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
7A Jorge et al., Phys. Rev. A 94 022710 (2016)
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
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
Method for 2 active electrons
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
Method for 2 active electrons
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
Method for 2 active electrons
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
Method for 2 active electrons
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
Method for 2 active electrons
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)
15A Jorge et al., Phys. Rev. A 94 022710 (2016)
16J D Talman, Comput. Phys. Commun. 54 85 (1989)
1RCM neutral 2017
Method for 2 active electrons
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
Method for 2 active electrons
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
Method for 2 active electrons
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
1RCM neutral 2017
Method for 2 active electrons
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
Method for 2 active electrons
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
H + H and H+ + H− collisions
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
H + H and H+ + H− collisions
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
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
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
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
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
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