Generic properties of the complementarity problem

Given f : R + n → R n , the complementarity problem is to find a solution to x ≥ 0, f(x) ≥ 0, and 〈 x, f(x) 〉 = 0. Under the condition that f is continuously differentiable, we prove that for a generic set of such an f , the problem has a discrete solution set. Also, under a set of generic nondegeneracy conditions and a condition that implies existence, we prove that the problem has an odd number of solutions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47915/1/10107_2005_Article_BF01584674.pd

Radiative lifetime of the 2P state of lithium

We determine the radial dipole moment between the 2S and 2P states of atomic lithium by analyzing the long-range vibrational eigenenergies of the singly excited diatomic molecule. The result can be expressed in terms of the 2P12 radiative lifetime of Li7, which is found to be 27.102(2)(7) ns. This result agrees with most current atomic-structure calculations and resolves the long-standing disagreement with previous experiment. The current level of precision is sensitive to relativistic effects in the atomic-structure calculation and to non-Born-Oppenheimer and radiation retardation effects in the molecule

Hyperfine structure in photoassociative spectra of 6Li2 and 7Li2

We present spectra of hyperfine resolved vibrational levels of the A1Σu+and 1 3Σg+ states of 6Li2 and 7Li2 obtained via photoassociation of colliding ultracold atoms in a magneto-optical trap. A simple first-order perturbation theory analysis accurately accounts for the frequency splittings and relative transition strengths of all observed hyperfine features. Assignment of the hyperfine structure allows accurate determination of a vibrational level center of gravity, which significantly decreases the experimental uncertainty of vibrational energies. Differences in the spectra of 6Li2 and 7Li2 are attributed to quantum statistics. The 1 3Σg+ series obeys Hund’s case bβS coupling and the hyperfine constant is extracted for both isotopes

Hyperfine structure in photoassociative spectra of 6Li2 and 7Li2

We present spectra of hyperfine resolved vibrational levels of the A1Σu+and 1 3Σg+ states of 6Li2 and 7Li2 obtained via photoassociation of colliding ultracold atoms in a magneto-optical trap. A simple first-order perturbation theory analysis accurately accounts for the frequency splittings and relative transition strengths of all observed hyperfine features. Assignment of the hyperfine structure allows accurate determination of a vibrational level center of gravity, which significantly decreases the experimental uncertainty of vibrational energies. Differences in the spectra of 6Li2 and 7Li2 are attributed to quantum statistics. The 1 3Σg+ series obeys Hund’s case bβS coupling and the hyperfine constant is extracted for both isotopes

Spectroscopic Determination of the s-Wave Scattering Length of Lithium

Two-photon photoassociation of colliding ultracold 7Li atoms is used to probe the Σu+3(a) ground state of 7Li2. The binding energy of the least-bound state of this triplet potential, υ=10, is found to be 12.47±0.04 GHz. This spectroscopic information establishes that the s-wave scattering length for 7Li atoms in the F=2, mF=2 state is (−27.3±0.8)a0. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation

Precise atomic radiative lifetime via photoassociative spectroscopy of ultracold lithium

We have obtained spectra of the high-lying vibrational levels of the 13Σg+ state of 6Li2 via photoassociation of ultracold 6Li atoms confined in a magneto-optical trap. The 13Σg+ state of the diatomic molecule correlates to a 2S1/2 state atom plus a 2P1/2 state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the 13Σg+ state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99±0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations

Singlet s-wave scattering lengths of Li6 and Li

Photoassociation of ultracold lithium atoms into bound vibrational levels of the AΣu+1 excited state is used to probe the XΣg+1 ground-state interaction potential of Li26 and Li27. It had been predicted that the s-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive s-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet s-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving Li7 atoms in different hyperfine states