Accurate calculation of the elastic scattering properties of ⁷Li atoms at ultralow temperatures

The elastic scattering properties for collisions between two ⁷Li atoms are investigated in the cold and ultracold regimes separately. Based on recent theoretical and experimental results, we present the improved hybrid potentials for the singlet X¹∑_g⁺ and triplet a³∑_u⁺ ground states of the Li₂. Our calculated values for the scattering lengths a and the effective ranges r_e are compared with previous ones and found them to be in good agreement. The scattering lengths are 34.6a₀ for the singlet state and ?27.6a₀ for the triplet state. Shape resonances occur in the collisions at low energies. We also calculate the total cross sections and the energy positions of shape resonances for both X¹∑_g⁺ and a³∑_u⁺ states.