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Talk given by Klaus Bartschat (Drake University) at DAMOP12, Anheim, California, USA (06 June 2012)
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BENCHMARK CALCULATIONS OF ATOMIC DATA
FOR MODELING APPLICATIONS
Klaus Bartschat, Drake University
DAMOP 2012 (GEC Session)
June 4-8, 2012
Special Thanks to:
Igor Bray, Dmitry Fursa, Arati Dasgupta,
Gustavo Garcia, Don Madison, Al Stauffer, ...
Michael Allan, Steve Buckman, Michael Brunger, Hartmut Hotop, Morty Khakoo,
and many other experimentalists who are pushing us hard ...
Andreas Dinklage, Dirk Dodt, John Giuliani, George Petrov, Leanne Pitchford, ...
Phil Burke, Charlotte Froese Fischer, Oleg Zatsarinny
National Science Foundation: PHY-0903818, PHY-1068140, TeraGrid/XSEDE
BENCHMARK CALCULATIONS OF ATOMIC DATA
FOR MODELING APPLICATIONS
OVERVIEW:
I. Introduction: Production and Assessment of Atomic Collision Data
II. Numerical Methods
• Special-Purpose Methods
• Distorted-Wave Methods
• The Close-Coupling Method: Recent Developments
CCC, RMPS, IERM, TDCC, BSR
III. Selected Results
• Energy Levels
• Oscillator Strengths
• Cross Sections for Electron-Impact Excitation
IV. GEC Application: What We Can Learn from Modeling a Ne Discharge
V. A Closer Look at Ionization
• Basic Idea
• Example Results
• Solution of the Excitation Mystery in e-Ne Collisions
VI. Conclusions and Outlook
Production and Assessment of Atomic Data
• Data for electron collisions with atoms and ions are needed for modeling processes in
• laboratory plasmas, such as discharges in lighting and lasers
• astrophysical plasmas
• planetary atmospheres
• The data are obtained through
• experiments
• valuable but expensive ($$$) benchmarks (often differential in energy, angle, spin, ...)
• often problematic when absolute (cross section) normalization is required
• calculations (Opacity Project, Iron Project, ...)
• relatively cheap
• almost any transition of interest is possible
• often restricted to particular energy ranges:
• high (→ Born-type methods)
• low (→ close-coupling-type methods)
• cross sections may peak at “intermediate energies” (→ ???)
• good (or bad?) guesses
• Sometimes the results are (obviously) wrong or (more often) inconsistent !
Basic Question: WHO IS RIGHT? (And WHY???)
Choice of Numerical Approaches• Which one is right for YOU?
• Perturbative (Born-type) or Non-Perturbative (close-coupling, time-
dependent, ...)?
• Semi-empirical or fully ab initio?
• How much input from experiment?
• Do you trust that input?
• Predictive power? (input ↔ output)
• The answer depends on many aspects, such as:
• How many transitions do you need? (elastic, momentum transfer, excitation,
ionization, ... how much lumping?)
• How complex is the target (H, He, Ar, W, H2, H2O, radical, DNA, ....)?
• Do the calculation yourself or beg/pay somebody to do it for you?
• What accuracy can you live with?
• Are you interested in numbers or “correct” numbers?
• Which numbers do really matter?
Who is Doing What?The list is NOT Complete or Arranged – concentrates on “GEC folks”
• “special purpose” elastic/total scattering: Stauffer, McEachran, Garcia, ...
• inelastic (excitation and ionization): perturbative
• Madison, Stauffer, McEachran, Dasgupta, Kim (NIST), ...
• inelastic (excitation and ionization): non-perturbative
• Fursa, Bray, Stelbovics, ... (CCC)
• Burke, Badnell, Pindzola, Ballance, Griffin, ... (“Belfast” R-matrix)
• Zatsarinny, Bartschat (B-spline R-matrix)
• Colgan, Pindzola, ... (TDCC)
• Molecules: Orel, McCurdy, Rescigno, Tennyson, McKoy, Winstead,
Madison, Kim (NIST), ...
Classification of Numerical Approaches• Special Purpose (elastic/total): OMP (pot. scatt.); Polarized Orbital
• Born-type methods• PWBA, DWBA, FOMBT, PWBA2, DWBA2, ...
• fast, easy to implement, flexible target description, test physical assumptions
• two states at a time, no channel coupling, problems for low energies and optically
forbidden transitions, results depend on the choice of potentials, unitarization
• (Time-Independent) Close-coupling-type methods• CCn, CCO, CCC, RMn, IERM, RMPS, DARC, BSR, ...
• Standard method of treating low-energy scattering; based upon the expansion
ΨLSπE (r1, . . . , rN+1) = A
∑i
∫ΦLSπ
i (r1, . . . , rN , r)1
rFE,i(r)
• simultaneous results for transitions between all states in the expansion;
sophisticated, publicly available codes exist; results are internally consistent
• expansion must be cut off (→→→ CCC, RMPS, IERM)
• usually, a single set of mutually orthogonal one-electron orbitals is used
for all states in the expansion (→→→ BSR with non-orthogonal orbitals)
• Time-dependent and other direct methods• TDCC, ECS
• solve the Schrodinger equation directly on a grid
• very expensive, only possible for (quasi) one- and two-electron systems.
Inclusion of Target Continuum (Ionization)
• imaginary absorption potential (OMP)
• final continuum state in DWBA
• directly on the grid and projection to continuum states (TDCC, ECS)
• add square-integrable pseudo-states to the CC expansion (CCC, RMPS, ...)
Inclusion of Relativistic Effects
• Re-coupling of non-relativistic results (problematic near threshold)
• Perturbative (Breit-Pauli) approach; matrix elements calculated between non-
relativistic wavefunctions
• Dirac-based approach
Numerical Methods: OMP for Atoms
• For electron-atom scattering, we solve the partial-wave equation
(d2
dr2−
ℓ(ℓ + 1)
r2− 2Vmp(k, r)
)uℓ(k, r) = k2uℓ(k, r).
• The local model potential is taken as
Vmp(k, r) = Vstatic(r) + Vexchange(k, r) + Vpolarization(r) + iVabsorption(k, r)with
• Vexchange(k, r) from Riley and Truhlar (J. Chem. Phys. 63 (1975) 2182);
• Vpolarization(r) from Zhang et al. (J. Phys. B 25 (1992) 1893);
• Vabsorption(k, r) from Staszewska et al. (Phys. Rev. A 28 (1983) 2740).
• Due to the imaginary absorption potential, the OMP method
• yields a complex phase shift δℓ = λℓ + iµℓ
• allows for the calculation of ICS and DCS for
• elastic scattering
• inelastic scattering (all states together)
• the sum (total) of the two processes
0 1 2 3 4 5 6 7 80
5 0
1 0 0
1 5 0
2 0 0
B P R M - C C 2 D B S R - C C 2 D B S R - C C 2 + p o l D A R C - C C 1 1 ( W u & Y u a n ) O M P
Cr
oss se
ction
(a2 o)
E l e c t r o n e n e r g y ( e V )
e + I ( 5 p 5 , J = 3 / 2 )
The (Time-Independent) Close-Coupling Expansion
• Standard method of treating low-energy scattering
• Based upon an expansion of the total wavefunction as
ΨLSπE (r1, . . . , rN+1) = A
∑
i
∫
ΦLSπi (r1, . . . , rN , r)
1
rFE,i(r)
• Target states Φi diagonalize the N -electron target Hamiltonian according to
〈Φi′ | HNT | Φi〉 = Ei δi′i
• The unknown radial wavefunctions FE,i are determined from the solution of a system of coupled integro-
differential equations given by
[
d2
dr2−
`i(`i + 1)
r2+ k2
]
FE,i(r) = 2∑
j
∫
Vij(r)FE,j(r) + 2∑
j
∫
Wij FE,j(r)
with the direct coupling potentials
Vij(r) = −Z
rδij +
N∑
k=1
〈Φi |1
|rk − r|| Φj〉
and the exchange terms
WijFE,j(r) =
N∑
k=1
〈Φi |1
|rk − r|| (A− 1)ΦjFE,j〉
Cross Section for Electron-Impact Excitation of He(1s2)
K. Bartschat, J. Phys. B 31 (1998) L469
n = 2 n = 3
21P
projectile energy (eV)4035302520
8
6
4
2
0
21S
4
3
2
1
0
23P
cros
sse
ctio
n(1
0−18cm
2)
4035302520
4
3
2
1
0
RMPSCCC(75)
DonaldsonHall
Trajmar
23S
6
5
4
3
2
1
0
31D
4035302520
0.3
0.2
0.1
0.0
31P
1.5
1.0
0.5
0.0
31S
1.0
0.8
0.6
0.4
0.2
0.0
33D
projectile energy (eV)4035302520
0.3
0.2
0.1
0.0
33P
cros
sse
ctio
n(1
0−18cm
2) 1.0
0.8
0.6
0.4
0.2
0.0
RMPSCCC(75)
experiment33S
2.0
1.5
1.0
0.5
0.0
In 1998, deHeer recommends (CCC+RMPS)/2 for uncertainty of 10% or better !
(independent of experiment)
Metastable Excitation Function in Kr
General B-Spline R-Matrix (Close-Coupling) Programs (D)BSR• Key Ideas:
• Use B-splines as universal
basis set to represent the
continuum orbitals
• Allow non-orthogonal or-
bital sets for bound and
continuum radial functions
• Consequences:
• Much improved target description possible with small CI expansions
• Consistent description of the N-electron target and (N+1)-electron collision
problems
• No “Buttle correction” since B-spline basis is effectively complete
• Complications:
• Setting up the Hamiltonian matrix can be very complicated and lengthy
• Generalized eigenvalue problem needs to be solved
• Matrix size typically 10,000 and higher due to size of B-spline basis
• Rescue: Excellent numerical properties of B-splines; use of (SCA)LAPACK et al.
List of calculations with the BSR code (rapidly growing)
hv + Li Zatsarinny O and Froese Fischer C J. Phys. B 33 313 (2000)hv + He- Zatsarinny O, Gorczyca T W and Froese Fischer C J. Phys. B. 35 4161 (2002)hv + C- Gibson N D et al. Phys. Rev. A 67, 030703 (2003)hv + B- Zatsarinny O and Gorczyca T W Abstracts of XXII ICPEAC (2003)hv + O- Zatsarinny O and Bartschat K Phys. Rev. A 73 022714 (2006)hv + Ca- Zatsarinny O et al. Phys. Rev. A 74 052708 (2006)e + He Stepanovic et al. J. Phys. B 39 1547 (2006)
Lange M et al. J. Phys. B 39 4179 (2006)e + C Zatsarinny O, Bartschat K, Bandurina L and Gedeon V Phys. Rev. A 71 042702 (2005)e + O Zatsarinny O and Tayal S S J. Phys. B 34 1299 (2001)
Zatsarinny O and Tayal S S J. Phys. B 35 241 (2002)Zatsarinny O and Tayal S S As. J. S. S. 148 575 (2003)
e + Ne Zatsarinny O and Bartschat K J. Phys. B 37 2173 (2004)Bömmels J et al. Phys. Rev. A 71, 012704 (2005)Allan M et al. J. Phys. B 39 L139 (2006)
e + Mg Bartschat K, Zatsarinny O, Bray I, Fursa D V and Stelbovics A T J. Phys. B 37 2617 (2004)e + S Zatsarinny O and Tayal S S J. Phys. B 34 3383 (2001)
Zatsarinny O and Tayal S S J. Phys. B 35 2493 (2002)e + Ar Zatsarinny O and Bartschat K J. Phys. B 37 4693 (2004)e + K (inner-shell) Borovik A A et al. Phys. Rev. A, 73 062701 (2006)e + Zn Zatsarinny O and Bartschat K Phys. Rev. A 71 022716 (2005)e + Fe+ Zatsarinny O and Bartschat K Phys. Rev. A 72 020702(R) (2005)e + Kr Zatsarinny O and Bartschat K J. Phys. B 40 F43 (2007)e + Xe Allan M, Zatsarinny O and Bartschat K Phys. Rev. A 030701(R) (2006)Rydberg series in C Zatsarinny O and Froese Fischer C J. Phys. B 35 4669 (2002)osc. strengths in Ar Zatsarinny O and Bartschat K J. Phys. B: At. Mol. Opt. Phys. 39 2145 (2006)osc. strengths in S Zatsarinny O and Bartschat K J. Phys. B: At. Mol. Opt. Phys. 39 2861 (2006)osc. strengths in Xe Dasgupta A et al. Phys. Rev. A 74 012509 (2006)
Structure Calculations with the BSR Code
Energy Levels in Heavy Noble Gases
Oscillator Strengths in Neon
Conclusions
• The non-orthogonal orbital technique allows us account for term-dependence and
relaxation effects practically to full extent. At the same time, this reduce the size of
the configuration expansions, because we use specific non-orthogonal sets of
correlation orbitals for different kinds of correlation effects.
• B-spline multi-channel models allow us to treat entire Rydberg series and can be
used for accurate calculations of oscillator strengths for states with intermediate
and high n-values. For such states, it is difficult to apply standard CI or MCHF
methods.
• The accuracy obtained for the low-lying states is close to that reached in large-scale
MCHF calculations.
• Good agreement with experiment was obtained for the transitions from the ground
states and also for transitions between excited states.
• Calculations performed in this work: s-, p-, d-, and f-levels up to n = 12.
Ne – 299 states – 11300 transitions
Ar – 359 states – 19000 transitions
Kr – 212 states – 6450 transitions
Xe – 125 states – 2550 transitions
• All calculations are fully ab initio.
• The computer code BSR used in the present calculations and the results for Ar
were recently published:
BSR: O. Zatsarinny, Comp. Phys. Commun. 174 (2006) 273
Ar: O. Zatsarinny and K. Bartschat, J. Phys. B 39 (2006) 2145
Introduction
• Using our semi-relativistic B-spline R-matrix (BSR) method [Zatsarinny andBartschat, J. Phys. B 37, 2173 (2004)], we achieved unprecendented agreementwith experiment for angle-integrated cross sections in e−Ne collisions.
Cro
ss S
ecti
on (
pm
/sr)
2
31S
10S
10S
d1
ed2
p
p
3p
3p4s4s2
3p2
4s4p
4s3d
4p
n1
n1
n2
n2
f1
f1
f2
f2
g1
g1
g2
g2
p
p
18.5 19.0 19.5 20.0 20.5
0
10
20
Electron Energy (eV)
q = 180°
0
1
2
3q = 135°
}
}
}
}
4p2
Expanded view of the resonant features in selected cross sections for the excitationof the 3p states. Experiment is shown by the more ragged red line, theory by thesmooth blue line. The present experimental energies, labels (using the notationof Buckman et al.et al.et al. (1983), and configurations of the resonances are given above thespectra. Threshold energies are indicated below the lower spectrum.
Metastable Excitation Function in Kr
Metastable Excitation Function in Kr
05 0
1 0 01 5 0
05
1 01 5
1 0 1 1 1 2 1 3 1 4 1 50
5 0
1 0 0
0
1 0 0
2 0 0
5 s [ 3 / 2 ] 2
e - K r θ = 3 0 o
5 s [ 3 / 2 ] 1
Cross
Secti
on (p
m2 /sr)
5 s ’ [ 1 / 2 ] 1
E l e c t r o n E n e r g y ( e V )
P h i l l i p s ( 1 9 8 2 ) A l l a n ( 2 0 1 0 ) D B S R 6 9
5 s ’ [ 1 / 2 ] 0
0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0
1 0 - 2
1 0 - 1
0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 00 . 0 0
0 . 0 2
0 . 0 4
0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 00 . 0 0 0
0 . 0 0 2
0 . 0 0 4
0 . 0 0 6
0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0
1 0 - 2
1 0 - 1�B S R 4 9 D B S R 6 9
T r a j m a r e t a l . ( 1 9 8 1 ) G u o e t a l . ( 2 0 0 0 ) � 0 . 3 7 A l l a n ( 2 0 1 0 )
��������
�
����������������������
�
��� ������
DC
S (a o2 /s
r) ��������
������
DCS (
a o2 /sr)
����������������������
Dirk Dodt for the 5th Workshop on Data Validation 5
Forward Model
intensity calibration
emission coefficient
radiance
spectral radiancespectrometer pixels
line of sightintegration
line profile (aparatus width)
Einstein's coefficients(radiation transport)
EEDF
population densities
collisional - radiative model
Dirk Dodt for the 5th Workshop on Data Validation 6
Collisional Radiative Model
● Balance equation for each excited state density
● Elementary processes:
– Electron impact (de)excitation
– Radiative transitions
– Atom collisions
– Wall losses● Linear equation for
Results: Treatment of Various Processes in the Model
Uncertainty Estimate of Oscillator Strengths
]-1 [skiA410 510 610 710 810
ki /
Aki
A∆
00.020.040.060.08
0.10.120.140.160.180.2
0.220.24
Uncertainty Estimate of Cross Sections
Modeled Spectrum With “Reasonable Uncertainty in Atomic Data”
[nm]λ560 580 600 620 640
] s
r m
2m
W [ λ
L 510
610
710
σre
sid
ual
/
-8-6-4-202468
[nm]λ680 700 720 740 760
] s
r m
2m
W [ λ
L 510
610
710
σre
sid
ual
/
-8-6-4-202468
[nm]λ800 820 840 860 880
] s
r m
2m
W [ λ
L 510
610
710
σre
sid
ual
/
-8-6-4-202468
Results: Are the Atomic Data Consistent?
0 0.5 1 1.5 2 2.52p1->3s42p1->3s32p1->3s22p1->3s1
2p1->3p102p1->3p92p1->3p82p1->3p72p1->3p62p1->3p52p1->3p42p1->3p32p1->3p22p1->3p1
3s4->3p103s4->3p93s4->3p83s4->3p73s4->3p63s4->3p53s4->3p43s4->3p33s4->3p23s4->3p13s4->3s33s4->3s23s4->3s13s3->3s23s3->3s13s2->3s1
3s3->3p103s3->3p93s3->3p83s3->3p73s3->3p63s3->3p53s3->3p43s3->3p33s3->3p23s3->3p1
3s2->3p103s2->3p93s2->3p83s2->3p73s2->3p63s2->3p53s2->3p43s2->3p33s2->3p23s2->3p1
3s1->3p103s1->3p93s1->3p83s1->3p73s1->3p63s1->3p53s1->3p43s1->3p33s1->3p23s1->3p13s3->4s43s3->4s33s3->4s23s3->4s1
3s3->3d123s3->3d113s3->3d103s3->3d93s3->3d8
0 0.5 1 1.5 2 2.53s3->3d73s3->3d63s3->3d53s3->3d43s3->3d33s3->3d23s3->3d13s2->4s43s2->4s33s2->4s23s2->4s1
3s2->3d123s2->3d113s2->3d103s2->3d93s2->3d83s2->3d73s2->3d63s2->3d53s2->3d43s2->3d33s2->3d23s2->3d13s1->4s43s1->4s33s1->4s23s1->4s1
3s1->3d123s1->3d113s1->3d103s1->3d93s1->3d83s1->3d73s1->3d63s1->3d53s1->3d43s1->3d33s1->3d23s1->3d12p1->4s42p1->4s32p1->4s22p1->4s1
2p1->3d122p1->3d112p1->3d102p1->3d92p1->3d82p1->3d72p1->3d62p1->3d52p1->3d42p1->3d32p1->3d22p1->3d13s4->4s43s4->4s33s4->4s23s4->4s1
3s4->3d123s4->3d113s4->3d103s4->3d93s4->3d83s4->3d73s4->3d63s4->3d53s4->3d43s4->3d33s4->3d23s4->3d1
Let’s Zoom In ...
0 0.5 1 1.5 2 2.52p1->3p10
2p1->3p9
2p1->3p8
2p1->3p7
2p1->3p6
2p1->3p5
2p1->3p4
2p1->3p3
2p1->3p2
2p1->3p1
3s4->3p10
3s4->3p9
3s4->3p8
3s4->3p7
3s4->3p6
3s4->3p5
3s4->3p4
3s4->3p3
3s4->3p2
0 0.5 1 1.5 2 2.52p1->3d122p1->3d11
2p1->3d10
2p1->3d92p1->3d8
2p1->3d72p1->3d6
2p1->3d5
2p1->3d42p1->3d3
2p1->3d2
2p1->3d13s4->3d12
3s4->3d113s4->3d10
3s4->3d9
3s4->3d83s4->3d7
3s4->3d63s4->3d5
3s4->3d4
3s4->3d33s4->3d2
3s4->3d1
Results: Significant Correction Factors for a Few Transitions
Fully Nonperturbative Treatment of Ionizationand Ionization with Excitation of Noble Gases
Overview:I. Motivation: Is Theory Really, Really, Really BAD?
II. Theoretical Formulations
• Perturbative Methods
• Plane-Wave and Distorted-Wave Treatments of the Projectile
• Second-Order Effects
• Ejected-Electron−Residual-Ion Interaction: The Hybrid Approach
• Fully Non-Perturbative Methods
• Time-Dependent Close-Coupling (TDCC), Exterior Complex Scaling (ECS)
• Convergent Close-Coupling (CCC)
• Convergent B-Spline R-matrix with Pseudostates (BSRMPS)
III. Example Results
• Ionization of He(1s222) → He+++(1s), He+++(nnn = 2)
• Ionization of Ne(2s2222p666) → Ne+++(2s2222p555), (2s2p666)
• Ionization of Ar(3s2223p666) → Ar+++(3s2223p555), (3s3p666)
IV. Conclusions and Outlook
The “Straightforward” Close-Coupling Formulation
• Recall: We are interested in the ionization process
e0(k0, µ0) + A(L0, M0; S0, MS0) → e1(k1, µ1) + e2(k2, µ2) + A+(Lf , Mf ; Sf , MSf
)
• We need the ionization amplitude
f(L0, M0, S0; k0 → Lf , Mf , Sf ; k1, k2)
• We employ the B-spline R-matrix method of Zatsarinny (CPC 174 (2006) 273)
with a large number of pseudo-states:
• These pseudo-states simulate the effect of the continuum.
• The scattering amplitudes for excitation of these pseudo-states are used to
form the ionization amplitude:
f(L0, M0, S0; k0 → Lf , Mf , Sf ; k1, k2) =∑
p
〈Ψk2
−
f |Φ(LpSp)〉 f(L0, M0, S0; k0 → Lp, Mp, Sp; k1p).
• Both the true continuum state |Ψk2
−
f 〉 (with the appropriate multi-channel
asymptotic boundary condition) and the pseudo-states |Φ(LpSp)〉 are consistently
calculated with the same close-coupling expansion.
• In contrast to single-channel problems, where the T -matrix elements can be
interpolated, direct projection is essential to extract the information in multi-
channel problems.
• For total ionization, we still add up all the excitation cross sections for the
pseudo-states.
Total Cross Section and Spin Asymmetry in e−H Ionization
(from Bartschat and Bray 1996)
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Total and Single-Differential Cross Section
1000.0
0.1
0.2
0.3
0.4
0.5
Montague et al. (1984) Rejoub et al. (2002) Sorokin et al. (2004) BSR-525 BSR with 1s2 correlation CCC with 1s2 correlation
300
Electron Energy (eV)
Ioni
zatio
n C
ross
Sec
tion
(10-
16 c
m2 )
30
e - He
0 10 20 30 40 50 60 700
1
2
3
Müller-Fiedler et al (1986) BSR227 - interpolation BSR227 - projection
SD
CS
(10-1
8 cm
2 /eV
)Secondary Energy (eV)
E=100 eVe - He
• Including correlation in the ground state reduces the theoretical result.
• Interpolation yields smoother result, but direct projection is acceptable.
• DIRECT PROJECTION is NECESSARY for MULTI-CHANNEL cases!
Triple-Differential Cross Section Ratio
experiment: Bellm, Lower, Weigold; measured directly
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
150
20 40 60 80 100 1200
50
100
1 = 24o
E1=44 eVE2=44 eV
expt. BSR DWB2-RMPS
1 = 36o
1 = 48o
1 = 32o
1 = 44o
2 (deg)
1 = 56o
1 = 28o
n=1/
n=2
Cro
ss S
ectio
n R
atio
1 = 40o
1 = 52o
Electron Impact Ionization of Ar(3p) with E0 = 71 eV
Electron Impact Ionization of Neon (from ground state)
0 20 40 60 80 100 120 140 160 180 2000
2
4
6
8
10
Rejoub et al. (2002) Krishnakumar & Strivastava (1988) Pindzola et al. (2000) BSR-679
Cro
ss s
ectio
n (1
0-17
cm2 )
Electron energy (eV)
e- + Ne - 2e- + Ne+
Electron Impact Ionization of Neon (from metastable states)
0 20 40 60 80 100 120 140 1600
10
20
30
40
50
60
70
80
Johnston et al. (1996) RMPS-243, Ballance et al. (2004) BSR-679
e- + Ne*(2p53s 3P) - 2e- + Ne+(2p5)
Cro
ss s
ectio
n (1
0-17
cm2 )
Electron energy (eV)
Total Cross Section for Electron Impact Excitation of NeonRMPS calculations by Ballance and Griffin (2004)
16 24 32 400.0
0.4
0.8
1.2
1.6
16 24 32 400.00
0.04
0.08
0.12
0.16
16 24 32 400.0
1.0
2.0
3.0
16 24 32 400.0
0.4
0.8
1.2
1.6
2.0
16 24 32 400
4
8
12
16 24 32 400.0
0.2
0.4
0.6 (2p53p)3D(2p53p)3S
Cro
ss s
ectio
n (1
0-18
cm2 )
(2p53d)3P
Electron energy (eV)
(2p53s)3P
RM-61 RMPS-243 BSR-679
(2p53d)1P
Electron energy (eV)
(2p53s)1P
Total Cross Section for Electron Impact Excitation of NeonEffect of Channel Coupling to Discrete and Continuum Spectrum
1000
3
6
9
12
1520 40 60 80 100
0.0
0.5
1.0
1.5
2.0
20 40 60 80 1000.0
0.1
0.2
0.3
0.4
1000.0
0.5
1.0
1.5
2.0
KatoSuzuki et al.
3s'[1/2]1
Electron Energy (eV)5020 30030050
BSR-457 BSR-31 BSR-5
3s[3/2]2
Cro
ss S
ectio
n (1
0-18 c
m2 )
20
Khakoo et al. Register et al. Phillips et al.
3s'[1/2]0
3s[3/2]1
Cro
ss S
ectio
n (1
0-18 c
m2 )
Electron Energy (eV)
Total Cross Section for Electron Impact Excitation of NeonEffect of Channel Coupling to Discrete and Continuum Spectrum
20 40 60 80 100
40
80
120
0
10
20
30
40
50
20 40 60 80 1000
100
200
300
0
20
40
60
80
Electron Energy (eV)
Cro
ss S
ectio
n (1
0-20 c
m2 )
3p[5/2]2
3p'[1/2]1
Electron Energy (eV)
3p'[1/2]0
BSR-31 BSR-457 RMPS-235 Chilton et al.
Cro
ss S
ectio
n (1
0-20 c
m2 )
3p[1/2]1
Total Cross Section for Electron Impact Excitation of NeonEffect of Channel Coupling to Discrete and Continuum Spectrum
1000
20
40
60
80
20 40 60 80 1000
1
2
3
20 40 60 80 1000
4
8
12
1000
10
20
30 3d[3/2]1
Electron Energy (eV)
BSR-31 BSR-46 BSR-457 RMPS-235
4020 20020040
3d[1/2]0
Cro
ss S
ctio
n (1
0-20 c
m2 )
20
3d[3/2]2
3d[1/2]1
Cro
ss S
ctio
n (1
0-20 c
m2 )
Electron Energy (eV)
Total Cross Section for Electron Impact Excitation of Metastable NeonEffect of Cascades
0 50 100 150 200 250 3000
1
2
3
0 50 100 150 200 250 3000
5
10
0 50 100 150 200 250 3000
2
4
6
0 50 100 150 200 250 3000
5
10
15
20
25
BSR-457 + cascade Boffard et al.
3p'[3/2]2
Cro
ss S
ectio
n (1
0-16
cm2 )
3p[3/2]2
3p[5/2]2
Cro
ss S
ectio
n (1
0-16
cm2 )
Electron Energy (eV)
3p[5/2]3
Electron Energy (eV)
Total Cross Section for e-Ne Collisions
0.01 0.1 1 10 100 10000
1
2
3
4
5
Wagenaar & de Heer (1980) Gulley et al. (1994) Szmitkowski et al. (1996) Baek & Grosswendt (2003) BSR-679, total elastic + excitation
Tota
l Cro
ss S
ectio
n (1
0-16
cm2 )
Electron Energy (eV)
e- + Ne
Differential Cross Section for Electron Impact Excitation of Neon at 30 eVExperiment: Khakoo group
0 20 40 60 80 100 120 140
100
101
102
0 20 40 60 80 100 120 1400.0
1.0
2.0
3.0
0 20 40 60 80 100 120 1400.0
0.2
0.4
0.6
0 20 40 60 80 100 120 140
10-1
100
101 3s'[1/2]1
Scattering Angle (deg)
Khakoo et al. x 0.55 BSR-457 BSR-31
30 eV 3s[3/2]2
D
CS
(10-1
9 cm
2 /sr
)
3s'[1/2]0
3s[3/2]1
DC
S (1
0-19
cm2 /
sr)
Scattering Angle (deg)
Differential Cross Section for Electron Impact Excitation of Neon at 40 eVExperiment: Khakoo group
0 20 40 60 80 100 120 140
100
101
102
0 20 40 60 80 100 120 1400.0
1.0
2.0
3.0
0 20 40 60 80 100 120 1400.0
0.2
0.4
0.6
0 20 40 60 80 100 120 140
10-1
100
1013s'[1/2]1
Scattering Angle (deg)
Khakoo et al. x 0.7 BSR-457 BSR-31
40 eV 3s[3/2]2
D
CS
(10-1
9 cm
2 /sr
)
3s'[1/2]0
3s[3/2]1
DC
S (1
0-19
cm2 /
sr)
Scattering Angle (deg)
DCS Ratios for Electron Impact Excitation of Neon at 30 and 40 eVExperiment: Khakoo group
0 20 40 60 80 100 120 1400
2
4
6
8
10
0 20 40 60 80 100 120 1400
2
4
6
8
10
0 20 40 60 80 100 120 1400.0
0.2
0.4
0.6
0.8
0 20 40 60 80 100 120 1400.0
0.1
0.2
0.3
0.4
0.5
0 20 40 60 80 100 120 1400.0
0.5
1.0
1.5
2.0
0 20 40 60 80 100 120 1400.0
0.5
1.0
1.5
3P2 / 3P0
30 eV
r
40 eV
3P1 / 1P1
r'
BSR-31 BSR-457 Khakoo et al.
3P2 / 3P1
r''
Scattering Angle (deg)
Scattering Angle (deg)
DCS Ratios for Electron Impact Excitation of Neon at 50 and 100 eVExperiment: Khakoo group
0 20 40 60 80 100 120 1400
2
4
6
8
10
0 20 40 60 80 100 120 1400
2
4
6
8
10
0 20 40 60 80 100 120 1400.0
0.1
0.2
0.3
0 20 40 60 80 100 120 1400.0
0.2
0.4
0.6
0 20 40 60 80 100 120 1400.0
0.5
1.0
1.5
0 20 40 60 80 100 120 1400.0
0.5
1.0
1.5
50 eV
r
3P2 / 3P0
100 eV
BSR-457 Khakoo et al.
r'3P1 / 1P1
r''
Scattering Angle (deg)
3P2 / 3P1
Scattering Angle (deg)
Conclusions and Outlook• Much progress has been made in calculating the structure of and electron-induced
collision processes in noble gases — and other complex targets (C, O, F, ..., Cu,
Zn, Cs, Au, Hg, Pb).
• Time-independent close-coupling (R-matrix) is the way to go for complete datasets.
• Other sophisticated methods (CCC, TDCC, ECS, ...) are still restricted to
simple targets. These methods are have essentially solved the (quasi-)one- and
(quasi-)two-electron problems for excitation and ionization.
• Special-Purpose and Perturbative (Born) methods are still being used, especially for
complex targets!
• For complex, open-shell targets, the structure problem should not be ignored !
• For such complex targets, the BSR method with non-orthonal orbitals has achieved
a breakthrough in the description of near-threshold phenomena. The major
advantages are:
• highly accurate target description
• consistent description of theN -electron target and (N+1)-electron collision problems
• ability to give “complete” datasets for atomic structure and electron collisions
• The most recent extension to anRMPS version allows for the treatment of ionization
processes.
Conclusions and Outlook (continued)
• After setting up a detailed model of a Ne discharge with a large number of observed
lines, we validated most atomic BSR input data (oscillator strengths and collision
cross sections) – and we got hints about areas to improve!
• The validation method provides a valuable alternative for data assessment and
detailed plasma diagnostics — especially when no absolute cross sections from beam
experiments are available.
• This is a nice example of a very fruitful and mutually beneficial collaboration between
data producers and data users.
• We can provide atomic data for (almost) any system. Practical limitations are:
• expertise of the operator/developer
• continued code development (parallelization, new architectures)
• computational resources (Many Thanks to Teragrid/XSEDE!)
• We are currently preparing fully relativistic R-matrix with pseudo-states
calculations on massively parallel platforms (→→→ Xe, W, ...).
• We don’t have a company (yet). If you really want/need specific data, you can
• ask us really nicely and hope for the best (preferred by most colleagues)
• give us $$$ and increase your priority on the list (preferred by us)
THANK YOU!
