Neutron quadrupole transition strength in ${}^{10}\mathrm{C}$ deduced from the ${}^{10}\mathrm{C}(\alpha ,{\alpha }^{\prime })$ measurement with the MAIKo active target

Elastic and inelastic alpha scatterings on ${}^{10}\mathrm{C}$ were measured using a 68-MeV/u radioactive ${}^{10}\mathrm{C}$ beam incident on the recently developed MAIKo active target system. The phenomenological effective $\alpha \text{−}N$ interaction and the point-nucleon density distribution in the ground state were determined from the elastic scattering data. The cross sections of the inelastic alpha scattering were calculated using this interaction and density distribution and were compared with the experiment to determine the neutron quadrupole transition matrix element $M_n$ between the ground state and the $2_1^{+}$ state at $E_x=3.35$ MeV in ${}^{10}\mathrm{C}$. The deduced neutron transition matrix element is $M_n=6.9\pm 0.7\left(\mathrm{fit}\right)\pm 1.2\left(\mathrm{sys}\right){\mathrm{fm}}^2$. The ratio of the neutron transition strength to proton transition strength was determined as $M_n/M_p=1.05\pm 0.11\left(\mathrm{fit}\right)\pm 0.17\left(\mathrm{sys}\right)$, which indicates that the quadrupole transition between the ground state and the $2_1^{+}$ state in ${}^{10}\mathrm{C}$ is less neutron dominant compared to that in ${}^{16}\mathrm{C}$.

Figure 1

Schematic view of the EN course and the beamline detectors. The inset shows the details of the detector setup at F3.

Figure 2

Schematic view of the MAIKo active target.

Figure 3

Example of (a) anode and (b) cathode images acquired in an $\alpha +{}^{10}\mathrm{C}$ event. The reconstructed trajectories of the recoil particle are drawn with the solid red lines. The vertex and the track endpoints are shown by the cyan circles. The shaded area in the cathode image was excluded from the trigger condition.

Figure 4

Same as Fig. 3, but track images in an inelastic scattering event exciting a highly excited state above the proton decay threshold at $E_x=3.82$ MeV. The trajectories of two protons and two alpha particles from the breakup of ${}^{10}\mathrm{C}$ are thin because of the small energy loss.

Figure 5

PID of recoil particles in the measurement at 500 hPa. (a) Correlation between the total charge collected by the $\mu$-PIC and the range of the recoil particle. (b) Correlation between the energy measured with a silicon detector and the charge collected with the 32 cathode strips near the silicon detector.

Figure 6

Scatter plots of kinematic energies versus angles of recoil alpha particles. (a) All of the $\alpha +{}^{10}\mathrm{C}$ events. (b) The elastic and inelastic scattering events to low excited states selected by the FADC data. The red, blue, and green dots show the “500 hPa,” “1000 hPa,” and “Si” events, respectively. Kinematically calculated energies and angles of recoil alpha particles at different excitation energies in ${}^{10}\mathrm{C}$ are shown by the solid lines.

Figure 7

Excitation energy spectrum in the $\alpha +{}^{10}\mathrm{C}$ scattering at $E=68$ MeV/u and $6.9^{\circ }<{\theta }_{\mathrm{c}.\mathrm{m}.}<7.2^{\circ }$. The solid lines represent the fit result of $0_1^{+}$ (blue), $2_1^{+}$ (green), and sum of the two states (red), respectively.

Figure 8

Differential cross sections for the $\alpha +{}^{10}\mathrm{C}$ elastic (solid circles) and inelastic scatterings to the $2_1^{+}$ state at $E_x=3.35$ MeV (open squares). The cross section of the elastic scattering calculated with the optical-model potential is shown by the solid line, while the cross section of the inelastic scattering obtained by the DWBA calculation is shown by the dashed line.

Figure 9

Differential cross sections for the $\alpha +{}^{12}\mathrm{C}$ elastic scattering at 94 MeV/u (solid circles) compared with the previous results measured under the normal kinematic condition at 96 MeV/u (open squares) [34]. The solid line connecting the open squares is drawn to guide the eyes.

Figure 10

Point-nucleon distribution of the ground state in ${}^{10}\mathrm{C}$. The density distribution obtained from the present work is shown by the solid blue line associated with the error band. The dashed black line represents the AMD calculation [47].