COMPILATION OF ELECTRON CROSS SECTIONS USED BY A. V. PHELPS

?

Please refer to these data using the sources cited for each gas.?

Please do not refer to any of them as "JILA cross sections",?

because a) the data shown here for a given gas may come from?

several sources that should be referred to by the respective?

authors names; b) in most cases no one else at JILA or NIST has?

approved the data or even looked at it.??Reference to this data as?

"JILA data" could be interpreted incorrectly as indicating NIST?

approval and could jepordize my Web site usage.

?

GASES COMPILED: O2, N2, CO, CO2, H2, H2O, NO, SF6, He, Ne, Ar,

Xe, Na, and Mg?

?

Comments are made on cross sections from other sources for some?

of these and other gases.

?

WE MAKE NO CLAIMS FOR THESE CROSS SECTIONS BEYOND THOSE STATED IN?

THE PAPERS WHERE THEY ARE PUBLISHED OR CITED.??IN MOST CASES THESE

CROSS SECTIONS WERE ASSEMBLED IN THE 1970'S AND 1980'S.??IN ONLY A?

FEW CASES HAVE THEY BEEN MODIFIED OR TESTED SINCE THAT TIME. I DO?

NOT PLAN ANY UPDATES.??ADDITIONS HAVE BEEN MADE WHEN CROSS

SECTIONS HAVE BEEN ASSEMBLED FOR OTHER PURPOSES.??SINCE THE JILA?

INFORMATION CENTER WAS CLOSED BY NIST, THERE IS NO ONE THERE TO?

HELP YOU.??OPINIONS EXPRESSED ARE THOSE OF A. V. PHELPS AND DO NOT?

IMPLY JILA, CU, OR NIST APPROVAL.

?

The cross sections are in 1E-16 cm2.??The two-term Boltzmann code,?

BACKPRO, used in deriving our cross sections employs linear?

interpolation between points in the cross section tables.??

Therefore linear interpolation should be applied when using them.?

Except as noted below for N2, the cross sections listed in JILA?

Information Center Reports 26, 27, and 28 for N2, H2, and O2?

should be the same as those listed here.??(This aspect has not?

been checked in detail, so please inform me of discrepancies.)

?

It should be kept in mind that the momentum transfer cross sections?

tabulated are effective values that include the effects of inelastic?

collisions as is appropriate for use in the two-tern spherical harmonic?

expansion.??See, for example, Baraff and Buchsbaum, Phys. Rev. 130,?

1007 (1963) and Sec. IIB of Pitchford and Phelps, Phys. Rev. A 25,?

540 (1982).??Where data is available, the effective Qm is set?

equal to the sum of the inelastic cross sections plus the elastic?

momentum transfer cross section. This is an approximate relation.

?

Some of the terms used in the tables and the BACKPRO code are:

?

QSCALE is a factor by which the input cross sections from the?

various sources were multiplied to get the values shown here?

and used in the Boltzmann equation.??

?

ENERGY LOSS is the inelastic energy loss in eV.

?

LOWER LIMIT and UPPER LIMIT were used by BACKPRO to limit

the range within which the tables were interpolated.??

Interpolation was the most time-consuming step in the code.

?

EBR is a parameter used to describe the sharing of energy

among the two electrons resulting from ionization.??It is

the parameter w in Yoshida, Phelps, and Pitchford, Phys. Rev.?

27, 1345 (1983) and its choice is based on the data of Opal,?

Peterson, and Beaty, Phys. Rev. 55, 4100 (1971).

?

BACKPRO is the FORTRAN code for the solution of the electron?

Boltzmann equation developed by Frost and Phelps, Phys. Rev.?

127, 1621 (1962) and modified by Phelps and coworkers in later?

papers.??A detailed analysis of the code as of 1975 has been

given by P.H. Luft, JILA Information Center Report No. 14,?

October 1975.??Changes since then are minimally documented,?

but include accounting for the electrons produced by electron

impact ionization during either a spatial or temporal?

exponential growth.??See Yoshida et al as cited above.

?

These cross sections were derived to give a good fit?

to published electron transport, excitation coefficient,?

attachment coefficient, and ionization coefficient data?

for the pure gases.??In many cases they have been tested?

satisfactorily against similar swarm data for gas mixtures,?

e.g., CO2 laser mixtures, H2-Ar mixtures, N2-SF6 mixtures,?

and atmospheric pressure dry and moist air.??In several?

cases, e.g., He, Ar, and Xe, we have not attempted to?

distinguish among the various excited states and find the

cross sections satisfactory for models of mixtures and of

ionization and transport in the pure gases.

?

Please refer to the published articles where possible.??

Also, please inform me of any errors or inconsistencies.

?

Original file preparation 10/29/95.

Last revision of file 06/24/08.

?

A. V. Phelps, Retired

JILA

University of Colorado

Boulder, CO 80309-0440

e-mail: avp@jila.colorado.edu

?

General remarks on electron collision cross sections:

?

For a recent review of electron cross sections see:

T. D. Mark, Y. Hatano, and F. Linder, "Electron Collision?

Cross Sections" in "Atomic and molecular data for?

radiotherapy and radiation research" IAEA-TECDOC-799, May?

1995, Chapt. 2. This chapter contains graphical compilations?

of cross sections for Ne, Ar, H2, H2O, CO2, CH4, and C3H8.?

These cross sections have not been compared to those given?

in this file.

?

M. Hayashi has prepared very extensive bibliographies of papers on?

electron collisions with Ar, H2, O2, N2, CO, H2O, halogen

molecules, hydrogen halide molecules, CO2, CH4, NH3, and PH3. Some

of these reoprts contain recommended cross sections. Available?

reports are entitled "Bibliography of electron and photon?

cross sections with atoms and molecules published in the 20th century?

- [name of gas] -", National Institute for Fusion Research, Report?

NIFS-Data Series NIFS-DATA-[??]. Unfortunately, most of these cross?

sections are not available on the Web. The Ar results are tabulated

in the accompanying file Hayashi.txt.

?

Very extensive reviews and compilations of published electron-atom?

and electron-molecule cross sections have been prepared by A.?

Zecca, G. P. Karwasz, and Brusa, Riv. Nuovo Cimento 19, No. 3,?

1-146 (1996) and G. P. Karwasz, R. S. Brusa, and A. Zecca, Riv.?

Nuovo Cimento 24, No. 1, 1-118 (2001) and No. 4, 1-101 (2001).?

Data shown are selected on the basis of???perceived quality?,?

but no recommended values are given.??Apparently floppy disk(s?)?

giving tabulations can be purchased from the Italian Physical?

Society.??I have not seen the disks, i.e., they are too expensive.??

Unfortunately for gas discharge modeling, the data ranges in?

the review papers are limited, especially for momentum transfer?

cross sections that can differ greatly from "total" cross sections

at the higher energies.?

?

Stephen Biagi at sfb@hep.ph.liv.ac.uk has derived a sets of?

cross sections for electron collisions with ~ 50 different gases?

that are required to be consistent with electron swarm data. The ~50?

gases include: N2, O2, H20, Ar, CO2, He, Ne, H2, D2, CH4, etc.

Unfortunately, the tabulations of these cross sections are not?

available on the Web.

?

A recent review of electron-molecule collisions is?

Hotop, Ruf, Allan, and Frabrikant, "Resonances and threshold?

phenomena in low energy electron collisions with molecules and?

clusters", in Advances in Atomic, Molecular and Optical Physics,

(Elsevier, 2003) Vol. 49.

?

A review of experimental integrated and differential cross section

data for electron collisions with some diatomic molecules is?

Brunger and Buckman, Physics Reports, 357, 215 (2002).??The gases?

discussed include H2, O2, N2, the halogens,NO, CO, and halogen?

halides.??This data is tabulated in Landolt-Bornstein, Vol. 17,?

Subvol. C, pp. 35-55 (2003).??Also, Vol 17, Subvol. A is concerned

with electron and photon collisions with atoms, but I do not have?

access to this volume or its data.

?

GENERAL WARNING TO GAS DISCHARGE MODELERS:

?

IF AUTHORS DO NOT EXPLICITLY STATE THAT THERE IS AGREEMENT BETWEEN?

A) IONIZATION, EXCITATION, ATTACHMMENT (IF APPLICABLE), AND TRANSPORT?

COEFFICIENTS CALCULATED USING THEIR CROSS SECTIONS AND B) RELIABLE?

EXPERIMENTAL MEASUREMENTS OF THESE COEFFICIENTS, YOU SHOULD BE

VERY SKEPTICAL OF ALL OF THEIR CROSS SECTIONS AND OF ELECTRON?

TRANSPORT AND REACTION COEFFICIENT RESULTS DERIVED FROM THEM.??

AGREEMENT WITH SWARM EXPERIMENTS SUCH AS IONIZATION COEFFICIENT,?

DRIFT VELOCITY, THE RATIO OF THE TRANSVERSE AND LOGITUDINAL DIFFUSION?

COEFFICIENT TO MOBILITY, ATTACHMENT COEFFICIENTS, AND EXCITATION?

COEFFICIENTS ARE CRICIAL EVIDENCE OF A RELIABLE SET OF INPUT CROSS?

SECTIONS FOR MODELING.??FOR EACH GAS IN THIS FILE WE HAVE SUMMARIZED?

OUR TESTS OF THE CROSS SECTIONS AGAINST EXPERIMENTAL SWARM DATA.

?

OXYGEN - O2 - 1978

These cross sections are those developed in Lawton and Phelps, J.

Chem. Phys. 69, 1055 (1978).??The agreement of the transport?

and reaction coefficients is good and is discussed in detail?

in this paper.??Information Center Report No. 28 is based on?

the same computer files as used to assemble the following data.??

As of 9/28/01 I know of no reason to change the cross sections.

?

Note that the "cross sections" listed under the heading of?

three-body attrachment are expressed as equivalent cross?

sections at an O2 density of 1 molecule/cm3.??This means?

that the rate coefficients k and spatial attachment?

coefficients alpha/n calculated using BACKPRO must be?

multiplied by the O2 density in molecules/cm3 to obtain the?

equivalent of the two-body coefficients per molecule calculated?

for other processes, such as excitation and ionization.??

?

O2 MOMENTUM-TRANSFER CROSS SECTION

?

????????????ENERGY????????Effective Qm - Defined in introduction

???1????????0.0000????????0.3500

???2????????0.0010????????0.3500

???3????????0.0020????????0.3600

???4????????0.0030????????0.4000

???5????????0.0050????????0.5000

???6????????0.0070????????0.5800

???7????????0.0085????????0.6400

???8????????0.0100????????0.7000

???9????????0.0150????????0.8700

??10????????0.0200????????0.9900

??11????????0.0300????????1.2400

??12????????0.0400????????1.4400

??13????????0.0500????????1.6000

??14????????0.0700????????2.1000

??15????????0.1000????????2.5000

??16????????0.1200????????2.8000

??17????????0.1500????????3.1000

??18????????0.1700????????3.3000

??19????????0.2000????????3.6000

??20????????0.2500????????4.1000

??21????????0.3000????????4.5000

??22????????0.3500????????4.7000

??23????????0.4000????????5.2000

??24????????0.5000????????5.7000

??25????????0.7000????????6.1000

??26????????1.0000????????7.2000

??27????????1.2000????????7.9000

??28????????1.3000????????7.9000

??29????????1.5000????????7.6000

??30????????1.7000????????7.3000

??31????????1.9000????????6.9000

??32????????2.1000????????6.6000

??33????????2.2000????????6.5000

??34????????2.5000????????6.1000

??35????????2.8000????????5.8000

??36????????3.0000????????5.7000

??37????????3.3000????????5.5000

??38????????3.6000????????5.4500

??39????????4.0000????????5.5000

??40????????4.5000????????5.5500

??41????????5.0000????????5.6000

??42????????6.0000????????6.0000

??43????????7.0000????????6.6000

??44????????8.0000????????7.1000

??45???????10.0000????????8.0000

??46???????12.0000????????8.5000

??47???????15.0000????????8.8000

??48???????17.0000????????8.7000

??49???????20.0000????????8.6000

??50???????25.0000????????8.2000

??51???????30.0000????????8.0000

??52???????50.0000????????7.7000

??53???????75.0000????????6.8000

??54??????100.0000????????6.5000

??55??????150.0000????????6.7000

??56??????200.0000????????6.0000

??57??????300.0000????????4.9000

??58??????500.0000????????3.6000

??59??????700.0000????????2.9000

??60?????1000.0000????????2.1200

??61?????1500.0000????????1.4800

??62?????2000.0000????????1.1400

??63?????3000.0000????????0.7900

??64?????5000.0000????????0.5100

??65?????7000.0000????????0.3800

??66????10000.0000????????0.2800

?

O2 THREE-BODY ATTACHMENT????????????????????????????????????????????????????????????????

ENERGY LOSS =????0.000 ,???LOWER LIMIT =????0.000 ,???UPPER LIMIT =????1.058 ,???

QSCALE =?????1.000000??(QSCALE USED ONLY FOR RECONSTRUCTING INPUT DATA)

?

??????????????ENERGY?????CROSS SECTION

?????1????????0.0000????????0.0000?

?????2????????0.0580????????0.0000????????????

?????3????????0.0730???????5.6E-21???????????

?????4????????0.0830??????18.0E-21??????????

?????5????????0.0890???????4.2E-21????????????

?????6????????0.0950???????8.4E-21????????????

?????7????????0.1030??????18.0E-21????????????

?????8????????0.1090????????0.0000????????????

?????9????????0.1500????????0.0000????????????

????10????????0.1700????????0.0000????????????

????11????????0.2000????????0.0000????????????

????12????????0.2100??????3.56E-21????????????

????13????????0.2300????????0.0000????????????

????14????????0.3200????????0.0000????????????

????15????????0.3300??????2.30E-21????????????

????16????????0.3500????????0.0000????????????

????17????????0.4400????????0.0000????????????

????18????????0.4500??????1.45E-21????????????

????19????????0.4700????????0.0000

????20????????0.5600????????0.0000

????21????????0.5700???????1.1E-21

????22????????0.5900????????0.0000

????23????????0.6800????????0.0000

????24????????0.6900???????8.0E-22

????25????????0.7100????????0.0000

????26????????0.7900????????0.0000

????27????????0.8000???????7.0E-22

????28????????0.8200????????0.0000

????29????????0.9000????????0.0000

????30????????0.9100???????5.5E-22

????31????????0.9300????????0.0000

????32????????1.0200????????0.0000

????33????????1.0300???????4.2E-22

????34????????1.0500????????0.0000

????35????????1.5000????????0.0000

????36????10000.0000????????0.0000

?

?

O2 TWO-BODY ATTACHMENT??????????????????????????????????????????????????????????????????

ENERGY LOSS =????0.000 ,???LOWER LIMIT =????0.000 ,???UPPER LIMIT =??100.001 ,???

QSCALE =?????1.200000

?

??????????????ENERGY?????CROSS SECTION

?????1????????0.0000????????0.0000????????????

? ???2????????4.4000????????0.0000????????????

?????3????????4.9000????????0.0000????????????

?????4????????5.3800????????0.0023????????????

?????5????????5.8600????????0.0072????????????

?????6????????6.1000????????0.0108????????????

?????7????????6.4800????????0.0138????????????

?????8????????6.7700????????0.0152????????????

?????9????????7.0500????????0.0156????????????

????10????????7.3000????????0.0148????????????

????11????????7.5300????????0.0131

????12????????7.7700????????0.0110

????13????????8.0000????????0.0084

????14????????8.2500????????0.0054

????15????????8.7300????????0.0028

????16????????9.2000????????0.0014

????17????????9.6800????????0.0008

????18???????10.1500????????0.0008

????19???????11.3500????????0.0008

????20????10000.0000????????0.0000

?

O2 SINGL LEVEL ROT PKQ FOR 300K??????????????????????????????????????????????????????????

ENERGY LOSS =????0.020 ,???LOWER LIMIT =????0.026 ,???UPPER LIMIT =????1.677 ,???

QSCALE =?????1.000000

?

??????????????ENERGY?????CROSS SECTION??????????????????ENERGY?????CROSS SECTION

?????1????????0.0000????????0.0000????????????

?????2????????0.0067????????0.0000????????????

?????3????????0.0700????????0.0000????????????

?????4????????0.0800????????0.0054????????????

?????5????????0.1000????????0.0000????????????

?????6????????0.2000????????0.0000????????????

?????7????????0.2100????????0.0216????????????

?????8????????0.2200????????0.0000????????????

?????9????????0.3200????????0.0000????????????

????10????????0.3300????????0.0384????????????

????11????????0.3500????????0.0000????????????

????12????????0.4400????????0.0000????????????

????13????????0.4500????????0.0540????????????

????14????????0.4700????????0.0000????????????

????15????????0.5600????????0.0000????????????

????16????????0.5700????????0.0672????????????

????17????????0.5900????????0.0000????????????

????18????????0.6800????????0.0000????????????

????19????????0.6900????????0.0804????????????

????20????????0.7100????????0.0000????????????

????21????????0.7900????????0.0000????????????

????22????????0.8000????????0.0936????????????

????23????????0.8100????????0.0000????????????

????24????????0.9000????????0.0000????????????

????25????????0.9100????????0.0840

????26????????0.9300????????0.0000

????27????????1.0200????????0.0000

????28????????1.0300????????0.0720

????29????????1.0500????????0.0000

????30????????1.1300????????0.0000

????31????????1.1400????????0.0468

????32????????1.1600????????0.0000

????33????????1.2300????????0.0000

????34????????1.2300????????0.0600

????35????????1.2600????????0.0000

????36????????1.3400????????0.0000

????37????????1.3500????????0.0360

????38????????1.3700????????0.0000

????39????????1.4400????????0.0000

????40????????1.4500????????0.0240

????41????????1.4700????????0.0000

????42????????1.5400????????0.0000

????43????????1.5500????????0.0120

????44????????1.5700????????0.0000

????45????????1.6400????????0.0000

????46????????1.6500????????0.0048

????47????????1.6700????????0.0000

????48????10000.0000????????0.0000

?

O2 V=1 LINDER AND SCHMIDT WITH SPLIT PK?????????????????????????????????????????????????

ENERGY LOSS =????0.190 ,???LOWER LIMIT =????0.181 ,???UPPER LIMIT =????5.005 ,???

QSCALE =?????2.500000

?

??????????????ENERGY?????CROSS SECTION????????

?????1????????0.0000????????0.0000????????????

?????2????????0.1900????????0.0000????????????

?????3????????0.2000????????0.0010????????????

?????4????????0.2100????????0.0010????????????

?????5????????0.2300????????0.0000????????????

?????6????????0.3200????????0.0000????????????

?????7????????0.3300????????0.4150????????????

?????8????????0.3500????????0.0000????????????

?????9????????0.4400????????0.0000????????????

????10????????0.4500????????1.3500????????????

????11????????0.4700????????0.0000????????????

????12????????0.5600????????0.0000????????????

????13????????0.5700????????1.8500????????????

????14????????0.5900????????0.0000????????????

????15????????0.6800????????0.0000????????????

????16????????0.6900????????1.6500????????????

????17????????0.7100????????0.0000????????????

????18????????0.7900????????0.0000????????????

????19????????0.8000????????1.0000????????????

????20????????0.8200????????0.0000????????????

????21????????0.9000????????0.0000????????????

????22????????0.9100????????0.6000????????????

????23????????0.9300????????0.0000????????????

????24????????1.0200????????0.0000????????????

????25????????1.0300????????0.2850

????26????????1.0500????????0.0000

????27????????1.1300????????0.0000

????28????????1.1400????????0.1125

????29????????1.1600????????0.0000

????30????????1.2300????????0.0000

????31????????1.2400????????0.0475

????32????????1.2600????????0.0000

????33????????1.3400????????0.0000

????34????????1.3500????????0.0165

????35????????1.3700????????0.0000

????36????????1.4400????????0.0000

????37????????1.4500????????0.0055

????38????????1.4700????????0.0000

????39????????1.5400????????0.0000

????40????????1.5500????????0.0019

????41????????1.5700????????0.0000

????42????????1.6300????????0.0000

????43????????1.6500????????0.0006

????44????????1.6700????????0.0000

????45????????3.5000????????0.0000

????46????????4.0000????????0.0000

????47????????5.0000????????0.0000

????48????10000.0000????????0.0000

?

O2 V=2 LINDER AND SCHMIDT X2????????????????????????????????????????????????????????????

ENERGY LOSS =????0.380 ,???LOWER LIMIT =????0.439 ,???UPPER LIMIT =????5.005 ,???

QSCALE =?????1.250000

?

??????????????ENERGY?????CROSS SECTION???????

?????1????????0.0000????????0.0000????????????

?????2????????0.3800????????0.0000????????????

?????3????????0.4400????????0.0000????????????

?????4????????0.4500????????0.0000????????????

?????5????????0.4700????????0.0000????????????

?????6????????0.5600????????0.0000????????????

?????7????????0.5700????????0.1400????????????

?????8????????0.5900????????0.0000????????????

?????9????????0.6800????????0.0000????????????

????10????????0.6900????????0.4150????????????

????11????????0.7100????????0.0000????????????

????12????????0.7900????????0.0000????????????

????13????????0.8000????????0.5350????????????

????14????????0.8200????????0.0000????????????

????15????????0.9000????????0.0000????????????

????16????????0.9100????????0.4650????????????

????17????????0.9300????????0.0000????????????

????18????????1.0200????????0.0000????????????

????19????????1.0300????????0.3150????????????

????20????????1.0500????????0.0000????????????

????21????????1.1300????????0.0000????????????

????22????????1.1400????????0.2000

????23????????1.1600????????0.0000

????24????????1.2300????????0.0000

????25????????1.2400????????0.0950

????26????????1.2600????????0.0000

????27????????1.3400????????0.0000

????28????????1.3500????????0.0400

????29????????1.3700????????0.0000

????30????????1.4400????????0.0000

????31????????1.4500????????0.0185

????32????????1.4700????????0.0000

????33????????1.5400????????0.0000

????34????????1.5500????????0.0085

????35????????1.5700????????0.0000

????36????????1.6300????????0.0000

????37????????1.6500????????0.0034

????38????????1.6700????????0.0000

????39????????3.5000????????0.0000

????40????????4.0000????????0.0000

????41????????5.0000????????0.0000

????42????10000.0000????????0.0000

...

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