Multiple ionization including post-collisional contributions Claudia Montanari Instituto de...

Multiple ionization including

post-collisional contributions

Multiple ionization including

post-collisional contributions

Claudia Montanari

Instituto de Astronomía y Física del Espacio

Buenos Aires, Argentina

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

10-18

sec

projectile

photon

3+

photon10-15 sec

10-5

sec

6+

Multiple ionization data includes PCI

PCI=time delayed electron emision

Independent of the projectile

)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

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)

Multiple ionization including PCIMultiple ionization including PCI


)(... 121 qqqq

N

i

iq ( pi x 1 )

qi

q

NbP

N

)1( qN

ip ii

n Fi,n = 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-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



)(... 121 qqqq

N

i

iq ( pi x 1 )

qi

q

NbP

N

)1( qN

ip ii

n Fi,n = 1



)(... 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

qq

PCIP

Xe

Kr

Ar

Ne

ResultsResultsE= (0.1-10) MeV/amu

Xe

Kr

Ar

Ne

ResultsResults

He2+

B2+

+2

Li2+, Be2+

+2

H+, He+

+1

Li3+

+3

E= (0.1-10) MeV/amu

Be3+, B3+

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

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

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

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

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

102 103 104

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Syage (1992) Mccallion (1992)


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

102 103

10-4

10-3

10-2

10-1

100

101

102


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

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

102 10310-3

10-2

10-1

100

101

102

103

CDW-EIS Born with PCI Born without PCI


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

102 103 104

10-3

10-2

10-1

100

101

102


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

102 103 104

10-3

10-2

10-1

100

101

102




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)

102 103 104

10-3

10-2

10-1

100

101

102



Galassi et al (2007)


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

102 103 104

10-3

10-2

10-1

100

101

102



Spranger et al (2004), includes capture Galassi et al (2007)


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

102 103 10410-1

100

101

102



Ne+2

Ne+4Ne+3

Mu

ltip

le-o

niz

atio

n c

ross

se

ctio

ns

(Mb

)

E (keV/amu)

Ne+

He2+ + Ne

102 103 10410-1

100

101

102

CDW-EISBorn with PCI , without PCI Kirchner et al (2000)


Ne+2

Ne+4Ne+3

Mu

ltip

le-o

niz

atio

n c

ross

se

ctio

ns

(Mb

)

E (keV/amu)

Ne+

He2+ + Ne

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

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+

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+

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+

)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

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

• 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

http://www.if.ufrj.br/

http://www.ufrj.br/

Thank you

102 103 104

10-3

10-2

10-1

100

101

102

Carlson, F0=0.87,F1=0.012,F2=0.008




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

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





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

102 103 104

10-3

10-2

10-1

100

101

102

with shake off 2s and 2p, F0=0.98,F1=0.02





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)

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

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

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

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

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

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)

Total ionization cross section Total ionization cross section

Miraglia and Gravielle, Phys. Rev A 81 (2010) 042709

Multiple ionization including post-collisional contributions Claudia Montanari Instituto de...

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