4 III. COMPUTATIONAL METHOD AND RESULTS R S$_{1}$ i R S$_{2}$ i ? = σ n 1 i σ n 1 R σ n 2 i σ n 2 R , (2) → σ n$_{1}$ i ? = σ n$_{2}$ i · σ n$_{1}$ R σ n$_{2}$ R · R S$_{1}$ i R S$_{2}$ i , ( i = fission or capture) . (3) kind of surrogate reactions, S$_{1}$ and S$_{2}$ , e.g., ( t, p ) reactions on different targets. If we know the neutron cross section σ n$_{2}$ i for the reaction leading to the same compound nucleus as the S$_{2}$ reaction, we can determine the neutron cross section ( σ n$_{1}$ i ) which leads to the same compound nucleus as S$_{1}$ reaction via the equality (with a question mark) Here, σ n$_{j}$ i denotes the neutron fission ( i =fission) or capture ( i =capture) reaction cross sec- tion, and σ n$_{j}$ R the total neutron reaction cross section for the reaction n$_{j}$ ( j = 1 or 2). Provided that the above equations hold, we can determine the neutron cross section σ n$_{1}$ i from this formula, since we know σ n$_{2}$ i , we measure the ratio R S$_{1}$ i /R S$_{2}$ i and we can calcu- late the ratio of the reaction cross sections σ n$_{1}$ R /σ n$_{2}$ R by the coupled-channel theory rather accurately[12, 13]. This method is referred to as the surrogate ratio method or relative surrogate method. It is naively expected to give a result better than the surrogate absolute method, since we do not need to know in the relative method all the experimental artifacts such as the detector efficiency and geometrical factor required to deduce the ratio in the ab- solute method. However, all these methods require a fact that the branching ratios are equal for the surrogate and the neutron-induced reactions. This is true only when 1) the ratios are independent of the spin-parity of the decaying nuclei (Weisskopf-Ewing condition[14]), or 2) the spin-parity distributions are equivalent for the surrogate and neutron reactions, or 3) the ratio is not sensitive to the difference of the spin-parity distributions between the neutron-induced and surrogate reactions. Below, we will investigate if these assumptions are justified or not, and when justified, what accuracy will be. We use the Hauser-Feshbach theory[15] to calculate the decay branching ratios of various spin-parity ( J $^{π}$) states of $^{239}$U by using CCONE code system[16]. It represents a nucleus produced by n+ $^{238}$U reactions and corresponding surrogate reactions such as $^{237}$U( t, p ) $^{239}$U. This nucleus was chosen just as an example. In the calculation, the same parameter val- ues for discrete level structures, transmission coefficients, level density, fission barrier and