We discover several magnetic Feshbach resonances in collisions of ultracold
K(39) atoms, by studying atom losses and molecule formation. Accurate
determination of the magnetic-field resonance locations allows us to optimize a
quantum collision model for potassium isotopes. We employ the model to predict
the magnetic-field dependence of scattering lengths and of near-threshold
molecular levels. Our findings will be useful to plan future experiments on
ultracold potassium atoms and molecules.Comment: 7 pages, 6 figure