(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 94591, 2626]*) (*NotebookOutlinePosition[ 95572, 2659]*) (* CellTagsIndexPosition[ 95528, 2655]*) (*WindowFrame->Normal*) Notebook[{ Cell["H3+ + H2 cross sections", "Subtitle", Evaluatable->False, CellHorizontalScrolling->False, TextAlignment->Center], Cell["\<\ A. V. Phelps, JILA 8/19/01\ \>", "Subsubtitle"], Cell["\<\ We wish to assemble a set of H3+ + H2 cross sections that is consistent with \ as many experiments as possible. We especially wish to fit Peko and Champion \ (1997). There is a large spread in the high energy (> 1 keV) dissociation \ data of Federenko (1954), McClure (1963), and Williams and Dunbar (1966). \ Our cross sections for ionization, Balmer alpha excitation, and Lyman alpha \ excitation remain unchanged from those recommended in Phelps (1992). We also \ include data for momentum transfer from mobility measurements of Miller et al \ (1968). The total scattering of Simons et al (1943) is much smaller than \ theory as expected because of their large detector angle. Note that we are \ unable to reconcile the observations of fast H and H2 production by McClure \ and Williams and Dunbar with the claim by Volger and Meierjohhann (1978) that \ the production of 2 fast H + fast H+ (or 3 fast H) is negligible at 10 keV \ compared to the production of fast H + fast H2.\ \>", "Subsubtitle"], Cell["\<\ A surprising thing to me about the experimental data was that measurements of \ the angular distributions of the products for H3+ + D2 show that for energies \ above a few tenths of an eV the velocities of the high energy products CM are \ almost always in the forward direction and that significant large angle \ scattering in occurs only for energies well below 1 eV. This seems to mean \ that the reactions occur at large range such that the incident projectile is \ only slightly deflected. More specific angular distributions are cited for \ the individual cross sections.\ \>", "Subsubtitle"], Cell[TextData[{ "One cannot hope to obtain a really good set of H3+ + H2 cross sections \ until experiments (or theories) become available for state selected H3+ \ projectiles. Published experiments show up to 50% changes in cross sections \ as the conditions are changed in the gas discharge sources of H3+. The \ changes are attributed to changes in the degree of vibrational relaxation of \ the H3+ following its initial production in an excited state from H2+ + H2 \ collisions. Generally, the H3+ + H2 cross sections are larger for conditions \ expected to yield greater populations of vibrationally excited H3+, but the \ data is extremely qualitative. A similar problem appears to arise from \ rotational excitation in electron-H3+ recombination experiments.", StyleBox["Here we have attempted to assemble cross sections appropriate to \ H3+ ions that are thermally relaxed, e.g., the ~1.5 eV of internal energy \ resulting from the H2+ H2 -> H3+* + H reaction has been dissipated in \ collisions with ambient temperature H2. It would be very desirable to \ assemble cross sections for collisions of H3+ with known degrees of internal \ energy with H2 of known internal energy, but there is little hope of doing so \ in the foreseeable future.", FontSize->13.5] }], "Subsubtitle"], Cell["\<\ One may wonder why a review of this topic is needed so soon after publication \ of the review of cross sections for collisions of hydrogenic species by \ Tabata and Shirai, Atomic Data and Nuclear Data Tables 76, 1 (2000). We \ undertook this compilation in order to provide a) cross sections with \ threshold behaviors consistent with the proposed processes, b) a set of cross \ sections that are consistent with the fact that Peko and Champion (1997) made \ only five independent measurements (not eight), and c) a cross section set \ consistent with the expected low energy behavior as modeled by Simko et al \ (1997).\ \>", "Subsubtitle", FontSize->16], Cell["\<\ We take a lead from Simko et al, Phys. Rev E 56, 5908 (1997) and consider the \ cross sections below the dissociation threshold at 4.4 eV to be made up of \ two components. a) The low energy component, which Simko et al call elastic scattering, \ results in elastic scattering and/or rotational excitation. Based on the \ differential scattering experiments of Vestal et al (1976) one is tempted to \ assume that this process results in elastic isotropic scattering in CM with \ the Langevin cross section. Another possibility is to ignore Vestal et al \ and assume that proton transfer dominates, results in rotational excitation, \ and causes 180 deg scattering in CM. A reason for doing this is the low \ mobility of H3+ in H2 at low E/N compared to Langevin. Probably a mixture of \ processes is best. b) The higher energy component, which Simko et al label as proton transfer \ scattering, is patched on to the proton transfer data of Peko and Champion at \ ~ 3 eV. In a modification of the model of Simko et al, we propose that all \ of this proton transfer results in vibrational excitation. It has a an \ absolute threshold equal to the energy of the lowest vibrational mode of H3+, \ e.g., deltaE = 0.31 eV. If the proton transfer model of the collision is \ valid, the actual threshold will be 9/5*deltaE = 0.56 eV. This process \ differs from the usual vibrational excitation collision in that the collision \ results in 180 deg scattering in CM.\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Setup notebook environment ", "SmallText", PageWidth->Infinity], Cell[BoxData[ \(\(a = 1;\)\)], "Input"], Cell["ClearAll[\"Global`*\"]; ", "Input"], Cell["Remove[\"Global`*\"]; ", "Input"], Cell["startclock = SessionTime[];", "Input", PageWidth->Infinity], Cell["Off[General::spell];", "Input", PageWidth->Infinity], Cell["Off[General::spell1];", "Input", PageWidth->Infinity], Cell["Needs[\"Graphics`Graphics`\"]", "Input", PageWidth->Infinity, FontFamily->"Times New Roman", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(Needs["\"]\)], "Input"] }, Closed]], Cell[BoxData[ \(SetDirectory["\"]\)], "Input"], Cell["\<\ Note: Double click on the arrows to open the various sections.\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["\<\ Procedure for importing, digitizing and exporting a graph read by the HP \ scanner.\ \>", "Subsubsection", Evaluatable->False], Cell["\<\ One way to scan and import the image to be analyzed is to: 1) enlarge image as much as possible with copier if it can be done without \ distortion 2) use the HP Deskscan II to Preview the image 3) select the portion of the image to be analyzed 4) use Final to make a *.bmp file of the image 5) start the desired Mathematica notebook 6) in Mathematica use Import[*.bmp] to place the image in the notebook. 7) use Show to display the image\ \>", "SmallText", Evaluatable->False], Cell["\<\ To read the points from the graph 1) enlarge the graph as much as possible while keeping all of image on \ screen. 2) click on the figure to get the frame. This activates the cursor for the \ nest step. 3) holding ^cntrl down, move mouse pointer to first point and control-click \ on the desired data point. If one then moves to the desired points in succession keeping ^cntrl down, \ the final list will be in the correct list format. 4) with ^cntrl still down, select Copy from the Edit menu 5) select the text insertion point and click on Paste from the Edit menu 6) note that it seems to work better if one uses only two points for the \ xscale and two for the yscale 7) after reading points, reduce the size of the image and make the Import and \ Show cells not evaluated to avoid reimporting and/or losing the image later.\ \>", "SmallText", Evaluatable->False, FontFamily->"Arial", FontSize->10, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->GrayLevel[0], Background->GrayLevel[1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Cross section for scattering by polarization potential for reference only.\ \>", "Section"], Cell["\<\ These cross sections for scattering by a polarization potential are not part \ of our recommended set and are shown for reference only.\ \>", "Text", FontColor->RGBColor[1, 0, 0]], Cell[BoxData[{ \(\(mramu\ = \ 3*2/\((3 + 2)\);\)\ \), "\[IndentingNewLine]", \(\(mr\ = \ mramu\ *\ 1.661*10^\(-27\);\)\), "\[IndentingNewLine]", \(\(qe\ = \ 1.602*10^\(-19\);\)\ \), "\[IndentingNewLine]", \(\(ng\ = \ 2.69*10^25;\)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*m^\(-3\)*) \ \), "\[IndentingNewLine]", \(\(alphaMcDaniel\ = \ 0.808\ *\ 10^\(-30\);\)\ \ \ \ \ \ \ \ \ (*m^3\ from\ McDaniel\ \((1993)\)*) \ \), "\[IndentingNewLine]", \(\(ao\ = \ 0.529*10^\(-10\);\)\ \ \ \ \ \ \ (*m*) \), "\[IndentingNewLine]", \(\(me\ = \ 9.11*10^\(-31\);\)\ (*kgm*) \), "\[IndentingNewLine]", \(\(ry\ = \ 27.211/2;\)\ \ (*eV*) \)}], "Input"], Cell[BoxData[ \(alphaau\ = \ alphaMcDaniel/ao^3\)], "Input"], Cell["Langevin cross section", "Subsubsection"], Cell[BoxData[ \(langevinQ\ = \ 2*Pi*ao^2*\((13.6/enrel*alphaau)\)^0.5\)], "Input"], Cell[BoxData[ \(kLLieberman\ = \ 8.99*10^\(-16\)*\(\((alphaau/mramu)\)\(^\)\(0.5\)\(\ \)\)\)], "Input"], Cell["Total cross section", "Subsubsection"], Cell["For a polarization potential ", "SmallText"], Cell[BoxData[ \(\(n\ = \ 4;\)\)], "Input"], Cell["The Landau-Lifshitz formula for gammaLL is ", "SmallText"], Cell[BoxData[ \(\(fn\ = \ Pi/4;\)\)], "Input"], Cell[BoxData[ \(\(\(gammaLL\)\(\ \)\(=\)\(\ \)\(N[ Pi^2*\((2 fn)\)^\((2/\((n - 1)\))\)* Csc[Pi/\((n - 1)\)]/Gamma[2/\((n - 1)\)]]\)\(\ \)\)\)], "Input"], Cell["\<\ Note that this formula is different than that given in Massey, Burhop, and \ Gilbody (1971) or in McDaniel, Mitchell, and Rudd (1993), but gives numbers \ in exact agreement with Massey et al Table 16.2.\ \>", "SmallText"], Cell[BoxData[ \(qtotal\ = \ gammaLL*ao^2* alphaau^\((2/3)\)*\((\(mr/me\)/4*ry/enrel)\)^\((1/3)\)\ \ // PowerExpand\)], "Input"], Cell[BoxData[ \(\(langevinQPlot\ = \ LogLogPlot[{Evaluate[10^20*langevinQ], Evaluate[10^20*qtotal]}, {enrel, 0.005, 10000}, \ \[IndentingNewLine]PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}}, ImageSize\ -> \ 432, \ PlotStyle\ -> \ {{Hue[1], \ Thickness[0.007]}, {Hue[1], Dashing[{0.05, 0.05}], \ Thickness[0.007]}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell["\<\ Here the Langevin is solid red, while the total cross section is dashed red. \ Again, These are not part of our recommended set of cross sections.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> ", StyleBox["fast H+", FontColor->RGBColor[1, 0, 0]], " + ", StyleBox["fast H2 ", FontColor->RGBColor[0, 1, 0]], "+ slow H2 by CID of H3+ ", StyleBox["meas. by P&C, McClure, Williams&Dunbar", FontColor->RGBColor[1, 0, 0]] }], "Section", Evaluatable->False], Cell["\<\ This cross section at relative energies from 3 to 115 eV is that obtained by \ a Peko and Champion (1997) using a retarding analysis of the ions produced in \ a H3+ + H2 collision. According to the collision induced dissociation (CID) \ model of P&C, the fast H+ are produced with an axial energy of approximately \ 1/3 of the energy of the incident ion. This argument seems to require that \ there is little scattering in angle. We force our fit to pass though the \ fast H+ results of Williams and Dunbar (1966) rather than those of McClure \ (1963) in order to keep down the total destruction of H3+. Another \ possibility would be to make this cross section to pass through McClure's \ much larger cross section for fast H2 production. We ignore the fast H+ \ results of Lange et al (1977) as being much too small to be consistent with \ those of Peko et al (1997). Prokof'ev et al (1978) agree with Peko and \ Champion for D3+ + H2 at 3 to 40 eV. The threshold for this reaction is 4.4 \ eV.\ \>", "Text"], Cell["\<\ This collision process is most easily visualized as a two step process, i.e., \ the excitation of the H3+ and then its dissociation. The collision process \ appears to be one in which the H3+ projectile and thermal H2 target are not \ significantly deflected during excitation of the H3+. The H3+ losses kinetic \ energy because of its excitation to a dissociating state, e.g., roughly 10 \ eV. Then the H+ and H2 fragments probably fly apart more or less \ isotropically with a few eV energy. The kinetics model should show that the \ final laboratory energy of the fast H+ is roughly 1/3 of the laboratory \ energy of the incident H3+. Similarly, the final laboratory energy of the \ fast H2 is approximately 2/3 of the laboratory energy of the incident H3+.\ \>", "Text"], Cell["\<\ Cross section from Peko and Champion (1997), Fig.2(a) reaction (1)\ \>", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Import["\"];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(Show[%];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(Quit[]\)], "Input", Evaluatable->False] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Record of desired data points and representative points for both axes.\ \>", "Subsubsection", Evaluatable->False], Cell["The cross section curve gives", "SmallText", Evaluatable->False], Cell["\<\ qtdata ={{338.954, 775.861}, {431.823, 800.778}, {488.451, 1006.9}, {533.754, 1072.59}, {569.996, 1136.02}, {599.442, 1111.1}, {624.358, 1136.02}, {644.744, 1111.1}, {674.191, 1097.51}, {744.41, 1045.41}, {794.242, 916.299}, {832.749, 968.396}, {862.196, 954.806}, {912.028, 929.889}};\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscaledata ={{144.153, 698.847}, {948.27, 696.582}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscalegraph = Log[10,{2.,200.}];", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscaledata ={{141.888, 698.847}, {146.419, 1217.56}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscalegraph = {0.0,2.0};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Subroutine for analyzing digitized data and its application to Peko and \ Champion data\ \>", "Subsubsection"], Cell[BoxData[ \(analyzeDigitizedData := Block[{xscaledata1, xscaledata2, xfit, yscaledata1, yscaledata2, yfit, data1, xdata, xdatagraph, ydata, ydatagraph, xdataout, ydataout}, xscaledata1 = Flatten[Take[Transpose[xscaledata], 1]]; \[IndentingNewLine]xscaledata2 = Transpose[{xscaledata1, xscalegraph}]; \[IndentingNewLine]xfit = Fit[xscaledata2, {1, x}, x]; \[IndentingNewLine]yscaledata1 = Flatten[Take[ Transpose[ yscaledata], \(-1\)]]; \[IndentingNewLine]yscaledata2 = Transpose[{yscaledata1, yscalegraph}]; \[IndentingNewLine]yfit = Fit[yscaledata2, {1, y}, y]; \[IndentingNewLine]data1 = Transpose[qtdata]; \[IndentingNewLine]xdata = Take[data1, 1]; \[IndentingNewLine]xdatagraph = Flatten[\((xfit /. x \[Rule] xdata)\)]; \[IndentingNewLine]ydata = Take[data1, \(-1\)]; \[IndentingNewLine]ydatagraph = Flatten[\((yfit /. y \[Rule] ydata)\)]; \[IndentingNewLine]xdataout = Power[10, xdatagraph]; \[IndentingNewLine]ydataout = ydatagraph; \[IndentingNewLine]dataout = Transpose[{xdataout, ydataout}];]\)], "Input"], Cell[BoxData[ \(analyzeDigitizedData\)], "Input"], Cell[BoxData[ \(\(LogLinearListPlot[dataout, PlotRange \[Rule] {{2. , 200. }, {0.0, 2.0}}, PlotStyle \[Rule] PointSize[0.02], PlotLabel \[Rule] {"\"}, \ ImageSize\ -> \ 432, DisplayFunction \[Rule] Identity];\)\)], "Input"] }, Closed]], Cell["\<\ data1Plot = LogLogListPlot[dataout, PlotRange -> \ {{0.02,10000},{0.01,200.0}}, PlotStyle->PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Data from Fig. 10 of McClure (1963) for fast H+ production as read in 1985\ \>", "Subsection"], Cell[BoxData[ \(\(mcClureDatafHp\ = \ {{2000. , \ 0.44}, {2800. , 0.64}, {4000. , 0.92}, {6000. , 1.25}, {8000. , 1.45}, {12000. , \ 1.75}, {20000. , 2. }, {28000. , 3.1}, {40000. , 3.1}};\)\)], "Input"], Cell["\<\ mcClurefHpPlot = LogLogListPlot[mcClureDatafHp, PlotRange -> \ {{0.02,100000},{0.01,200.0}}, PlotStyle->{Hue[0.5],PointSize[0.02]},ImageSize -> 432,DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Data from higher source pressure points of Fig. 8 of Williams and Dunbar \ (1966) for fast H+ production\ \>", "Subsection"], Cell[BoxData[ \(\(williamsfHp\ = {{2000. , \ 0.11}, {3000. , 0.165}, {5000. , 0.28}, {7000. , 0.4}, {10000. , 0.55}, {14000. , \ 0.8}, {20000. , 1.15}, {25000. , 1.3}};\)\)], "Input"], Cell["Scale to CM energy", "Text"], Cell[BoxData[ \(\(williamsfHp1\ = \ Table[{williamsfHp[\([j, 1]\)]*2/5, williamsfHp[\([j, 2]\)]}, {j, 1, Length[williamsfHp]}];\)\)], "Input"], Cell["\<\ williamsfHpPlot = LogLogListPlot[williamsfHp1, PlotRange -> \ {{0.02,100000},{0.01,200.0}}, PlotStyle-> {Hue[0.8], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["Fit to data and compare", "Subsection"], Cell["Fit to McClure at high energies", "Text"], Cell[BoxData[ \(\(fastHpFit\ = \ UnitStep[ enrel - 4.4]*\(11/ Sqrt[enrel]\)/\((1 + \((12/\((enrel - 4.4)\))\)^2)\)*\((1 + \((enrel/ 1870)\)^3.0)\)/\((1 + \((enrel/4000)\)^2.5)\) + 1. *10^\(-30\);\)\)], "Input", Evaluatable->False], Cell["Fit to Williams at high energies", "Text"], Cell[BoxData[ \(\(fastHpFit\ = \ UnitStep[ enrel - 4.4]*\(\(11/ Sqrt[enrel]\)/\((1 + \((12/\((enrel - 4.4)\))\)^2)\)\)/\((1 + \((enrel/ 300)\)^3)\)*\((1 + \((enrel/ 550)\)^4.5)\)/\((1 + \((enrel/20000)\)^2.5)\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ StyleBox[\(Note\ that\ the\ 1. *10^\(-30\)\ in\ this\ and\ later\ cross\ \ sections\ is\ added\ to\ prevent\ problems\ with\ Log \((0)\)\ when\ making\ \ Log\ plots . \ \ It\ has\ no\ physical\ \(\(significance\)\(.\)\)\), FormatType->StandardForm, FontFamily->"Courier New", FontSize->13.5, FontColor->RGBColor[0.996109, 0, 0]]], "Input", Evaluatable->False], Cell[BoxData[ \(\(fastHpPlot\ = LogLogPlot[fastHpFit, {enrel, 0.01, 10000}, PlotStyle\ -> {\ Hue[0.1], \ Thickness[0.007]}, PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}}, PlotPoints\ -> \ 500, \ DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[data1Plot, mcClurefHpPlot, fastHpPlot, williamsfHpPlot, \ langevinQPlot, PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"] }, Open ]], Cell["Estimate of angular momentum quantum number, etc.", "Subsubsection"], Cell["\<\ In order to get some feel for the probability that the the protontransfer \ collision will succed in exciting rotational levels of the product H3+ Leone \ suggested that I estimate the angular momentum quantum number and spacing of \ the rotational levels for H3+. The lower rotational energy levels are shown \ in Fig. 2 of McCall, Phil. Trans. Roy. Soc. Lond. 358, 2385 (2000). The \ lowest levels, J = 1 -> J=2, are separated by roughly 80 cm^-1 = 0.01 eV. We \ estimate the internuclear separation from the collsion cross section ra = \ Sqrt[Q/Pi] ~ Sqrt[1E-20/Pi] ~ 5e-11 m ~ 1 au. The angular momentum of a \ collision at maximum radius is mr*vrel/ra and must equal J*hbar. At 1 eV\ \>", "Text"], Cell[BoxData[ \(\(enrel1\ = \ 1. ;\)\)], "Input"], Cell[BoxData[ \(Sqrt[2*qe*enrel1/mr]\)], "Input"], Cell[BoxData[ \(j\ = \ mr*vrel*ra/hbar\ /. \ {vrel\ -> \ Sqrt[2*qe*enrel1/mr], ra\ -> \ ao, \ hbar\ -> \ 1.054*10^\(-34\)}\)], "Input"], Cell["The rigid rotator energy levels for this j are at", "Text"], Cell[BoxData[ \(levelEnergy\ = \ j \((j + 1)\)*0.08/4\)], "Input"], Cell["\<\ This energy is large compared to the energy that proton transfer theory says \ is transferred, i.e., 4/9 = 0.44 eV. The energy level spacing is \ \>", "Text"], Cell[BoxData[ \(rotEnergyChange = \ \((2 j + 2)\)*0.08/4\)], "Input"], Cell["\<\ This energy is comparable with the energy that proton transfer theory says is \ transferred,i.e.,4/9=0.44 eV, but the lower level needs to be occupied for a \ transition to take place.\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> ", StyleBox["fast H2+", FontColor->RGBColor[1, 0, 0]], " +", StyleBox[" fast H", FontColor->RGBColor[0, 0, 1]], " + slow H2 by CID of H3+ ", StyleBox["meas. by McClure & by Williams", FontColor->RGBColor[0, 0, 1]] }], "Section", Evaluatable->False], Cell["\<\ This cross section is that obtained by a Peko et al (1997) using a retarding \ analysis of the ions produced in a H3+ + H2 collision and represents the \ middle energy group, i.e., those ions with an axial energy of approximately \ 2/3 of the energy of the incident ion. This argument seems to assume that \ there is little scattering in angle. We force our fit to pass though the \ fast H2+ results of McClure (1963). An alternative would be to make our \ cross section to pass through McClure's very large cross section for fast H \ production, as would be appropriate if McClure missed some of the fast H2+. \ We ignore the fast H2+ results of Lange et al (1977) as being much too small \ to be consistent with those of Peko et al (1997).\ \>", "Text"], Cell["\<\ It may help to think of this as a two step process. The first step is an \ excitation process in which the H3+ projectile and thermal H2 target are not \ significantly deflected. During excitation of the H3+ to a dissociating \ state, the H3+ losses roughly 10 eV. In the second step, the H+ and H2 \ fragments fly apart more or less isotropically with a few eV energy. The \ kinetics model should show that the axial component of the final laboratory \ energy of the fast H2+ is approximately 2/3 of the laboratory energy of the \ incident H3+. Similarly, the final laboratory energy of the fast H is roughly \ 1/3 of the laboratory energy of the incident H3+.\ \>", "Text"], Cell["Cross section from Peko et al (1997), Fig.2a reaction (2)", "Subsection"], Cell[CellGroupData[{ Cell["Digitize Peko and Champion.", "Subsubsection", Evaluatable->False], Cell["The cross section curve gives", "SmallText", Evaluatable->False], Cell["\<\ qtdata ={{483.921, 984.252}, {513.368, 941.215}, {538.284, 877.792}, {558.67, 875.527}, {565.465, 850.61}, {590.382, 812.103}, {597.177, 798.513}, {622.093, 773.596}, {644.744, 773.596}, {660.6, 798.513}, {671.926, 771.331}, {710.433, 787.187}, {742.144, 787.187}, {748.94, 775.861}, {782.917, 775.861}, {791.977, 771.331}, {832.749, 798.513}, {830.484, 787.187}, {864.461, 784.922}, {912.028, 773.596}};\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscaledata ={{141.888, 698.847}, {948.27, 698.847}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscalegraph = Log[10,{2.,200.}];", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscaledata ={{144.153, 698.847}, {146.419, 1217.56}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscalegraph = {0.0,2.0};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(analyzeDigitizedData\)], "Input"], Cell["\<\ LogLinearListPlot[dataout, PlotRange -> {{2.,200.},{0.0,2.0}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, \ ImageSize -> 432, DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Closed]], Cell["\<\ pekofH2pPlot = LogLogListPlot[dataout, PlotRange -> \ {{0.01,10000},{0.01,200.0}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, PlotStyle->PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Data from McClure (1963) for fast H2+ production as read in 1985\ \>", "Subsubsection"], Cell[BoxData[ \(\(mcClureDatafH2p\ = \ {{2000. , \ 0.69}, {2800. , 0.85}, {4000. , 0.97}, {6000. , 1.10}, {8000. , 1.20}, {12000. , \ 1.23}, {20000. , 1.18}, {28000. , 1.09}, {40000. , 0.93}};\)\)], "Input"], Cell["\<\ mcClurefH2pPlot = LogLogListPlot[mcClureDatafH2p, PlotRange -> \ {{0.02,100000},{0.01,200.0}}, PlotStyle->{Hue[0.7],PointSize[0.02]},ImageSize -> 432 ,DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Data from higher source pressure points of Fig. 8 of Williams and Dunbar \ (1966) for fast H2+ production\ \>", "Subsubsection"], Cell[BoxData[ \(\(williamsfH2p\ = {{2000. , \ 0.2}, {3000. , 0.28}, {5000. , 0.45}, {7000. , 0.6}, {10000. , 0.83}, {14000. , \ 1.05}, {20000. , 1.3}, {25000. , 1.35}};\)\)], "Input"], Cell["Scale to CM energy", "Text"], Cell[BoxData[ \(\(williamsfH2p1\ = \ Table[{williamsfH2p[\([j, 1]\)]*2/5, williamsfH2p[\([j, 2]\)]}, {j, 1, Length[williamsfH2p]}];\)\)], "Input"], Cell["\<\ williamsfH2pPlot = LogLogListPlot[williamsfH2p1, PlotRange -> \ {{0.02,100000},{0.01,200.0}}, PlotStyle-> {Hue[0.8], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["Fit and compare ", "Subsubsection"], Cell["Fit to McClure", "Text"], Cell[BoxData[ \(\(fastH2pFit\ = \ 1.3*UnitStep[ enrel - 6.2]*\(enrel^0.6/\((1 + \((25/\((enrel - 6.2)\)^1.1)\))\)\)/\((1 + \((enrel/ 16)\)^6)\)^1.0*\(\((1 + \((enrel/ 27)\)^6)\)^0.9/\((1 + \((enrel/ 500)\)^2)\)^0.4\)/\((1 + \((enrel/70000)\))\) + 1. *10^\(-30\);\)\)], "Input"], Cell["Fit to Williams and Dunbar", "Text"], Cell[BoxData[ \(\(fastH2pFit\ = \ 1.3*UnitStep[ enrel - 6.2]*\(enrel^0.6/\((1 + \((25/\((enrel - 6.2)\)^1.1)\))\)\)/\((1 + \((enrel/ 15)\)^5.5)\)^1.0*\((1 + \((enrel/ 27)\)^5.5)\)^0.9/\((1 + \((enrel/ 210)\)^4.5)\)^0.4*\((1 + \((enrel/ 480)\)^2.8)\)/\((1 + \((enrel/12000)\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(fastH2pPlot\ = \ LogLogPlot[fastH2pFit, {enrel, 2.5, 10000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.3], \ Thickness[0.007], Dashing[{0.05, 0.05}]}, \ PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[pekofH2pPlot, mcClurefH2pPlot, \ fastH2pPlot, williamsfH2pPlot, \ langevinQPlot, PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> ", StyleBox["sum of slow ions", FontColor->RGBColor[1, 0, 0]], " = INC = slow H3+* + slow H+ + slow H2+" }], "Section", Evaluatable->False], Cell[TextData[{ "This cross section is that obtained by a Peko and Champion (1997) using a \ retarding analysis of the ions produced in a H3+ + H2 collision and \ represents the slowest group, i.e., those ions with an axial energy of much \ less than that of the incident ion. This interpretation seems to make no \ specific assumption as to the scattering in angle. In the next three \ sections we discuss how P&C divide this component into three reactions based \ on a c", StyleBox["rossed beam experiment that collects only slow ions and analyzes \ them by mass into H3+, H2+, and H+. P&C claim that the \"spectator\" model \ of proton transfer leads to conversion of up to 5/9 of the CM energy (2/9 of \ the LAB energy for a cold target H2) into internal energy of the H3+. This \ could be an efficient means of vibrational excitation (and dexcitation) of \ the H3+ and is observed by P&C to lead to dissociation at CM collision \ energies above about 6 eV.", CellOpen->False] }], "Text"], Cell["\<\ Measurements of the differential cross sections for H3+ + D2 -> D2H+* + H2 by \ Vestal et al (1976) show that this proton transfer process produces D2H+* \ with velocities near 180 deg in CM, but with kinetic energies somewhat higher \ than predicted by the spectator stripping model. The higher than expected \ energy of the product ion is attributed to initial internal energy of the \ projectile H3+. The \"spectator stripping\" model is described, for \ example, in Sec. 1.4 of Levine and Bernstein, \"Molecular Reaction Dynamics\" \ (Oxford Univ. Press, Oxford, 1974). See Peko and Champion (1997) for a \ statement as to its significance for H3+ + H2. A model of the internal energy distribution for the H3+ produced in the H2+ + \ H2 relaxation is discussed by Anicich and Futrell, Int. J. Mass. Spectrom. \ and Ion Processes 55, 189 (1983). They find approximate agreement with a \ statistical distribution of H3+ in the excited states. These considerations \ could serve as a guide to the internal energy distribution in the H3+ \ produced in the reaction of fast H3+ with H2. These authors also consider the \ relaxation of this energy in collisions with H2 and seem to assume 60% of the \ maximum rate (Langevin?) for the lowest excited state. I do not uderstand! \ The most recent reference on H2= + H2 that I have found is Pollard et al, J. \ Chem. Phys. 95, 4877 (1991). The most interesting new result appears to be \ that much of the translational energy ends up as rotational energy of the \ H3+, whereas most of the reaction energy is found in vibration. The recoil \ energy is ~ 30% of the available energy.\ \>", "Text"], Cell["\<\ Angular distributions, etc. will be discussed wth the individual processes.\ \>", "Text"], Cell["\<\ Total proton transfer cross section from Peko et al (1997), Fig.2b reacrions \ (3), (4a), and (4b)\ \>", "Subsection"], Cell[CellGroupData[{ Cell["\<\ Record of desired data points and representative points for both axes.\ \>", "Subsubsection", Evaluatable->False], Cell[BoxData[ \(\(Import["\"];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(Show[%];\)\)], "Input", Evaluatable->False], Cell["The cross section curve Q gives", "SmallText", Evaluatable->False], Cell["\<\ qtdata ={{236.308, 585.552}, {275.794, 567.605}, {308.1, 520.94}, {333.227, 443.764}, {338.611, 404.279}, {358.354, 379.152}, {378.096, 354.025}, {390.66, 337.872}, {406.813, 318.129}, {424.761, 296.592}, {433.735, 285.823}, {464.246, 260.696}, {518.09, 223.006}, {552.191, 210.442}, {571.933, 206.853}, {604.239, 203.263}, {631.161, 201.468}, {647.314, 201.468}, {670.647, 203.263}, {744.233, 210.442}, {796.282, 215.827}, {837.562, 223.006}, {869.868, 230.185}};\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscaledata ={{141.185, 149.419}, {947.044, 149.419}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscalegraph = Log[10,{2.,200.}];", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscaledata ={{142.979, 149.419}, {144.774, 594.526}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscalegraph = {0.0,5.0};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(analyzeDigitizedData\)], "Input"], Cell["\<\ data3Plot1 =LogLinearListPlot[dataout, PlotStyle -> PointSize[0.02], PlotRange -> {{2.,200.},{0.0,6.0}},PlotLabel -> {\"Cross section (10^-20 m^2) \ versus relative energy (eV)\"}, DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(Show[data3Plot1, PlotLabel\ -> \ {"\"}, ImageSize \[Rule] 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"] }, Closed]], Cell["Note that this data is plotted versus CM energy.", "Text"], Cell["\<\ dataPTPlot2 = LogLogListPlot[dataout, PlotRange -> \ {{0.01,10000},{0.01,200.0}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, PlotStyle->PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(fitPT\ = \ \(9.5/ enrel^0.5\)/\((1 + \((enrel/7)\)^4)\)^0.35*\((1 + \((enrel/ 21.5)\)^4)\)^0.58/\((1 + \((enrel/400)\)^2)\)^0.5 + 1. *10^\(-30\);\)\)], "Input"], Cell[BoxData[ \(\(fitPTPlot\ = \ LogLogPlot[fitPT, {enrel, 0.01, 10000}, PlotPoints\ -> \ 1000, \ PlotRange\ -> \ {{0.01, 1000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[dataPTPlot2, fitPTPlot, langevinQPlot, PlotLabel\ -> \ "\", ImageSize \[Rule] 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell["\<\ The portion of this cross section at energies above ~200 eV is adjusted to \ give the production of fast H2 as observed by McClure (1963). See plot \ below. This fitting seems inconsistent with my fitting of Williams and Dunbar \ (1966), rather than McClure, for fast H+ and fast H2+, but McClure is our \ only source of fast H2 data.\ \>", "Subsubtitle"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> ", StyleBox["slow, bound H3+*", FontColor->RGBColor[1, 0, 0]], " + ", StyleBox["fast H2", FontColor->RGBColor[0, 1, 0]], " = vibrational excitation of slow H3+ by proton transfer (3) " }], "Section", Evaluatable->False], Cell[TextData[{ "This cross section is that obtained by a Peko and Chanpion (1997) (P&C) \ based on a c", StyleBox["rossed beam experiment that collects only slow ions and analyzes \ them by mass into H3+. The results are presented as a fraction of the total \ slow component of the initial H3+ + H2 reaction. P&C and others say that the \ H3+ produced by this process is vibrationally (and rotationally?) excited, \ i.e., in this energy range H3+ + H2 -> H3+* + H2 is an inelastic collision. \ P&C say that in the \"spectator\" model the H3+* is left with an internal \ energy of 5/9 of the collision energy and that this energy can lead to a \ competition between dissociation into H+ + H2 or H2+ + H and vibrational \ relaxation. ", CellOpen->False] }], "Text"], Cell["\<\ This is the higher energy component of Simko et al.(1997). If this really is \ a proton transfer collision, it results in vibrational excitation and in 180 \ deg scattering in CM mass and presumably has a threshold at the vibrational \ bending mode, i.e., at 0.31 eV. I have not found any theory relevant to \ H3+ + H2 collisions and so have no guidance as to the vibrational-rotational \ excitation (or anything else). For the somewhat related system of H2+ +H2, \ Bates and Reid, Proc. Roy. Soc. A 310, 1 (1969) seem to find a slow onset to \ vibrational excitation. On the other hand, Krstic and Schultz, J. Phys. B \ 32, 2515 (1999) find a rather sharp onset for vibrational excitation in \ collisions of H+ and H with H2.\ \>", "Text"], Cell["\<\ Why doesn't proton transfer result in vibrational excitation of the H2 at the \ proper threshold? Why don't I show the cross section as smaller by a factor \ of two as found by P&C and then double it to get the momentum transfer \ contribution? Why not do the same for the apparent elastic contribution at \ enegies below the vibrational threshold? What about Futrell's data.\ \>", "Subsubtitle", FontColor->RGBColor[1, 0, 0], Background->None], Cell[TextData[StyleBox["As far as mobility of H3+ in H2 at low and moderate \ E/N is concerned, this ion-molecule combination behaves like that for elastic \ scattering in a potential similar to that of an alkali ion in H2 or in a rare \ gas with a weak repulsive core. However at E/N ~ 400 Td there is an \ anomalous behavior in which the mobility of H3+ and H+ approach each other. \ Phelps (1990) proposed this is caused by H3+* breakup. Peko at al (1997) \ noted that at low energies the cross section for proton transfer was \ approximately half the Langevin value. We expect that the contribution of \ this process to the effective momentum transfer cross section is twice the \ proton transfer value (as in the case of charge transfer by an electron) \ because of the observed production of a slow H3+ ion, i.e., effectively 180 \ deg scattering in CM.", CellOpen->False]], "Text"], Cell["\<\ In summary, we treat this process as a single step vibrational and rotational \ excitation in which the product H3+* has more internal energy than the \ incident H3+. The product H3+* is directed at 180 deg in CM and the product \ H2 is directed a 0 deg in CM. Their relative translational energy at the end \ of the first step is 4/9 times the initial relative translational energy. As \ discussed by P&C, this proton transfer model predicts that 5/9 of the initial \ relative translational energy ends up as internal energy of the product H3+*, \ rather than the fixed energy usually associated with inelastic collisions. \ This simplified model neglects the discrete nature of the vibrational and \ rotational levels of H3+*. I do not know of any quantum mechanical theory of \ this collision process.\ \>", "Text"], Cell["\<\ Relative cross section from Peko and Champion (1997), Fig. 3a reaction (3)\ \>", "Subsection"], Cell[CellGroupData[{ Cell["Digitize data from Peko and Champion (1995).", "Subsubsection", Evaluatable->False], Cell["This relative cross section curve Qt gives", "SmallText", Evaluatable->False], Cell["\<\ qtdata ={{274.572, 1207.76}, {319.974, 1178.57}, {355.647, 1141.27}, {379.97, 1094.25}, {407.536, 1042.36}, {430.237, 1021.28}, {443.209, 982.364}, {461.046, 958.042}, {480.504, 941.826}, {490.233, 932.097}, {521.042, 920.747}, {579.417, 902.91}, {618.333, 888.316}, {639.413, 886.695}, {673.465, 885.073}, {702.652, 883.452}, {720.489, 885.073}, {744.811, 883.452}, {825.887, 880.209}, {881.019, 883.452}, {923.178, 881.83}, {957.23, 883.452}};\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscaledata ={{177.28, 880.209}, {947.501, 883.452}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscalegraph = Log[10,{2.0,120.}];", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscaledata ={{175.659, 881.83}, {178.902, 1219.11}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscalegraph = {0.0,1.0};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(analyzeDigitizedData\)], "Input"], Cell["\<\ data4Plot1 = LogLinearListPlot[dataout, PlotRange -> {{2.0,150.},{0.0,1.0}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, \ ImageSize -> 432, PlotStyle -> PointSize[0.02]];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(dataout\)], "Input", Evaluatable->False] }, Closed]], Cell[BoxData[ \(\(normData\ = \ Abs[Table[{dataout[\([j, 1]\)], \((fitPT\ /. \ enrel\ -> dataout[\([j, 1]\)])\)*\ dataout[\([j, 2]\)]}, {j, 1, Length[dataout]}]\ ];\)\)], "Input"], Cell["\<\ data4Plot = LogLogListPlot[normData, PlotRange -> \ {{0.01,10000},{0.01,200.}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, \ ImageSize -> 432, PlotStyle->PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(protonTransferFit = 10*UnitStep[ enrel - 0.31]*\(enrel^\(-0.5\)/\((1 + \((0.6/\((enrel - 0.31)\))\)^2)\)\)/\((1 + \((enrel/ 6.2)\)^3.95)\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(protonTransferPlot\ = \ LogLogPlot[protonTransferFit, {enrel, 0.01, 10000}, PlotPoints\ -> \ 5000, \ PlotStyle\ -> \ {Hue[0.5], \ Thickness[0.007]}, \ PlotRange\ -> \ {{0.01, 10000. }, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[data4Plot, protonTransferPlot, langevinQPlot, PlotLabel\ -> \ "\", ImageSize \[Rule] 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> ", StyleBox["slow H+", FontColor->RGBColor[1, 0, 0]], " + slow H2 +", StyleBox[" fast H2", FontColor->RGBColor[0, 1, 0]], " = slow H3+*by proton transfer then dissoc. (4a)" }], "Section", Evaluatable->False], Cell[TextData[{ "This relative cross section is that obtained by a Peko et al (1997) based \ on a c", StyleBox["rossed beam experiment that collects only slow ions and analyzes \ them by mass into H+ and H2+. The results are presented as a fraction of the \ total slow component of the initial H3+ + H2 reaction. I have not found \ measurements of the production of slow H+ other than P&C. The principle \ difference between this process and the previous one is that the internal \ energy of the H3+ after the collision is high enough so the H3+ is unstable \ and disintegrates.", CellOpen->False] }], "Text"], Cell["\<\ We think of this as a two step process. The first step is the proton \ transfer process and is an inelastic collision in which the product H3+* has \ more internal energy than the incident H3+. The proton transfer process is \ one in which the product H3+* is directed at 180 deg in CM and the product H2 \ is directed a 0 deg in CM. Their relative translational energy at the end of \ the first step is 4/9 times the initial relative translational energy. As \ discussed by P&C, this proton transfer model predicts that 5/9 of the initial \ relative translational energy ends up as internal energy of the product H3+*. \ In the second step, the excited H3+* dissociates with a relative energy \ approximately equal to the excess of the excitation energy over the binding \ energy of 4.4 eV and with the usual conservation of momentum, etc. This \ simplified model neglects the discrete nature of the vibrational and \ rotational levels of H3+*. I do not know of any quantum mechanical theory of \ this collision process.\ \>", "Text"], Cell["\<\ Relative cross section from Peko et al (1998), Fig.3 reaction (4a)\ \>", "Subsection"], Cell[CellGroupData[{ Cell["Digitize data of Peko and Champion.", "Subsubsection", Evaluatable->False], Cell[BoxData[ \(\(Import["\"];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(Show[%];\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(Quit[]\)], "Input", Evaluatable->False], Cell["The cross section curve gives", "SmallText", Evaluatable->False], Cell["\<\ qtdata ={{272.95, 889.938}, {316.731, 912.639}, {354.026, 948.313}, {379.97, 993.715}, {405.914, 1048.85}, {428.616, 1060.2}, {443.209, 1102.36}, {461.046, 1112.09}, {477.261, 1118.57}, {490.233, 1120.19}, {521.042, 1066.68}, {577.795, 1032.63}, {618.333, 1014.79}, {641.034, 1003.44}, {671.843, 996.958}, {702.652, 995.337}, {722.11, 992.093}, {744.811, 987.229}, {825.887, 979.121}, {881.019, 979.121}, {923.178, 975.878}, {957.23, 966.149}};\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscaledata ={{177.28, 881.83}, {947.501, 883.452}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscalegraph = Log[10,{2.,120.}];", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscaledata ={{177.28, 880.209}, {178.902, 1219.11}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscalegraph = {0.0,1.0};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(analyzeDigitizedData\)], "Input"], Cell["\<\ data5Plot = LogLinearListPlot[dataout, PlotRange -> {{2.,150.},{0.0,1.0}}, \ PlotStyle -> PointSize[0.02], ImageSize -> 432, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(dataout\)], "Input", Evaluatable->False] }, Closed]], Cell[BoxData[ \(\(normData5\ = \ Table[{dataout[\([j, 1]\)], \((fitPT\ /. \ enrel\ -> dataout[\([j, 1]\)])\)*\ dataout[\([j, 2]\)]}, {j, 1, Length[dataout]}];\)\)], "Input"], Cell["\<\ data5Plot = LogLogListPlot[normData5, PlotRange -> \ {{0.01,10000},{0.01,200.}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, \ ImageSize -> 432, PlotStyle->PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Note that the following Huber et al data have been reduced from their Fig. 1 \ data to give the slow H2+ formation only.\ \>", "Text"], Cell[BoxData[ \(\(huberHpData\ = \ {{90. , 0.15}, {450. , 0.2}};\)\)], "Input"], Cell[BoxData[ \(\(huberHpPlot\ = \ LogLogListPlot[huberHpData, PlotRange \[Rule] {{0.01, 10000}, {0.01, 200. }}, \ ImageSize \[Rule] 432, PlotStyle \[Rule] {Hue[0.3], PointSize[0.02]}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(slowHpFit\ = \ 1.3*UnitStep[ enrel - 4.4]*\(enrel^0.6/\((1 + \((2/\((enrel - 4.4)\)^1.1)\))\)\)/\((1 + \((enrel/ 8. )\)^4.05)\)^1.0*\((1 + \((enrel/ 21. )\)^4)\)^0.9*\((1 + \((enrel/ 120)\)^3.5)\)^0.4/\((1 + \((enrel/350)\)^1.9)\)^2 + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(slowHpPlot\ = \ LogLogPlot[slowHpFit, {enrel, 0.01, 10000. }, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.7], \ Thickness[0.007]}, \ PlotRange\ -> \ {{0.01, 10000. }, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[data5Plot, slowHpPlot, langevinQPlot, huberHpPlot, \ PlotLabel\ -> \ "\", ImageSize \[Rule] 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 \[Rule] ", StyleBox["slow H2+", FontColor->RGBColor[1, 0, 0]], " + slow H +", StyleBox[" fast H2", FontColor->RGBColor[0, 1, 0]], " = slow H3+*by proton transfer then dissoc. (4b)" }], "Section"], Cell[TextData[{ "This relative cross section is that obtained by a Peko et al (1997) based \ on a c", StyleBox["rossed beam experiment that collects only slow ions and analyzes \ them by mass into H2+ and H+. The results of P&C are presented in their Fig. \ 3a as a fraction of the total slow component of the initial H3+ + H2 reaction \ labeled INC. Huber et al measure the slow H2+ formation cross section at \ energies from 120 to 500 eV in CM.", CellOpen->False] }], "Text"], Cell["\<\ In the first step of this two step model, the collision appears to be one in \ which the H3+ projectile and H2 target are not significantly deflected during \ proton transfer to H2. In CM the unstable H3+ is at 180 deg and the H2 is at \ 0. Then the H and H2+ fragments fly apart more or less isotropically with a \ few eV relative energy. There is much uncertainty in this model, e.g., the \ amount of internal energy of the molecular fragments.\ \>", "Text"], Cell[TextData[{ "Peko and Champion had no way to distinguish the products slow H2+ + slow H \ + fast H2 from the products slow H2+ + fast H + fast H2, i.e., no way to \ distinguish proton abstraction followed by dissociation of the H3+ (the \ present process) from electron charge transfer followed by dissociation of \ the H3 (the next process).", StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox[" It seems to me that Vogel and Meierjohann (1978) should have \ seen this fast H2 at their theta1 = theta2 = 0 for 10 keV H3+ + H2.", CellOpen->False] }], "Text"], Cell["\<\ Cross section from Peko et al (1997), Fig. 3 reaction (4b), (5), and (6)\ \>", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell["Digitize data points and reconstruct plot.", "Subsubsection", Evaluatable->False], Cell["The relative cross section curve gives", "SmallText", Evaluatable->False], Cell["\<\ qtdata ={{272.95, 880.209}, {316.731, 886.695}, {354.026, 886.695}, {379.97, 888.316}, {404.293, 888.316}, {426.994, 896.424}, {443.209, 891.559}, {459.424, 907.775}, {477.261, 917.504}, {490.233, 925.611}, {521.042, 988.85}, {579.417, 1042.36}, {618.333, 1074.79}, {639.413, 1091.01}, {673.465, 1099.11}, {702.652, 1100.74}, {722.11, 1103.98}, {744.811, 1110.46}, {827.509, 1118.57}, {881.019, 1120.19}, {923.178, 1121.81}, {958.852, 1133.17}};\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscaledata ={{175.659, 881.83}, {947.501, 883.452}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["xscalegraph = Log[10,{2.0,120.}];", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscaledata ={{177.28, 880.209}, {178.902, 1219.11}};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["yscalegraph = {0.0,1.0};", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(analyzeDigitizedData\)], "Input"], Cell["\<\ data3Plot1 =LogLinearListPlot[dataout, PlotRange -> {{2.,150.},{0.0,1.0}}, \ ImageSize -> 432, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, PlotStyle -> PointSize[0.02]];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(dataout\)], "Input", Evaluatable->False] }, Closed]], Cell[BoxData[ \(\(normData6\ = \ Abs[Table[{dataout[\([j, 1]\)], \((fitPT\ /. \ enrel\ -> dataout[\([j, 1]\)])\)*\ dataout[\([j, 2]\)]}, {j, 1, Length[dataout]}]];\)\)], "Input"], Cell["\<\ data6Plot = LogLogListPlot[normData6, PlotRange -> \ {{0.01,10000},{0.01,200.}}, PlotLabel -> {\"Cross section (10^-20 m^2) versus relative energy (eV)\"}, \ ImageSize -> 432, PlotStyle->PointSize[0.02], DisplayFunction -> Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(slowH2pFit\ = \ 0.3*UnitStep[ enrel - 6.2]/\((1 + \((5/\((enrel - 6.2)\)^2)\))\)*\((1 + \((enrel/ 10)\)^2)\)^0.12/\((1 + \((enrel/2000)\)^1)\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(slowH2pPlot\ = \ LogLogPlot[slowH2pFit, {enrel, 2.5, 10000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.8], \ Thickness[0.007]}, \ PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell["\<\ Note that the following Huber et al data have been reduced from their Fig. 1 \ data to give the slow H2+ formation only.\ \>", "Text"], Cell[BoxData[ \(\(huberH2pData\ = \ {{90. , 0.3}, {450. , 0.4}};\)\)], "Input"], Cell[BoxData[ \(\(huberH2pPlot\ = \ LogLogListPlot[huberH2pData, PlotRange \[Rule] {{0.01, 10000}, {0.01, 200. }}, \ ImageSize \[Rule] 432, PlotStyle \[Rule] {Hue[0.3], PointSize[0.02]}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[data6Plot, \ huberH2pPlot, \ slowH2pPlot, langevinQPlot, PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell["\<\ Check of sum of proton transfer fits versus total proton transfer\ \>", "Subsubsection"], Cell[BoxData[ \(\(checkPTPlot\ = \ LogLogPlot[{fitPT, slowH2pFit + slowHpFit\ + protonTransferFit, slowH2pFit, slowHpFit, protonTransferFit}, \ {enrel, 1. , 100000}, PlotPoints\ -> \ 5000, \ ImageSize\ -> \ 432, PlotStyle\ -> \ {{\ Thickness[0.007]}, {Hue[0.1], \ Thickness[0.007]}, {Hue[0.8], \ Thickness[0.007]}, {Hue[0.5], \ Thickness[0.007]}, {Hue[0.6], \ Thickness[0.007]}}, \ PlotRange\ -> \ {{1. , 100000}, {0.01, 200}}, \ PlotLabel\ -> \ "\"];\)\)], \ "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 \[Rule] ", StyleBox["slow H2+", FontColor->RGBColor[1, 0, 0]], " + ", StyleBox["fast H ", FontColor->RGBColor[0, 0, 1]], "+", StyleBox[" fast H2", FontColor->RGBColor[0, 1, 0]], " = slow H2+ by charge transfer + dissoc. of fast H3 (5)" }], "Section"], Cell[TextData[{ "Peko and Champion had no way to distinguish the products slow H2+ + slow H \ + fast H2 from the products slow H2+ + fast H + fast H2, i.e., no way to \ distinguish proton abstraction followed by dissociation of the slow H3+ (the \ previous process) from electron charge transfer followed by dissociation of \ the fast H3 (the present process).", StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox[" They propose that the charge transfer is important only at \ energies above 50 eV because it is a nonresonant process. Vogel and \ Meierjohann (1978) attribute all of their signal at 10 keV to charge \ transfer. ", CellOpen->False], "Probably one could transform the fragment velocity distributions of Volger \ and Meierjohann (1978) for 10 keV collisions from rectangular LAB coordinates \ to spherical CM coordinates, but I do not have plans to try. ", StyleBox["Note that we prefer to assume that only the observed H2+ by Huber \ et al (1980) belongs here, not their total apparent charge transfer signal. \ Huber et al raise the possibility of H3+ dissociation to form H2+ that \ immediately undergoes resonant charge transfer.", CellOpen->False] }], "Text"], Cell["\<\ I do not know what to assume for this cross section and have taken a guess \ that leads to rough agreement below. Presumably one could use the theory of \ Rapp and Francis J. Chem. Phys. 37, 2631 (1962) as a best guess. I do not \ know whether the correction of Pullins et al, Z. Phys. Chem. 214, 1279 (2000) \ applies. Because this is a nonresonant charge transfer collision, Peko and \ Champion predict that it will only be important at energies above 50 eV. At \ low energies, it should be significantly smaller than that for the P&C fast H \ production process.\ \>", "Text"], Cell["\<\ In the first step of this two step model, the collision is one in which the \ H3+ projectile and H2 target are not significantly deflected during electron \ transfer from the H2 to the H3+. In CM the unstable H3 is at 0 deg and the \ H2+ is at 180. Then the H and H2 fragments fly apart more or less \ isotropically with a few eV relative energy. There is much uncertainty in \ this model, e.g., the amount of internal energy of the molecular fragments.\ \>", "Text"], Cell[BoxData[ \(\(fastHctFit\ = 0.025*\ UnitStep[ enrel - 6.2]*\(enrel^0.53/\((1 + \((50/\((enrel - 6.2)\)^1.1)\))\)\)/\((1 + \((enrel/ 15000)\)^2)\)^0.9 + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[TextData[{ "According to Rapp and Francis, J. Chem. Phys. 37, 2631 (1962), the \ nonresonant charge transfer cross section varies as enrel^2 at low energies \ and as (a + b*ln(v))^2, i.e., as the resonant charge transfer cross section, \ for high energies. The following function is an approximation to this model. \ However, it is much too sharply peaked in energy to give a good fit to \ experiment. Probably one could get a reasonable fit to experiment if there \ were other similar functions with a spread in the energies at which they \ peaked. ", " We will not use the following formula.", StyleBox["\n", FontSize->12] }], "Text"], Cell[BoxData[ \(\(fastHctFit2\ = 15. *\ \(\(UnitStep[enrel - 6.2]/ enrel^0.2\)/\((1 + \((2000. /\((enrel - 6.2)\))\)^4)\)^0.5\)/\((1 + \((enrel/ 150000)\)^2)\)^1.1 + 1. *10^\(-30\);\)\)], "Input"], Cell[BoxData[ \(fastHctFit2\ /. \ enrel\ -> \ 100\)], "Input"], Cell[BoxData[ \(\(fastHctFitPlot\ = \ LogLogPlot[{fastHctFit, fastHctFit2}, {enrel, 2.5, 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.8], \ Thickness[0.007], Dashing[{0.05, 0.05}]}, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}} (*\(,\)\(DisplayFunction\ -> \ Identity\)*) ];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> ", StyleBox["fast H+", FontColor->RGBColor[1, 0, 0]], " + ", StyleBox["2 fast H", FontColor->RGBColor[0, 0, 1]], " + slow H2 - CID of H3+ - similar to (1)" }], "Section"], Cell["\<\ The reason for invoking this process is to fit try to both the sum of the H3+ \ destruction cross sections of Williams et al (1984) and the fast H atom \ production as measured by Williams and Dunbar (1966), i.e., we want a process \ producing more fast H atoms per collision than those discussed above. The \ assumption of a significant cross section appears to be inconsistent with the \ observation by Volger and Meierjohann (1978) that the production of fast H+ + \ 2 fast H atoms \"makes only a negligible contribution\" to the fast particle \ production compared to fast H + fast H2 production at 10 keV. I do not know \ how to resolve this problem.\ \>", "Text"], Cell["\<\ Here the first step is the excitation of the H3+ and the second is the \ dissociation into fast H+ and 2 fast H atoms. This collision is assumed to \ be one in which the H3+ projectile and H2 target are not significantly \ deflected during excitation of the H3+ to a dissociating state. The loss of \ energy by the H3+ in the first step is expected to be roughly 10 eV. Then \ the H+ and 2 H fragments probably fly apart more or less isotropically in the \ H3+ CM with a few eV energy. There is much uncertainty in the applicability \ of this model.\ \>", "Text"], Cell["\<\ Data from McClure (1963) for fast H production as read in 1985\ \>", "Subsection"], Cell[BoxData[ \(\(mcClureDatafH\ = \ {{2000. , \ 4.2}, {2800. , 5.2}, {4000. , 6.0}, {6000. , 7.2}, {8000. , 8.3}, {12000. , \ 9.5}, {20000. , 9.1}, {28000. , 8.4}, {40000. , 6.8}};\)\)], "Input"], Cell["\<\ mcClurefHPlot = LogLogListPlot[mcClureDatafH, PlotRange -> \ {{0.02,100000},{0.01,200.0}}, PlotStyle->{Hue[0.1], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(fast2HFit\ = 0.017*\ UnitStep[ enrel - 8.8] \(enrel^0.53/\((1 + \((50/\((enrel - 8.8)\)^1.1)\))\)\)/\((1 + \((enrel/ 24000)\)^2)\)^0.9 + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(fast2HFitPlot\ = \ LogLogPlot[2*fast2HFit, {enrel, 2.5, 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.1], \ Thickness[0.007], Dashing[{0.05, 0.05}]}, \ PlotRange\ -> \ {{0.01, 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(totalfHFitPlot\ = \ LogLogPlot[\((2*fast2HFit + fastH2pFit + fastHctFit)\), {enrel, 2.5, 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.5], \ Thickness[0.007]}, \ PlotRange\ -> \ {{0.01, 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> total fast H production ", StyleBox["measured by McClure & by Williams", FontColor->RGBColor[0, 0, 1]] }], "Section"], Cell["\<\ Here we compare the fast H results with the present high energy models. This \ is a check and not a new cross section for the set.\ \>", "Text"], Cell[BoxData[ \(\(Show[mcClurefHPlot, pekofH2pPlot, mcClurefH2pPlot, \ fastHctFitPlot, \ fastH2pPlot, williamsfH2pPlot, \ langevinQPlot, fast2HFitPlot, totalfHFitPlot, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell["\<\ The fit here is not perfect, but it did not seem worthwhile to try harder to \ adjust the various component cross sections. The energy dependences of \ several components are almost pure guesses. Also, there is considerable \ disagreement as to some of the measured cross sections.\ \>", "Subsubtitle"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 -> total fast H2 production ", StyleBox["measured by McClure & by Williams", FontColor->RGBColor[0, 1, 0]] }], "Section"], Cell["\<\ Here we compare our model cross sections for fast H2 production with \ experiment. This is a test of the recommended cross sections and is not a \ cross section to be added to the set.\ \>", "Text"], Cell["From our previous fits", "Text"], Cell[BoxData[ \(\(totalfH2Fit\ = \ fastHpFit\ + \ fitPT\ + \ fastHctFit;\)\)], "Input"], Cell[BoxData[ \(\(totalfH2FitPlot\ = \ LogLogPlot[totalfH2Fit, {enrel, 1. , 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.8], \ Thickness[0.007]}, \ PlotRange\ -> \ {{1. , 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell["\<\ Data from McClure (1963) for fast H2 production as read in 1985\ \>", "Subsubsection"], Cell[BoxData[ \(\(mcClureDatafH2\ = \ {{2000. , \ 2.35}, {2800. , 2.75}, {4000. , 3.15}, {6000. , 3.6}, {8000. , 4.0}, {12000. , \ 4.3}, {20000. , 3.6}, {28000. , 3.05}, {40000. , 2.1}};\)\)], "Input"], Cell["\<\ mcClurefH2Plot = LogLogListPlot[mcClureDatafH2, PlotRange -> \ {{1.,100000},{0.01,200.0}}, PlotStyle->{Hue[0.3], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(Show[mcClurefH2Plot, \ totalfH2FitPlot, \ fastHpPlot, \ fitPTPlot, \ fastHctFitPlot, protonTransferPlot, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell["\<\ The fit here is not perfect, but it did not seem worthwhile to try harder to \ adjust the various component cross sections. The energy dependences of \ several components are almost pure guesses. Also, there is considerable \ disagreement as to some of the measured cross sections.\ \>", "Subsubtitle"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "fast H3+ + H2 \[Rule] ", StyleBox["slow H2+", FontColor->RGBColor[1, 0, 0]], " + fast H3+ + e ionization" }], "Section"], Cell["\<\ We assume that this is a long range stripping collision where there is no \ significant deflection of the fast H3+ as it losses an energy equal to the \ ionization potential of H2, i.e., 15.6 eV, plus the energy of the free \ electron, e.g., 30 eV, at high collision energies.\ \>", "Text"], Cell["\<\ From Gordeev et al (1958) as tabulated in the \"old\" Oak Ridge Red Book. The \ threshold is the ionization potential of H2, i.e., 15.6 eV.\ \>", "Text"], Cell[BoxData[ \(\(gordeevQe\ = \ {{1000*2/5, \ 0.13}, {3000*2/5, \ 0.36}, {6000*2/5, 0.72}, {10000*2/5, 1.1}, {30000*2/5, 2.6}, {60000*2/5, 3.6}, {100000*2/5, 4.3}};\)\)], "Input"], Cell["\<\ gordeevQePlot = LogLogListPlot[gordeevQe, PlotRange -> \ {{1.,100000},{0.01,200.0}}, PlotStyle->{Hue[0.3], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(ionizationFit\ = 0.0006*\ UnitStep[ enrel - 15.6] \(enrel^0.9/\((1 + \((5/\((enrel - 15.6)\)^1)\))\)\)/\((1 + \((enrel/ 42000)\)^1.5)\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(ionizationFitPlot\ = \ LogLogPlot[ionizationFit, {enrel, 1. , 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.8], \ Thickness[0.007]}, \ PlotRange\ -> \ {{1. , 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[gordeevQePlot, \ ionizationFitPlot, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"] }, Open ]], Cell["\<\ fast H3+ + e \[Rule] 3 H or H2 + H dissociative recombination\ \>", "Section"], Cell[TextData[{ "There is much current discussion about the dissociative recombination of \ electrons with H3+. A recent review by M. Larsson, Phil. Trans. Royal Soc. \ Lond. A 358, 2433 (2000) cite merged-beam, storage-ring results as giving \ alpha(300 K) = 1.15E-7 cm^3/s while flowing afterglow experiments currently \ give 1E-8 to 2E-8 cm^3/s. It has been proposed (apparently not published) \ that the recombination coefficient is very sensitive to rotational excitation \ of the H3+ and that the merged beam apparatus has \ \[OpenCurlyDoubleQuote]rotationally excited\[CloseCurlyDoubleQuote] (not \ vibrationally excited) H3+ with a large recombination coefficient. Even more \ recently papers by Glosik et al, Chem. Phys. Lett. 331. 209 (2000) and J. \ Phys. B (subnitted) (2001) claim that electron recombination to vibrationally \ relaxed H3+ is a three-body process in which H2 removes energy from a \ metastable H3 to produce a dissociationg state. The merged beam experiments \ give the neutral products as 3 H (75%) and H2 + H (25%).", StyleBox[" ", FontSize->12], "The beam experiments yielding a large recombination coefficients show a \ lot of structure with a roughly 1/enrel behavior or a T^(-0.5) variation.", StyleBox["\n", FontSize->12] }], "Text"], Cell[CellGroupData[{ Cell["\<\ fast H3+ + H2 \[Rule] Balmer alpha dissociation and excitation\ \>", "Section"], Cell["\<\ From Table 5 of Williams et al (1982). The threshold is the excitation \ potential of H2, i.e., 12.1 eV plus the threshold for H formation of 6.2 eV, \ i.e., 18.3 eV. The cross section given here is the sum of the \"projectile \ excitation- sigma P\" in which the emission is Doppler shifted by an amount \ determined by an H atom with the unperturbed projectile velocity plus the \ \"target excitation - sigmaT\" in which the there is no measurable Doppler \ shift as if the emitting H atom is randomly directed with a low velocity. \ From Williams et al, these components are roughly equal. I would assume the \ same angular distribution of products as for the second reaction in our list, \ i.e., no deflection of the projectile and target.\ \>", "Text"], Cell[BoxData[ \(\(!! Halpha2.txt\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(halphaTable\ = \ Drop[Import["\", "\"], 4];\)\)], "Input"], Cell[BoxData[ \(Dimensions[%]\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(williamsQHalpha\ = \ Table[{halphaTable[\([j, 1]\)]*1000*2/ 5, \((halphaTable[\([j, 2]\)] + halphaTable[\([j, 8]\)])\)*0.01}, {j, 1, 29}];\)\)], "Input"], Cell["\<\ williamsQHalphaPlot = LogLogListPlot[williamsQHalpha, PlotRange -> \ {{1.,100000},{0.01,200.0}}, PlotStyle->{Hue[0.3], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(halphaFit\ = 0.0027*\ UnitStep[ enrel - 18.3]*\(enrel^0.47/\((1 + \((5/\((enrel - 18.3)\)^1)\))\)\)/\((1 + \((enrel/ 70000)\)^2. )\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(halphaFitPlot\ = \ LogLogPlot[halphaFit, {enrel, 1. , 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.8], \ Thickness[0.007]}, \ PlotRange\ -> \ {{1. , 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[williamsQHalphaPlot, \ halphaFitPlot, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell["\<\ Note that the contributions of the target excitation sigmaT, not Doppler \ shifted, and the projectile excitation sigmaP, Doppler shifted, are \ comparable. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ fast H3+ + H2 \[Rule] Lyman alpha dissociation and excitation\ \>", "Section"], Cell["\<\ From Fig. 8 of Dunn, Geballe, and Pretzer, Phys. Rev. 128? 2200 (1962). The \ threshold is the excitation potential of H(n=3), i.e., 10.2 eV plus the \ threshold for H formation of 6.2 eV, i.e., 16.4 eV. The data points are form \ my visual digitization in 1985. These authors did not measure a Doppler \ shift. I would assume the same angular distribution of products as for the \ second reaction in our list, i.e., no deflection of the projectile and \ target. Note that these photons (along with the Lyman band from H2) can \ contribute to the electron production at the cathode.\ \>", "Text"], Cell[BoxData[ \(\(dunnLymanData\ = \ {{240. , 0.196}, {400. , 0.246}, {800. , 0.272}, {1200. , 0.28}, {1600. , 0.304}, {2000. , 0.33}};\)\)], "Input"], Cell["\<\ dunnQHLymanPlot = LogLogListPlot[dunnLymanData, PlotRange -> \ {{1.,100000},{0.01,200.0}}, PlotStyle->{Hue[0.3], PointSize[0.02]}, ImageSize -> 432, DisplayFunction -> \ Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[BoxData[ \(\(lymanFit\ = 0.0012*\ UnitStep[ enrel - 16.4]*\(enrel^1. /\((1 + \((50/\((enrel - 16.4)\)^1)\))\)\)/\((1 + \((enrel/ 250)\)^4. )\)^0.26*\((1 + \((enrel/ 1800)\)^4)\)^0.25/\((1 + \((enrel/20000)\)^2)\) + 1. *10^\(-30\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(lymanFitPlot\ = \ LogLogPlot[lymanFit, {enrel, 1. , 100000}, PlotPoints\ -> \ 1000, \ PlotStyle\ -> \ {Hue[0.8], \ Thickness[0.007]}, \ PlotRange\ -> \ {{1. , 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[dunnQHLymanPlot, \ lymanFitPlot, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell["\<\ Here there is a lot of guessing as to the low energy behavior.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Momentum transfer cross section for H3+ + H2 from mobility data\ \>", "Section"], Cell["\<\ Note that this momentum transfer cross section is not part of our recommended \ set. At low E/N elastic collisions and vibrational excitation via proton \ transfer are assumed to determine the H3+ mobility in H2. The fit to \ mobility data could probably be improved, but I do not have an ion transport \ code for taking all of the necessary factors into account.\ \>", "Subsubtitle"], Cell["Potential models for mobility", "Subsubsection"], Cell["\<\ From the ratio of the peak mobility to the low E/n limit one seems to need \ either a 16-4 potential or a gamma = 0.1 with a 12-6-4 potential. See Fig. \ 5-3-1 of McDaniel and Mason (1973) and the corresponding figure of Mason and \ McDaniel (1988). The peak mobility of 16 cm^2/V-s at NTP occurs at E/n = 150 \ Td, a drift velocity of 64e4 cm/s, and Teff = 4000 K. The later is roughly \ consistent with a dissociation energy of H5+ -> H3+ + H2 of 0.35 eV from \ Johnsen and Biondi (1976). Elford and Miloy get 0.25 eV and cite an \ equilibrium distance of 3 Ang.. A problem in fitting mobility theory to the \ H3+ in H2 data, as pointed out in the literature, is the low mobility at low \ E/N compared to Langevin. \ \>", "Text"], Cell[BoxData[{ \(\(mramu\ = \ 3*2/\((3 + 2)\);\)\ \), "\[IndentingNewLine]", \(\(amu\ = \ \ 1.661*10^\(-27\);\)\), "\[IndentingNewLine]", \(\(mr\ = \ mramu\ *\ amu\ ;\)\), "\[IndentingNewLine]", \(\(qe\ = \ 1.602*10^\(-19\);\)\ \), "\[IndentingNewLine]", \(\(ng\ = \ 2.69*10^25;\)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (*m^\(-3\)*) \ \)}], "Input"], Cell[BoxData[ \(\(!! h3ph2mobility.txt\)\)], "Input", Evaluatable->False], Cell[BoxData[ \(\(mobilityExpt1\ = \ Table[Take[\(Drop[ Drop[Import["\", "\"], 4], \(-5\)]\)[\([j]\)], 2], {j, 1, 20}];\)\)], "Input"], Cell["\<\ We need to normalize the mobility to unit density and MKS units.\ \>", "Text"], Cell[BoxData[ \(\(mobilityExpt2\ = \ Table[{mobilityExpt1[\([j, 1]\)], \ mobilityExpt1[\([j, 2]\)]*2.69*10^19*10^2}, {j, 1, 20}];\)\)], "Input"], Cell[BoxData[ \(\(mobilityExptPlot\ = \ LogLinearListPlot[mobilityExpt2, \ PlotRange\ -> \ {{1. , \ 1000. }, {0. , 5. *10^22}}, PlotStyle\ -> \ PointSize[0.02], DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell["\<\ We need the energy at the highest E/n for which we believe the data, E/n = \ 300 Td.\ \>", "Text"], Cell[BoxData[ \(kTeffHigh\ = \ 0.0258\ + \ 1/3*\((2* amu)\)*\((mobilityExpt2[\([19, 1]\)]*10^\(-21\)* mobilityExpt2[\([19, 2]\)])\)^2/qe\)], "Input"], Cell[BoxData[ \(kTeffLow\ = \ 0.0258\ + \ 1/3*\((2* amu)\)*\((mobilityExpt2[\([1, 1]\)]*10^\(-21\)* mobilityExpt2[\([1, 2]\)])\)^2/qe\)], "Input"], Cell["Theoretical mobility to be fit to experiment", "Subsubsection"], Cell[BoxData[ \(\(!! omegaN-4.txt\)\)], "Input", Evaluatable->False], Cell["We choose N = 14, although 12 might be better.", "Text"], Cell[BoxData[ \(\(omegaN4\ = \ Transpose[ Drop[Import["\", "\"], 4]];\)\)], "Input"], Cell[BoxData[ \(\(omega1\ = \ Transpose[{omegaN4[\([1]\)], omegaN4[\([4]\)]}];\)\)], "Input"], Cell["Now we try N = 12", "Text"], Cell[BoxData[ \(\(omega12\ = \ Transpose[ Drop[Import["\", "\"], 4]];\)\)], "Input"], Cell[BoxData[ \(\(omega1\ = \ Transpose[{omega12[\([1]\)], omega12[\([2]\)]}];\)\)], "Input"], Cell["\<\ The well depth for the H3+-H2 potential has been determined by Johnsen and \ Biondi (1976) from H5+ stability measurements as 0.35 eV, so we will use that \ as a first guess for our mobility model. These Omega(1,1) are normalized to \ Pi*rmin^2 versus the temperature in units of the well depth. The rmin and \ well depth epsilon are adjustable parameters that are to be found by trial \ and error. The final epsilon and rmin are the first entries in the following \ lists.\ \>", "Text"], Cell[BoxData[ \(\(\(epsilon\ = \ {0.3, 0.3, 0.3, 0.3, 0.25}[\([1]\)]\ ;\)\(\ \)\( (*eV*) \)\)\)], "Input"], Cell[BoxData[ \(\(\(kTgas\ = \ 0.0258;\)\(\ \ \)\( (*eV*) \)\)\)], "Input"], Cell[BoxData[ \(\(\(rmin\ = \ {2.22, 2.25, 2.3, 2.35, 2.35}[\([1]\)]*10^\(-10\);\)\(\ \ \)\( (*m*) \)\)\)], "Input"], Cell[BoxData[ \(\(mgas\ = \ 2*amu;\)\)], "Input"], Cell["\<\ Next we calculate a table of Teff and mobility normalized to unit gas \ density.\ \>", "Text"], Cell[BoxData[ \(\(mobilityTheor1\ = \ Table[{omega1[\([j, 1]\)]*epsilon, 3*qe/\((8*Pi* rmin^2)\) \((Pi/\((2*mr*epsilon*omega1[\([j, 1]\)]* qe)\))\)^0.5/omega1[\([j, 2]\)]}, {j, 1, Length[omega1]}];\)\)], "Input"], Cell["\<\ We now convert the kTeff/e into E/N values using the Wannier expression to \ find the drift velocity and the mobility to find E/N.\ \>", "Text"], Cell[BoxData[ \(vd[kTeff_]\ := \ If[kTeff - kTgas\ > \ 0, \ Sqrt[2*qe/mgas*\((kTeff - kTgas)\)], 1]\)], "Input"], Cell[BoxData[ \(\(mobilityTheor2\ = \ Table[{10^21* vd[mobilityTheor1[\([j, 1]\)]]/mobilityTheor1[\([j, 2]\)], mobilityTheor1[\([j, 2]\)]}, {j, 1, Length[omega1]}];\)\)], "Input"], Cell[BoxData[ \(\(mobilityTheorPlot\ = \ LogLinearListPlot[mobilityTheor2, \ PlotJoined\ -> \ True, PlotRange\ -> \ {{1. , \ 1000. }, {0. , 5. *10^22}}, PlotStyle\ -> \ {Hue[1], PointSize[0.02]}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[mobilityExptPlot, mobilityTheorPlot, PlotLabel\ -> \ "\", ImageSize\ -> \ 432, DisplayFunction\ -> $DisplayFunction];\)\)], "Input"], Cell["\<\ These plots show that we do not fit the apparent turn up in experimental \ mobility at E/n > ~ 300 Td. I propose that the behavior is caused by H3+ \ breakup into H+ and H2 and the the breakup is facilitated by the build up of \ internal energy of the drifting H3+.\ \>", "Subsubtitle"], Cell["Cross section corresponding to theoretical mobility", "Subsubsection"], Cell[BoxData[ \(\(!! QViehlandN-4.txt\)\)], "Input", Evaluatable->False], Cell["Here we are using N = 14", "Text"], Cell[BoxData[ \(\(qmN4\ = \ Transpose[ Drop[Import["\", "\"], 4]];\)\)], "Input"], Cell[BoxData[ \(\(qm1\ = \ Transpose[{qmN4[\([1]\)], qmN4[\([4]\)]}];\)\)], "Input"], Cell["Here we are trying N = 12", "Text"], Cell[BoxData[ \(\(qm12\ = \ Transpose[ Drop[Import["\", "\"], 3]];\)\)], "Input"], Cell[BoxData[ \(\(qm1\ = \ Transpose[{qm12[\([1]\)], qm12[\([2]\)]}];\)\)], "Input"], Cell["\<\ Note that the following table is limited to energies from near the minimum of \ 0.026 to the maximum of kTeff = 0.9 eV, corresponding to the range of the \ experimental E/N.\ \>", "Subsubtitle"], Cell[BoxData[ \(\(qm2\ = \ Table[{qm1[\([j, 1]\)]*epsilon, 10^20*qm1[\([j, 2]\)]*Pi*rmin^2}, {j, 5, 16}];\)\)], "Input"], Cell[BoxData[ \(\(qmFitPlot\ = \ LogLogListPlot[qm2, PlotRange \[Rule] {{0.01, 10000}, {0.01, 200. }}, \ ImageSize \[Rule] 432, PlotStyle\ -> {Hue[0.6], PointSize[0.02]}, DisplayFunction\ -> \ Identity];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Elastic cross section (including rotational excitation)", "Section"], Cell[TextData[{ "Following Simko et al (1997) we need generate an elastic cross section \ that fits the cross section derived from mobility data at low energies and \ drops rapidly at the onset of vibrational excitation.", " The details of the transfer from this \[OpenCurlyDoubleQuote]elastic\ \[CloseCurlyDoubleQuote] scattering to the vibrational excitation roughly \ follow the cross sections chosen by Simko et al (1997) to fit H3+ mobility \ and diffusion data in H2.", StyleBox["\n", FontSize->12] }], "Text"], Cell[BoxData[ \(\(qElasticFit\ = \ \(22/ enrel^0.5\)/\((1 + \((enrel/0.4)\)^4)\);\)\)], "Input", FontSize->16, FontColor->RGBColor[1, 0, 0]], Cell[BoxData[ \(\(qElasticFitPlot\ = \ LogLogPlot[qElasticFit\ , {enrel, 0.01, 10000}, PlotPoints\ -> \ 5000, \ PlotStyle\ -> \ {Hue[0.3], \ Thickness[0.007]}, \ PlotRange\ -> \ {{0.01, 100000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell["\<\ Note that at the lowest energies shown, this cross section is significantly \ larger (~30%) than Langevin. Perhaps proton transfer and rotational \ excitation are large enough to effectively increase the momentum transfer \ scattering.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Summary", "Section"], Cell["\<\ Compare the sum of our H3+ destruction with Williams et al (1984) H3+ \ destruction\ \>", "Subsubsection"], Cell[BoxData[ \(\(williamsH3pDestData\ = \ {{2500. *2/5, 2.96}, {5000. *2/5, 3.47}, {7500. *2/5, 4.13}, {10000. *2/5, 4.72}, {15000. *2/5, 5.3}, {20000. *2/5, 6.02}, {30000. *2/5, 7.2}, {40000. *2/5, 7.6}, {60000. *2/5, 7.0}, {80000. *2/5, 6.4}, {100000. *2/5, 5.7}};\)\)], "Input"], Cell[BoxData[ \(\(williamsH3pDestPlot\ = \ LogLogListPlot[williamsH3pDestData, PlotRange \[Rule] {{0.02, 100000}, {0.01, 200. }}, \ ImageSize \[Rule] 432, PlotStyle\ -> PointSize[0.02], DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(sumFits\ = \ fastHpFit + \ fastH2pFit + \ 2*protonTransferFit + \ slowHpFit + \ slowH2pFit\ + \ fast2HFit\ + \ fastHctFit\ + qElasticFit;\)\)], "Input"], Cell[BoxData[ \(\(sumFitsPlot1\ = \ LogLogPlot[Evaluate[sumFits], {enrel, 0.01, 5. }, PlotPoints\ -> 50000, \ PlotStyle\ -> \ Thickness[0.007], \ PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}}, DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(sumFitsPlot2\ = \ LogLogPlot[Evaluate[sumFits], {enrel, 10. , 10000. }, PlotPoints\ -> 50000, \ PlotStyle\ -> \ {Thickness[0.007], Dashing[{0.03, 0.03}]}, \ PlotRange\ -> \ {{0.01, 10000}, {0.01, 200}}, \ DisplayFunction\ -> \ Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[qmFitPlot, williamsH3pDestPlot, langevinQPlot, \ fastHpPlot, \ fastH2pPlot, \ protonTransferPlot, \ slowHpPlot, \ slowH2pPlot, \ \ fast2HFitPlot, \ sumFitsPlot1, sumFitsPlot2, fastHctFitPlot, qElasticFitPlot, \ GridLines\ -> Automatic, \ PlotLabel\ -> \ "\", ImageSize\ -> \ 432, \[IndentingNewLine]DisplayFunction \[Rule] \ $DisplayFunction];\)\)], "Input"], Cell[BoxData[ \(\(ShowLegend[ qmFitPlot, \ {{{Hue[1.0], "\"}, {Hue[ 0.3], "\"}}, LegendPosition\ -> {1.2, 0.5}, \[IndentingNewLine]LegendSize\ -> \ {1. , .3}, \ LegendLabel\ -> "\", \ PlotStyle -> \ Thickness[0.07], LegendOrientation\ -> \ Vertical, \ LegendShadow\ -> \ None}];\)\)], "Input", Evaluatable->False], Cell["\<\ Note that the black curve is equal to the effective momentum transfer cross \ section at energies below about 5 eV. At higher energies, the dashed black \ curve is the sum of the cross sections leading to attenuation of an H3+ beam.\ \ \>", "Subsubtitle"], Cell["\<\ There are many uncertainties in these results. For example the dip in the \ sum of the elastic and vibrational excitation cross sections just below 1 eV \ seems much too narrow in energy, although the \"area\" seems roughly OK and \ the structure is comparable to that shown by Simko et al (1997).\ \>", "Subsubtitle"] }, Open ]], Cell["\<\ A crucial question in the modeling of the behavior of H3+ in H2 under the \ influence of an electric field or in an afterglow situation is whether a \ significant fraction of the collisions lead to vibrational cooling of the H3+ \ that is excited by proton transfer collisions. Proton transfer measurements \ give cross sections between 1/4 (Vestal et al at low energies) and 1/2 (Peko \ and Champion at 4 eV) of Langevin. The proton transfer reaction is \ envisioned as a long range collision with nearly straight line trajectories. \ We are left asking whether there is a short range part of the Langevin \ scattering that could cause vibrational relaxation, e.g., scattering from the \ repulsive part of the potential barrier. A problem with vibrational \ relaxation in H3+ + H2 collisions is that the vibrational spacings seem very \ different so that resonant energy transfer (VV) seems unlikely and one must \ invoke vibrational-translational transfer (VT) or rotational excitation (VR). This listing of reactions for H3+ has not considered H3+ + H. The possible \ proton transfer reaction H3+ + H -> H2+ + H2 appears to be exothermic by \ about 1.7 eV. I have no idea as to its energy dependence. The energy to be \ dissipated in the product H2+ could lead to dissociation at relatively low \ collision energies. Other possible reactions are vibrational relaxation of \ the H3+ and collisional dissociation of the H3+. Hopefully, the models will \ not have to consider H3+ + H collisions.\ \>", "Subsubtitle"], Cell[BoxData[ \(TeXSave["\", "\"]\)], "Input", Evaluatable->False], Cell[BoxData[ \(HTMLSave["\", "\", ConversionOptions\ -> \ {"\"\ -> \ "\"}]\)], \ "Input", Evaluatable->False], Cell["runtime = SessionTime[] - startclock", "Input", PageWidth->Infinity] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{838, 597}, WindowMargins->{{-1, Automatic}, {Automatic, 9}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, CellLabelAutoDelete->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, StyleDefinitions -> "AvpStyle.nb" ] (******************************************************************* Cached data follows. 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