Calculation of the elastic scattering properties for cold and ultracold ³⁹K atoms in a triplet state

The elastic scattering properties for collisions between cold and ultracold ³⁹K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet a³\Sigma_u⁺ ground state of K₂. Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578a₀ and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the a³\Sigma_u⁺ state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the a³\Sigma_u⁺ state are calculated.