Transmission coefficients in compound-nucleus reaction theory

A recent article [D. A. Brown, G. P. A. Nobre, and M. W. Herman, Phys. Rev. C 98, 024616 (2018)] proposed a modification of the cross section formula used in practical calculations of compound nucleus reactions. We discuss the main concepts and approximations of statistical reaction theory and conclude that the standard practical implementations of the cross section formula remain the preferred choice.

Figure 1

Transmission coefficient $T_c$ for an incoming channel $c$ in the GOE model with six equivalent reaction channels as a function of $x_c$. Solid line: Eq. (9). Solid circles: results obtained by sampling $H$ from the GOE.

Figure 2

Ratio of entrance channel cross section calculated from Eqs. (13) and (14) to the GOE statistical theory cross section for the two-channel example described in the text. Black circles: $f_c=T_c$; Red circles: $f_c=T_c/\sqrt{1-T_c}$. (a) and (b) show the ratios as a function of $x_a$ and $x_b$, respectively.