Cold and ultracold collisions involving open-shell diatomic molecules
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1 Lunteren 2005 p. 1/31 Cold and ultracold collisions involving open-shell diatomic molecules Gerrit C. Groenenboom Institute of Theoretical Chemistry University of Nijmegen The Netherlands
2 Lunteren 2005 p. 2/31 Cold and ultracold Cold atoms and molecules 1K can be trapped Ultracold regime µk - nk by evaporative cooling Cold molecules Buffer-gas cooling CaH( 2 Σ + ) John Doyle et al., Harvard, 1998 Stark deceleration CO(a 3 Π) Gerard Meijer et al., Nijmegen, 1999 Trapped molecules ultra high resolution spectroscopy High resolution scattering Manipulation with electric and magnetic fields
3 Lunteren 2005 p. 3/31 Buffer gas cooling and magnetic trapping Systems 3 He + CaH( 2 Σ + ) 3 He + NH( 3 Σ ) 3 He + OH( 2 Π 3/2 ) Collaborators (ITAMP, Harvard-Smithsonian center for Astrophysics) Alex Dalgarno Roman Krems Naduvalath Balakrishnan
4 Lunteren 2005 p. 4/31 Zeeman interaction Ĥ Zeeman = µ B µ = 1µ B B = 1 T } E 0.5 cm K ground state magnetic moment CaH 2 Σ + 1µ B NH 3 Σ 2µ B OH 2 Π 3/2 1.4µ B
5 Lunteren 2005 p. 5/31 Low field seekers ( 2 Σ) 2 S,M S > = 1/2, 1/2> Energy/cm σ inelastic (Spin flipping) Ĥ Zeeman = µ B µ = 2m e es) E(S, M S ) = 2m e g ebm S S,M S > = 1/2, 1/2> B/tesla Elastic momentum transfer cross section: σ tr (E) = 2π π 0 dσ(e) (1 cos χ)d cos χ dχ
6 Lunteren 2005 p. 6/31 Ab initio calculations Supermolecular approach: E AB = E AB E A E B Energies with RCCSD(T) method (MOLPRO) Complex and fragments in the same one electron basis: CaH( 2 Σ + ) He NH( 3 Σ ) He OH( 2 Π) He d-aug-cc-pvtz; Ca: 6-311G++(3df) aug-cc-pvqz aug-cc-pvtz (A and A PES) + bond orbitals CaH/NH He (3s3p2d1f 1g) OH( 2 Π) He (3s3p2d2f1g) He-OH: H.-S. Lee et al., J. Chem. Phys. 113, 5736 (2000)
7 Lunteren 2005 p. 7/31 Grid He R Ca Θ r R (a 0 ) r (a 0 ) # points He-CaH (3D) He-NH (2D) He-OH (2D) H
8 Lunteren 2005 p. 8/31 Coordinates used in the fit He X R b R R a Θ b Θ Ca H r V (R, θ, r) = V lr (R, θ, r) + V sr (R a, θ a, r) + V sr (R b, θ b, r) Θ a
9 Lunteren 2005 p. 9/31 Expansion of the potential Long range (n + l is even): V lr = 13 n=6 n 4 l=0 f n (βr) R n P l (cos θ)c nl (r) Short range (x = a, b): V sr (R x, θ x, r) = 2 l=0 + e βr x P l (cos θ x )s (x) l 3 n=0 3 l=0 R n xe βr x P l (cos θ x )s (x) nl (r)
10 He-CaH ( 2 Σ + ) potential (µeh) (a) r=3 a y He (a 0 ) (b) r=r e = a y He (a 0 ) (c) r=5 a y He (a 0 ) x He (a 0 ) Groenenboom and Balakrishnan J. Chem. Phys. 188, 7380 (2003) Lunteren 2005 p. 10/31
11 Lunteren 2005 p. 11/31 He CaH: coupled channel calculation Hamiltonian: Ĥ = 2 2µR Spin-rotation term: d 2 dr 2 R + ˆl 2 2µR 2 + ˆN 2 2µ CaH r 2 + V (R, r e, θ) + ˆV SR ˆV SR = γ ˆN Ŝ (γ = cm 1 ) Channel basis: (NS)jl; JM = M N,M S,m j,m l NM N SM S lm l NM N SM S jm j jm j lm l JM
12 Lunteren 2005 p. 12/31 3 He+CaH(N = 0): spin flip mechanism N = 1 j = 3/2 j = 1/2 N = 0 j = 1/2
13 Lunteren 2005 p. 13/31 He CaH(N=0): elastic cross sections 10 5 Cross section (10 16 cm 2 ) l=2 l= Kinetic energy (cm 1 ) Open circles: Solid curve: Dotted curve: 3 He-CaH with spin-rotation 3 He-CaH 1 Σ-calculation 4 He-CaH 1 Σ-calculation
14 Lunteren 2005 p. 14/31 He CaH: modified potential Spherically averaged potential 5 Original potential Modified potential (f=0.15) Energy (cm 1 ) R (a 0 ) Ṽ = V CCSD(T) + f (V CCSD(T) V CCSD ) f = 0.15: van der Waals minimum 3% more attractive
15 Lunteren 2005 p. 15/31 3 He CaH(N=0): elastic cross sections 10 5 Cross section (10 16 cm 2 ) original modified (f=0.1) modified (f=0.15) Kinetic energy (cm 1 ) Ṽ = V CCSD(T) + f (V CCSD(T) V CCSD )
16 Lunteren 2005 p. 16/31 3 He CaH: comparison with experiment Thermal averaged elastic momentum transfer cross section Theory (modified potential) Theory Experiment Cross section (cm 2 ) Temperature (K) Experiment: J. D. Weinstein et al., Nature 395, 148 (1998) Theory: Balakrishnan, Groenenboom, Krems, Dalgarno, J. Chem. Phys. 118, 7386 (2003)
17 Lunteren 2005 p. 17/31 He+CaH: Spin-flipping σ jm j m = π k 2 j J 1 J 2 lm l M 1 M 2 ( ( l m l T J 1 jl j l T J 2 jl j l (2J 1 + 1)(2J 2 + 1) j l J 1 m m l M 1 ) ( j l J 1 m m l M 1 ) ( j l J 2 m m l M 2 ) j l J 2 m m l M 2 )
18 Lunteren 2005 p. 18/31 3 He+CaH(N = 0): spin flip cross sections Cross section (Ang 2 ) Elastic Modified potential 3γ Spin flip l= Collision energy (cm 1 ) k(t = 0.4K) = σv = cm 3 s 1 (with resonance) cm 3 s 1 (modified potential) Experiment: k(0.4k) cm 3 s 1 Theory: Krems, Dalgarno, Balakrishnan, and Groenenboom, Phys. Rev. A 67, (2003)
19 Lunteren 2005 p. 19/31 He-NH( 3 Σ ) hamiltonian Ĥ = 2 2µR d 2 ˆl 2 R+ dr2 2µR 2 + ˆN 2 2µ NH r 2 +V (R, r e, θ)+ ˆV SR + ˆV SS +ĤZeeman Spin-rotation term (γ = cm 1 ): ˆV SR = γ ˆN Ŝ Spin-spin term (λ SS = cm 1 ): ˆV SS = 2 3 λ SS Zeeman term: [ 4π 5 ] q Ĥ Zeeman = g e µ 0 ˆB Ŝ ( 1) q Y 2, q (ˆr) [S S] (2) q
20 Lunteren 2005 p. 20/31 He NH ( 3 Σ ) potential (cm 1 ) 180 θ (degrees) R (a ) 0 Cybulski, Krems, Sadeghpour, Dalgarno, Kłos, Groenenboom, van der Avoird, Zgid, and Chałasiński, J. Chem. Phys. 122, 1 (2005)
21 Lunteren 2005 p. 21/31 He NH bound states (cm 1 ) J Parity l 4 He-NH γ = λ SS = 0 3 He-NH B ( 4 He-NH) Theory: cm 1 (-4%) Experiment: cm 1 G. Kerenskaya et al., J. Chem. Phys. 121, 7549 (2004)
22 Lunteren 2005 p. 22/31 3 He-NH: elastic and Zeeman cross sections (B = 100 G = 0.01 T) elastic Cross section (Å 2 ) inelastic without the N = 2 level Collision energy (cm 1 ) Effect of omitting γ ˆN Ŝ is negligible Krems, Sadeghpour, Dalgarno, Zgid, Kłos, Chałasiński, Phys. Rev. A, , (2003)
23 Lunteren 2005 p. 23/31 3 He-NH: elastic/inelastic ratio Elastic-to-inelastic ratio B = 0 B = 0.01 T B = 1 T B = 2 T B = 3 T Collision energy (cm -1 ) Cybulski et al. J. Chem. Phys. 122, 1 (2005)
24 Lunteren 2005 p. 24/31 Ongoing work Buffer-gas cooling of NH via the beam loaded buffer-gas method Egorov, Campbell, Friedrich, Maxwell, Tsikata, van Buuren, Doyle, Eur. Phys. J. D 31, 307 (2004) NH molecules thermalized in He at T < 6K Trapping and evaporative cooling in progress Can NH be made ultracold? Guillaume Dhont et al. (RU Nijmegen), Theory Session.
25 He OH( 2 Π) potentials (cm 1 ) He OH (A ) He OH (A ) R (a 0 ) θ (degrees) R (a 0 ) θ (degrees) H.-S. Lee et al., J. Chem. Phys. 113, 5736 (2000) Lunteren 2005 p. 25/31
26 Lunteren 2005 p. 26/31 He OH( 2 Π) hamiltonian Ĥ = 2 2µR d 2 ˆl 2 R+ dr2 2µR 2 +Ĥrot+ĤΛ doubling+ĥso+ĥzeeman+ ˆV (R, θ) Ĥ rot B = 18.5 cm 1 Ĥ Λ doubling p = 0.2, q = 0.04 (cm 1 ) A = cm 1 Ĥ SO ˆV (R, θ) = Λ,Λ Λ V Λ,Λ(R, θ) Λ V Λ,Λ = 1 2 (V A + V A ) V Λ, Λ = 1 2 (V A V A )
27 Lunteren 2005 p. 27/31 He OH( 2 Π): channel basis Uncoupled space-fixed channel eigen functions: njm j lm l ; p = njm j ; ɛ lm l, p = ɛ( 1) l Diatom eigen functions: njm j ; ɛ = Ω ΛΩjm j ; ɛ U (j,ɛ) Ω,n Hund s case (a) functions: ΛΩ; jm j ɛ, Λ = 1, Ω = 3/2, 1/2, ɛ = ±1 Initial state: Ω = 3/2, ɛ = 1(e), m j = 3/2
28 Lunteren 2005 p. 28/31 3 He+OH: elastic and Zeeman cross sections Cross section (Ang 2 ) He+OH Elastic, B=0 T B=2 T B=0.5 T B=0.1 T B=0.01 T B=0 T Collision energy (cm 1 )
29 Lunteren 2005 p. 29/31 3 He+OH: elastic and Zeeman cross sections 3 He+OH 10 2 Cross section (Ang 2 ) Collision energy (cm 1 ) B = 0.00 T B = 0.01 T B = 0.10 T B = 0.50 T B = 2.00 T
30 Lunteren 2005 p. 30/31 Conclusions He+CaH( 2 Σ + ) [Experiment 1998] Spin-flip mechanism: spin-rotation, indirect Calculated elastic cross section too big Huge resonance in spin-flip cross section He+NH( 3 Σ ) [Ongoing experiment] Spin-flip mechanism: spin-spin, direct Favorable Elastic/inelastic ratio predicted He+OH( 2 Π) [Experiment??] Elastic/inelastic ratio unfavorable Spin-flip mechanism: spin-orbit, direct Many interesting resonance features
31 Lunteren 2005 p. 31/31 Acknowledgements Nijmegen: Ad van der Avoird Paul Wormer Jacek Kłos Wilfried Zeimen Guillaume Dhont Gerrit Groenenboom ITAMP: Balakrishnan Roman Krems Alex Dalgarno Hossein Sadeghpour Warsaw: Hubert Cybulski Dominika Zgid Grzegorz Chałasiński Emory University Atlanta: Michael Heaven Udo Schnupf
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