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
RRee (Å) (Å) e e (cm(cm-1-1)) DDe e (eV)(eV)
19841984 1.34281.3428 2063.182063.18 2.1622.162
20082008 1.3451.345 2055.522055.52 2.1332.133
Exp. Exp. 20062006
1.342391.3423944
2061.232061.2355
2.1812.181
JCP 2008
Dissociative recombinationDissociative recombination
BeH+ + e Be + H
Results for diatomic Results for diatomic hydrideshydrides
HH22++ HeHHeH
++
LiHLiH++ BeHBeH++ BHBH++ CHCH++ NHNH++ OHOH++ FHFH++
The.The. yesyes yesyes yesyes nono nono yesyes nono yesyes yesyes
Exp.Exp. yesyes yesyes yesyes nono nono yesyes yesyes yesyes yesyes
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
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