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