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Benchmark calculations for electron collisions with complex atoms
Oleg Zatsarinny and Klaus BartschatDrake University, Des Moines, Iowa, USA
supported by the NSF under PHY-1520970,
PHY-1212450, Teragrid/XSEDE-090031
Benchmark calculations for electron collisions with
general B-spline R-matrix package (BSR)
OVERVIEW:
1. General features of BSR:
R−matrix method (close−coupling expansion)
B-splines as universal basis
Non-orthogonal orbitals technique
Continuum pseudo−state approach (RMPS)
2. Examples
Scattering on neutral atoms (Ar, C, N, O, F, Be, Mg)
Scattering on ions (Be-like N3+, O-like Mg4+)
4. Summary
Benchmark results:
• maximum accuracy
• possible source of uncertainties
• convergence
• uncertainty estimations
Benchmark calculations for electron collisions with
general B-spline R-matrix package (BSR)
OVERVIEW:
1. General features of BSR:
R−matrix method (close−coupling expansion)
B-splines as universal basis
Non-orthogonal orbitals technique
Continuum pseudo−state approach (RMPS)
2. Examples
Scattering on neutral atoms (Ar, C, N, O, F, Be, Mg)
Scattering on ions (Be-like N3+, O-like Mg4+)
4. Summary
The B-Spline R-Matrix (BSR) Method[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]
• The method is based on the non-perturbative close-coupling expansion.
• The close-coupling equations are solved using the R-matrix method.
• Atomic-structure calculations − frozen-core approximation
Distinctive feature:
Allows for non-orthogonal orbital sets to represent both bound andcontinuum radial functions
• independent generation of target states – much more accurate target
representation (term-dependence, relaxation effects, correlation)
• no artificial orthogonality constraints for continuum orbitals –
more consistent treatment of N-electron target and (N+1)-electron
collision system −> no pseudo−resonances
• Standard method of treating low-energy scattering
• Based upon an “exact” expansion of the total scattering wavefunction over target states
• Simultaneous results for transitions between all states in the expansion
• Problems:
• close−coupling expansion must be cut off• accuracy (expansions) of target states are limited
),...,()(1
)ˆ,,...,(),...,( 11,111
Nj
LS
jiENi
LS
iN
LS rrrFr
rrrArrE
Main source of uncertainties
The B-Spline R-Matrix (BSR) Method[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]
• The method is based on the non-perturbative close-coupling expansion.
• The close-coupling equations are solved using the R-matrix method.
• Atomic-structure calculations − frozen-core approximation
Distinctive feature:
Allows for non-orthogonal orbital sets to represent both bound andcontinuum radial functions
• Basic Idea: indirect calculations – inner ( r < a) and outer regions ( r > a).
• Complete set of inner-region solutions is found from diagonalization of total
Hamiltonian modified with Bloch operator
• Scattering parameters can then obtained from matching with solutions in external
region − allows us obtain cross sections at many energy points rather cheaply
The B-Spline R-Matrix (BSR) Method[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]
• The method is based on the non-perturbative close-coupling expansion.
• The close-coupling equations are solved using the R-matrix method.
• Atomic-structure calculations − frozen-core approximation
Distinctive feature:
Allows for non-orthogonal orbital sets to represent both bound andcontinuum radial functions
• independent generation of target states – much more accurate target
representation (term-dependence, relaxation effects, correlation)
• no artificial orthogonality constraints for continuum orbitals –
more consistent treatment of N-electron target and (N+1)-electron
collision system −> no pseudo−resonances
• Computer Codes:
• RMATRX–I : Berrington et al (1995)
• PRMAT - parallelized version of RMARX-I
• Badnell's Rmax complex - http: //amdpp.phys.strath.ac.uk/,
with possibility for radiative damping
• DARC – relativistic version, http://web.am.qub.ac.uk/DARC/
• Enormous number of calculations
Principal ingredient: a single set of orthogonal one-electron orbitals
• < Pnℓ | Pn'ℓ > = 0 → difficulties to achieve accurate target representation
for different states
• < Pnℓ | Fkℓ > = 0 → large (N+1)-electron expansions needed for completeness
(may lead to appearance of pseudo-resonances)
),...,()(1
)ˆ,,...,(),...,( 11,111
Nj
LS
jiENi
LS
iN
LS rrrFr
rrrArrE
The B-Spline R-Matrix (BSR) Method[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]
• The method is based on the non-perturbative close-coupling expansion.
• The close-coupling equations are solved using the R-matrix method.
• Atomic-structure calculations − frozen-core approximation
Distinctive feature:
Allows for non-orthogonal orbital sets to represent both bound andcontinuum radial functions
• independent generation of target states – much more accurate target
representation (term-dependence, relaxation effects, correlation)
• no artificial orthogonality constraints for continuum orbitals –
more consistent treatment of N-electron target and (N+1)-electron
collision system −> no pseudo−resonances
It allows us to considerably (almost completely) reduce the uncertainties
due to the accuracy of the target states
The B-Spline R-Matrix (BSR) Method[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]
• The method is based on the non-perturbative close-coupling expansion.
• The close-coupling equations are solved using the R-matrix method.
• Atomic-structure calculations − frozen-core approximation
Distinctive feature:
Allows for non-orthogonal orbital sets to represent both bound andcontinuum radial functions
• independent generation of target states – much more accurate target
representation (term-dependence, relaxation effects, correlation)
• no artificial orthogonality constraints for continuum orbitals – more
consistent treatment of N-electron target and (N+1)-electron collision
system −> (no pseudo−resonances, improved convergence)
Additional source of uncertainties
),...,()(1
)ˆ,,...,(),...,( 11,111
Nj
LS
jiENi
LS
iN
LS rrrFr
rrrArrE
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
n+k
n+1nk+1k
1
Bi(r): k = 8, n = 17, h = 0.5
• excellent numerical properties − machine accuracy with Gaussian quadratures.
• flexibility in the choice of radial grid.
• effective completeness of B-spline basis − no Buttle correction required;
finite representation of whole Rydberg series or continuum spectra.
• avoid finite-difference algorithms − established Linear Algebra packages can be used.
i
ii rBcr )()( ScHc EEH
Why B−splines ?
• first R-matrix calculation with B-splines: e-H scattering (van der Hart 1997)
However − scattering calculations require relatively big basis: n ~ 50−100
BSR – general B-spline R-matrix package
1. First implementation: Li photoionization (2000)
2. First presentation: ICPEAC XXX, Rosario, Argentina (2005)
3. First version published: Comp.Phys.Comm. (2006)
4. Fully−relativistic version: e−Cs scattering (2008)
5. RMPS extension and e−He,Ne scattering (2011−2012)
ionization:
6. Topical review: J.Phys.B 46, 112001 (2013)
Calculations:
1. Electron scattering from neutrals (including inner−core excitations)
He, Be,C, N, O, F, S, Cl, Ne, Na, Mg, Al, Si, Ar, K, Ca, Zn,
Cu, I, Kr, Rb, Xe, Cs, Kr, Xe, Cs, Au, Hg, Pb
2. Electron−ion collisions (rate coefficients)
S II, K II, Fe II, Fe VII, Fe VIII, Fe IX
3. Photodetachment and photoionization
He−, Li−, B−, O−, Ca−, Li, K, Zn
4. Atomic structure: energies, oscillator strengths, polarizabilities
C, Ne, S, SII, F, CL, Ar, Kr, Xe
8.4 8.8 9.2 9.6 10.00.0
0.4
0.8
1.2
17 18 190.00
0.05
0.10
0.15
11.5 12.0 12.5 13.0 13.50.0
0.1
0.2
0.3
0.4
9.5 10.0 10.5 11.0 11.5 12.0 12.50.0
0.2
0.4
0.6
BPRM-41
BSR-31
Xe
Electron Energy (eV)
BPRM-31
BSR-31
Ne
C
ross S
ection
(a
2 o )
BPRM-41
BSR-31`
Ar
BPRM-31
BPRM-51
BSR-31
Kr
Cro
ss S
ection
(a
2 o )
Electron Energy (eV)
Metastable production in Electron Collisions with noble gasesBSR calculations
BSR with pseudo−states
V(r)
r
continuum spectrum discrete spectrum
V(r)
rr = a
We use the box−based approach:
Both physical and pseudo−states are found by direct solving the close−coupling
(frozen−cores) equations for N−electron atomic wavefunctions with zero boundary
conditions.
?
),...,()(1
)ˆ,,...,(),...,( 111,
1
1111
Nj
LS
jNiE
N
NNi
LS
iN
LS rrrFr
rrrArrE
How many pseudo−states do we need in this approach to simulate
the target continuum?
Electron-impact excitation of neon at intermediate energies(PHYSICAL REVIEW A 86, 022717, 2012)
J
ji
LSij
ij
J
ji
LSij
ij
LSslrBpsaA
LSslrBpsaAJnlps
},|)()S;22({
},|)()P;22({),22(
26
,
252
,
52
Target states:
Total number of states − 457
Bound states − 87
Continuum pseudostates − 370
(l = 0 − 3)
Continuum energy coverage− 40eV
Number of channels − 2260
R−matrix radius − 30ao
Number of B−splines − 70
Hamiltonian matrix − 150000
Number of processors used − up to 1000
Resources used − 200000 PU (1 hour x 1 processor)
(for 50 partial waves)
Do we really need such big computational efforts?
Effect of Channel Coupling to Discrete and Continuum spectrum in Ar
10 1000
4
8
12
10 1000
10
20
30
10 20 30 40 500
2
4
6
8
10
10 20 30 40 500.0
0.4
0.8
1.2
1.6
2.0
BSR-31
BSR-500
Electron Energy (eV)
50205020 300
4s[3/2]1
Cro
ss S
ection
(10-1
8 c
m-2
)
Kato et al (2011)
Khakoo et al (2004)
Filipovic et al (2000)
Chutjian & Cartwright (1981)
4s'[1/2]1
Electron Energy (eV)
Cro
ss S
ectio
n (
10
-18 c
m-2
)
4s[3/2]2
300
4s'[1/2]0
How to estimate uncertainties here?
10 1000
4
8
12
10 1000
10
20
30
10 20 30 40 500
2
4
6
8
10
10 20 30 40 500.0
0.4
0.8
1.2
1.6
2.0
Electron Energy (eV)
50205020 300
4s[3/2]1
Cro
ss S
ectio
n (
10
-18
cm
-2)
4s'[1/2]1
Electron Energy (eV)
BSR-5
BSR-31
BSR-78
BSR-160
BSR-500
BSR-600
Cro
ss S
ectio
n (
10
-18 c
m-2
)
4s[3/2]2
300
4s'[1/2]0
Total Cross Section for Electron Impact Excitation of ArgonConvergence study
Final uncertainty within 5−10 percent, just based on the convergence study.
• Ne(2p6) , Ar(3p6) - extremely big influence of target continuum.
• What about other atoms with open p-shells:
B(2p), C(2p2), N(2p3), O(2p4), F(2p5) - ?
20 40 60 80 1000
1
2
3
4
5
BSR-690 - Gedeon et al. (2014)
BSR-39 - the same target states
RM-11 - Boliyan & Bhatia (1994)
Cro
ss S
ectio
n (
10
-16 c
m2) F (2p5 2Po - 3s' 2D)
Electron Energy (eV)
20 40 60 80 1000
2
4
6
8
Vaughan & Doering (1987)
Kanik et al. (2001)
BSR-26 - Tayal & Zatsarinny (2002)
RMPS-52 - Tayal (2005)
BSR-1116 - Tayal & Zatsarinny (2016)
O (2p4 3P - 2p33s' 3Do)
Electron Energy (eV)
Cro
ss S
ectio
n
(10
-18cm
2)
20 40 60 80 1000.0
0.2
0.4
0.6
0.8
expt. - Doering & Goembel (1992)
BSR-12 - Tayal & Zatsarinny (2005)
BSR-39 - polarized pseudostates
BSR-690 - Wang et al. (20015)
BSR-61 - the same target states
Electron Energy (eV)
Cro
ss S
ectio
n (
10
-16 c
m2)
N (2p3 4So - 2p23s 4P)
15 30 45 600
1
2C
ross S
ectio
n (
10
-16 c
m2)
RM-28 Dunseath et al. (1997)
BSR-28 Zatsarinny et al. (2005)
BSR-696 Wang et al. (2013)
BSR-25 (the same target states)
C (2p2 3P - 2p3s 3Po)
Electron Energy (eV)
• Inclusion of the target continuum – mandatory condition for the neutral atoms, at least.
• But first check target − then CC convergence !
• Uncertainties – the upper limit – may be estimated as difference between CC models with the
same target w.f.
Motivation:
1. Big interest in plasma applications (JET project, ITER).
2. No experimental data.
3. What accuracy can be achieved for this ‘simple’ system?
4. Complete set of scattering data (first 21 levels).
5. Joint work of CCC and BSR teams.
0 20 40 60 80 1000
4
8
12
RMPS-280
CCC-409
BSR-660
Cro
ss S
ection
(1016 c
m2)
(2s2)1S - (2s2p)1Po
0 20 40 60 80 1000
2
4
6
Cro
ss S
ection
(1016 c
m2)
Electron Energy (eV) Electron Energy (eV)
(2s2p)3Po - (2p2)3P
0.0 0.5 1.0 1.5 2.0 2.50
100
200
300
400 BSR-01
BSR-02
BSR-03
BSR-29
BSR-660
CCC-409
model potential
Ela
stic C
ross S
ection
(1
0-1
6 c
m2)
Electron Energy (eV)
0 20 40 60 80 1000
1
2
3
CCC
BSR
RMPS (Ballance et al. 2003)
TDCC (Colgan et al. 2003)
Be+(2p)Io
niz
atio
n C
ross S
ectio
n (
10
-16 c
m2)
Electron Energy (eV)
e - Be(2s2)
• A complete and consistent set of scattering data for Be, with a high level of
confidence in a small uncertainty (5-10 %).
• A good example of team work (CCC + BSR) to get accurate results.
• New similar calculations for e-Mg are now in progress
Electron-impact excitation of N3+ (2s2)
(2snl, 2pnl, n ≤ 8)
RM-238 (ICFT - Intermediate Coupling Frame Transformation)
Fernandez-Menchero et al. 2014, Astron. Astroph. 566 A104)
DARC-238 (Dirac Atomic R-matrix Code)
Aggarwal et al. 2016 Mon. Not. R. Astr. Soc. 461 3997)
BSR-238 with improved structure description
(submitted to J.Phys.B)
Electron-impact excitation of Mg4+ (2p4)
Big difference between existing datasets:
• RM-37 (Hudson et al., 2009, A \& A 494, 729)
• BSR-86 (Tayal & Sossah, 2015, A&A, 574, 87) { 2s22p4, 2s2p5, 2s22p33l }
• DARC-86 (Aggarwal & Keenan, 2016, Can. J. Phys., online)
statement: DARC calculations are much more accurate;
BSR results are completely wrong (possibly because
BSR code is not able to avoid pseudo resonances)
Electron-impact excitation of Mg4+ (2p4)
Big difference between existing datasets:
• RM-37 (Hudson et al., 2009, A \& A 494, 729)
• BSR-86(TS) (Tayal & Sossah, 2015, A&A, 574, 87) { 2s22p4, 2s2p5, 2s22p33l }
• DARC-86 (Aggarwal & Keenan, 2016, Can. J. Phys., online)
statement: DARC calculations are much more accurate;
BSR results are completely wrong (possibly because
BSR code is not able to avoid pseudo resonances )
Really ???
New calculations:
• BSR-86 with improved structure description
• BSR-316 with additional 2s22p34l and 2s2p53l states
10-5 10-4 10-3 10-2 10-1 10010-5
10-4
10-3
10-2
10-1
100
GRASP (DARC)
BSR
OT
HE
RS
MCHF
f-values
0 10 20 30 40 50 60 70 80 900.0
0.5
1.0
1.5
2.0
GRASP
BSR
Ra
tio
to
MC
HF
Level Index
lifetimes
f-values and lifetimes of Mg4+ (2p4)
MCHF - Tachiev & Froese Fischer (2004)
GRASP - Aggarwal & Keenan (2016), DARC-86
Effective collision strengths of Mg4+ (2p4)
BSR-86 vs. BSR-86(TS), DARC-86, RM-37
BSR(TS)
DARC
RM
BSR
Electron-impact excitation of Mg4+ (2p4)
7.2 7.4 7.6 7.8 8.00
1x10-4
2x10-4
3x10-4
4x10-4
7.2 7.4 7.6 7.8 8.00
1x10-4
2x10-4
3x10-4
4x10-4
Colli
sio
n S
trength
(10 - 30) (2p6)1S0 - (2s22p33p)3D3
BSR-86
BSR-86 (TS)
Colli
sio
n S
trength
Electron Energy (Ry)
DARC
Effective collision strengths of Mg4+ (2p4)
CC – convergence: BSR-86 vs. BSR-316
The 2s22p4 → 2s22p33l are mainly converged.
Difference mainly for weak two-electron transitions 2s2p5, 2p6 → 2s22p33l
or for transitions between close-lying levels
Electron-impact excitation of Mg4+ (2p4)
Big difference between existing datasets:
• RM-37 (Hudson et al., 2009, A \& A 494, 729)
• BSR-86 (Tayal & Sossah, 2015, A&A, 574, 87) { 2s22p4, 2s2p5, 2s22p33l }
• DARC-86 (Aggarwal & Keenan, 2016, Can. J. Phys., 11, 111)
statement: DARC calculations are much more accurate and the best;
BSR results are completely wrong
BSR code is not able to avoid pseudo resonances
New calculations
• BSR-86 with improved structure description
• BSR-316 with additional 2s22p34l and 2s2p53l states
Our conclusions:
• Good agreement our oscillator strengths with the extensive MCHF calculations indicate
that our target description is more accurate than used before.
• We essentially confirm the previous BSR calculations by Tayal & Sossah (2015)
(except #10 and #86 levels – computational bugs)
• Big disagreement with DARC calculations is mainly due to the target description
(and possible pseudo resonances).
• RM-37 calculations of Hudson et al. (2009) for some transitions are clearly wrong
due to evident appearance of pseudo resonances.
• Comparison of BSR-86 and BSR-316 indicate convergence for the lower levels.
For complex targets, the BSR method with non-orthogonal orbitals has advantages:
• highly accurate target description
• more consistent description of (N+1)-electron scattering system
• considerable improvement for low-energy region and near-threshold resonance phenomena
• improvement for intermediate energies with RMPS approach (MPI version)
• BSR code is able to provide benchmark results for uncertainty estimation
► considerable reduction (elimination) of target description uncertainty
► absence of pseudo resonances
► systematic check of convergence (including target continuum)
Summary
requires large-scale computations using supercomputers (i.e., extensive and expensive)
For complex targets, the BSR method with non-orthogonal orbitals has advantages:
• highly accurate target description
• more consistent description of (N+1)-electron scattering system
• considerable improvement for low-energy region and near-threshold resonance phenomena
• improvement for intermediate energies with RMPS approach (MPI version)
• BSR code is able to provide benchmark results for uncertainty estimation
► considerable reduction (elimination) of target description uncertainty
► absence of pseudo resonances
► systematic check of convergence (including target continuum)
Summary
requires large-scale computations using supercomputers (i.e., extensive and expensive)
My main point: The importance of accurate target descriptions is
highly underestimated in most scattering calculations.
This leads to lower accuracy and larger uncertainties.
10-5 10-4 10-3 10-2 10-1 100 101 10210-5
10-4
10-3
10-2
10-1
100
101
102
DW (Bhatia et al. 2006)
RM-37 (Hudson et al. 2009)
BSR-316
(
OT
HE
RS
)
(BSR-86)
E = 20 Ry
Electron-impact excitation of Mg4+ (2p4)
Background collision strengths: BSR-86 vs. DW, RM, BSR-316
0 1 2 3 4 5 6 7 80
1
2
3
4
5
Colli
sio
n s
trength
Electron Energy (Ry)
(1 - 2) (2s22p4)3P2 - (2s22p4)3P1
4 5 6 7 8
2
3
4
5
Colli
sio
n S
treng
th (
)
Electron Energy (Ry)
(4 - 9) (2s22p4)1D2 - (2s2p5)1P1
Electron-impact excitation of Mg4+ (2p4)
• We used 71000 energy points to resolve resonance structure
Description of target states
(GRASP_2K – DBSR_CI, DBSR_HF)
target1.c, target1.bsw
target2.c, target2.bsw
……………………….
knot.dat dbsr_par target_jj
DBSR_PREP
DBSR_CONF
DBSR_BREIT
DBSR_MAT
DBSR_HD
DBSR_MULT
DBSR_DMAT
h.nnn, bound.nnn
jnt_bnk.nnn
cfg.001
cfg.002
…….
cfg.nnn
target_jj..bsw
dbsr_mat.nnn
H.DAT
FARM,STGF, etc. d.nnn BSR_PHOT zf_res
rsol.nnn
mult_bnk.nnn
Energies
Oscillator strengths Cross sections
MPI
DBSR
Description of target states
(HF, MCHF, CI_BNK. BSR_HF)
target1.c, target1.bsw
target2.c, target2.bsw
……………………….
knot.dat bsr_par target
BSR_PREP
BSR_CONF
BSR_BREIT
BSR_MAT
BSR_HD
BSR_MULT
BSR_DMAT
h.nnn, bound.nnn
jnt_bnk.nnn
cfg.001
cfg.002
…….
cfg.nnn
target.bsw
dbsr_mat.nnn
H.DAT
FARM, STGF, etc. d.nnn BSR_PHOT zf_res
rsol.nnn
mult_bnk.nnn
Energies
Oscillator strengths Electron-impact
cross sections
MPI
Photoionization
BSR
[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]
Many existing databases for neutrals should be re−evaluated
Comparison of different codes and models is crucial.
• Repeating calculations are encouraged.
• Non−critical using the existing codes − expert proof is still important.
Each atom − unique!
(the automatic calculations for whole iso-electronic or iso−nuclear series can be deceptive)
Comparison of published results or different databases is very time consuming:
(It is desirable to encourage development of new software for extracting and
comparison of data in different databases and sharing the results)
For more confident results - comprehensive comparison with included ALL transitions,
not just the selected ones.
Uncertainty’s questions
My main point: The importance of accurate target descriptions is
very much underestimated in most scattering calculations. This
leads to lower accuracy and larger uncertainties.
Electron-impact excitation of Mg (3s2)
(in progress)
• Numerous measurements and calculations but for selected transitions or energies
(DCS)
• Modeling of non-equilibrium plasma requires complete set of data
(Mauas et al. 1988 - collection from different sources with unclear uncertainties)
• BSR-37 (Zatsarinny et al. 2009) - most complete set of data for all transitions
between first 37 levels (n ≤ 8) except triplet-triplet transitions
• Merle et al. (2015) - rate coefficients based on BSR-37
• Osorio et al. (2015) – new RMPS calculations for transitions between first 10 levels
(noticeable differences with existing results)
• 2016, new project – parallel CCC and BSR-712 (RMPS) calculations to get
complete set with uncertainty estimations
0 20 40 60 80 1000
4
8
12
16
20
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
0 20 40 60 80 1000.0
0.5
1.0
1.5
2.0
0 20 40 60 80 1000.0
0.5
1.0
1.5
2.0
BSR-712
BSR-37 - Zatsarinny et al. (2009)
CCC - Bray (2016)
RMPS - Osorio et al. (2015)
3s2 1S - 3s3p 1P 3s2 1S - 3s4s 1S
Electron Energy (eV)
3s2 1S - 3s4p 1P
Cro
ss S
ectio
n (
10
16cm
2)
Electron Energy (eV)
3s2 1S - 3s3d 1D
Electron-impact excitation of Mg (3s2)
0 20 40 60 80 1000
1
2
3
4
5
6
7
Boivin & Strivastava (1998)
Freund et al. (1990)
BSR
CCC (Bray et al. 2015)
RMPS (Ludlow et al. 2009)
TDCC (Ludlow et al. 2009)
Cro
ss S
ectio
n (
10
-16 c
m2)
Electron Energy (eV)
e + Mg - Mg+ + 2e
Electron-impact ionization of Mg (3s2)
Electron-impact excitation of Mg (3s2)
• The agreement between the CCC and BSR712 calculations differ by on average
only 6%, with a scatter of 27% for ALL transitions between first 25 levels.
• Another example of team work to get accurate results from independent
calculations
T = 5000 K
For complex targets, the BSR method with non-orthogonal orbitals has advantages:
• highly accurate target description
• more consistent description of (N+1)-electron scattering system
• considerable improvement for low-energy region and near-threshold resonance phenomena
• improvement for intermediate energies with RMPS approach (MPI version)
• BSR code is able to provide benchmark results for uncertainty estimation
► considerable reduction (elimination) of target description uncertainty
► absence of pseudo resonances
► systematic check of convergence (including target continuum)
Summary
Goal: can we finally get accurate cross sections for complex atoms?
my main point: the important of accurate target description is very
underestimated in the most scattering calculations and leads to
lower accuracy and big uncertainties
Electron-impact excitation of N3+ (2s2)
Big difference between existing datasets:
• Fernandez-Menchero et al. 2014, Astron. Astroph. 566 A104
RM-238 (ICFT - Intermediate Coupling Frame Transformation)
• Aggarwal et al. 2016 Mon. Not. R. Astr. Soc. 461 3997)
DARC -238 (Dirac Atomic R-matrix Code)
statement: DARC calculations are much more accurate and
the ICFT results might even be wrong
• BSR-238 with improved structure description (2snl, 2pnl, n ≤ 8)
Electron-impact excitation of N3+ (2s2)
Big difference between existing datasets:
• Fernandez-Menchero et al. 2014, Astron. Astroph. 566 A104
RM-87 (ICFT - Intermediate Coupling Frame Transformation)
• Aggarwal et al. 2016 Mon. Not. R. Astr. Soc. 461 3997)
DARC -87 (Dirac Atomic R-matrix Code)
statement: DARC calculations are much more accurate and
the ICFT results might even be wrong
Our conclusions:• The differences in the final results for the collision strengths are mainly due to
differences in the structure description, specifically the inclusion of correlation
effects, rather than the treatment of relativistic effects.
• Hence there is no indication that one approach is superior to another,
until the convergence of both the target configuration and the close-coupling
expansions have been fully established.
• Due to the superior target structure generated, we believe the BSR results are the
currently best for electron collisions with N+3 .
• The differences between the BSR and the DARC / ICFT results may in fact serve as an
uncertainty estimate for the available excitation rates.
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