MAPPED FOURIER METHODS FOR LONG-RANGE MOLECULES : APPLICATION TO PERTURBATIONS IN THE RB2(0U+) PHOTOASSOCIATION SPECTRUM

Numerical calculations of vibrational levels of alkali dimers close to the dissociation limit are developed in the framework of a Fourier Grid Hamiltonian method. The aim is to interpret photoassociation experiments in cold atom samples. In order to avoid the implementation of very large grids we propose a mapping procedure adapted to the asymptotic R−n behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to 500a0 using a minimal number of grid points. Calculations with two electronic states, A 1Σu+ and b 3Πu states, both correlated to the Rb(5s)+Rb(5p) dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the Rb2(0u+) spectrum, manifested under the 5s, 5p 2P1/2 dissociation limit by an oscillatory behavior of the rotational constants.

[1]  Gabriel G. Balint-Kurti,et al.  The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions , 1989 .

[2]  Robert W. Field,et al.  Perturbations in the Spectra of Diatomic Molecules , 1986 .

[3]  S. F. Rice,et al.  The predissociation of Li2 b3Πu by a3Σ+u , 1986 .

[4]  P. Millié,et al.  Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations , 1993 .

[5]  R. Meyer.  Trigonometric Interpolation Method for One‐Dimensional Quantum‐Mechanical Problems , 1970 .

[6]  Weiner,et al.  Accuracy of molecular data in the understanding of ultracold collisions. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[7]  Eli Turkel,et al.  Mappings and accuracy for Chebyshev pseudo-spectral approximations , 1992 .

[8]  Julienne,et al.  Cold collisions of ground- and excited-state alkali-metal atoms. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[9]  L. Schlie,et al.  Absorption spectra of the Cs2 molecule , 1977 .

[10]  Weiner,et al.  Laser-induced photoassociation of ultracold sodium atoms. , 1987, Physical review letters.

[11]  R. F. Barrow,et al.  Interactions between A 1Su+ and b 3?u states of Na2 , 1985 .

[12]  J. H. Müller,et al.  Direct measurement of fine-structure collisional losses from a Cs magneto-optical trap , 1997 .

[13]  R. Kosloff,et al.  Quasibound states in long-range alkali dimers: Grid method calculations , 1997 .

[14]  Phillips,et al.  Spectroscopy of Na2 by photoassociation of laser-cooled Na. , 1993, Physical review letters.

[15]  R. Wyatt,et al.  Dynamics of molecules and chemical reactions , 1996 .

[16]  P. Gould,et al.  Fine-Structure Predissociation of Ultracold Photoassociated K 2 39 Molecules Observed by Fragmentation Spectroscopy , 1998 .

[17]  C. Amiot,et al.  The Cs2 A1Σu+ → X1Σg+ fluorescence excited by the Ar+ 1.09-μm laser line , 1987 .

[18]  M. Monnerville,et al.  Optical potential coupled to discrete variable representation for calculations of quasibound states: Application to the CO(B 1Σ+–D’1 Σ+) predissociating interaction , 1994 .

[19]  P. Millié,et al.  Nonperturbative method for core–valence correlation in pseudopotential calculations: Application to the Rb2 and Cs2 molecules , 1992 .

[20]  Daniel Neuhauser,et al.  Extraction, through filter‐diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short‐time segment of a signal. I. Theory and application to a quantum‐dynamics model , 1995 .

[21]  Dalgarno,et al.  Dispersion forces and long-range electronic transition dipole moments of alkali-metal dimer excited states. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[22]  E. M. Lifshitz,et al.  Quantum mechanics: Non-relativistic theory, , 1959 .

[23]  W. Meyer,et al.  Predissociation lifetimes of the b3Πu state of Li2 and the accidental predissociation of its A1Σu+ state , 1985 .

[24]  W. Preuss,et al.  Time spectroscopy in theA1∑u+ state of Li2. Perturbations by thea3Πu state , 1985 .

[25]  Baer,et al.  Phase space approach for optimizing grid representations: The mapped Fourier method. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  F. Gygi,et al.  Adaptive Riemannian metric for plane-wave electronic-structure calculations , 1992 .

[27]  A. Fioretti,et al.  Formation of Cold Cs 2 Molecules through Photoassociation , 1998 .

[28]  Y. Band,et al.  Hermiticity of the Hamiltonian matrix in a discrete variable representation , 1997 .

[29]  J. A. Coxon,et al.  CW all-optical triple-resonance spectroscopy of K2: Deperturbation analysis of the A1Σu+ (v ≤ 12) and b3Πu (13 ≤ v ≤ 24) states , 1992 .

[30]  Miller,et al.  Study of Rb2 long-range states by high-resolution photoassociation spectroscopy. , 1994, Physical review letters.

[31]  Carl J. Williams,et al.  PHOTOASSOCIATIVE SPECTROSCOPY OF HIGHLY EXCITED VIBRATIONAL LEVELS OF ALKALI-METAL DIMERS : GREEN-FUNCTION APPROACH FOR EIGENVALUE SOLVERS , 1998 .

[32]  R. Kosloff.  Time-dependent quantum-mechanical methods for molecular dynamics , 1988 .

[33]  V. Flambaum,et al.  Calculation of the scattering length in atomic collisions using the semiclassical approximation. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[34]  John M. Blatt,et al.  Practical points concerning the solution of the Schrödinger equation , 1967 .