theoretical studies of ionization, charge transfer and ...1rcm neutral 2017 ion-h collisions total...

1RCM neutral 2017

Theoretical studies of ionization, charge transfer

and excitation in ion-H, He collisions in the energy

range of 25-500 keV/amu

Clara Illescas

UNIVERSIDAD AUTONOMA DE MADRID

June 2017

1RCM neutral 2017

Contents

1 Motivation

2 Method

3 Ion-H collisions

4 Method for 2 active electrons

5 H + H and H+ + H− collisions

6 Final Remarks

1RCM neutral 2017

Motivation

Motivation

In the framework of this CRP on Data for Atomic Processes of Neutral Beams in

Fusion Plasmas we are interested in calculating:

Fully (and partially) stripped impurity ions colliding with atomic hydrogen

The processes relevant to neutral beam diagnostics of fusion plasmas are:

Target Ionization: Aq+ + H(nlm) −→ Aq+ + H+ + e−

Electron Capture: Aq+ + H(nlm) −→ A(q−1)+(n′l ′m′) + H+

Target Excitation: Aq+ + H(nlm) −→ Aq+ + H(n′′l ′′m′′)

1RCM neutral 2017

Motivation

Motivation

Purpose I.: Detailed data for atomic processes involving neutral hydrogen

Data found in ADAS1 at 100 keV/amu

Collisions with H(1s): Several sets of data: A need to asses their uncertainties

and to provide a well recommended data set.

Be4+ + H(1s) → Be3+(6lm) + H+: ∼ 33%

Collisions with H(n = 2): Significant gaps, especially related to processes

initiated from an excited state of the neutral atom.

C6+ + H(n = 2) → C5+(8lm) + H+: 1 set of data

1http://open.adas.ac.uk

1RCM neutral 2017

Motivation

Motivation

Methods to be employed:

CTMC (Classical Trajectory Monte Carlo Method) 2

Wide experience in the treatment of one-active electron collisions with H(1s)

Stripped ions:3 He2+, Li3+, Be4+, B5+, C6+, N7+, O8+, Ne10+

Highly charged ions:4 Ar16+,17+,18+, Kr36+, W60+

GTDSE (Grid Time Dependent Schrodinger Equation)5

A complete study of state-selective cross sections of Be4+ + H(1s) collisions6

2R Abrines & I C Percival, Proc. Phys. Soc. 88, 861 (1966)

3Phys. Rev. A 60 4546 (1999), Phys. Rev. A 70 052713 (2004), Eur. Phys. J. D. 68, 227 (2014)

4J. Phys. B. 39, L91 (2006), Phys. Scr. T156 014033 (2013)

5J Suarez et al., Comput. Phys. Commun. 150 2025 (2009)

6A Jorge et al., Phys. Rev. A 94 032707 (2016)

1RCM neutral 2017

Motivation

Motivation

Purpose II.: Detailed data for atomic processes involving neutral beams of helium and

lithium.

Very scarce data

Proposed method: the Switching CTMC Approach

↪→ implementation of a new approach especially designed to classically treat

two-active electron systems7


1RCM neutral 2017

Method

Method

In this talk,

Eikonal CTMC8

The projectile follows straight-line trajectories: R = b + vt

The electronic motion is described by a classical distribution function

ρ(r, p, t) =1

N

N∑j=1

δ(r − rj )δ(p− pj )

solution of the Liouville’s equation:

∂ρ

∂t= −[ρ,Hel ]

where Hel is the target electronic Hamiltonian and N ≈ 105

8Illescas and Riera, Phys. Rev. A 60 (1999)

1RCM neutral 2017

Method

Method

Eikonal CTMC

Hamilton’s equations are solved for each electron trajectory:

rj =∂H

∂pj

; pj = −∂H

∂rj

Including the total collision Hamiltonian:

H =p2

2−

ZT

rT−

ZP

rP

Energy criterion is applied at tfin = 500a.u.v

to select ionized (ET > 0, EP > 0),

captured (ET > 0, EP < 0) or (ET < 0) elastic or excited trajectories.

1RCM neutral 2017

Method

Method

The classical phase space of captured (or excited, then referred to the target)

electrons is partitioned into exclusive subspace9

[(n − 1) (n −1

2) n]1/3 < nc ≤ n (n +

1

2) (n + 1)]1/3

l <n

nclc ≤ l + 1

with nc = ZP/√−2EP and lc = |(r − b− vt) ∧ (p− v)|.

Electron probabilities:

P i,c,e (v , b) =

∫dr

∫dp ρi,c,e (r, p, v , b, tfin)

Total cross sections:

σi,c,e (v) = 2π

∫ ∞0

db b P i,c,e (v , b)

9R L Becker & A D MacKellar, J. Phys. B 17 3923 (1984)

1RCM neutral 2017

Method

Initial distributions: construction

Microcanonical (standard):

ρM (r, p,Z ,E) =1

Kδ(Hel − E) =

1

8π3δ

(p2

2−

1

r+

1

2

)

All the particles have the same binding energy.

Hydrogenic10:

ρH (r, p,Z , ε) =M∑

k=1

ak · ρM (r, p,Z , εk ) =M∑

k=1

(−2ε5/2k )

8π3ak δ

(p2

2−

1

r− εk

)

A linear combination of M microcanonicals with an averaged energy < ε >' − 12

.

10D J Hardie and R E Olson, J. Phys. B 16 1983 (1983)

1RCM neutral 2017

Method

Phase space initial distributions for H(1s)

0 1 2 3 4p (a.u.)

1.25

0.5

1

Mom

entu

m p

roba

bilit

y di

stri

butio

n

ρΜρΗQuantal

0 2 4 6 8r (a.u.)

0

0.2

0.4

0.6

0.8

Rad

ial p

roba

bilit

y di

stri

butio

n

ρΜρΗQuantal

1RCM neutral 2017

Method

Phase space initial distributions for H(n =2)

0 0.5 1 1.5 2p (a.u.)

0

1

2

Mom

entu

m d

istr

ibuti

on p

robab

ilit

y

ρΗ(p)

ρΜ

(p)

Quantum

0 2 4 6 8 10 12 14 16 18 20r (a.u.)

0

0.05

0.1

0.15

0.2

Rad

ial

dis

trib

uti

on p

robab

ilit

y

ρΗ(r)

ρΜ

(r)

Quantum

1RCM neutral 2017

Ion-H collisions

Some CTMC results for Aq+ + H collisions

B5+, C6+, N7+ + H(1s) with neutral hydrogen.

C6+, N7+ + H(n = 2) with excited hydrogen.

Total and n-partial cross sections.

Highly charged ions: Ar16+,17+,18+, Kr36+, W60+ + H(1s)

Total, n-partial and n, l-partial cross sections. Scaling.

1RCM neutral 2017

Ion-H collisions

Total cross sections for B5+, C6+, N7+ + H(n=1)

1 10 100 1000E (keV/amu)

0,1

1

10

100

σ (

10

-16 c

m2)

OEDM capture

CTMC capture

CTMC ionization

Shah et al

Toshima, σcap

Toshima, σion

B5+

+ H(1s)

10 100E (keV/amu)

0,1

1

10

100

Miraglia et al (CDW-EIS)

CTMC ionization

CTMC capture

Igenbergs et al (AOCC)

Shah et al

Toshima 1994 (AOCC)

C6+

+ H(1s)

10 100E (keV/amu)

0,1

1

10

100

CTMC

Igenbergs et al

Toshima 1994

N7+

+ H(1s)

1RCM neutral 2017

Ion-H collisions

Total cross sections C6+ + H(n=2)

(—–) hydrogenic-CTMC, (- - -) microcanonical-CTMC 11 and (—N—) AOCC results from Igenbergs12

11A Jorge et al. EPJD 68 227 (2014)

12K Igenbergs et al. J. Phys. B 45 065203 (2012)

1RCM neutral 2017

Ion-H collisions

Total cross sections N7+ + H(n=2)

(—–) hydrogenic-CTMC, (- - -) microcanonical-CTMC and (—N—) AOCC results from Igenbergs.

1RCM neutral 2017

Ion-H collisions

n-partial cross sections for C6+ and N7+ + H(n = 1)

500100

E (keV/amu)

0.01

1

100

10000

σn (

10

-16 c

m2)

500100

E (keV/amu)

0.01

1

100

10000

σn (

10

-16 c

m2)

n = 6 (x10)

n = 7

n = 8 (x0.1)

n = 7 (x10)

n = 8

n = 9 (x0.1)

n=5 (x100) n=6 (x100)

n=5 (x1000)n=4 (x1000)

(—–) hydrogenic-CTMC, (- - -) AOCC results from Igenbergs and (- • -) MOOC results13.

13Harel et al., At. Data. Nucl. Data Tables, 68 279 (1998)

1RCM neutral 2017

Ion-H collisions

n-partial cross sections for C6+ and N7+ + H(n = 2)

10 100

E (keV/amu)

0.1

4000

1

10

100

1000

σn (

10

-16 c

m 2

)

10 100

E (keV/amu)

0.1

4000

1

10

100

1000

n = 9 (x10)

n = 8

n = 8 (x10)n = 7

n = 6 (x0.1) n = 7 (x0.1)

(—–) hydrogenic-CTMC compared to (- - -) AOCC results from Igenbergs.

1RCM neutral 2017

Ion-H collisions

Arq+ ions + H collisions: Total cross sections

Hydrogenic versus microcanonical initial distribution: its importance in the TCS

50 100 150E (keV/amu)

0

50

100

150

σ

(10

-16 c

m2)

0

50

100

150

M-CTMC e-loss

H-CTMC e-loss

OEDM e-loss

50 100 150 200 250 300E (keV/amu)

0

50

100

150

2000

50

100

150

Ar18+

Ar17+

Ar16+

Ar18+

, Hung et al

Ar17+

, Hung et al

Ar16+

, Hung et al

Ar18+

, present micro

Ar18+

+ H

σion

σcap

In Errea et al. J. Phys. B 39 L91 (2006)

1RCM neutral 2017

Ion-H collisions

Arq+ + H collisions: n-partial cross sections, σn

Focus on capture to very high-lying states of the projectile n = 14− 17, triggering the

visible radiative decay analysed in 2012 ASDEX diagnostic experiments.

40 60 80 100 120 140

E (keV/amu)

0

2

4

6

8

10

12

σn (

10

-16 c

m2)

40 60 80 100 120 140

E (keV/amu)

0

2

4

6

8

10

12

40 60 80 100 120 140

E (keV/amu)

0

2

4

6

8

10

12

n=14

n=15

n=16

n=17

σion

Ar18+

+ H Ar17+

+ H Ar16+

+ H

1RCM neutral 2017

Ion-H collisions

σn,l : ` distributions in Ar18+ + H collisions

E ranging from 40 to 144 keV/amu and 3 typical n-shells.

Capture to high-n shells⇒ captured orbits of large ` values. The shifts of σn,lmax are larger as n and E increase.

0 1 2 3 4 5 6 7 8 9 10 11 12 130

1

2

3σ

14,l (

10

-16 c

m2)

0 5 100

1

2

3 e=40 keV/amu

e=70 keV/amu

e=100 keV/amu

e=144 keV/amu

0 2 4 6 8 10 12 14 160

0,2

0,4

0,6

0,8

1

σ18,l (

10

-16 c

m2)

0

0,2

0,4

0,6

0,8

1

0 4 8 12 16 20

l

0

0,1

0,2

0,3

σ 2

2,l (

10

-16 c

m2)

n=14

n=18

n=22

1RCM neutral 2017

Ion-H collisions

Ar18+, Kr36+, W60+ + H collisions: Total cross sections

100 1000E (keV/amu)

0.01

0.1

1

10

100

1000σ

(10-1

6 cm

2 )

W60+

Kr36+

Ar18+

IONIZATION

CAPTURE

In Illescas et al., Phys. Scr. T156 014033 (2013)

1RCM neutral 2017

Ion-H collisions

Scaling for total electron capture cross sections

100

E*

(keV/amu)

0,01

0,1

1

10

σ∗

(10

-16 c

m2)

W60+

Kr36+

Ar18+

σ∗ = σ Z−α

E∗ = E Z−β ,

with α = 1.05 and β = 0.30

(Foster, PhD Thesis, 2008)

↪→ Good agreement of our results with the empirical scaling law which

allow to predict σEC for collisions of high Z without performing detailed calculations.

1RCM neutral 2017

Ion-H collisions

n-partial cross sections

σn/Z as functions of scaled n∗ = n Z−γ(E∗)

γ= 0.8 for E = 150 keV/amu; γ= 1.0 for E = 225 keV/amu

0 1 2 3 4n*

0

0.05

0.1

σ n/ Z (

10-1

6 cm

2 )

W60+

+ H

Kr36+

+ H

Ar18+

+ H

150 keV/amu

225 keV/amu

n-partial cross sections exhibit a maxima at nmax ≈ Z/2, as predicted by COBM.

1RCM neutral 2017

Ion-H collisions

n-partial cross sections

0 1 2 3 4n*

0

0.05

0.1

σ n/ Z (

10-1

6 cm

2 )

W60+

+ H

Kr36+

+ H

Ar18+

+ H

150 keV/amu

225 keV/amu

The Oppenheimer n−3 rule holds for E > 100 keV/amu for the three systems.

1RCM neutral 2017

Method for 2 active electrons

Four-body & Switching CTMC treatments

Two-active electrons and two-nuclei:

We have studied the most simple 2e− systems:

H(1s) + H(1s) −→ Electrons initially in different centers

H+ + H−(1s, 1s) −→ Electrons initially in the same center

↪→ Our idea: To apply these methods to explicitly treat e1 and e2

ion-He(1s, 1s) collisions.

1RCM neutral 2017


Two-active electron processes

H(1s) + H(1s) →

H + H elastic/excitation

H + H+ + e target ionization

H+ + H + e projectile ionization

H+ + H+ + 2e double ionization

H+ + H− target electron capture

H− + H+ projectile electron capture

H+ + H−(1s, 1s) →

H+ + H− elastic/excitation

H + H mutual neutralization

H + H+ + e transfer ionization

H+ + H + e detachment

H+ + H+ + 2e double ionization

H− + H+ charge exchange

1RCM neutral 2017


Four-body CTMC method

Classical initial distribution function:

→ The electronic motion of each electron is described by a microcanonical

initial distribution, ρM (r, p,Z ,E), solution of the Liouville’s equation.

→ The initial two electron distribution consists of the product of two

microcanonical sets of N = NH · NH

We solve the Hamilton equations for each pair of electrons {e1, e2}:

Rj =∂H2e

∂Pj; Pj = −

∂H2e

∂Rj

using Jacobi coordinates {R1, R2, R3} and {P1, P2, P3}.

1RCM neutral 2017


Classical autoionization problem

An isolated classical H− anion is described by the hamiltonian:

H =p2

1

2+

p22

2+

p23

2M−

1

re1

−1

re2

+1

r12

The system is not classically stable due to the interelectronic repulsion14:

E1 =p2

e1

2−

1

re1

E2 =p2

e2

2−

1

re2

14See F. Guzman et al. Phys Rev. A 80 (2009)

1RCM neutral 2017


Classical autoionization problem

H(1s) + H (1s) collisions: H− formation

0 2000 4000 6000 8000 10000Z (a.u.)

10-4

10-3

10-2

10-1

Pro

bab

ilit

y o

f H

- fo

rmat

ion

0 20 40 60 80 10010

-2

10-1 A Four-body CTMC

calculation yields a H−

formation probability which

depends on the final time of

integration.

Processes such

H+ + H−

H− + H+are understimated while the others are overestimated.

1RCM neutral 2017


How can we describe a H− anion?

We propose two independent systems to describe the H−, one for each electron15:

H−(e1, e2)

e2 interacting with {H+ + e1} ≡ α −→ VH+−e1mod

e1 interacting with {H+ + e2} ≡ β −→ VH+−e2mod

V H+−emod = −

(1 + αr) exp(−2αr)

r

↪→ is a model potential which represents the nucleus and one frozen electron.

The parameter α has been fitted to α= 0.65 (a.u.)−1(16)


16J D Talman, Comput. Phys. Commun. 54 85 (1989)

1RCM neutral 2017


A classical stable description of the H− anion

The construction of H− is

performed by using two ρM :

• Uion= -0.027 a.u.

• ` = 0

• VH+−emod

Under no external perturbation, we let the electron evolve in time and we calculate the

total energy from the full hamiltonian: H =p2

12

+p2

22

+p2

32M− 1

re1− 1

re2+ 1

r12

We obtain 〈H〉H−= 0.450 a.u. close to εH

−exp= 0.503 a.u.

1RCM neutral 2017


A classical stable description of the He atom

Similarly, we can describe the He atom with two active electrons:

We obtain 〈H〉He = -2.89 a.u. very close to εHeexp = -2.90 a.u.

1RCM neutral 2017


A classical stable description multielectronic atoms

This same approach has been applied to other atoms: Li, Be, B and C,

where each electron is represented by a different initial distribution

[different VH+−emod , ` and Uion values]

↪→ Good description with this approach

HF and CI values from NIST, https://www.nist.gov

https://www.nist.gov

1RCM neutral 2017


The Switching CTMC Approach

Application to collisions: a combined 4-body and 2x3-body CTMC

We propose to perform the time evolution of:

The 4-body system if the electrons are not bound to the same nucleus:

V4b = −ZT

rTe1

−ZT

rTe2

−ZP

rPe1

−ZP

rPe2

+1

r12

Two 3-body systems if the electrons are bound to the same nucleus:

Target

V e1

3b = − ZPrPe1− (ZT−1)

rTe1−

(1+αrTe1)

rTe1exp(−2αrTe1

)

V e23b = − ZP

rPe2− (ZT−1)

rTe2−

(1+αrTe2)

rTe2exp(−2αrTe2

)

or

Projectile

V e1

3b = − ZTrTe1− (ZP−1)

rPe1−

(1+αrPe1)

rPe1exp(−2αrPe1

)

V e23b = − ZT

rTe2− (ZP−1)

rPe2−

(1+αrPe2)

rPe2exp(−2αrPe2

)

1RCM neutral 2017


The Switching CTMC Approach

H(1s) + H(1s) collisions: correct H− formation

0 2000 4000 6000 8000 10000Z (a.u.)

10-4

10-3

10-2

10-1

Pro

bab

ilit

y o

f H

- fo

rmat

ion

0 20 40 60 80 10010

-2

10-1

(—–) Switching calculation

(- - -) Four-body CTMC

⇓

converged probability after

t ∼ 200 a.u.

1RCM neutral 2017

H + H and H+ + H− collisions

Results for H(1s) + H(1s) collisions: Projectile H− formation

20 50 100 200E (keV)

0

0,05

0,1

0,15

0,2

σ

(10

-16 c

m2)

(—–) Switching, (- - -) 4-body, (- - -) 4-body CTMC17, (- - · - -) AOCC18. Measurements: (�)19 and (N)20.

17K Dimitriu et al., J. Phys. IV (France) 10 299 (2000)

18J Wang et al., J. Phys. B 33 241 (2000)

19G W McClure, Phys. Rev. 166 22 (1968)

20J Hill et al., J. Phys. B 12 3341 (1979)

1RCM neutral 2017


Results for H+ + H− collisions

H+ + H−(1s2) → H(nlm) + H(n′l ′m′)

20 50 100 200E (keV)

0,01

0,1

1

10

Mutu

al

neutr

ali

zati

on c

ross

secti

on 1

0-1

6 c

m2

(—–) Switching CTMC and (- - · - -) Coupled-channel calculations21. Measurements. (•) from Schon et al.22.

21R Shingal and B H Bransden, J. Phys. B 23 1203 (1990)

22W Schon et al., J. Phys. B 20 L759 (1987)

1RCM neutral 2017


Results for H+ + H− collisions

H+ + H−(1s2) → H(nlm) + H(1s)

20 50 100 200E (keV)

0,01

0,1

1

10

σ (

10

-16 c

m2)

(—–) Switching CTMC, (- - · - -) AOCC23, (· · · )24 and (- - - - -) CB1-4B calculations from Mancev et al.25

23J Wang et al., J. Phys. B 33 241 (2000)

24L Ling and J Wang, Chin. Phys. Lett. 24 3115 (2007)

25I Mancev et al., Europhys. Lett. 103 23001 (2013)

1RCM neutral 2017

Final Remarks

Final remarks

CTMC methods for treating one- and two-active electron collisions at impact

energies of interest in fusion research.

Obtaining of accurate total and n, `−partial CROSS SECTIONS in low- and

highly charged ions in collision with H.

New Switching CTMC Approach which improves the computed cross sections

for electron capture processes when two electron are involved.

1 Classical stable description of multielectronic atoms throught independent systems (Vmod).

2 Avoid the underestimation of H−(1s, 1s) formation due to the unphysical classical autoionization.

3 Mutual neutralization cross sections in good agreement with experiments.

1RCM neutral 2017

Final Remarks

Coworkers

L. F. Errea

A. Jorge

L. Mendez

B. Pons (U. Bordeaux, FR)

J. Suarez

I. Rabadan

theoretical studies of ionization, charge transfer and ...1rcm neutral 2017 ion-h collisions total...

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