Study of the A 1  + u and b 3  0u states in Cs 2 : New data and global analysis Houssam Salami, Tom Bergeman, Olivier Dulieu, Dan Li, Feng Xie and LiLi 63 rd International Symposium on Molecular Spectroscopy, Colombus, June 18, 2008

S+S Cold molecules Cold Atoms X1+X1+ a3+a3+ b3b3 X 1  + is the state where « really » cold molecules are produced. photoassociation "dump" "fluorescence" A1+A1+ Description of the A 1  u + and b 3  0u states correlated to the atomic asymptote Cs(6s)+Cs(6p) S+P E/cm -1 R/Å

Cs 2, A 1  + and b 3  0u data Fourier Transform Spectroscopy (FTS) data from the Laboratoire Aimé Cotton website, from the work of Claude Amiot and Olivier Dulieu, J. Chem. Phys. 117, 5155 (2002). Fluorescence spectroscopy data from Tsinghua University, from the work of Feng Xie, Dan Li, Luke Tyree, Li Li, Vladimir Sovkov, Valery Ivanov, Sylvie Magnier and A. Marjatta Lyyra, recently submitted to J. Chem. Phys Rotational quantum number, J Very recent measurements of excitation from Feshbach resonance states by J. Danzl and H. C. Nägerl at Innsbruck Energy/cm -1

The DVR Method * DVR method computes perturbed wavefunctions to a high degree of accuracy, because all mesh points are used to obtain d 2 /dR 2 Kinetic Energy is represented by a full matrix over the mesh points, The potential energies are diagonal, V ii’ =  ii’  (R i ) Hamiltonian matrix, n × n n=number of R mesh points × number of channels (, etc). * Colbert and Miller, Journal of Chemical Physics 96, 1982 (1992)

Coupled Channel Analysis Hamiltonian matrix: Potential: Spin-orbit functions: Atomic fine structure interval Hannover or: Morse/long-range

Modified Morse Potential/Long-Range (MLR) Dispersion coefficients: C 3 (A) = 6.8×10 5 cm -1 Å 3, C 3 (b) = 3.4×10 5 cm -1 Å 3 Derevianko, Babb, Dalgarno, PRA 63, (2001) C 6 (A) = 8.4 ×10 7 cm -1 Å 6, C 6 (A) = 8.4 ×10 7 cm -1 Å 6 Porsev, Derevianko, J. Chem. Phys. 119 (2003) 844 Dissociation energy: D e (A)= 5283 cm -1, R e (A)= Å; D e (b)= 6404 cm -1,R e (b)= Å With theoretically predicted form at Long Range * * Published model: R. Le Roy, D. Henderson, Mol. Phys. 105, 663, 2007

with y p → 1 when for R ≤ R e or (R > R e ) p (integer) > 3 imposed by C n constraints OPTIMIZE N S, N L, p,   OTHER VARIABLES ? 

Fitted MLR potentials and Morse SO function E/cm -1 R/Å A1u+A1u+ b 1  0u Spin orbit function Morse-type R/Å E/cm -1 Adiabatic potentials Diabatic potentials Potential Energy Curves have been performed using DVR method

Parameters in the MLR potential: N s, N L, p,  and in S.O functions p=4, N s =4, N L =10p=4, N s =4, N L =11 1 (11)D (75)D+01 2 (10)D D+04* 3 (21)D (73)D+04 4 (37)D (15)D+01  (34)D (60)D+01  (26)D (76)D+02  (72)D (26)D+02  (677)D (26)D+02  (590)D (52)D+05   (56)D (36)D+06   0.360(20)D (12)D+06  (34)D (21)D+07  D (21)D+07  D (86)D (26)D+06 b 3  0u A1u+A1u+ Spin-Orbit Function:

Fitted MLR potentials and Morse S.O. function E/cm -1 R/Å Potential Energy Curves have been performed using DVR method A1u+A1u+ b 1  0u Rms deviation (using Morse/Long-Range) = 0.07 cm -1 Rms deviation (using Hannover potential) =0.12 cm -1 Rms deviation (using Morse/Long-Range) = 0.07 cm -1 Rms deviation (using Hannover potential) =0.12 cm -1 Adiabatic potentials Diabatic potentials

Fit of the complete data set: Interpolation across the gap gap

b state, low resolution data (~ 2 cm -1 ) High resolution data on the A ~ b state (resolution ~ cm -1 ) High resolution data on the A ~ b state (resolution ~ cm -1 ) Fit until cm -1, rmsd= 0.07 cm -1 Fit ALL the data, rmsd= 0.2 cm -1 rmsd= 0.2 cm -1 rmsd/cm -1 E/cm -1 Hannover MLR

Tom Bergeman, State University of New York Olivier Dulieu, Laboratoire Aimé Cotton Li Li, Dan Li, Feng Xie, Tsinghua U. Acknowledgements Thank you for your attention

p=1 (Lennard-Jones) p=2 p=3 p=4 p=5 R / R e The power p in the expansion variable y p (R) is very important ! For p too small, most of the domain y p (R) is outside the region where the polynomial in y p (R) is determined, so polynomial may misbehave there. For p too large, y p (R) is too flat in the outer parts of the data region to allow a good fit to the data. Cs 2, A 1  + u and b 3  u0 data

Term Values Root mean square = 0.08 cm -1, for the high resolution data. (experimental uncertainty = cm -1 ) Rms = 1.65 cm -1 for the low resolution data (~ exp. Uncertainty) E/cm -1 J(J+1) b(0) b(5) b(10) b(40) b(45) A(0) A(4) A(6) A(15) b(58) b(60) b(66) A(17) A(23)A(20) b(63) A(13) A(11) J(J+1) E/cm -1