IV. FORMAL VERIFICATION OF THE SURROGATE RATIO METHOD 6 only a level of several % nominally, while that was about 50 % in Fig. 1. This means that we can determine the unknown fission cross sections by taking this kind of ratio if we know one of the other neutron cross section. The convergence seems to be valid also for somewhat higher value of spins. Similar convergence, although less dramatic, can be seen in Fig. 4 for capture probabilities. At 5 MeV, the ratios of the capture branching ratios for the 2 nuclei scatter only by about ± 5 % around those for the neutron capture reaction. At energies from 2.5 to 4 MeV, the surrogate ratios are all larger than the neutron ratio, but the deviation is still only 10 %. The same ratios were compared for various J + states produced in the neutron-induced reactions on $^{197}$Au and $^{193}$Ir in Fig. 5. We can notice that very good mutual convergence up to 8 + and equivalence to the neutron ratio are obtained in this mass region as well. Therefore, these data can be used to determine the GDR parameters at an energy region of, e.g., 2 to 5 MeV to normalize the calculated neutron capture cross section, and these parameters can be used to calculate the capture cross sections at lower energies since the Hauser-Feshbach theory can predict the shape of the energy dependent cross section rather accurately if normalization is given correctly at certain energies. Therefore, there is a fair possibility that we can determine the neutron capture cross section with accuracy of several % by the surrogate ratio method in combination with a theoretical calculation. The convergence of the ratios of fission and capture probabilities are very important to validate the surrogate technique and can be a base of the validity of surrogate ratio method. In the previous section, we have seen that the ratios of fission and capture probabilities at various values of J π between 2 nuclei have a dramatic convergence to the ratios of the neutron reactions. This can be utilized to verify the surrogate ratio method as follows. Let 2 surrogate reactions used for the ratio method be denoted as S$_{1}$ and S$_{2}$ , and corresponding neutron reactions as n$_{1}$ and n$_{2}$ . The reactions S$_{j}$ and n$_{j}$ ( j =1,2) are chosen to lead to the same compound nucleus. Let us assume that we know the neutron cross section σ n$_{2}$ i for the n$_{2}$ reaction . The branching ratio of the surrogate reaction for channel i ( i = fission or capture) may be written as B S$_{j}$ i ( U, J $^{π}$), where U denotes the equivalent neutron energy ( U can be the excitation energy as well). Then, the identity of the branching ratios shown in