Three-body model calculations for the ${}^{16}\mathrm{C}$ nucleus

We apply a three-body model consisting of two valence neutrons and the core nucleus ${}^{14}\mathrm{C}$ in order to investigate the ground state properties and electric quadrupole transition of the ${}^{16}\mathrm{C}$ nucleus. The discretized continuum spectrum within a large box is taken into account by using a single-particle basis obtained from a Woods-Saxon potential. The calculated $B(E2)$ value from the first $2^{+}$ state to the ground state shows good agreement with the observed data with the core polarization charge which reproduces the experimental $B(E2)$ value for ${}^{15}\mathrm{C}$. We also show that the present calculation accounts well for the longitudinal momentum distribution of the ${}^{15}\mathrm{C}$ fragment from the breakup of the ${}^{16}\mathrm{C}$ nucleus. We point out that the dominant ($d_{5/2}){}^2$ configuration in the ground state of ${}^{16}\mathrm{C}$ plays a crucial role in these agreements.

Figure 1

Upper panel: Two-particle density for the ground state of ${}^{16}\mathrm{C}$ obtained with parameter set D for single-particle potential as a function of $r_1=r_2=r$ and the angle between the valence neutrons, θ. It is weighted with a factor of $8{\pi }^2{r}^4\sin \theta$. Lower panel: Corresponding angular density weighted with a factor of $2\pi \sin \theta$. Solid line is the result of the three-body model calculation with the Minnesota potential. Dotted and dashed lines are for the pure configurations, as shown.

Figure 2

Same as Fig. 1, but for the second $0^{+}$ state of ${}^{16}\mathrm{C}$.

Figure 3

Longitudinal momentum distribution of the ${}^{15}\mathrm{C}$ fragment from the breakup reaction of ${}^{16}\mathrm{C}$ on ${}^{12}\mathrm{C}$ target at 83 MeV/nucleon, obtained with parameter set D. Contributions from the ${1/2}^{+}$ and ${5/2}^{+}$ states of ${}^{15}\mathrm{C}$ are also shown. Experimental data are from Ref. [21].