Progress report: Progress report: Calculations on BeH Calculations on BeH + + Åsa Larson, Stockholm Åsa Larson, Stockholm University University Johanna Roos, Stockholm Johanna Roos, Stockholm University University Ann Orel, UC Davis Ann Orel, UC Davis Mats Larsson, Stockholm Mats Larsson, Stockholm University University
Progress report: Calculations on BeH +. Åsa Larson, Stockholm University Johanna Roos, Stockholm University Ann Orel, UC Davis Mats Larsson, Stockholm University. Motivation. Beryllium used for the first wall and limiter BeH + formed in the plasma - PowerPoint PPT Presentation
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Progress report:Progress report:Calculations on BeHCalculations on BeH++
Åsa Larson, Stockholm UniversityÅsa Larson, Stockholm UniversityJohanna Roos, Stockholm Johanna Roos, Stockholm
UniversityUniversityAnn Orel, UC DavisAnn Orel, UC Davis
Mats Larsson, Stockholm Mats Larsson, Stockholm UniversityUniversity
MotivationMotivation
• Beryllium used for the first wall and Beryllium used for the first wall and limiterlimiter
• BeHBeH+ + formed in the plasmaformed in the plasma
• How fast does it recombine with How fast does it recombine with electrons?electrons?
• Problem: toxicity of Be; experiments not Problem: toxicity of Be; experiments not the preferred choicethe preferred choice
What has been doneWhat has been done
• Theoretical work on BeTheoretical work on BexxHHyy was reported by was reported by Stefan Matejcik at the CRP-meeting in June Stefan Matejcik at the CRP-meeting in June 20072007
• High resolution spectroscopy work on BeH High resolution spectroscopy work on BeH published in 2006 (Le Roy et al. published in 2006 (Le Roy et al. J.Mol.Spec.)J.Mol.Spec.)
• High resolution work on BeHHigh resolution work on BeH++ published by published by Coxon & Colin, J. Mol. Spec. 1997Coxon & Colin, J. Mol. Spec. 1997
• Theoretical calculations by several groupsTheoretical calculations by several groups
MRCI calculations on the excited states of the ion:
0 3 6 9 12-15.0
-14.7
-14.4
-14.1
-13.8
-13.5
-13.2
-12.9
-12.6
Ground and excited states of BeH+E
ne
rgy
(H)
R (au)
11+
21+
31+
13+
13+
13+
11 21 31 13 23 33
MRCI calculations on the excited states of BeH (2A1 symmetry)
0 2 4 6 8 10 12 14-15.3
-15.0
-14.7
-14.4
-14.1
-13.8
Bound and resonant states of BeH of 2A1 symmetry
En
erg
y (H
)
R (au)
MRCI calculations on the excited states of BeH (2A2 symmetry)
0 2 4 6 8 10
-14.9
-14.8
-14.7
-14.6
-14.5
-14.4
-14.3
-14.2
-14.1
-14.0
-13.9
-13.8
-13.7
Bound and resonant states of BeH of 2A2 symmetry
En
erg
y (h
)
R (au)
MRCI calculations on the excited states of BeH (2B1 symmetry)
0 1 2 3 4 5 6 7 8 9 10 11-15.2
-15.1
-15.0
-14.9
-14.8
-14.7
-14.6
-14.5
-14.4
-14.3
-14.2
-14.1
-14.0
-13.9
-13.8
-13.7Bound and resonant states of BeH of 2B
1 symmetry
En
erg
y (H
)
R (au)
Using the Using the Complex Kohn variational methodComplex Kohn variational method, the , the resonant states of BeH are calculated.resonant states of BeH are calculated.Trial wave function:Trial wave function:
Insert into a variational functional for the T-matrix Insert into a variational functional for the T-matrix ccii, d, dμμ, T, T
Eigenphase sum of the T-matrix: Eigenphase sum of the T-matrix: EEres(R), Γres(R)
Electron scattering calculationsElectron scattering calculations
)...()()...( 11110
00
NNN dFA rrrrr
Target wave function MRCI
rYrkfTrkfcF mllmmllmmlllii
i /)ˆ()]()([)()( ,0
0000
0
0rrr
Correlation and polarization
Eigenphase sum: 2A1 symmetry (2Σ+, 2∆) R = 2.5 a0
0.00 0.02 0.04 0.06 0.08 0.10 0.12
-3
-2
-1
0
1
2
3
Eig
en
ph
ase
su
m
Energy (eV)
21
)(2tan)()()( cEbEa
EEEEE
resbgres
Γ(R)REres ),(
Combine resonant potentials obtained with the electron scattering calculation with the electronically bound states obtained with structure calculation.
Quasidiabatization
2Σ+ symmetry:
0 2 4 6 8 10-15.3
-15.2
-15.1
-15.0
-14.9
-14.8
-14.7
-14.6
-14.5
-14.4
-14.3
-14.2
-14.1
-14.0 Resonant states for BeH of 2+ symmetry
En
erg
y (H
)
R (a0)
2Π symmetry
0 2 4 6 8 10
-15.0
-14.8
-14.6
-14.42 resonant states of BeH
En
erg
y (H
)
R (au)
2∆ symmetry
0 2 4 6 8 10 12 14-15.0
-14.8
-14.6
-14.4
-14.2
-14.0
Be(1D)+H
Be++H
BeH+ X1+
BeH 12
Resonant states for BeH of 2 symmetryE
ne
rgy
(H)
R (a0)
Molecular Dynamics with a Molecular Dynamics with a time-independent nonlocal time-independent nonlocal modelmodel• The driven time-The driven time-
independent SEindependent SE
• The resonant state The resonant state potentialpotential
PRA PRA 7171, 052714 (2005), 052714 (2005)
• The driving term or The driving term or ”entry amplitude””entry amplitude”
• Partial cross sectionPartial cross section
• Total cross sectionTotal cross section
iiiresR VKE )( )(
2
)()( 0 R
RR v
ii
X
2
2
2
)(lim2
)( RK
kgE i
R
ii
2
)()()(
RiRERV ii
resires
i
itot EE )()(
Cross sectionsCross sections
0.01 0.1 1 101E-21
1E-20
1E-19
1E-18
1E-17
1E-16
1E-15
1E-14
1E-13
Cro
ss s
ect
ion
(cm
2)
Interaction energy (eV)
Total
0.01 0.1 1 101E-23
1E-22
1E-21
1E-20
1E-19
1E-18
1E-17
1E-16
1E-15
1E-14
C
ross
se
ctio
n (
cm2)
Interaction energy (eV)
Delta1
0.01 0.1 1 101E-32
1E-30
1E-28
1E-26
1E-24
1E-22
1E-20
1E-18
1E-16
1E-14
Cro
ss s
ect
ion
(cm
2)
Interaction energy (eV)
Pi1 Pi2 Pi3 Pi4 Pi5
0.1 1 101E-26
1E-24
1E-22
1E-20
1E-18
1E-16
1E-14
Cro
ss s
ect
ion
(cm
2)
Interaction energy (eV)
Sigma1 Sigma2 Sigma3 Sigma4 Sigma5
Partial cross section for Δ states
Partial cross section for Σ states
Partial cross section for Π states
Total cross section
Concluding remarksConcluding remarks
• The calculations will be finalized with The calculations will be finalized with nonadiabatic couplings includednonadiabatic couplings included
• CRYRING will be used for a few CRYRING will be used for a few experiments during 2009, and then experiments during 2009, and then in 2010 moved to Darmstadt (FAIR)in 2010 moved to Darmstadt (FAIR)
• A new double electrostatic storge A new double electrostatic storge ring, Desiree, will be commissioned ring, Desiree, will be commissioned in Stockholm during 2009in Stockholm during 2009