Low-lying excited states of ${}^{24}\mathrm{O}$ investigated by a self-consistent microscopic description of proton inelastic scattering

The proton inelastic scattering of ${}^{24}\mathrm{O}$($p,p^{\prime }$) at 62 MeV/nucleon is described by a self-consistent microscopic calculation with the continuum particle-vibration coupling (cPVC) method. The SLy5, SkM*, and SGII parameters are adopted as alternative effective nucleon-nucleon interactions. For all the Skyrme parameters the cPVC calculation reproduces reasonably well the absolute values of the first and second peaks of the excitation energy spectrum of ${}^{24}\mathrm{O}$ and the absolute value of the angular distribution corresponding to the first peak at 4.65 MeV. The relative energy between the two peaks is well reproduced by the cPVC method with SLy5 and SkM*. The role of the cPVC self-energy strongly depends on the effective interactions. The second peak around 7.3 MeV is suggested to be a superposition of the $3^{-}$ and $4^{+}$ states by the results with SLy5 and SGII, whereas the SkM* calculation indicates it is a pure $3^{-}$ state. This difference gives a rather strong interaction dependence of the angular distribution corresponding to the second peak.

Figure 1

The Feynman diagram corresponding to the double differential cross section for the nucleon-nucleus inelastic scattering expressed by Eq. (1). ${\varphi }^{\mathrm{HF}}$ and $\psi$ are the HF and cPVC scattering wave functions, respectively. $\kappa$ is the residual force. $R\left(E_x\right)$ is the continuum RPA response function. The half part of the diagram expresses the transition matrix.

Figure 2

The differential cross section $d\sigma /d{E}_x$ plotted as a function of the excitation energy $E_x$ of ${}^{24}\mathrm{O}$ for the $(p,p^{\prime })$ reaction at 62 MeV/nucleon, and compared with the experimental data [1]. The results were calculated by the cPVC method with the SLy5, SkM*, and SGII Skyrme interactions. The lines show the total energy spectrum and contributions from the $1^{-},2^{+},3^{-}$, and $4^{+}$ states of ${}^{24}\mathrm{O}$. The lower horizontal axis is the experimental excitation energies of ${}^{24}\mathrm{O}$, $E_x^{\mathrm{expt}}$, and the upper axis is the theoretical one, $E_x^{\mathrm{cPVC}}$. See the text for detail.

Figure 3

The angular distribution of the cross section $d\sigma /d\Omega$ corresponding to the first $2^{+}$ state of ${}^{24}\mathrm{O}$ at $E_x=4.65\pm 0.14$ MeV compared with the experimental data [1]. The panels show the results for the SLy5, SkM*, and SGII interactions obtained with the cPVC and one-step transition calculations (see text).

Figure 4

The angular distributions corresponding to 7 $\le E_x\le$ 7.5 MeV and 7.5 $\le E_x\le$ 8 MeV for the SLy5 and SkM* interactions.

Figure 5

The contributions of the $3^{-}$ and $4^{-}$ states to the angular distribution for $7.0\le E_x\le 7.5$ MeV shown in Fig. 4, for the results obtained with SLy5 and SkM*.