Number of virtual photons in the Coulomb dipole excitation

Abstract

In this study, the number of virtual photons obtained through general, relativistic, nonrelativistic, and intermediate methods was investigated, which is an important factor in obtaining the Coulomb dipole strength distribution. The number of virtual photons was studied according to the incident energy ${E}_{\text{lab}}$ using five methods. The general method, which has two different forms (integral and differential), is valid for all energy regions, whereas the relativistic method is effective for regions with high $\ensuremath{\beta}$ values. In addition, the validity of the nonrelativistic approximation was tested by comparing it with the general method in the low-incident-energy region, and the intermediate method was shown to be not effective in the high-excitation-energy region. Further, an investigation was conducted on the dependence of the number of virtual photons on the charges of the projectile and target nuclei. Using the same $R$ value, target nuclei, and incident energy, it was found that the number of virtual photons does not depend on the charge number of the projectile in the relativistic method. With the same $R$ value, projectile, and incident energy, in contrast it can be seen that the number of virtual photon depends on the square of the charge number of target nuclei.