B S$_{j}$ i ( U, J $^{π}$) = B S$_{j}$ i ( U ) = R n$_{j}$ i ( U ) . (10) R S$_{1}$ i ( P + Q ) = ∑$_{J}$ π ˆ Qσ $^{S$_{1}$}$( U, J $^{π}$) · B S$_{1}$ i ( U, J $^{π}$) ∑$_{J}$ π ( ˆ P + ˆ Q ) σ $^{S$_{1}$}$( U, J $^{π}$) ≤ R S$_{1}$ i ( U ) = ∑$_{J}$ π ˆ Qσ $^{S$_{1}$}$( U, J $^{π}$) · B S$_{1}$ i ( U, J $^{π}$) ∑$_{J}$ π ˆ Qσ $^{S$_{1}$}$( U, J $^{π}$) , (11) 8 The essential point in the verification is the equality given in Eq. (4) and equality of the J π spectra of the 2 surrogate reactions. The latter implies that the J π distributions in the surrogate reactions can be different from those of the neutron-induced reactions. What is important is that 2 surrogate reactions should yield equivalent J π distributions. It can be easily achieved in experiments by selecting targets having similar structure and using the same reaction for the both surrogate reactions. However, the difference of the representative spin between the neutron- induced and surrogate reactions should not be much larger than about 10 ¯ h . We define the equality given in Eq. (4) as “ weak Weisskopf-Ewing condition ”. This condition is different from the standard Weisskopf-Ewing condition, which is written as If this standard condition is satisfied, we can determine the branching ratios by the surrogate absolute method. Unfortunately, it is not the case for the reactions investigated in this paper, especially it is a poor assumption for the capture reaction as shown in Fig. 2. The surrogate ratio method has another advantage over the absolute method. Since the surrogate method uses multi-nucleon transfer reactions very often, there is a possibility, when the corresponding neutron energy increases, that the nucleons expected to be transferred to bound states of the target is actually transferred to an unbound state, eventually leading to the breakup (or preequilibrium) reactions such as $^{238}$U( t, np ) $^{239}$U instead of expected reaction $^{238}$U( t, p ) $^{240}$U. This effect can be also canceled out by the surrogate ratio method as follows. Let us denote the bound states as “Q”, and unbound ones as “P”. Since we measure the ejectile (e.g., p ), the production cross section of it contains transitions to both the Q- and P-states of the residual nuclei. On the contrary, the true decay occurs only via the Q- states. Therefore, the decay probabilities measured in the surrogate method in the presence of breakup reaction, R S$_{1}$ i ( P + Q ), can be written as where the ˆ Q and ˆ P denote fractions of transitions to the Q- and P-states, respectively, and ˆ P + ˆ Q =1. The same is true for the S$_{2}$ reaction Therefore, the ratio of the measured surrogate