Core excitation in three-body nuclear reactions: Improved nucleon-core potential

Three-body nuclear reactions in two-nucleon plus core systems are described in the framework of exact scattering equations including the core excitation. A nucleon-core optical potential is constructed that can be easily adjusted to the reference potential and thereby to the experimental two-body data, if available. This constitutes an important improvement over the simple deformation of the potential used previously that violated the original fit to the data. Predictions for elastic, inelastic, and transfer reactions involving ${}^{10}\mathrm{Be}$ and ${}^{24}\mathrm{Mg}$ nuclear cores are obtained. The new optical potential leads to a moderate increase of cross sections.

Figure 1

Nucleon-core potential in the three-body Hilbert space. The particles are represented by vertical lines, the core in its excited state is distinguished by thick lines, and the potential is represented by horizontal dashed lines. The diagrams (a), (b), (c), and (d) correspond to $V_{gg},V_{xg},V_{gx}$, and $V_{xx}$.

Figure 2

Diagrammatic representation of the contributions at the two lowest orders subtracted from the nucleon-core potential.

Figure 3

Differential cross section for ${}^{10}\mathrm{Be}(p,p){}^{10}\mathrm{Be}$ and ${}^{10}\mathrm{Be}(p,p^{\prime }){}^{10}{\mathrm{Be}}^{*}$ reactions at $E_p=39$ MeV. Results including the CeX with and without subtraction, i.e., CX and CX(no subtr), are given by solid and dash-dotted curves, respectively. CX predictions coincide with SP results neglecting the CeX for the elastic scattering and with DWBA results for the inelastic reaction. The elastic experimental data are from Ref. [31].

Figure 4

Differential cross section for $p+{}^{11}\mathrm{Be}$ elastic scattering at $E_p=35.3$ MeV. Results of SP, CX, and CX(no subtr) potential models are given by dotted, solid, and dash-dotted curves, respectively. The experimental data are from Ref. [31].

Figure 5

Differential cross section for transfer reactions ${}^{10}\mathrm{Be}(d,p){}^{11}\mathrm{Be}$ at $E_d=21.4$ MeV leading to the ground $\left({\frac{1}{2}}^{+}\right)$ and excited $\left({\frac{1}{2}}^{-}\right)$ states of ${}^{11}\mathrm{Be}$. Curves are as in Fig. 4 and experimental data are from Ref. [32].

Figure 6

Differential cross section for ${}^{11}\mathrm{Be}(p,d){}^{10}\mathrm{Be}$ transfer reactions at $E_p=35.3$ MeV leading to the ground $\left(0^{+}\right)$ and excited $\left(2^{+}\right)$ states of ${}^{10}\mathrm{Be}$. Curves are as in Fig. 4 and experimental data are from Ref. [33].

Figure 7

Differential cross section for ${}^{11}\mathrm{Be}(p,d){}^{10}\mathrm{Be}$ transfer reactions at $E_p=35.3$ MeV leading to the ground $\left(0^{+}\right)$ and excited $\left(2^{+}\right)$ states of ${}^{10}\mathrm{Be}$. CX predictions based on CH89 (solid curves), Koning-Delaroche (double-dot-dashed curves), and Watson (dashed curves) potentials are compared with the experimental data from Ref. [33].

Figure 8

Differential cross-section ratios $R_x$ for ${}^{10}\mathrm{Be}(d,p){}^{11}\mathrm{Be}$ transfer reactions leading to ground (thick curves) and excited (thin curves) states of ${}^{11}\mathrm{Be}$. CX and CX(no subtr) predictions are given by solid and dash-dotted curves, respectively.

Figure 9

Differential cross section for $d+{}^{24}\mathrm{Mg}$ elastic (left) and inelastic (right) scattering at $E_d=70$ MeV. Results of SP, CX, and CX(no subtr) models based on the CH89 potential are given by dotted, solid, and dash-dotted curves, respectively, while CX results based on the Koning-Delaroche potential are given by double-dot-dashed curves. The experimental data are from Ref. [34].