Isomer effect in electron collisions with small hydrocarbons
Transcript of Isomer effect in electron collisions with small hydrocarbons
Isomer effect in electron collisions
with small hydrocarbons
Marcio H. F. BettegaDepartamento de Fısica, Universidade Federal do Parana,
Caixa Postal 19044, 81531-990, Curitiba Parana, Brazil
Adriana R. Lopes, Sergio d’A. Sanchez,Marcio T. do N. Varella, Marco A. P. Lima, Luiz G. Ferreira
Instituto de Fısica “Gleb Wataghin”,
Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970,
Campinas, Sao Paulo, Brazil
XXIV ICPEAC - Rosario 2005 1
Outline
• Motivation.
• The Schwinger multichannel method.• Results: static-exchange (SE) approximation.
• C3H4: allene, propyne and cyclopropene.• C3H6: propene and cyclopropane.• C4H6: 1,3-butadiene, 2-butyne and cyclobutene.• C4H8: isobutene, trans-2- and cis-2-butene, syn-1- and
skew-1-butene.• C4H10: butane and isobutane.• Isocarbons.• Alkanes.• Shadow model.
• Final remarks
XXIV ICPEAC - Rosario 2005 2
Outline
• Motivation.• The Schwinger multichannel method.
• Results: static-exchange (SE) approximation.• C3H4: allene, propyne and cyclopropene.• C3H6: propene and cyclopropane.• C4H6: 1,3-butadiene, 2-butyne and cyclobutene.• C4H8: isobutene, trans-2- and cis-2-butene, syn-1- and
skew-1-butene.• C4H10: butane and isobutane.• Isocarbons.• Alkanes.• Shadow model.
• Final remarks
XXIV ICPEAC - Rosario 2005 2
Outline
• Motivation.• The Schwinger multichannel method.• Results: static-exchange (SE) approximation.
• C3H4: allene, propyne and cyclopropene.• C3H6: propene and cyclopropane.• C4H6: 1,3-butadiene, 2-butyne and cyclobutene.• C4H8: isobutene, trans-2- and cis-2-butene, syn-1- and
skew-1-butene.• C4H10: butane and isobutane.
• Isocarbons.• Alkanes.• Shadow model.
• Final remarks
XXIV ICPEAC - Rosario 2005 2
Outline
• Motivation.• The Schwinger multichannel method.• Results: static-exchange (SE) approximation.
• C3H4: allene, propyne and cyclopropene.• C3H6: propene and cyclopropane.• C4H6: 1,3-butadiene, 2-butyne and cyclobutene.• C4H8: isobutene, trans-2- and cis-2-butene, syn-1- and
skew-1-butene.• C4H10: butane and isobutane.• Isocarbons.• Alkanes.
• Shadow model.
• Final remarks
XXIV ICPEAC - Rosario 2005 2
Outline
• Motivation.• The Schwinger multichannel method.• Results: static-exchange (SE) approximation.
• C3H4: allene, propyne and cyclopropene.• C3H6: propene and cyclopropane.• C4H6: 1,3-butadiene, 2-butyne and cyclobutene.• C4H8: isobutene, trans-2- and cis-2-butene, syn-1- and
skew-1-butene.• C4H10: butane and isobutane.• Isocarbons.• Alkanes.• Shadow model.
• Final remarks
XXIV ICPEAC - Rosario 2005 2
Outline
• Motivation.• The Schwinger multichannel method.• Results: static-exchange (SE) approximation.
• C3H4: allene, propyne and cyclopropene.• C3H6: propene and cyclopropane.• C4H6: 1,3-butadiene, 2-butyne and cyclobutene.• C4H8: isobutene, trans-2- and cis-2-butene, syn-1- and
skew-1-butene.• C4H10: butane and isobutane.• Isocarbons.• Alkanes.• Shadow model.
• Final remarks
XXIV ICPEAC - Rosario 2005 2
Motivation
• Our main goal is to investigate the isomer effect in the elasticcross sections of isomers of small hydrocarbons → differencesthat allow one to distinguish between the different isomers
• Shape resonances (position, symmetry);• Differences in the shape and/or in the magnitude of the elastic
cross sections of the isomeric compounds.
• Previous experimental works motivated us to perfom thissystematic study.
XXIV ICPEAC - Rosario 2005 3
Motivation
• Our main goal is to investigate the isomer effect in the elasticcross sections of isomers of small hydrocarbons → differencesthat allow one to distinguish between the different isomers• Shape resonances (position, symmetry);• Differences in the shape and/or in the magnitude of the elastic
cross sections of the isomeric compounds.
• Previous experimental works motivated us to perfom thissystematic study.
XXIV ICPEAC - Rosario 2005 3
Motivation
• Our main goal is to investigate the isomer effect in the elasticcross sections of isomers of small hydrocarbons → differencesthat allow one to distinguish between the different isomers• Shape resonances (position, symmetry);• Differences in the shape and/or in the magnitude of the elastic
cross sections of the isomeric compounds.• Previous experimental works motivated us to perfom this
systematic study.
XXIV ICPEAC - Rosario 2005 3
Motivation
• Experimental studies:
Total cross sections: C. Szmytkowski, S. Kwitnewski, JPB 35, 2612(2002); JPB 35, 3781 (2002); JPB 36, 2129 (2003).
0.1 1 10 1000
10
20
30
40
50
C3H4
allenepropyne
0.1 1 10 100energy (eV)
0
10
20
30
40
50
cross section (10-16cm2)
C3H6
cyclopropanepropene
0.1 1 10 1000
10
20
30
40
50
60
C4H6
1,3-butadiene2-butyne
XXIV ICPEAC - Rosario 2005 4
Motivation
• Experimental studies:
Total cross sections: C. Szmytkowski, S. Kwitnewski, JPB 35, 2612(2002); JPB 35, 3781 (2002); JPB 36, 2129 (2003).
0.1 1 10 1000
10
20
30
40
50
C3H4
allenepropyne
0.1 1 10 100energy (eV)
0
10
20
30
40
50
cross section (10-16cm2)
C3H6
cyclopropanepropene
0.1 1 10 1000
10
20
30
40
50
60
C4H6
1,3-butadiene2-butyne
XXIV ICPEAC - Rosario 2005 4
Motivation
Total cross sections: C. Makochekanwa, H. Kawate, O. Sueoka, M.Kimura, M. Kitajima, M. Hoshino and H. Tanaka, CPL 368, 82 (2003).
0.1 1 10 100 1000energy (eV)
0
10
20
30
40
50
cross section (10-16cm2)
allenepropyne
XXIV ICPEAC - Rosario 2005 5
Motivation
Differential cross sections: Y. Nakano, M. Hoshino, M. Kitajima, H.Tanaka, M. Kimura, PRA 66, 032714 (2002).
5 eV
propyneallene
7 eV
0 30 60 90 120 150 180
scattering angle (degrees)
0.1
1
10
100
cross section (10-16cm2/sr)
10 eV 12 eV
15 eV 20 eV
25 eV 30 eV
XXIV ICPEAC - Rosario 2005 6
Motivation
• Experiment and theory.
• C3H6 and C4H10 isomers: K. Floeder, D. Fromme, W. Raith, A.Schwab and G. Sinapius, JPB 18, 3347 (1985).• The isomers have similar total cross sections over the energy
range studied.
• C3H6 isomers: H. Nishimura and H. Tawara, JPB 24, L363 (1991).• The isomers present differences in the total cross sections for
energies below 40 eV.• Isomer effect → differences in the molecular structures.
• C3H6 isomers (theory): C. Winstead, Q. Sun, and V. McKoy, JCP96, 4246 (1992).• The isomers present differences in the elastic cross sections
below 40 eV.
XXIV ICPEAC - Rosario 2005 7
Motivation
• Experiment and theory.• C3H6 and C4H10 isomers: K. Floeder, D. Fromme, W. Raith, A.
Schwab and G. Sinapius, JPB 18, 3347 (1985).• The isomers have similar total cross sections over the energy
range studied.
• C3H6 isomers: H. Nishimura and H. Tawara, JPB 24, L363 (1991).• The isomers present differences in the total cross sections for
energies below 40 eV.• Isomer effect → differences in the molecular structures.
• C3H6 isomers (theory): C. Winstead, Q. Sun, and V. McKoy, JCP96, 4246 (1992).• The isomers present differences in the elastic cross sections
below 40 eV.
XXIV ICPEAC - Rosario 2005 7
Motivation
• Experiment and theory.• C3H6 and C4H10 isomers: K. Floeder, D. Fromme, W. Raith, A.
Schwab and G. Sinapius, JPB 18, 3347 (1985).• The isomers have similar total cross sections over the energy
range studied.• C3H6 isomers: H. Nishimura and H. Tawara, JPB 24, L363 (1991).
• The isomers present differences in the total cross sections forenergies below 40 eV.
• Isomer effect → differences in the molecular structures.
• C3H6 isomers (theory): C. Winstead, Q. Sun, and V. McKoy, JCP96, 4246 (1992).• The isomers present differences in the elastic cross sections
below 40 eV.
XXIV ICPEAC - Rosario 2005 7
Motivation
• Experiment and theory.• C3H6 and C4H10 isomers: K. Floeder, D. Fromme, W. Raith, A.
Schwab and G. Sinapius, JPB 18, 3347 (1985).• The isomers have similar total cross sections over the energy
range studied.• C3H6 isomers: H. Nishimura and H. Tawara, JPB 24, L363 (1991).
• The isomers present differences in the total cross sections forenergies below 40 eV.• Isomer effect → differences in the molecular structures.
• C3H6 isomers (theory): C. Winstead, Q. Sun, and V. McKoy, JCP96, 4246 (1992).• The isomers present differences in the elastic cross sections
below 40 eV.
XXIV ICPEAC - Rosario 2005 7
Motivation
• Experiment and theory.• C3H6 and C4H10 isomers: K. Floeder, D. Fromme, W. Raith, A.
Schwab and G. Sinapius, JPB 18, 3347 (1985).• The isomers have similar total cross sections over the energy
range studied.• C3H6 isomers: H. Nishimura and H. Tawara, JPB 24, L363 (1991).
• The isomers present differences in the total cross sections forenergies below 40 eV.• Isomer effect → differences in the molecular structures.
• C3H6 isomers (theory): C. Winstead, Q. Sun, and V. McKoy, JCP96, 4246 (1992).• The isomers present differences in the elastic cross sections
below 40 eV.
XXIV ICPEAC - Rosario 2005 7
SMC method
Takatsuka and McKoy, PRA 24, 2473 (1981)Takatsuka and McKoy, PRA 30, 1734 (1984)
• Variational approach;• Formulated for applications to low-energy electron-molecule
collisions;• Capable of addressing important aspects of these collisions as:
• molecular targets of general geometry;• exchange interactions (ab initio);• effects arising from the polarization of the target by the
incident electron (ab initio);• electronic excitation.
• Pseudopotentials LDA/norm-conserving from Bachelet, Hamannand Schlüter [PRB 26, 4199 (1982)].Bettega, Ferreira and Lima, PRA 47, 1111 (1993).
XXIV ICPEAC - Rosario 2005 8
SMC method
Takatsuka and McKoy, PRA 24, 2473 (1981)Takatsuka and McKoy, PRA 30, 1734 (1984)
• Variational approach;
• Formulated for applications to low-energy electron-moleculecollisions;
• Capable of addressing important aspects of these collisions as:• molecular targets of general geometry;• exchange interactions (ab initio);• effects arising from the polarization of the target by the
incident electron (ab initio);• electronic excitation.
• Pseudopotentials LDA/norm-conserving from Bachelet, Hamannand Schlüter [PRB 26, 4199 (1982)].Bettega, Ferreira and Lima, PRA 47, 1111 (1993).
XXIV ICPEAC - Rosario 2005 8
SMC method
Takatsuka and McKoy, PRA 24, 2473 (1981)Takatsuka and McKoy, PRA 30, 1734 (1984)
• Variational approach;• Formulated for applications to low-energy electron-molecule
collisions;
• Capable of addressing important aspects of these collisions as:• molecular targets of general geometry;• exchange interactions (ab initio);• effects arising from the polarization of the target by the
incident electron (ab initio);• electronic excitation.
• Pseudopotentials LDA/norm-conserving from Bachelet, Hamannand Schlüter [PRB 26, 4199 (1982)].Bettega, Ferreira and Lima, PRA 47, 1111 (1993).
XXIV ICPEAC - Rosario 2005 8
SMC method
Takatsuka and McKoy, PRA 24, 2473 (1981)Takatsuka and McKoy, PRA 30, 1734 (1984)
• Variational approach;• Formulated for applications to low-energy electron-molecule
collisions;• Capable of addressing important aspects of these collisions as:
• molecular targets of general geometry;• exchange interactions (ab initio);• effects arising from the polarization of the target by the
incident electron (ab initio);• electronic excitation.
• Pseudopotentials LDA/norm-conserving from Bachelet, Hamannand Schlüter [PRB 26, 4199 (1982)].Bettega, Ferreira and Lima, PRA 47, 1111 (1993).
XXIV ICPEAC - Rosario 2005 8
SMC method
Takatsuka and McKoy, PRA 24, 2473 (1981)Takatsuka and McKoy, PRA 30, 1734 (1984)
• Variational approach;• Formulated for applications to low-energy electron-molecule
collisions;• Capable of addressing important aspects of these collisions as:
• molecular targets of general geometry;• exchange interactions (ab initio);• effects arising from the polarization of the target by the
incident electron (ab initio);• electronic excitation.
• Pseudopotentials LDA/norm-conserving from Bachelet, Hamannand Schlüter [PRB 26, 4199 (1982)].
Bettega, Ferreira and Lima, PRA 47, 1111 (1993).
XXIV ICPEAC - Rosario 2005 8
SMC method
Takatsuka and McKoy, PRA 24, 2473 (1981)Takatsuka and McKoy, PRA 30, 1734 (1984)
• Variational approach;• Formulated for applications to low-energy electron-molecule
collisions;• Capable of addressing important aspects of these collisions as:
• molecular targets of general geometry;• exchange interactions (ab initio);• effects arising from the polarization of the target by the
incident electron (ab initio);• electronic excitation.
• Pseudopotentials LDA/norm-conserving from Bachelet, Hamannand Schlüter [PRB 26, 4199 (1982)].Bettega, Ferreira and Lima, PRA 47, 1111 (1993).
XXIV ICPEAC - Rosario 2005 8
Results
• Elastic integral, differential and momentum transfer cross sectionsat the static-exchange (SE) approximation.
• References:• C3H4 isomers: Lopes and Bettega, PRA 67, 032711 (2003).• C4H6 isomers: Lopes et al., PRA 69, 014702 (2004).• C4H8 and C4H10 isomers: Lopes et al., JPB 37, 997 (2004).• C3H4 (SEP): Sanchez et al., PRA 71 , 062702 (2005).• C3H4 (rotational excitation): Lopes et al., to be submitted.• C3H6 (SE and SEP): Bettega et al., to be submitted.
XXIV ICPEAC - Rosario 2005 9
Results
• Elastic integral, differential and momentum transfer cross sectionsat the static-exchange (SE) approximation.
• References:• C3H4 isomers: Lopes and Bettega, PRA 67, 032711 (2003).• C4H6 isomers: Lopes et al., PRA 69, 014702 (2004).• C4H8 and C4H10 isomers: Lopes et al., JPB 37, 997 (2004).• C3H4 (SEP): Sanchez et al., PRA 71 , 062702 (2005).• C3H4 (rotational excitation): Lopes et al., to be submitted.• C3H6 (SE and SEP): Bettega et al., to be submitted.
XXIV ICPEAC - Rosario 2005 9
Results: C3H4 isomers
(b)
(a)
(c)
Geometrical structure of the C3H4 isomers: (a) allene (D2d), (b) propyne (C3v), and (c)cyclopropene (C2v).
XXIV ICPEAC - Rosario 2005 10
Results: C3H4 isomers
5 eV 7 eV
0 30 60 90 120 150 180
angle (degrees)
0.1
1
10
100
cross section (10-16cm2/sr)
10 eV 12 eV
15 eV 20 eV
25 eV 30 eV
Differential cross sections for propyne. Solid lines, our results at the SE approximation;circles, experimental data of Nakano et al..
XXIV ICPEAC - Rosario 2005 11
Results: C3H4 isomers
5 eV 7 eV
0 30 60 90 120 150 180
angle (degrees)
0.1
1
10
100
cross section (10-16cm2/sr)
10 eV 12 eV
15 eV 20 eV
25 eV 30 eV
Differential cross sections for allene. Solid lines, our results at the SE approximation;circles, experimental data of Nakano et al..
XXIV ICPEAC - Rosario 2005 12
Results: C3H4 isomers
0 10 20 30 40 500
10
20
30
40
50
D2d (allene)
0 10 20 30 40 50
energy (eV)
0
10
20
30
40
50
cross section (10-16cm2)
C3v (propyne)
Integral cross section for C3H4 isomers propyne and allene. Solid lines, our results atthe SE approximation; stars, total cross section of Szmytkowski and Kwitnewski;
crosses, total cross section of Makochekanwa et al..
XXIV ICPEAC - Rosario 2005 13
Results: C3H4 isomers
0 10 20 30 40 50
energy (eV)
0
10
20
30
40
50
cross section (10-16cm2)
(a)
C3v (propyne)
D2d (allene)
C2v (cyclopropene)
0 10 20 30 40 500
10
20
30
40
(b)
(a) Integral and (b) momentum transfer cross sections for C3H4 isomers at the SEapproximation.
XXIV ICPEAC - Rosario 2005 14
Results: C3H4 isomers
10-3
10-2
10-1
100
101
10-3
10-2
10-1
100
101
10-3
10-2
10-1
100
101
cross section (10-16 cm2/sr)
10-3
10-2
10-1
100
101
0 30 60 90 120 150 180scattering angle (degrees)
10-4
10-2
100
0 30 60 90 120 150 18010-4
10-2
100
5 eV 7 eV
10 eV 15 eV
20 eV 30 eV
Differential rotationally elastic cross sections (00 → 00) for allene (solid line), propyne(dashed line) and cyclopropene (dot-dashed line).
XXIV ICPEAC - Rosario 2005 15
Results: C3H6 isomers
(a)(b)
Geometrical structure of the C3H6 isomers: (a) cyclopropane (D3h) and (b) propene(Cs).
XXIV ICPEAC - Rosario 2005 16
Results: C3H6 isomers
0 10 20 30 40 50 60energy (eV)
0
10
20
30
40
50cross section (10-16cm2)
(a)
0 10 20 30 40 50 600
10
20
30
40
50
(b)
Integral cross sections for C3H6 isomers at the SE approximation. (a) Cyclopropane and(b) propene. Solid lines, our results at the SE approximation. Total cross sections:
crosses, Floeder et al.; pluses, Nishimura and Tawara; stars, Szmytkowski andKwitnewski.
XXIV ICPEAC - Rosario 2005 17
Results: C3H6 isomers
0 10 20 30 40 50 60energy (eV)
0
10
20
30
40
50cross section (10-16cm2)
(a)
0 10 20 30 40 50 600
5
10
15
20
25
30
(b)
(a) Integral and (b) momentum transfer cross sections for C3H6 isomers at the SEapproximation. Solid line (PP) and dot-dashed line (AE), cyclopropane; dashed line (PP)
and dotted line (AE), propene.
XXIV ICPEAC - Rosario 2005 18
Results: C3H6 isomers
0 3 6 9 12 15energy (eV)
0
10
20
30
40
50
cross section (10-16cm2)
(a)
0 3 6 9 12 150
10
20
30
40
50
(b)
Integral cross sections for C3H6 isomers: (a) cyclopropane and (b) propene. Dashedlines, our results at the SE approximation; solid lines, our results at the SEP
approximation; dotted line, results of Curik and Gianturco at the SEP approximation;dot-dashed lines, results of Beyer et al. at the SEP approximation; stars, total cross
section of Szmytkowski and Kwitnewski.
XXIV ICPEAC - Rosario 2005 19
Results: C4H6 isomers
(a)(b)
(c)
Geometrical structure of the C4H6 isomers: (a) trans-1,3-butadiene (C2h), (b) 2-butyne(D3h), and (c) cyclobutene (C2v).
XXIV ICPEAC - Rosario 2005 20
Results: C4H6 isomers
0 10 20 30 40 50 600
20
40
60
D3h - 2-butyne
0 10 20 30 40 50 60
energy (eV)
0
20
40
60cross section (10-16cm2)
C2h - 1,3-butadiene
Integral cross sections for C4H6 isomers 2-butyne and 1,3-butadiene at the SEapproximation. Solid lines, our resuls; stars, total cross sections of Szmytkowski and
Kwitnewski.
XXIV ICPEAC - Rosario 2005 21
Results: C4H6 isomers
0 10 20 30 40 50 60
energy (eV)
0
20
40
60cross section (10-16cm2)
(a)
2-butyne1,3-butadienecyclobutene
0 10 20 30 40 50 600
10
20
30
40
(b)
(a) Integral and (b) momentum transfer cross sections for C4H6 isomers at the SEapproximation.
XXIV ICPEAC - Rosario 2005 22
Results: C4H8 isomers
(a)
(b)
(c)
Geometrical structure of the C4H8 isomers: (a) isobutene (C2v), (b) cis-2-butene (C2v),and (c) skew-1-butene (Cs).)
XXIV ICPEAC - Rosario 2005 23
Results: C4H8 isomers
0 10 20 30 40 50
energy (eV)
0
20
40
60cross section (10-16cm2)
(a)
isobutenecis-2-buteneskew-1-butene
0 10 20 30 40 500
10
20
30
40
(b)
(a) Integral and (b) momentum transfer cross sections for C4H8 isomers at the SEapproximation.
XXIV ICPEAC - Rosario 2005 24
Results: C4H10 isomers
(a)(b)
Geometrical structure of the C4H10 isomers: (a) butane (C2h), (b) isobutane (C3v).
XXIV ICPEAC - Rosario 2005 25
Results: C4H10 isomers
0 10 20 30 40 50
energy (eV)
0
20
40
60
cross section (10-16cm2)
butaneisobutane
0 10 20 30 40 500
10
20
30
40
Integral (left panel) and momentum transfer (right panel) cross sections for C4H10
isomers at the SE approximation.
XXIV ICPEAC - Rosario 2005 26
Results: Isocarbons.
0 10 20 30 40 50
energy (eV)
0
10
20
30
40
50cross section (10-16cm2) C
3H4
C3H6
C3H8
0 10 20 30 40 50
energy (eV)
0
20
40
60
cross section (10-16cm2)
C4H6
C4H8
C4H10
Comparison of the integral cross sections for left panel: C3H4 (propyne), C3H6
(propene), and C3H8 (propane); right panel: C4H6 (1,3-butadiene), C4H8
(trans-2-butene), and C4H10 (butane).
[For the comparison of C3H4, C3H6 and C3H8 we observe the same behavior reportedby Szmytkowski and Kwitnewski, JPB 35, 3781 (2002)]
XXIV ICPEAC - Rosario 2005 27
Results: Isocarbons.
0 10 20 30 40 50
energy (eV)
0
10
20
30
40
50cross section (10-16cm2) C
3H4
C3H6
C3H8
0 10 20 30 40 50
energy (eV)
0
20
40
60
cross section (10-16cm2)
C4H6
C4H8
C4H10
Comparison of the integral cross sections for left panel: C3H4 (propyne), C3H6
(propene), and C3H8 (propane); right panel: C4H6 (1,3-butadiene), C4H8
(trans-2-butene), and C4H10 (butane).[For the comparison of C3H4, C3H6 and C3H8 we observe the same behavior reported
by Szmytkowski and Kwitnewski, JPB 35, 3781 (2002)]
XXIV ICPEAC - Rosario 2005 27
Results: Alkanes.
0 10 20 30 40 50
energy (eV)
0
20
40
60
cross section (10-16cm2)
CH4
C2H6
C3H8
C4H10
Comparison of the integral cross sections for alkanes: CH4, C2H6, C3H8, C4H10.
[Winstead et al., JCP 94 , 5455 (1991) - we added C4H10]
XXIV ICPEAC - Rosario 2005 28
Results: Alkanes.
0 10 20 30 40 50
energy (eV)
0
20
40
60
cross section (10-16cm2)
CH4
C2H6
C3H8
C4H10
Comparison of the integral cross sections for alkanes: CH4, C2H6, C3H8, C4H10.[Winstead et al., JCP 94 , 5455 (1991) - we added C4H10]
XXIV ICPEAC - Rosario 2005 28
Shadow model
• Model based on Geometrical Optics:
• Atoms = spheres, molecules = rigid assembly of thesespheres.
• Sphere radii: depend on the atomic species and on theelectron impact energy.
• The molecules are illuminated by light coming from differentorientations. The shadow cross sections are computed.
• The ratio σSMC/σshadow is computed.
• The shadow cross sections are proportional to the hydrocarboncross sections.
• This model provides an “scaling law” for the hydrocarbon crosssections.
XXIV ICPEAC - Rosario 2005 29
Shadow model
• Model based on Geometrical Optics:• Atoms = spheres, molecules = rigid assembly of these
spheres.• Sphere radii: depend on the atomic species and on the
electron impact energy.• The molecules are illuminated by light coming from different
orientations. The shadow cross sections are computed.• The ratio σSMC/σshadow is computed.
• The shadow cross sections are proportional to the hydrocarboncross sections.
• This model provides an “scaling law” for the hydrocarbon crosssections.
XXIV ICPEAC - Rosario 2005 29
Shadow model
• Model based on Geometrical Optics:• Atoms = spheres, molecules = rigid assembly of these
spheres.• Sphere radii: depend on the atomic species and on the
electron impact energy.• The molecules are illuminated by light coming from different
orientations. The shadow cross sections are computed.• The ratio σSMC/σshadow is computed.
• The shadow cross sections are proportional to the hydrocarboncross sections.
• This model provides an “scaling law” for the hydrocarbon crosssections.
XXIV ICPEAC - Rosario 2005 29
Shadow model
• Model based on Geometrical Optics:• Atoms = spheres, molecules = rigid assembly of these
spheres.• Sphere radii: depend on the atomic species and on the
electron impact energy.• The molecules are illuminated by light coming from different
orientations. The shadow cross sections are computed.• The ratio σSMC/σshadow is computed.
• The shadow cross sections are proportional to the hydrocarboncross sections.
• This model provides an “scaling law” for the hydrocarbon crosssections.
XXIV ICPEAC - Rosario 2005 29
Shadow model - Results
10 15 20 25 30 35 40 45
energy (eV)
1.5
2
2.5
3
σ(SMC)/
σ(shadow)
CH4
C2H6
C2H4
C2H2
C3H8
C3H4a
C3H4b
C3H4c
C4H10a
C4H10b
C4H8a
C4H8b
C4H8c
C4H8d
C4H8e
C4H6a
C4H6b
C4H6c
Cross section ratios: CH4, C2H6, C2H4, C2H2, propane (C3H8), cyclopropene (C3H4a),propyne (C3H4b), allene (C3H4c), butane (C4H10a), isobutane (C4H10b), syn-1-butene
(C4H8a), skew-1-butene (C4H8b), trans-2-butene (C4H8c), isobutene (C4H8d),cis-2-butene (C4H8e), 2-butyne (C4H6a), 1,3-butadiene (C4H6b), cyclobutene (C4H6c).
XXIV ICPEAC - Rosario 2005 30
Final Remarks
• Conclusions
• Isomer effect: isomeric molecules have similar cross sectionsabove a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work
• Investigate the influence of polarization effects in the isomerscross sections.
• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31
Final Remarks
• Conclusions• Isomer effect: isomeric molecules have similar cross sections
above a given energy, which is different for different isomericgroups.
• In general the isomer effect is more evident at low energies,where the hydrocarbons cross sections present shaperesonances and different shape and magnitude.
• The isomer effect is more evident for cyclic hydrocarbons(cyclopropene, cyclopropane, cyclobutene - cyclobutane?).
• Isocarbons: larger molecules have larger cross sections (thedifferences being small for energies above 10 eV).
• Shadow model: the hydrocarbons cross sections becomesimilar after a “scaling”.
• Future work• Investigate the influence of polarization effects in the isomers
cross sections.• Rotational excitations.
XXIV ICPEAC - Rosario 2005 31