Long Range Potentials for TwoNa(3p)Atoms Including Ionic-Covalent Interaction and Fine Structure: Application to Two-Color Photoassociation Spectroscopy

Abstract

In the framework of ab initio pseudopotential calculations, a method is presented to compute an effective spin-orbit Hamiltonian within a nonorthogonal diabatic representation separating the ionic and covalent subspaces. The resulting Hund's case c adiabatic curves display long range structures. We predict that a small ͑ഠ1 cm 21 ͒ fine-structure splitting of an ionic 3 P u curve is manifested in the spectrum of the excited Na 2 molecule slightly below the ͑3p 2 P 1͞2 1 3p 2 P 1͞2 ͒ asymptote as a series of well identified quadruplets. They should be observed in two-color photoassociation spectroscopy experiments using cold atoms. PACS numbers: 31.15.Ar, 32.80.Pj, 34.50.Rk The fundamental problem of the accurate description of long range interaction between two atoms (van der Waals forces), which has been extensively studied in the past [1,2], is presently reopened due to rapid progress in laser cooling and trapping of atoms [3,4]. Photoassociative spectroscopy (PAS) in a cold atom medium [5], as well as elaborate developments in traditional laser spectroscopy [6], are now capable of providing data on weakly bound states of diatomic molecules, for which the vibrational motion extends towards interatomic distances of several hundreds of atomic units (1 a.u. a 0 5.29177 3 10 29 m) that is much larger than in all previous investigations. Up to now, most experimental results are related to the electronic states of Li 2 [7], Na 2 [6,8], and Rb 2 [9] dimers that are correlated to the ns 1 np dissociation limit, where one atom is in the ground state and the other one in the first excited state. The long range potentials deduced from such measurements are in good agreement with theoretical calculations [10,11] using asymptotic methods. However, more recent two-color PAS experiments investigate upper excited electronic states, correlated to the Na͑3p͒ 1 Na͑3p͒ asymptote [12,13]; they detect the ion signal produced from short range autoionizing doubly excited states correlated to a given long range state. The interpretation of such spectra is a challenge because the pattern of electronic states is much more complicated than for the 3s 1 3p asymptote. Although the short range autoionizing states are now well identified [14], the correct evaluation of intermediate and long range potentials, typically in the 20a 0 50a 0 range of internuclear distances, is still an open problem. Indeed, as the ͑3p 1 3p͒ asymptote cannot be considered as an isolated energy level, second order perturbation theory is no longer a valid approximation to compute the dispersion forces. The asymptotic estimation of tunneling exchange forces cannot follow the usual treatment [15,16], since the covalent states are perturbed by several ionic states [17], some of which correspond to excited states of the negative ion. Finally, the correct treatment of spin-orbit coupling [18] appears difficult in this context of strong configuration mixing.However, recent results seem to indicate that quantum chemistry calculations using effective potentials can provide...

Photoassociation of Ultracold Atoms: A New Spectroscopic Technique

“…Fortunately, the complex correlation diagram was worked out (120) for the analogous case of B (2p) ϩ B(2p); see also the calculations for Na(3p) ϩ Na(3p) (81,151). Moreover, accurate C n coefficients are now available (164).…”

“…The doubly excited 4p ϩ 4p atomic limit and the corresponding molecular states are important and have recently been calculated at longrange for the first time in our group. Of particular interest are extrema outside 30a 0 : 0 g ϩ minima at 33 and 34a 0 at the (1/2, 1/2) asymptote and a 1 g maximum at 42a 0 at the (1/2, 3/2) asymptote (the Na 2 states at the 3p ϩ 3p asymptotes have also been discussed in detail (81,151)). …”

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

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Characterization of Frictional Properties of Single-Layer Molybdenum-Disulfide Film Based on a Coupling of Tip Radius and Tip–Sample Distance by Molecular-Dynamics Simulations

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