Electron-Atom Collisions:
Benchmark Comparisons between Experiment and Theory
Klaus Bartschat, Drake University
(+ Oleg Zatsarinny + many others)
IAEA Technical Meeting
Vienna, May 6-8, 2013
$$$: PHY-1068140, PHY-1212450, XSEDE
I. Production and Assessment of Atomic Collision Data
II. Computational Methods for electron (positron) collisions with atoms
• Special-Purpose Methods: Polarized Orbital, Optical Model Potential
• Distorted-Wave Methods: DWBA and RDW
• Close-Coupling Methods: CCC, RMPS, IERM, TDCC, ECS, BSR
III. Illustrative Results
• Electron-Impact Excitation: H, He, Be; Ne, Ar, Kr, Xe;
I, Au, Hg; C, Fe+ , Mo
• Electron-Impact Ionization: H, He, Ne, C
IV. Conclusions
Production and Assessment of Atomic Data
• Data for electron collisions with atoms, ions, and molecules are needed for modeling
and interpreting
• laboratory plasmas (fusion devices, discharges in lighting, lasers, plasma etching, ...)
• astrophysical observations
• planetary atmospheres
• The data are obtained through
• experiments
• valuable but expensive ($$$) 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 ???)
For complete data sets, theory is often the "only game in town"!
Production and Assessment of Atomic Data
• Data for electron collisions with atoms, ions, and molecules are needed for modeling
and interpreting
• laboratory plasmas (fusion devices, discharges in lighting, lasers, plasma etching, ...)
• astrophysical observations
• planetary atmospheres
• The data are obtained through
• experiments
• valuable but expensive ($$$) benchmarks (often differential in energy, angle, spin, ...)
• often problematic when absolute (cross section) normalization is required
• calculations (Opacity Project, Iron Project, ...)
• relatively cheap
• almost any transition of interest is possible
• often restricted to particular energy ranges:
• high (→ Born-type methods)
• low (→ close-coupling-type methods)
• cross sections may peak at “intermediate energies” (→ ???)
• good (or bad ?) guesses
• Sometimes the results are (obviously) wrong or (more often) inconsistent !
Basic Question: WHO IS RIGHT ? (And WHY ???)
For complete data sets, theory is often the "only game in town"!
Production and Assessment of Atomic Data
• Data for electron collisions with atoms, ions, and molecules are needed for modeling
and interpreting
• laboratory plasmas (fusion devices, discharges in lighting, lasers, plasma etching, ...)
• astrophysical observations
• planetary atmospheres
• The data are obtained through
• experiments
• valuable but expensive ($$$) 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 ???)
For complete data sets, theory is often the "only game in town"!
Production and Assessment of Atomic Data
• Data for electron collisions with atoms, ions, and molecules are needed for modeling
and interpreting
• laboratory plasmas (fusion devices, discharges in lighting, lasers, plasma etching, ...)
• astrophysical observations
• 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 ???)
For complete data sets, theory is often the "only game in town"!
Classification of Computational 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
Z
X
1
LSπ
ΨLSπ
(r
,
.
.
.
,
r
)
=
A
Φ
(r
,
.
.
.
,
r
,
r̂)
F (r)
E
1
N +1
i
1
N
r E,i
i
• simultaneous results for transitions between all states in the expansion;
sophisticated, publicly available codes exist; results are internally consistent
→ CCC, RMPS, IERM)
• expansion must be cut off (→
• usually, a single set of mutually orthogonal one-electron orbitals is used
→ BSR with non-orthogonal orbitals)
for all states in the expansion (→
•
Time-dependent and other direct methods
• TDCC, ECS
• solve the Schrödinger equation directly on a grid
• very expensive, only possible for (quasi) one- and two-electron systems.
Classification of Computational 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
Z
X
1
LSπ
ΨLSπ
(r
,
.
.
.
,
r
)
=
A
Φ
(r
,
.
.
.
,
r
,
r̂)
F (r)
E
1
N +1
i
1
N
r E,i
i
• simultaneous results for transitions between all states in the expansion;
sophisticated, publicly available codes exist; results are internally consistent
→ CCC, RMPS, IERM)
• expansion must be cut off (→
• usually, a single set of mutually orthogonal one-electron orbitals is used
→ BSR with non-orthogonal orbitals)
for all states in the expansion (→
•
Time-dependent and other direct methods
• TDCC, ECS
• solve the Schrödinger equation directly on a grid
• very expensive, only possible for (quasi) one- and two-electron systems.
Classification of Computational 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
Z
X
1
LSπ
ΨLSπ
(r
,
.
.
.
,
r
)
=
A
Φ
(r
,
.
.
.
,
r
,
r̂)
F (r)
E
1
N +1
i
1
N
r E,i
i
• simultaneous results for transitions between all states in the expansion;
sophisticated, publicly available codes exist; results are internally consistent
→ CCC, RMPS, IERM)
• expansion must be cut off (→
• usually, a single set of mutually orthogonal one-electron orbitals is used
→ BSR with non-orthogonal orbitals)
for all states in the expansion (→
•
Time-dependent and other direct methods
• TDCC, ECS
• solve the Schrödinger equation directly on a grid
• very expensive, only possible for (quasi) one- and two-electron systems.
Numerical Methods: OMP for Atoms
• For electron-atom scattering, we solve the partial-wave equation
d2
ℓ(ℓ + 1)
2
−
−
2V
(k,
r)
u
(k,
r)
=
k
uℓ (k, r).
mp
ℓ
dr 2
r2
• 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
It's great if this
is all you want!
Comparison with "ab initio" Close-Coupling
2 0 0
e + I (5 p 5 , J = 3 /2 )
PRA 83 (2011) 042702
C r o s s s e c t i o n ( a 2o )
1 5 0
1 0 0
B P R M
D B S R
D B S R
D A R C
O M P
5 0
-C
-C
-C
-C
C 2
C 2
C 2 + p o l
C 1 1 (W u & Y u a n )
0
0
1
2
3
4
5
E le c tro n e n e rg y (e V )
6
7
8
momentum transfer cross section (10
-16
2
cm )
Polarized Orbital – an "Ab Initio Special Purpose" Approach
10
nonrel-pol
nonrel-pol+DD
rel-pol+DD
recommended expt.
1
e-Ar
0.1
0.01
0.1
1
10
energy (eV)
Extension to account for inelastic effects:
J. Phys. B 42 (2009) 075202
BEf-scaling; Plane-Wave Born with Experimental Optical
Oscillator Strength and Empirical Energy Shift
works well, but is limited to optically allowed transitions
Similar idea works even better for ionization of complex targets :=)
Semi-Relativistic DWBA
polarization and absorption potentials
may also be included
Ar 3p54s –> 3p54p: DWBA vs. R-matrix
unitarization problem!
(can be fixed; e.g., Dasgupta's NRL code)
Phys. Rev. A 61 (2000) 022701
Theoretical results depend on
wavefunctions and potentials
Relativistic DWBA; Semi-Relativistic DWBA; R-Matrix; Experiment
Ar 3d1 (J=1)
0.1
RDW
RM15
DW-a
DW-b
Chutjian + Cartwright
?
cross section (a02)
cross section (a02)
1
Ar 3d4 (J=2)
0.1
RDW
RM15
DW-a
DW-b
0.01
?
0.001
0.0001
Chutjian + Cartwright
Chilton + Lin
0.01
20
40
60
energy (eV)
80
100
20
40
60
energy (eV)
80
Key Message:
Sometimes BIG Differences between Theories
and HUGE Experimental Error Bars!
100
Time-Independent Close-Coupling
The (Time-Independent) Close-Coupling Expansion
HΨ=EΨ
• Standard method of treating low-energy scattering
• Based upon an expansion of the total wavefunction as
Z
X
1
LSπ
ΨE (r1 , . . . , rN +1 ) = A
ΦLSπ
(r1 , . . . , rN , r̂) FE,i (r)
i
r
i
• Target states Φi diagonalize the N -electron target Hamiltonian according to
hΦi0 | HTN | Φi i = Ei δi0 i
good start – remember
your QM course?
• The unknown radial wavefunctions FE,i are determined from the solution of a system of coupled integrodifferential equations given by
2
Z
Z
X
X
`i (`i + 1)
d
2
−
+ k FE,i (r) = 2
Vij (r) FE,j (r) + 2
Wij FE,j (r)
dr2
r2
j
j
with the direct coupling potentials
N
X
Z
1
Vij (r) = − δij +
hΦi |
| Φj i
r
|rk − r|
k=1
and the exchange terms
Wij FE,j (r) =
N
X
k=1
hΦi |
1
| (A − 1) Φj FE,j i
|rk − r|
Close-coupling can yield complete data sets, and the results are
internally consistent (unitary theory that conserves total flux)!
Benchmark Results for e-H Excitation
Bartschat,Benchmark
Bray, Burke,
and Scott,
Phys. B 29 (1996) 5493
Results
for e−HJ.Scattering
• Using a variational method, Schwartz solved the low-energy elastic e−H scattering problem
with high accuracy in the early 1960’s.
• As seen in further benchmark work in the inelastic regime, CCC, RMPS, and IERM predictions
agree extremely well with each other, and also with the experimental data (dots on 2s, 2p) of Williams
(1988). [From Bartschat, Bray, Burke, and Scott, J. Phys. B 29 (1996) 5493.]
cross section (πa20)
7.2
7.0
6.8
6.6
6.4
6.2
6.0
5.8
0.5
1s
light quasi-one and
quasi-two electron
systems; theory
looks very good :-)
0.4
2s
0.3
0.2
0.1
0.0
0.8
2p
0.6
0.4
0.2
0.0
0.75
0.77
0.79
0.81
0.83
0.85
0.86
projectile energy (Ryd)
0.87
0.88
0.89
CrossCross
Section
for Electron-Impact
Excitation
of He(1s2)of Helium
Total
Sections
for Electron-Impact
Excitation
K.Bartschat,
Bartschat,
J. Phys.
B 31 L469
(1998) L469
K.
J. Phys.
B 31 (1998)
n=2
6
Trajmar
Hall
Donaldson
CCC(75)
RMPS
5
3
2.0
3S
3
1.5
2
1.0
1.0
experiment
CCC(75)
RMPS
3
0.8
31 S
0.6
0.4
2
1
1
0.5
23 S
0
4
0
8
3
6
2
4
1
2
21 P
23 P
0
20
25
30
0.2
21 S
0
35
40
20
25
projectile energy (eV)
30
35
40
cross section (10−18cm2)
cross section (10−18cm2)
4
n=3
4
0.0
1.0
0.8
0.0
1.5
33 P
31 P
1.0
0.6
0.4
0.5
0.2
0.0
0.3
0.0
33 D
0.3
31 D
0.2
0.2
0.1
0.1
0.0
0.0
20
25
30
35
40
20
25
30
35
40
projectile energy (eV)
In 1998,
deHeerrecommends
recommends (CCC+RMPS)/2
for uncertainty
of 10% or better
In 1998,
de Heer
0.5 x (CCC+RMPS)
for uncertainty
of! 10%
(independent of
— independent
ofexperiment)
experiment!
So far, so good ...
3S
3S
Total Cross
CrossSection
Sections
Electron-Impact
Excitation
from He(1s2s)
for for
Electron-Impact
Excitation
of He(1s2s)
K.K.
Bartschat,
Phys.
B (1998)
31 (1998)
Bartschat, J.J.Phys.
B 31
L469 L469
n=2
300
3
2P
200
n=3
Piech et al. 1998
Piech et al. 1997
Lagus et al. 1996
FBA
RM(11)
CCC(75)
RMPS
33 S
10
5
100
0
10
cross section (10−16cm2)
cross section (10−16cm2)
10
15
Piech et al. 1998
Piech et al. 1997
EA10
RM5
CCC(75)
RMPS
1
0.1
21 S
0.01
10
31 S
1
0.1
0.01
0.001
1
0
5
31 P
33 P
4
3
0.1
2
1
0
15
0.01
1
31 D
33 D
10
1
0.1
0.1
5
21 P
0
0.01
0
5
10
15
projectile energy (eV)
20
0.01
0
5
10
15
20
0
5
10
15
20
projectile energy (eV)
There are BIG discrepancies in excitation from the metastable!
There is significant disagreement between theory and experiment !?!?!?
Who is right?
It looks
may from
be correct
New like
Trap theory
Measurement
Australiaafter all!
upper limit to
excitation XS
e-Be: coupling to continuum most important for
i) optically forbidden transitions and/or ii) small cross sections
good agreement between CCC, RMPS, TDCC — no experiment !
But not everything looks that good ...
Metastable Excitation Function in Kr
Oops — maybe we need
to try a bit harder?
We have a great new program :):):)
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 orbital sets for bound and
continuum radial functions
not just the numerical basis!
O. Zatsarinny, CPC 174 (2006) 273
• 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 record:150,000
• Generalized eigenvalue problem needs to be solved
to do 50-100 times;
• Matrix size typically 10,000
50,000 and higher due to size of B-spline basis
100 - 200 kSU
• Rescue: Excellent numerical properties of B-splines; use of (SCA)LAPACK et al.
We also have to solve the problem outside the box for each energy (from 100's to 1,000,000's).
List of early calculations
with
BSRcode
code
(rapidly
growing)
List of calculations
withthe
the BSR
(rapidly
growing)
hv + Li
hv + Hehv + Chv + Bhv + Ohv + Cae + He
e+C
e+O
e + Ne
e + Mg
e+S
e + Ar
e + K (inner-shell)
e + Zn
e + Fe+
e + Kr
e + Xe
Rydberg series in C
osc. strengths in Ar
osc. strengths in S
osc. strengths in Xe
Zatsarinny O and Froese Fischer C J. Phys. B 33 313 (2000)
Zatsarinny O, Gorczyca T W and Froese Fischer C J. Phys. B. 35 4161 (2002)
Gibson N D et al. Phys. Rev. A 67, 030703 (2003)
nearly 100
Zatsarinny O and Gorczyca T W Abstracts of XXII ICPEAC (2003)
papers by now
Zatsarinny O and Bartschat K Phys. Rev. A 73 022714 (2006)
Zatsarinny O et al. Phys. Rev. A 74 052708 (2006)
(Topical Review
Stepanovic et al. J. Phys. B 39 1547 (2006)
in press)
Lange M et al. J. Phys. B 39 4179 (2006)
Zatsarinny O, Bartschat K, Bandurina L and Gedeon V Phys. Rev. A 71 042702 (2005)
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)
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)
Bartschat K, Zatsarinny O, Bray I, Fursa D V and Stelbovics A T J. Phys. B 37 2617 (2004)
Zatsarinny O and Tayal S S J. Phys. B 34 3383 (2001)
Zatsarinny O and Tayal S S J. Phys. B 35 2493 (2002)
Zatsarinny O and Bartschat K J. Phys. B 37 4693 (2004)
Borovik A A et al. Phys. Rev. A, 73 062701 (2006)
Zatsarinny O and Bartschat K Phys. Rev. A 71 022716 (2005)
Zatsarinny O and Bartschat K Phys. Rev. A 72 020702(R) (2005)
Zatsarinny O and Bartschat K J. Phys. B 40 F43 (2007)
Allan M, Zatsarinny O and Bartschat K Phys. Rev. A 030701(R) (2006)
Zatsarinny O and Froese Fischer C J. Phys. B 35 4669 (2002)
Zatsarinny O and Bartschat K J. Phys. B: At. Mol. Opt. Phys. 39 2145 (2006)
Zatsarinny O and Bartschat K J. Phys. B: At. Mol. Opt. Phys. 39 2861 (2006)
Dasgupta A et al. Phys. Rev. A 74 012509 (2006)
Resonances in Electron Impact Excitation of He
Experiment (not absolute): Williams group (Western Australia)
Theory: B-Spline R-matrix
cm )
0.8
Cross Section (10
1
He 3 S
BSR-69 (convoluted)
2
-18
experiment
0.6
0.4
0.2
n=4
n=3
n=5
0.0
23.0
23.5
Electron Energy (eV)
24.0
Resonances in Electron Impact Excitation of He
Resonance Resolution in BSR Theory
1.2
He
1
3 S
n=5
n=4
n=3
0.4
Cross Section [10
-18
2
cm ]
0.8
0.0
2
e
S
-0.4
2
o
P
-0.8
2
-1.2
22.8
23.0
D
23.2
e
23.4
23.6
Electron Energy [eV]
23.8
24.0
heavy noble gases
Metastable Excitation Function in Kr
JPB 43 (2010) 074031
What a difference :):):)
–> let's go to more detail!
Resonances in the excitation of the Ne (2p53p) states
Allan, Franz, Hotop, Zatsarinny, Bartschat (2009), J. Phys. B 42, 044009
expt.
BSR31 n
1
p
3
f1
1
S0
q = 135°
g1 g2
p
n2
3p2
}
d1
0
20
it's looking
good :):):)
3
S1
4p2
}
e d2
3p 4s
p
4s2
g1 g2
4s 4p
q = 180°
}
}
Cross Section (pm2/sr)
2
1
f2
1
S0
p
n1 n2 f1 f2
10
4p
3p
0
18.5
19.0
3d
4s
19.5
Electron Energy (eV)
20.0
20.5
Expanded view of the resonant features in selected cross sections for the excitation
of the 3p states. Experiment is shown by the more ragged red line, theory by the
smooth blue line. The present experimental energies, labels (using the notation
of Buckman et al. (1983), and configurations of the resonances are given above the
spectra. Threshold energies are indicated below the lower spectrum.
M. Allan, O. Zatsarinny, and K.B., J. Phys. B 44 (2011) 065201
(selected as a JPB "highlight")
excitation at fixed energy
5s[3/2]2
15 eV
5s'[1/2]0
0 .0 0 6
D C S (a
o
2
/s r)
0 .0 4
0 .0 0 4
0 .0 2
0 .0 0 2
0 .0 0
0
3 0
6 0
9 0
1 2 0
1 5 0
1 8 0
1 0
T ra jm 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 lla n (2 0 1 0 )
-1
0
3 0
6 0
9 0
now confirmed
1 0
-1
1 0
-2
B S R 4 9
D B S R 6 9
1 2 0
1 5 0
1 8 0
5s'[1/2]1
D C S (a
o
2
/s r)
5s[3/2]1
0 .0 0 0
1 0
-2
0
3 0
6 0
9 0
1 2 0
1 5 0
Scattering Angle (deg)
1 8 0
0
3 0
6 0
9 0
1 2 0
1 5 0
Scattering Angle (deg)
1 8 0
Ionization in Close-Coupling:
Excitation
of and
Positive-Energy
Pseudo-States
Total Cross
Section
Spin Asymmetry
in e−H Ionization
Total
Cross
Sectionand
in e-H
Ionization
(from
Bartschat
Bray
1996)
K. Bartschat and I. Bray, J. Phys. B 29 (1996) L577
#'
"
*
.
,
&'
$'
%'
"
"
"
6 45 3 2 1 0 / 0 /
+
*
"'
"
"
!"
%"
#"
%"
&"
$" &"
$'
"
('
)'
%'
"
"
"
!'
&'
"
"
"'
"
"
!"
#"
$" Phys. Rev. Lett. 107 (2011) 023203
Total and Single-Differential Cross Section
e - He
0.4
e - He
correlation drops
the theoretical ICS
E=100 eV
3
BSR227 - interpolation
BSR227 - projection
2
cm /eV)
Müller-Fiedler et al (1986)
2
-18
0.3
0.2
Montague et al. (1984)
Rejoub et al. (2002)
SDCS (10
-16
2
Ionization Cross Section (10
cm )
0.5
definitely looks o.k.
Absolute1 experiments are tricky!
Sorokin et al. (2004)
That's a lot of states!
BSR-525
0.1
2
BSR with 1s
correlation
2
CCC with 1s
correlation
0
0.0
30
100
Electron Energy (eV)
300
0
10
20
30
40
50
60
Secondary Energy (eV)
• 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!
70
Electron Impact Ionization of Neon (from ground state)
10
-
+ Ne
-
2e
-
+ Ne
+
8
Cross section (10
-17
2
cm )
e
6
Absolute experiments are tricky!
4
Rejoub et al. (2002)
Krishnakumar & Strivastava (1988)
2
BSR-679
0
TDCC; target description?
That's again a lot of states!
Pindzola et al. (2000)
0
20
40
60
80
100
120
140
Electron energy (eV)
160
180
200
Electron Impact Ionization of Neon (from metastable states)
80
e
Cross section (10
-17
2
cm )
70
-
5
+ Ne*(2p 3s
3
P)
-
2e
-
+
5
+ Ne (2p )
60
Johnston et al. (1996)
50
RMPS-243, Ballance et al. (2004)
BSR-679
40
30
20
10
0
0
20
40
60
80
100
Electron energy (eV)
120
140
160
Total Cross Section for Electron Impact Excitation of Neon
RMPS calculations by Ballance and Griffin (2004)
5
3.0
2.0
8
1.0
4
0.0
16
24
32
40
0
16
5
1
(2p 3s) P
The Excitation Mystery!
24
32
40
Cross section (10
-18
2
cm )
12
3
(2p 3s) P
5
5
1.6
3
(2p 3p) D
1.2
There is a BIG drop in the
cross sections due to the
coupling to pseudo-states!
0.4
0.8
0.2
0.4
0.0
16
24
0.16
This result is AGAINST
the message in
standard textbooks!
3
(2p 3p) S
0.6
32
5
40
0.0
16
24
2.0
3
32
5
(2p 3d) P
40
1
(2p 3d) P
We seriously underestimated the
uncertainty to only 60% !?!?!?
1.6
0.12
1.2
0.08
RM-61
0.8
RMPS-243
0.04
0.00
16
BSR-679
0.4
24
32
Electron energy (eV)
40
0.0
16
24
32
Electron energy (eV)
40
Total Cross Section for Electron Impact Excitation of Neon
2.0
0.4
Cross Section (10
-18
2
cm )
Effect of Channel Coupling to Discrete and Continuum Spectrum
3s[3/2]
1.5
0.3
Register et al.
BSR-31
BSR-5
1.0
0
Khakoo et al.
BSR-457
Phillips et al.
0.2
0.5
0.1
0.0
0.0
20
2.0
40
60
80 100
20
40
We had some indication that something
might
be 60
15
wrong with models containing
only discrete states.
80 100
Cross Section (10
-18
2
cm )
3s'[1/2]
2
3s[3/2]
3s'[1/2]
1
1.5
12
1
9
1.0
6
0.5
Kato
3
0.0
Suzuki et al.
0
20
50
100
Electron Energy (eV)
300
20
50
100
300
Electron
Energy (eV)
BIG drop also
in fine-structure-resolved
results, especially at "intermediate" energies.
Total Cross Section for Electron Impact Excitation of Neon
60
120
3p[1/2]
50
3p'[1/2]
1
1
40
BSR-31
BSR-457
30
RMPS-235
40
Chilton et al.
20
20
10
0
0
Again, a BIG drop!
3p[5/2]
2
300
3p'[1/2]
0
Cross Section (10
-20
2
Cross Section (10
80
cm )
-20
2
cm )
Effect of Channel Coupling to Discrete and Continuum Spectrum
80
200
40
100
20
40
60
80
Electron Energy (eV)
100
0
20
40
60
80
Electron Energy (eV)
100
Total Cross Section for Electron Impact Excitation of Neon
3d[1/2]
3
0
3d[3/2]
12
2
BSR-31
2
Cross Sction (10
8
BSR-46
BSR-457
RMPS-235
1
4
0
0
20
40
60
80 100
20
40
60
80 100
The 2p53d states are really affected - factors of 5-10 — not just 60% !!!
80
30
3d[3/2]
3d[1/2]
1
1
-20
2
cm )
Cross Sction (10
-20
2
cm )
Effect of Channel Coupling to Discrete and Continuum Spectrum
60
20
40
Repeat: This result is
AGAINST the20message
in standard textbooks!
10
0
20
40
100
Electron Energy (eV)
200
0
20
40
100
Electron Energy (eV)
200
Total Cross Section for e-Ne Collisions
5
-
BSR-679 can do this as a SINGLE theory
for energies between 0.01 eV and 200 eV!
+ Ne
2
cm )
e
Total Cross Section (10
-16
4
Wagenaar & de Heer (1980)
Gulley et al. (1994)
3
Szmitkowski et al. (1996)
Baek & Grosswendt (2003)
BSR-679, total
elastic
+ excitation
2
1
0
0.01
0.1
1
10
100
1000
Electron Energy (eV)
These results (and more) are now in the LXCAT database.
http://www.lxcat.laplace.univ-tlse.fr/database.php
Differential Cross Section for Electron Impact Excitation of Neon at 30 eV
DCS (10
-19
2
cm /sr)
Experiment: Khakoo group
3.0
0.6
3s[3/2]
3s'[1/2]
0
2
0.4
2.0
0.2
1.0
0.0
0.0
0
20
40
60
80
1
10
100
120
140
10
3s[3/2]
0
20
40
60
80
100
2
120
140
3s'[1/2]
1
1
DCS (10
-19
2
cm /sr)
30 eV
Theory: Breit-Pauli BSRMPS
Khakoo et al. x 0.55
Here is the effect on angle1
differential cross sections.
10
0
10
BSR-457
BSR-31
renormalize
experimental DCS?
10
10
-1
0
20
40
60
80
100
Scattering Angle (deg)
120
140
0
0
20
40
60
80
100
Scattering Angle (deg)
120
140
0.4
0.15
2
Cross Section (ao )
Near-Threshold Excitation of Heavy Noble Gases Ne, Ar, Kr, Xe
(experiment normalized to semi-relativistic BSR)
Ar
Ne
0.3
0.10
0.2
0.05
0.1
BPRM-41
BPRM-31
BSR-31`
BSR-31
2
Cross Section (ao )
0.00
0.0
17
18
19
11.5
12.0
12.5
13.0
13.5
1.2
0.6
Kr
Xe
0.8
0.4
0.4
0.2
BPRM-31
BPRM-41
BPRM-51
BSR-31
BSR-31
0.0
9.5
0.0
10.0
10.5
11.0
11.5
12.0
Electron Energy (eV)
12.5
8.4
8.8
9.2
9.6
Electron Energy (eV)
10.0
Breit-Pauli vs. Dirac-Coulomb in Xe
(experiment normalized to full-relativistic DBSR)
1.4
e-Xe: 6s[3/2]2 + 6s[1/2]0
expt.
2
Cross Section (ao)
1.2
BSR-31
1.0
DBSR-31
DBSR-75
0.8
0.6
0.4
0.2
0.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
Electron Energy (eV)
9.6
9.8
10.0
Electron Impact Excitation of Resonance Transition in Gold
Experiment (not absolute): Teubner group (Flinders, Australia)
(5d10 6s)2 S1/2 → (5d10 6p)2 P3/2
Heavy Targets
Electron Impact Excitation of Forbidden Transition in Gold
Experiment (not absolute): Teubner group (Flinders, Australia)
complex, open-shell targets
from P.G. Burke's Allis Prize Lecture
“The Rosetta Stone Element”
Quote from Lawrence Aller, UCLA
Fe
“Iron offers us unparalleled opportunities.
I call it the Rosetta Stone Element
because its spectrum offers the
wherewithal to interpret physical
conditions in such a wide variety of
sources… Much data pertains to the low
ionization stages Fe I, Fe II, Fe III ”
from P.G. Burke's Allis Prize Lecture
Fe II Energy Level Diagram
Lowest 5 terms = 261 LS or 716 fine-structure states
from P.G. Burke's Allis Prize Lecture
Electron Fe II Collisions
fine-structure transition
262-state calculation by Ramsbottom et al (2007)
Some validation through independent (non-relativistic)
calculation; effective collision strengths agreed to within 10%
More on Fe II (BSR vs. Standard R-Matrix)
8
5
D
7
e
6
3d 4s
6
7
D - 3d
4
F
Collision Strength
6
5
4
3
2
1
0
0.00
0.05
0.10
0.15
0.20
0.25
Energy (Ry)
8
5
e
G
6
3d 4s
6
D - 3d
7 4
F
7
Collision Strength
6
5
4
3
2
1
0
0.02
0.03
0.04
0.05
Energy (Ry)
0.06
0.07
A Grand Challenge: Electron Collisions with Molybdenum
Spectrum from a Moly-Oxide Lamp
Petrov, Giuliani, Dasgupta, Bartschat and Pechacek, J. of Appl. Phys, 95 (2004) 5284
11
Mo 380
Mo 311
Mo 430
-1
6
photopic
curve
-2
7
-1
I(mW cm st nm )
8
IR detector
Mo 551
+
9
Mo 282
10
VIS detector
UV detector
5
4
Ar 750
3
2
1
0
200
300
400
500
600
λ (nm)
700
Ar 802
O 777
800
R-matrix Results for Electron Collisions with Molybdenum
K. Bartschat, A. Dasgupta, and J.L. Giuliani, J. Phys. B 35 (2002) 2899
]
Y
6
45
3
7
6
c5
3
.
,/
2
1
.
,0
]
Z
.
,
`
^b_
W
`
^a_
[
`
^X_
\
]
[
W
X
Y
Z
[
\
:
49
8
7
6
45
3
]
X
\

{
]
]
\
g
f
ed
h
g
—˜
d

|
”
’–“
y
]
”
’•“
}
”
’z“
~

}
W
X
G
F
=
Y E
D
@C
=
Z B
;
B
A
[ @
?
>
=<
;
\
]

~
Œ ‹„ ‰ˆ‡† ……„ƒ
Š
‚
Ž
]
X
]
]
]
]
]
]
\
]
X
]
Z
[
[
V USR QJ NML KKJI
PO
H
T
+ *(' & #"! %$
)


~
y

~
{
z
}
Œ ‹„ ‰ˆ‡† ……„ƒ
Š
‚
Ž
‘
k

e
€
h
g
f
ed
y
k
ej
i
h
z
g
x
f
ed
w
n
{ v
u
qt
n 
z
| s }
~
l
s
r
} q
p
o
nm
l
~

Does theory have any chance?
67-state R-matrix
(close-coupling)


y
z
x
w
n
{ v
u
qt
n
| s
l
s
r
} q
p
o
nm
l
~

y
z
x
w
n
{ v
u
qt
n
| s
l
s
r
} q
p
o
nm
l
~

Moly-Lines from a Moly-Oxide Lamp
Petrov, Giuliani, Dasgupta, Bartschat and Pechacek, J. of Appl. Phys, 95 (2004) 5284
Bartschat, Dasgupta, Petrov and Giuliani, New Journal of Physics 6 (2004) 145
experiment
6
-2
-1
P (mW cm st )
8
4
2
0
300
350
400
450
500
550
650
model
15
-2
-1
P (mW cm st )
600
10
5
YES !
0
300
350
400
450
500
λ (nm)
550
600
650
Conclusions
• 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) and their ions.
• 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-)twoelectron 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 big advantages are:
• highly accurate target description (relative to other collision models)
• reduced pseudo-resonance problems
• consistent description of the N -electron target and (N +1)-electron collision problems
• ability to give “complete” datasets for atomic structure and electron collisions
• A final word of caution: ABSOLUTE experimental data are difficult to obtain!
THANK YOU !
Conclusions
• 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) and their ions.
• 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-)twoelectron 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 big advantages are:
• highly accurate target description (relative to other collision models)
• reduced pseudo-resonance problems
• consistent description of the N -electron target and (N +1)-electron collision problems
• ability to give “complete” datasets for atomic structure and electron collisions
• A final word of caution: ABSOLUTE experimental data are difficult to obtain!
THANK YOU !
Conclusions
• 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) and their ions.
• 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-)twoelectron 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 big advantages are:
• highly accurate target description (relative to other collision models)
• reduced pseudo-resonance problems
• consistent description of the N -electron target and (N +1)-electron collision problems
• ability to give “complete” datasets for atomic structure and electron collisions
• A final word of caution: ABSOLUTE experimental data are difficult to obtain!
THANK YOU !
Conclusions
• 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) and their ions.
• 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-)twoelectron 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 big advantages are:
• highly accurate target description (relative to other collision models)
• reduced pseudo-resonance problems
• consistent description of the N -electron target and (N +1)-electron collision problems
• ability to give “complete” datasets for atomic structure and electron collisions
• A final word of caution: ABSOLUTE experimental data are difficult to obtain!
THANK YOU !