multiple ionization including post-collisional contributions claudia montanari instituto de...
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Multiple ionization including
post-collisional contributions
Multiple ionization including
post-collisional contributions
Claudia Montanari
Instituto de Astronomía y Física del Espacio
Buenos Aires, Argentina
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102 103 104
10-2
10-1
100
101
102
103
Syage (1992) for e+Kr Schram (1966) for e + Kr
Mul
tiple
ioni
zatio
n cr
oss
sect
ions
(M
b)
Rejoub (2002) for e + Kr Krishnakumar et al (1988)
Cavalcanti et al (2003) DuBois et al (1984), DuBois, PRL (1984)
Energy (keV/amu)
Kr4+x 10-2
Kr3+x 10-1
Kr2+
Kr+
H+ + Kr
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10-18
sec
projectile
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photon
3+
photon10-15 sec
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10-5
sec
6+
Multiple ionization data includes PCI
PCI=time delayed electron emision
Independent of the projectile
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)1()(... 121
qNi
qi
qqqq
N
i i
iq pp
q
NbP iii
N
Multinomial distributionMultinomial distribution
Direct multiple ionizationDirect multiple ionization
Cross section for ionization of q target electronsCross section for ionization of q target electrons
dbbb Pqq )(2
Independent particle model (IPM)Independent particle model (IPM)
ionization probability per electronionization probability per electronppii(b), of the i-subshell(b), of the i-subshell
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0.01 0.1 1 10
2
3
4
5
2
3
4
5
Zeff
P(r)
Zeff
P(q)
B+2 (1s2 2s)
First BornFirst Born bpi
)1()(... 121
qNi
qi
qqqq
N
i i
iq pp
q
NbP iii
N
Multinomial Multinomial
distributiondistribution
CDW-EISCDW-EIS
Angular expansion in spherical harmonics
The radial Scrödinger eq. is numericallly solved initial boundfinal continuum states
Ortogonality, asymptotic condicions
T-matrix expanded in Fourier series
Projectile:
Hartree-Fock positive ions
2
2
q
qZqV
effP
P)(
)(
nlmiqr
nlmPeffP eZZ
Miraglia & Gravielle Phys Rev A 78 (2008)
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Multiple ionization including PCIMultiple ionization including PCI
Multinomial distributionMultinomial distribution
)(... 121 qqqq
N
i
iq ( pi x 1 )
qi
q
NbP
N
)1( qN
ip ii
n Fi,n = 1
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CDW-EIS for multiple ionization of Ne, Ar, Kr, and Xe 7
Table 1. Compilation of experimental photoionization branching ratios.
N e
1s 2s 0 0.0193 1.00 1 0.921 0.00 2 0.0571 0.00 3 0.0028 0.00 4 0.000 0.00
A r
2s 2p 3s 0 0.000 0.005 1.00 1 0.010 0.863 0.00 2 0.890 0.128 0.00 3 0.100 0.003 0.00 4 0.000 0.001 0.00
K r
3s 3p 3d 4s 0 0.00 0.00 0.005 1.00 1 0.01 0.02 0.670 0.00 2 0.12 0.60 0.320 0.00 3 0.66 0.36 0.005 0.00 4 0.21 0.02 0.00 0.00
Xe
4s 4p 4d 5s 0 0.00 0.00 0.00 1.00 1 0.01 0.05 0.80 0.00 2 0.165 0.89 0.20 0.00 3 0.774 0.06 0.00 0.00 4 0.051 0.00 0.00 0.00
In Table 1, we present a rather complete compilation of di¤erent experimentalbranching ratios, of equation (8), for Ne, Ar, Kr and Xe, due to an initial singlevacancy in the -subshell. The vertical sumof each column is equal to 1. In this work,weusetheratios indicated with bold numbers in Table 1.
Auger emission in these targets is energetically possible for initial vacancies fromthedeepest to the subvalence shells [43]. This fact, already mentioned by Krause andCarlson [4, 6] and Saito et al [20], is expressed in Table 1 in thecolumns 2 for Ne, 3for Ar, 4 for Kr and 5 for Xewith = 0 (meaning that single ionization of theseshells does not contributeto PCI [4, 6, 7, 21, 23, 28, 43]).
This is an important point because, in recent works [9, 10, 12, 42], thePCI of Neand Ar targets were included by using the experimental data of Table IV by Carlsonet al [3]. These values represent the charge-state distribution after photoabsortion ofx-rays with energies chosen in order to determine theshell that dominates thevacancy
nF,n = 1
no of Auger electrons
Single ionization of an electron in
the subshell
Fn
Landers et al 2009, Phys. Rev Lett
Krause & Carlson in the 60s
Brünken et al 2002, Phys. Rev A
Tamenori et al 2004, J. Phys. B
Hikosaka et al 2004, Phys. Rev. AHayaishi et al 2002, J.Phys. B
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3p-2
3s-1
CDW-EIS for multiple ionization of Ne, Ar, Kr, and Xe 7
Table 1. Compilation of experimental photoionization branching ratios.
N e
1s 2s 0 0.0193 1.00 1 0.921 0.00 2 0.0571 0.00 3 0.0028 0.00 4 0.000 0.00
A r
2s 2p 3s 0 0.000 0.005 1.00 1 0.010 0.863 0.00 2 0.890 0.128 0.00 3 0.100 0.003 0.00 4 0.000 0.001 0.00
K r
3s 3p 3d 4s 0 0.00 0.00 0.005 1.00 1 0.01 0.02 0.670 0.00 2 0.12 0.60 0.320 0.00 3 0.66 0.36 0.005 0.00 4 0.21 0.02 0.00 0.00
Xe
4s 4p 4d 5s 0 0.00 0.00 0.00 1.00 1 0.01 0.05 0.80 0.00 2 0.165 0.89 0.20 0.00 3 0.774 0.06 0.00 0.00 4 0.051 0.00 0.00 0.00
In Table 1, we present a rather complete compilation of di¤erent experimentalbranching ratios, of equation (8), for Ne, Ar, Kr and Xe, due to an initial singlevacancy in the -subshell. The vertical sumof each column is equal to 1. In this work,weusetheratios indicated with bold numbers in Table 1.
Auger emission in these targets is energetically possible for initial vacancies fromthedeepest to the subvalence shells [43]. This fact, already mentioned by Krause andCarlson [4, 6] and Saito et al [20], is expressed in Table 1 in thecolumns 2 for Ne, 3for Ar, 4 for Kr and 5 for Xewith = 0 (meaning that single ionization of theseshells does not contributeto PCI [4, 6, 7, 21, 23, 28, 43]).
This is an important point because, in recent works [9, 10, 12, 42], thePCI of Neand Ar targets were included by using the experimental data of Table IV by Carlsonet al [3]. These values represent the charge-state distribution after photoabsortion ofx-rays with energies chosen in order to determine theshell that dominates thevacancy
nF,n = 1
no of Auger electrons
Single ionization of an electron in
the subshell
Fn
Landers et al 2009, Phys. Rev Lett
Krause & Carlson in the 60s
Brünken et al 2002, Phys. Rev A
Tamenori et al 2004, J. Phys. B
Hikosaka et al 2004, Phys. Rev. AHayaishi et al 2002, J.Phys. B
3p
3s
ArPCI o
f valence electro
ns ?
L-shell0.810.1120.0080.000.00
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Multiple ionization including PCIMultiple ionization including PCI
Multinomial distributionMultinomial distribution
)(... 121 qqqq
N
i
iq ( pi x 1 )
qi
q
NbP
N
)1( qN
ip ii
n Fi,n = 1
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Multiple ionization including PCIMultiple ionization including PCI
Multinomial distributionMultinomial distribution
)(... 121 qqqq
N
i
iq ( pi n Fi,n)
qi
q
NbP
N
)1( qN
ip ii
n Fi,n = 1
P(b)= P PCI
i1s2s…
PCI
including PCI
Number of total emitted electron (direct+PCI) )()( bbP
PCIP
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Xe
Kr
Ar
Ne
ResultsResultsE= (0.1-10) MeV/amu
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Xe
Kr
Ar
Ne
ResultsResults
He2+
B2+
+2
Li2+, Be2+
+2
H+, He+
+1
Li3+
+3
E= (0.1-10) MeV/amu
Be3+, B3+
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102 10310-4
10-3
10-2
10-1
100
101
102
103
CDW-EISBorn with PCI, without PCI
Xe5+x 10-3
Rejoub (2002) , e + Xe Syage (1992) , e + Xe Krishnakumar et al (1988), e + Xe
Cavalcanti et al (2003)
Mul
tiple
ioni
zatio
n cr
oss
sect
ion
(Mb)
Energy (keV/amu)
Xe4+x 10-2
Xe3+x 10-1
Xe2+
Xe+
Bornwithout PCI
H+ + Xe
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102 103 104
10-2
10-1
100
101
102
103
Syage (1992) for e+Kr Schram (1966) for e + Kr
Mu
ltip
le io
niz
atio
n c
ross
se
ctio
ns
(Mb
) CDW-EIS Born (Mb)
Rejoub (2002) for e + Kr Krishnakumar et al (1988)
Cavalcanti et al (2003) DuBois et al (1984), DuBois, PRL (1984)
Energy (keV/amu)
Kr4+x 10-2
Kr3+x 10-1
Kr2+
Kr+
Bornwithout PCI
H+ + Kr
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102 10310-4
10-3
10-2
10-1
100
101
102
103
Born with PCI CDW-EIS with PCI
DuBois, Phys Rev A 39, 4440 (1989) Santos et al, Phys Rev A 63, 062717 (2001)
Mul
tiple
ioni
zatio
n cr
oss
sect
ion
(Mb)
Kr5+x10-3
Energy (keV/amu)
Kr4+x10-2
Kr3+x10-1
Kr2+
Kr+
Bornwithout PCI
He+ + Kr
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102 103
10-3
10-2
10-1
100
101
102
103
DuBois (1987)
Born (Mb) CDW-EIS
Mu
ltip
le io
niz
atio
n c
ross
se
ctio
ns
(Mb
)
Kr5+x 10-3
Energy (keV/amu)
Kr4+x 10-2
Kr3+x 10-1
Kr2+
Kr+
Born
He+2 + Kr
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102 103 104
10-5
10-4
10-3
10-2
10-1
100
101
102
103
Syage (1992) Mccallion (1992)
CDW-EISBorn with PCI , without PCI
Belic (2010) Rejoub (2002)
Ar5+x 10-3
DuBois et al (1984), capture Cavalcanti et al (2002) Andersen et al (1987)
Ar4+x 10-2
Ar3+x 10-1
Ar2+
Ar+
Mul
tiple
ioni
zatio
n cr
oss
sect
ions
(M
b)
Energy (keV/amu)
Born
H+ + Ar
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102 103 104
10-5
10-4
10-3
10-2
10-1
100
101
102
103
Syage (1992) Mccallion (1992)
CDW-EISBorn with PCI , without PCI
BGM by Spranger et al (2004), includes capture
Belic (2010) Rejoub (2002)
Ar5+x 10-3
DuBois et al (1984), capture Cavalcanti et al (2002) Andersen et al (1987)
Ar4+x 10-2
Ar3+x 10-1
Ar2+
Ar+
Mul
tiple
ioni
zatio
n cr
oss
sect
ions
(M
b)
Energy (keV/amu)
Born
H+ + Ar
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102 103
10-4
10-3
10-2
10-1
100
101
102
CDW-EISBorn with PCI , without PCI
Santos et al (2001) DuBois (1989)
Mu
ltip
le io
niz
atio
n c
ross
se
ctio
n (
Mb
)
Ar5+x 10-3
Energy (keV/amu)
Ar4+x 10-2
Ar3+x 10-1
Ar2+
Ar+
Born
He+ + Ar
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102 10310-3
10-2
10-1
100
101
102
103
CDW-EIS Born with PCI Born without PCI
DuBois (1987) Andersen et al (1987)
Ar5+x 10-2
Ar4+x 10-1
Ar3+
Ar2+
Ar+
M
ultip
le io
niza
tion
cros
s se
ctio
ns (
Mb)
Energy (keV/amu)
Born
He+2 + Ar
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102 10310-3
10-2
10-1
100
101
102
103
CDW-EIS Born with PCI Born without PCI
DuBois (1987) Andersen et al (1987)
Kirchner et al (2002)
Ar5+x 10-2
Ar4+x 10-1
Ar3+
Ar2+
Ar+
M
ultip
le io
niza
tion
cros
s se
ctio
ns (
Mb)
Energy (keV/amu)
Born
He+2 + Ar
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102 103 104
10-3
10-2
10-1
100
101
102
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984)
Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
H+ + Ne
K-shell PCI
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102 103 104
10-3
10-2
10-1
100
101
102
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984)
Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
H+ + Ne
2s & 2p – PCI ?
Shake-off ?
Carlson & Nestor (1973)
Kochur et al (2006)
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102 103 104
10-3
10-2
10-1
100
101
102
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Galassi et al (2007)
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984)
Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
H+ + Ne
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102 103 104
10-3
10-2
10-1
100
101
102
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Spranger et al (2004), includes capture Galassi et al (2007)
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984)
Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
H+ + Ne
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102 103 10410-1
100
101
102
CDW-EISBorn with PCI , without PCI
DuBois (1987) Andersen et al (1987)
Ne+2
Ne+4Ne+3
Mu
ltip
le-o
niz
atio
n c
ross
se
ctio
ns
(Mb
)
E (keV/amu)
Ne+
He2+ + Ne
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102 103 10410-1
100
101
102
CDW-EISBorn with PCI , without PCI Kirchner et al (2000)
DuBois (1987) Andersen et al (1987)
Ne+2
Ne+4Ne+3
Mu
ltip
le-o
niz
atio
n c
ross
se
ctio
ns
(Mb
)
E (keV/amu)
Ne+
He2+ + Ne
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102 103100
101
102
Ne+4
Ne+3
Ne+2
E (keV/amu)
Wolf et al (2011) XXVII ICPEAC, Poster Fr071M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)Ne+
B2+ + Ne
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102 103
100
101
102
103
Wolf et al (2011), XXVII ICPEAC, Poster Fr071
DuBois (1987)
He2+ B2+
Ne+3 0.1
Mul
tiple
ioni
zatio
n cr
oss
sect
ions
(M
b)
Energy (keV/amu)
Ne+
Ne+2
B2+
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102 103
100
101
102
103
He2+ B2+ Li3+
Wolf et al (2011), XXVII ICPEAC, Poster Fr071
DuBois (1987)
Ne+3 0.1
Mul
tiple
ioni
zatio
n cr
oss
sect
ions
(M
b)
Energy (keV/amu)
Ne+
Ne+2
B2+
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102 103
100
101
102
103
He2+ B2+ Li3+
Wolf et al (2011), XXVII ICPEAC, Poster Fr071 Luna et al (2011), XXVII ICPEAC, Poster We073 DuBois (1987)
Ne+3 0.1
Mul
tiple
ioni
zatio
n cr
oss
sect
ions
(M
b)
Energy (keV/amu)
Ne+
Ne+2
B2+
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)1(2
ZZZnn Nen
ionNe
neffn He
BZ
2
1
2
2
2
200 400 600 800 1000
2.0
2.5
3.0
n=4
n=3
n=2
Zeff
n (
a.u
.)
Energy (keV/amu)
n=1
Ion effective charge for multiple ionizationIon effective charge for multiple ionization
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Summary Summary
Multiple ionization cross sections, independent particle model, multinomial
distribution, CDW-EIS
PCI is included using photoionization branching ratios.
Good description of Ar, Kr and Xe targets. Overestimation of Ne in the
intermediate energy region (direct ionization)
Effective ion charge for multiple ionization, lower for single than for multiple
Open questions that deserve research
+Limits of the IPM?: Multinomial statistic? Importance of correlation?
Changes in the target potential? Why a different answer for Ne and Kr?
+Other PCI contributions in Ne, shake off? Again, why a different answer for
Ne and Kr?
More experimental data is needed for different ions in gases
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• Maria Silvia Gravielle• Diego Arbo• Dario Mitnik• Claudio Archubi
Dep Physics, University of Missouri, USA
• Robert DuBois
Instituto de Astronomia y Física del Espacio, Buenos Aires, Argentina
• Jorge MiragliaUniversidad Federal de Rio de Janeiro,
Rio de Janeiro, Brasil
• Eduardo Montenegro• Wania Wolf• Hugo Luna• Antonio Santos
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Thank you
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102 103 104
10-3
10-2
10-1
100
101
102
Carlson, F0=0.87,F1=0.012,F2=0.008
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Spranger et al (2004), includes capture Galassi et al (2007)
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984) Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
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102 103 104
10-3
10-2
10-1
100
101
102
with shake off 2s and 2p, F0=0.98,F1=0.02 Carlson, F0=0.87,F1=0.012,F2=0.008
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Spranger et al (2004), includes capture Galassi et al (2007)
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984)
Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
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102 103 104
10-3
10-2
10-1
100
101
102
with shake off 2s and 2p, F0=0.98,F1=0.02
CDW-EISBorn with PCI, without PCI
Rejoub et al (2002), for e + Ne Schram et al (1966), for e + Ne
Spranger et al (2004), includes capture Galassi et al (2007)
Cavalcanti et al (2002) Andersen et al (1987) DuBois et al (1984) DuBois, PRL (1984)
Ne3+x 10-1
ne3+x 10-1
Ne2+
Ne+
M
ultip
le io
niza
tion
cros
s se
ctio
n (M
b)
Energy (keV/amu)
Born
shake off
Carlson & Nestor (1973)
Mukoshama (1989)
Kochur et al (2006)
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102 10310-2
10-1
100
101
102
Born
CDW-EISBorn with PCI withou PCI
Santos et al (2001)
Mul
tiple
ioni
zatio
n cr
oss
sect
ion
(Mb)
Xe3+x 10-1
Xe4+x 10-2
Energy (keV/amu)
Xe2+
Xe+
He+ + Xe
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102 10310-4
10-3
10-2
10-1
100
101
102
DuBois (1989) Santos et al (2001)
Mu
ltip
le io
niz
atio
n c
ross
se
ctio
n (
Mb
)
Energy (keV/amu)
Ne4+x 10-2
Ne3+x 10-1
Ne2+
Ne+
Born
He+ + Ne
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102 10310-4
10-3
10-2
10-1
100
101
102
DuBois (1989) Santos et al (2001)
Kirchner et al (2001)M
ulti
ple
ion
iza
tion
cro
ss s
ect
ion
(M
b)
Energy (keV/amu)
Ne4+x 10-2
Ne3+x 10-1
Ne2+
Ne+
Born
He+ + Ne
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102 103
10-4
10-3
10-2
10-1
100
101
102
103
Santos et al, PRA 63 062717 (2001) DuBois PRA 39, 4440 (1989)
Mu
ltip
le io
niz
atio
n c
ross
se
ctio
n (
Mb
)
Ar5+x 10-3
Energy (keV/amu)
Ar4+x 10-2
Ar3+x 10-1
Ar2+
Ar+
He+ + Ar
Born
Born
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0 2 4 6 8 100.00
0.02
0.04
0.06
0.08
0.10
0.12
Cro
ss S
ect
ion
(M
b)
Proton energy (MeV)
CDW-EIS for Kshell ionization
H + Ne
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200 400 600 800 1000
2.8
3.0
3.2
3.4
3.6
3.8
4.0
2.8
3.0
3.2
3.4
3.6
3.8
4.0
Ne1+
Ne2+
Ne3+
Ne4+
Z
eff
(a
.u.)
E (keV/amu)
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Total ionization cross section Total ionization cross section
Miraglia and Gravielle, Phys. Rev A 81 (2010) 042709