Repulsive three-body force and channel-coupling effects via ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering at $100A$ MeV

The angular distributions of differential cross sections of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ elastic and inelastic scattering populating the ground and excited states in ${}^{12}\mathrm{C}$ up to 15 MeV excitation energy are precisely measured for the first time at an incident energy of $100A$ MeV to study the effect of repulsive three-body forces. Using the high-resolution spectrometer Grand Raiden at the Research Center for Nuclear Physics (RCNP), Osaka University, we have obtained the differential cross sections for the ground state ($0_1^{+}$) and 4.44 MeV ($2_1^{+}$) excited state, as well as the summed differential cross sections for the states between 4.44 and 15 MeV in the angular range of $1.0^{\circ }–7.5^{\circ }$. The results are compared with microscopic coupled-channel calculations. The potential between the colliding nuclei is determined by the double folding method with three different complex $G$-matrix interactions, the ESC, CEG07b, and MPa interactions. The CEG07b and MPa interactions, which include repulsive three-body forces, describe the data well, whereas the ESC interaction, which does not include repulsive three-body forces, fails to reproduce the data. The results provide evidence of repulsive three-body forces in ${}^{12}\mathrm{C}$ and demonstrate the possible sensitivity of elastic scattering to three-body forces.

Figure 1

Schematic view of the magnetic spectrometer Grand Raiden (left) and focal plane detector system setup (right). The spectrometer consists of two dipole magnets (D1 and D2), two quadrupoles (Q1 and Q2), a sextupole (SX), a multipole (MP), and an additional dipole (DSR) magnet.

Figure 2

Particle identification during ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering experiment.

Figure 3

Two-dimensional plot of excitation energy and laboratory angles for outgoing ${}^{12}\mathrm{C}$ particles for the spectrometer central angle of $2.0^{\circ }$.

Figure 4

Example excitation spectrum obtained at scattering angle of $1.5^{\circ }$. The horizontal and vertical axes represent excitation energy and counts, respectively. The fitted spectrum for the 4.44 MeV excited state with the target and projectile excitation components is shown. The spectral shape for the ground state is used as the lineshape. The red and green curves show the phenomenological components of the projectile and target excitations, respectively. The arrows numbered 1, 2, and 3 show the peak positions for the 7.65 MeV ($0_2^{+}$) state, the 9.64 MeV ($3_1^{-}$) state, and the 10.30 MeV state, respectively.

Figure 5

Saturation curves obtained based on ESC, CEG07b, and MPa interactions. The horizontal and vertical axes represent the Fermi momentum and the binding energy per nucleon, respectively. The box shows the empirical value [36].

Figure 6

Calculated ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction cross sections for different complex $G$-matrix interactions and ${\sigma }_R$ data as a function of beam energy. The filled circles represent the reaction cross section experimental data of Takechi [51]; the other open symbols denote 1-ch calculations for the three kinds of interaction models.

Figure 7

1-ch calculation results for elastic-scattering differential cross sections for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering at $100A$ MeV based on ESC (solid curve), CEG07b (dashed curve), and MPa (dot-dashed curve) interaction models in center-of-mass frame.

Figure 8

Calculated reaction cross sections for the full-CC calculation with three kinds of interaction model. The results for several $N_W$ values are also shown.

Figure 9

Experimental and calculated differential cross sections with ESC model (without the 3BF) for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering at $100A$ MeV with $N_W=0.57$ in full-CC calculation.

Figure 10

Experimental and calculated differential cross sections with CEG07b model (with the 3BF) for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering at $100A$ MeV with $N_W=0.57$ in full-CC calculation.

Figure 11

Experimental and calculated differential cross sections with MPa model (with 3BF) for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering at $100A$ MeV with $N_W=0.57$ in full-CC calculation.

Figure 12

Experimental and calculated differential cross sections with MPa model (with the 3BF) for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering at $100A$ MeV with several $N_W$ values in full-CC calculation. The meaning of the curves is described in the text.

Figure 13

Elastic cross section for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ at $E/A=100$ MeV. The dotted and solid curves are the results with the ESC and MPa interactions, respectively. The dashed and dot-dashed curves are the results of the 2-ch (elastic and singe $2_1^{+}$ excited channels) and full-CC calculations with MPa, respectively.

Figure 14

Inelastic cross section for 4.44 MeV. The dotted and solid curves are the 2-ch (elastic and singe excited channels) results with ESC and MPa interactions, respectively. The dashed and dot-dashed curves are the 5-ch [elastic, singe $2_1^{+}$ excited, mutual $2_1^{+}$ excited ($J=0,2,4$) channels] and full-CC results with the MPa interaction, respectively.

Figure 15

Elastic and inelastic cross sections for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ at $E/A=100$ MeV. The dotted and dot-dot-dashed curves are the results with the ESC and MPa interactions, respectively. The meanings of the curves are described in the text.