In this paper, we use the quantum field theory to solve the generation process of particle-anti-particle pairs (PAPs), and study the generation characteristics of PAPs by changing the profile of the field combining an oscillating field and a static electric field. We find a way to increase the generation of PAPs and change the energy distribution. As the field strength of the oscillating field increases, the quantity of particle pairs generated increases. Increasing the field strength of a static electric field yields higher energy pairs of particles. If the frequency of the oscillating field becomes higher, the peak of the energy distribution shifts to higher energy but the width of the peak remains unchanged. The reduction of the field width of the oscillating field increases the generated quantity of PAPs on the one hand, and reduces the peak width of the energy distribution on the other hand. Therefore, we can obtain a narrower range of the energy distribution and more PAPs at less energy cost. Meanwhile, the relationship among the generation yield, the width of energy distribution and the width of the oscillation field is obtained. The width of the oscillating field only significantly narrows the peak width of the energy distribution in a range and reaches a limit after that. This provides useful details for future experiments, and suggests an appropriate width of the oscillating field to produce enough quantity of PAPs with concentrated energy distribution. According to previous studies, varying field width will inevitably lead to the change in the intensity of the electric field. It will be shown that the concentrating of the energy distribution is induced by narrowing the oscillating field instead of increasing the electric field intensity. Therefore, more concentrated PAPs will be obtained and their mutual annihilation will lead to the generation of -ray, which can be used as a -ray in experiments that follow. We suggest reducing the width of the oscillating field to improve the energy concentration of both particles and anti-particles while their quantities are still large enough.