Precision calculation of low-energy electron-impact excitation cross sections of helium among the ground and excited states

Low-energy electron-impact cross sections of helium among the ground and some low excited states are calculated using the $R$-matrix method. The convergences of the cross sections are checked systematically by using five sets of high-quality target states; i.e., including 5, 11, 19, 29, and 39 physical target states, respectively. Our calculated cross sections are in excellent agreement with the benchmark high-resolution experimental data. Compared with the recommended theoretical data, there is a deviation of about 6%, which suggests the recommended data may need a revision. Based on our calculation results, the influence of the Rydberg target states on the collision cross sections of the excited states is found to be similar to the case of the ground state; i.e., the amplitude of resonance structures will decrease with respect to the principal quantum number $n$ of Rydberg target states. This result should be very useful for providing the cross-section data in the whole energy regions with high quality, which would be of great importance in related scientific fields.