At low photon energies, the potential models of nucleus-nucleus bremsstrahlung are based on electric transition multipole operators, which are derived either only from the nuclear current or only from the charge density by making the long-wavelength approximation and using the Siegert theorem. In the latter case, the bremsstrahlung matrix elements are divergent and some regularization techniques are used to obtain finite values for the bremsstrahlung cross sections. From an extension of the Siegert theorem, which is not based on the long-wavelength approximation, a new potential model of nucleus-nucleus bremsstrahlung is developed. Only convergent integrals are included in this approach. Formal links between bremsstrahlung cross sections obtained in these different models are made. Furthermore, three different ways to calculate the regularized matrix elements are discussed and criticized. Some prescriptions for a proper implementation of the regularization are deduced. A numerical comparison between the different models is done by applying them to the $alpha+alpha$ bremsstrahlung.
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