multiple ionization of ne, ar, kr, and xe by different ions c. c. montanari 1, j. e. miraglia 1 and...

Multiple ionization of Ne, Ar, Kr, and Xe by

different ions

Multiple ionization of Ne, Ar, Kr, and Xe by

different ions

C. C. Montanari1, J. E. Miraglia1 and E. Montenegro2

1Instituto de Astronomía y Física del Espacio and Universidad de Buenos Aires, Buenos Aires, Argentina

2Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil

CAARI 2010-Fort Worth

102 103

10-3

10-2

10-1

100

101

102

103M

ultip

le io

niza

tion

cros

s se

ctio

ns (

Mb)

Cavalcanti et al (2002) DuBois (1984) Syage for e+Kr (1992)

Energy (keV/amu)

Kr4+x 10-3

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

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

2p

2s

1s

Ne

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

PCI

onlysubvalence electrons

Hikosaka et al 2004, Phys. Rev. AHayaishi et al 2002, J.Phys. B

Direct multiple ionizationDirect multiple ionization

Cross section for ionization of q target electronsCross section for ionization of q target electrons

dbbbPqq )(2

independent electron modelindependent electron model

Binomial distributionBinomial distribution

)1()(... 121

qNi

qi

qqqq

N

i i

iq pp

q

NbP iii

N

single ionization probability per electron single ionization probability per electron for the i atomic subshellfor the i atomic subshell

Multiple ionization including PCIMultiple ionization including PCI

Binomial distributionBinomial distribution

)(... 121 qqqq

N

i

iq ( pi x 1 )

qi

q

NbP

N

)1( qN

ip ii

n Fi,n = 1

Multiple ionization including PCIMultiple ionization including PCI

Binomial distributionBinomial 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) P PCI

1s (2) = P1s (1) F1s,1 + P1s (2)[F1s,0 ]2

Montanari et al J. Phys B 43, 165201 (2010)

Ne

102 103 104

10-3

10-2

10-1

100

101

102

CDW-EIS

CDW-EIS

Cavalcanti (2002) Andersen (1987) DuBois (1984) Schram for e+Ne (1966)

Ne3+x 10-1

ne3+x 10-1

Ne2+

Ne+

M

ulti

ple

ion

iza

tion

cro

ss s

ect

ion

(M

b)

Energy (keV/amu)

H+ + Ne

Born

CDW-EIS

102 10310-5

10-4

10-3

10-2

10-1

100

101

102

CDW-EIS

CDW-EIS

Santos (2001) DuBois (1989)

Energy (keV/amu)M

ultip

le io

niza

tion

cros

s se

ctio

n (M

b)

Ne4+x 10-2

Ne3+x 10-1

Ne2+

Ne+

Born

CDW-EIS

He+ + Ne

100 100010-5

10-4

10-3

10-2

10-1

100

101

102

103

CDW-EIS

CDW-EIS

CDW-EIS

Born

Born

Born, including PCI CDW, including PCI CDW direct DuBois, PRA36.2585 (1987)

Ne+5 x 10-2

Ne+4 x 10-2

Ne+3 x 10-1

Ioni

zatio

n cr

oss

sect

ions

(M

b)

E (keV/amu)

Ne+

Ne+2

He+2 on Ne

without PCI

Born

CDW-EIS

Ar

102 103 10410-4

10-3

10-2

10-1

100

101

102

103

Andersen (1987) Cavalcanti (2002) DuBois (1984)

Ar4+x 10-2

Ar3+x 10-1

Ar2+

Ar+

M

ulti

ple

ion

iza

tion

cro

ss s

ect

ion

s (M

b)

Energy (keV/amu)

H+ + Ar

102 103

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

He+ + Ar

DuBois (1987) Santos (2002)

Ar5+x 10-5

Mu

ltip

le io

niz

atio

n c

ross

se

ctio

n (

Mb

)

Energy (keV/amu)

Ar4+x 10-3

Ar3+x 10-1

Ar2+

Ar+

Kr

102 10310-4

10-3

10-2

10-1

100

101

102

103

H+ + Kr

Cavalcanti et al (2002) DuBois (1984) Syage for e+Kr (1992)

Mu

ltip

le io

niz

atio

n c

ross

se

ctio

ns

(Mb

)

Energy (keV/amu)

Kr4+x 10-3

Kr3+x 10-1

Kr2+

Kr+

102 10310-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Santos et al (2001) DuBois (1989)

Kr5+x10-5

Energy (keV/amu)

Mu

ltip

le io

niz

atio

n c

ross

se

ctio

n (

Mb

)

Kr4+x10-3

Kr3+x10-1

Kr2+

Kr+

He+ + Kr

Xe

102 10310-3

10-2

10-1

100

101

102

103

Santos et al (2001)

He+ + Xe

Xe3+x 10-2

Xe4+x 10-3

Mu

ltip

le io

niz

atio

n c

ross

se

ctio

n (

Mb

)

Energy (keV/amu)

Xe2+x 10-1

Xe+

102 10310-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Cavalcanti (2002) Syage for e+Xe (1992)

Xe5+x 10-5

Energy (keV/amu)

Mu

ltip

le io

niz

atio

n c

ross

se

ctio

ns

(Mb

)

Xe4+x 10-3

Xe3+x 10-1

Xe2+

Xe+

H+ + Xe

Concluding remarks Concluding remarks

Multiple ionization with CDW-EIS and first Born approx.

Concluding remarks Concluding remarks

Multiple ionization with CDW-EIS and first Born approx.

Auger type contributions

Concluding remarks Concluding remarks

Multiple ionization with CDW-EIS and first Born approx.

Auger type contributions

Kr and Xe for the first time (within independent electron model)

Concluding remarks Concluding remarks

Multiple ionization with CDW-EIS and first Born approx.

Auger type contributions

Kr and Xe for the first time (within independent electron model)

Ar and Kr CDW-EIS very good for E>200 keV/amu

H impact, very good!

Born He+, little high for E<70 keV

Ne CDW-EIS good for E>300 keV/amu

Born good even intermediate energies for H+

not so good for He2+

Xe good for H+ impact but not for He+

more experimental data is needed!

Concluding remarks Concluding remarks

Multiple ionization with CDW-EIS and first Born approx.

Auger type contributions

Kr and Xe for the first time (within independent electron model)

Ar and Kr CDW-EIS very good for E>200 keV/amu

H impact, very good!

Born He+, little high for E<70 keV

Ne CDW-EIS good for E>300 keV/amu

Born good even intermediate energies for H+

not so good for He2+

underestimate PCI for H+ + Ne (excitation-ionization channel? Shake-off?)

Xe good for H+ impact but not for He+

more experimental data is needed!

Thank you!

Buenos Aires, Argentina

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

102 103 104

10-3

10-2

10-1

100

101

102

Cavalcanti (2002) Andersen (1987) DuBois (1984) Schram for e+Ne (1966)

Ne3+x 10-1

ne3+x 10-1

Ne2+

Ne+

Mu

ltip

le io

niz

atio

n c

ross

se

ctio

n (

Mb

)

Energy (keV/amu)

H+ + Ne