Progress report Calculations on BeH+

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 • How fast does it recombine with electrons? • Problem: toxicity of Be; experiments not the preferred choice What has been done • Theoretical work on BexHy was reported by Stefan Matejcik at the CRP-meeting in June 2007 • High resolution spectroscopy work on BeH published in 2006 (Le Roy et al. J.Mol.Spec.) • High resolution work on BeH+ published by Coxon & Colin, J. Mol. Spec. 1997 • Theoretical calculations by several groups Re (Å) 1984 2008 e (cm-1) De (eV) 1.3428 1.345 2063.18 2055.52 2.162 2.133 Exp. 2006 1.342394 2061.235 2.181 JCP 2008 Dissociative recombination BeH+ + e Be + H Results for diatomic hydrides H2+ HeH+ LiH+ BeH+ BH+ CH+ NH+ OH+ FH+ The. yes yes yes no no yes no yes yes Exp. yes yes yes no no yes yes yes yes MRCI calculations on the excited states of the ion: + Ground and excited states of BeH -12.6 -12.9 -13.2 -13.5 -13.8 -14.1 -14.4 -14.7 -15.0 0 3 6 1 1 + 2 1 + 3 3 + 1 3 + 1 3 + 1 1 1 1 2 1 3 3 1 3 2 3 3 1 + Energy (H) 9 12 R (au) MRCI calculations on the excited states of BeH (2A1 symmetry) Bound and resonant states of BeH of A1 symmetry -13.8 2 -14.1 Energy (H) -14.4 -14.7 -15.0 -15.3 0 2 4 6 8 10 12 14 R (au) MRCI calculations on the excited states of BeH (2A2 symmetry) Bound and resonant states of BeH of A2 symmetry -13.7 -13.8 -13.9 -14.0 -14.1 2 Energy (h) -14.2 -14.3 -14.4 -14.5 -14.6 -14.7 -14.8 -14.9 0 2 4 6 8 10 R (au) MRCI calculations on the excited states of BeH (2B1 symmetry) Bound and resonant states of BeH of B1 symmetry 2 -13.7 -13.8 -13.9 -14.0 -14.1 -14.2 -14.3 -14.4 -14.5 -14.6 -14.7 -14.8 -14.9 -15.0 -15.1 -15.2 0 Energy (H) 1 2 3 4 5 6 7 8 9 10 11 R (au) Electron scattering calculations Using the Complex Kohn variational method, the resonant states of BeH are calculated. Trial wave function:  0   A   (r1...rN ) F0 (rN 1 )   d 0   (r1...rN 1 )     Target wave function MRCI Correlation and polarization ˆ F0 (r)   ci0 i (r)  [ f l  (k r ) ll0  mm0  Tll0 0 f l  (k r )]Yl ,m (r) / r 0 mm i Insert into a variational functional for the T-matrix Eigenphase sum of the T-matrix: Eres(R), Γres(R) ci, dμ, T Eigenphase sum: 2A1 symmetry (2Σ+, 2∆) R = 2.5 a0      a  bE  cE 2  ( E )   res ( E )   bg ( E )  tan    2( E  Eres )  1  Eres ( R ), Γ(R) 3 2 Eigenphase sum 1 0 -1 -2 -3 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Energy (eV) Combine resonant potentials obtained with the electron scattering calculation with the electronically bound states obtained with structure calculation. Quasidiabatization 2 Σ+ symmetry: -14.0 -14.1 -14.2 -14.3 -14.4 Resonant states for BeH of  symmetry 2 + Energy (H) -14.5 -14.6 -14.7 -14.8 -14.9 -15.0 -15.1 -15.2 -15.3 0 2 4 6 8 10 R (a0) 2Π symmetry 2 -14.4  resonant states of BeH -14.6 Energy (H) -14.8 -15.0 0 2 4 6 8 10 R (au) 2∆ symmetry Resonant states for BeH of  symmetry -14.0 2 -14.2 BeH X  2 BeH 1  + 1 + Energy (H) -14.4 -14.6 -14.8 Be +H Be( D)+H 1 + -15.0 0 2 4 6 8 10 12 14 R (a0) Molecular Dynamics with a timeindependent nonlocal model • The driven timeindependent SE i ( E  K R  Vres ) i  i • The driving term or ”entry amplitude” i ( R )  i ( R ) X v 0 ( R) 2 • The resonant state potential i i Vres ( R)  Eres ( R)  i • Partial cross section 2 2 K i 2  i (E)  g 2 lim  i ( R ) k  R  i ( R) 2 • Total cross section  tot ( E )    i ( E ) i  PRA 71, 052714 (2005) Partial cross section for Δ states 1E-14 Cross sections Partial cross section for Π states 1E-14 1E-16 1E-18 Delta1 1E-15 1E-16 Cross section (cm ) 1E-17 1E-18 Cross section (cm ) Pi1 Pi2 Pi3 Pi4 Pi5 2 1E-19 1E-20 1E-21 1E-22 1E-23 0.01 1E-20 1E-22 1E-24 1E-26 1E-28 0.1 1 10 2 Interaction energy (eV) 1E-30 1E-32 0.01 0.1 1 10 Interaction energy (eV) Partial cross section for Σ states 1E-14 Total cross section 1E-13 1E-16 Cross section (cm ) 1E-18 Cross section (cm ) Sigma1 Sigma2 Sigma3 Sigma4 Sigma5 Total 1E-14 1E-15 2 2 1E-16 1E-17 1E-18 1E-19 1E-20 1E-22 1E-24 1E-20 1E-26 0.1 1E-21 1 10 0.01 0.1 1 10 Interaction energy (eV) Interaction energy (eV) Concluding remarks • The calculations will be finalized with nonadiabatic couplings included • CRYRING will be used for a few experiments during 2009, and then in 2010 moved to Darmstadt (FAIR) • A new double electrostatic storge ring, Desiree, will be commissioned in Stockholm during 2009