Practical method for decomposing discretized breakup cross sections into components of each channel

Background: In the continuum-discretized coupled-channel method, a breakup cross section (BUX) is obtained as an admixture of several components of different channels in multichannel scattering.

Purpose: Our goal is to propose an approximate way of decomposing the discretized BUX into components of each channel. This approximation is referred to as the “probability separation (P separation).”

Method: As an example, we consider ${}^{11}\mathrm{Be}$ scattering by using the three-body model with core excitation (${}^{10}\mathrm{Be}+n+T$, where $T$ is a target). The structural part is constructed by the particle-rotor model and the reaction part is described by the distorted-wave Born approximation.

Results: The validity of the P separation is tested by comparing with the exact calculation. The approximate way reproduces the exact BUXs well regardless of the configurations and/or the resonance positions of ${}^{11}\mathrm{Be}$.

Conclusion: The method proposed here can be an alternative approach for decomposing discretized BUXs into components in four- or five-body scattering where the strict decomposition is hard to perform.

Figure 1

Decomposition of the breakup cross sections for the scattering of ${}^{11}\mathrm{Be}+p$ at 63.7 MeV/nucleon. The solid lines represent the exact BUXs ($\sigma$), whereas the solid circles correspond to the approximate BUXs ($\widehat{\sigma }$). The results of the approximate decomposition without Eq. (20) are also shown by the open squares.

Figure 2

Energy distribution of the BUXs for the scattering of ${}^{11}\mathrm{Be}+p$ at 63.7 MeV/nucleon. The discretized and exact BUXs are represented by the bars and the line, respectively. The total, core-ground, and core-excited BUXs are shown from the bottom panel. Note that Eq. (20) is not imposed in this figure. Each discretized BUX is multiplied by the density of states ${\sum }_{{\ell }_f{j}_f{I}_f}{\left|\langle {\mathrm{\Psi }}_{JM}^{\left({\varepsilon }_{n_f}{\ell }_f{j}_f{I}_f\right)}|{\widehat{\mathrm{\Psi }}}_{JM}^{\left(n_f\right)}\rangle \right|}^2$ to make it comparable with the exact one in the same unit of millibarns/MeV.