Investigation of multistep effects for proton inelastic scattering to the $2_1^{+}$ state in ${}^6\mathrm{He}$

Multistep effects among bound, resonant, and nonresonant states have been investigated by the continuum-discretized coupled-channels method (CDCC). In the CDCC, a resonant state is treated as multiple states fragmented in a resonance energy region, although it is described as a single state in usual coupled-channels calculations. For such the fragmented resonant states, one-step, and multistep contributions to the cross sections should be carefully discussed because the cross sections obtained by the one-step calculation depend on the number of those states, which corresponds to the size of the model space. To clarify the role of the multistep effects, we propose the one-step calculation without model-space dependence for the fragmented resonant states. Furthermore, we also discuss the multistep effects among the ground, $2_1^{+}$ resonant, and nonresonant states in ${}^6\mathrm{He}$ for proton inelastic scattering.

Figure 1

Pseudostates of ${}^6\mathrm{Li}$ for $I^{\pi }$ = $2^{+}$ calculated with sets I and II. On the vertical axis, 0 MeV corresponds to the $d+\alpha$ threshold. States in the area between the two lines represent fragmented resonant states.

Figure 2

Breakup cross section for ${}^6\mathrm{Li}+{}^{40}\mathrm{Ca}$ scattering calculated with set I. The bars represent the breakup cross sections to discretized states, and the absolute values are shown on the right vertical axis.

Figure 3

Inelastic cross sections for the ${}^6\mathrm{Li}+{}^{40}\mathrm{Ca}$ reaction at $E=26\mathrm{MeV}/\mathrm{nucleon}$ obtained from the CDCC. The pseudostates considered in the results are calculated with parameter set I for Gaussian bases.

Figure 4

Inelastic cross sections for the ${}^6\mathrm{Li}+{}^{40}\mathrm{Ca}$ reaction at $E=26\mathrm{MeV}/\mathrm{nucleon}$ obtained from the one-step calculations with Eqs. (5) and (8). The pseudostates considered in the results are calculated with parameter sets I or II for Gaussian bases.

Figure 5

Breakup cross section for the ${}^6\mathrm{He}+p$ reaction at $E=41\mathrm{MeV}/\mathrm{nucleon}$ describing the transition to the $2^{+}$ continuum states obtained from the CDCC. States in the area between the two lines represent fragmented resonant states.

Figure 6

Inelastic cross sections for the ${}^6\mathrm{He}+p$ reaction at $E$ = 41 and 25 MeV/nucleon obtained from the CDCC including only the fragmented resonant states and one-step calculations using Eqs. (5) and (8).

Figure 7

Inelastic cross sections for the ${}^6\mathrm{He}+p$ reaction at $E=41$ and 25 MeV/nucleon obtained from the CDCC and one-step calculations using Eq. (8).

Figure 8

The radial wave functions of ${}^6\mathrm{Li}$ in sets I and II.

Figure 9

The radial wave functions of ${}^6\mathrm{Li}$ and the probability densities in set I.