px;" id="M4" height="17.4" version="1.1" viewBox="0 0 17.65 17.4" width="17.65" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path id="x1D453" d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19&#xA;q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" /></g><g transform="matrix(.012,-0,0,-.012,10.975,17.2)"><use xlink:href="#x1D458" /></g></svg>, experienced by the molecule in a collision. For most of (Lewis,  2008) it was assumed that <svg style="vertical-align:-4.15506pt;width:51.9375px;" id="M5" height="17.049999" version="1.1" viewBox="0 0 51.9375 17.049999" width="51.9375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.813)"><use xlink:href="#x1D707" /></g><g transform="matrix(.012,-0,0,-.012,9.5,16.838)"><use xlink:href="#x1D458" /></g><g transform="matrix(.017,-0,0,-.017,20.825,11.813)"><path id="x221D" d="M774 30q-34 -42 -87 -42q-142 0 -215 159q-39 -81 -84.5 -120t-125.5 -39q-94 0 -151.5 66t-57.5 154q0 113 66.5 176.5t142.5 63.5q79 0 132.5 -41t94.5 -119q30 58 88 103q74 57 149 57q20 0 32 -13t12 -29q0 -25 -18 -41q-7 -5 -15 0q-18 9 -35 9q-70 0 -112.5 -32.5&#xA;t-75.5 -102.5q47 -96 93 -143.5t125 -47.5q19 0 37 10q4 -17 5 -28zM451 198q-19 48 -35 80t-40.5 67t-56 52.5t-69.5 17.5q-44 0 -74.5 -47t-30.5 -128q0 -96 35 -157.5t92 -61.5q107 0 179 177z" /></g><g transform="matrix(.017,-0,0,-.017,39.592,11.813)"><use xlink:href="#x1D41F" /></g><g transform="matrix(.012,-0,0,-.012,45.262,15.888)"><use xlink:href="#x1D458" /></g></svg> and <svg style="vertical-align:-4.15506pt;width:57.1875px;" id="M6" height="17.4" version="1.1" viewBox="0 0 57.1875 17.4" width="57.1875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D707" /></g><g transform="matrix(.012,-0,0,-.012,9.5,17.2)"><use xlink:href="#x1D458" /></g><g transform="matrix(.017,-0,0,-.017,20.825,12.162)"><use xlink:href="#x221D" /></g><g transform="matrix(.017,-0,0,-.017,39.592,12.162)"><use xlink:href="#x1D453" /></g><g transform="matrix(.012,-0,0,-.012,50.525,17.2)"><use xlink:href="#x1D458" /></g></svg>, but it proved to be possible to extend the models, so that the magnitude of the
induced dipole moment is equal to an arbitrary power or sum of powers of the intermolecular force. 
This allows estimates of the infilling of the interference dip by the disproportionality of the induced
dipole moment and force. One particular such model, using data from (Herman and Lewis,  2006), leads to the most realistic
estimate for the infilling of the vector interference dip yet obtained. 
In (Lewis,  2008) the drastic assumption was made that collision times occurred at equal intervals. In the
present paper that assumption is removed: the collision times are taken to form a Poisson process. 
This is much more realistic than the equal-intervals assumption. 
The interference dip is found to be a Lorentzian in this model.

John Courtenay Lewis

Elementary Statistical Models for Vector Collision-Sequence Interference Effects with Poisson-Distributed Collision Times

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International Journal of Spectroscopy - Table of contents 2010

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International Journal of Spectroscopy