Diproton correlation in the proton-rich Borromean nucleus ${}^{17}\mathrm{Ne}$

We carry out three-body-model calculations for a proton-rich Borromean nucleus ${}^{17}\mathrm{Ne}$ by assuming a ${}^{15}\mathrm{O}+p+p$ structure. To this end, we use a density-dependent contact interaction between the valence protons, explicitly treating also the Coulomb interaction. We find that the two-particle density distribution for ${}^{17}\mathrm{Ne}$ is similar to that for ${}^{16}\mathrm{C}$, which has two valence neutrons outside the $N=8$ core. That is, the two protons take a spatially compact configuration, while the Coulomb repulsion plays a minor role. This indicates that there is a strong diproton correlation in the ground state of the ${}^{17}\mathrm{Ne}$ nucleus. We also show that the Coulomb interaction reduces the expectation value of the proton-proton interaction by about $14\%$.

Figure 1

A low-lying level scheme of the ${}^{16}\mathrm{F}$ nucleus. Spin-averaged levels for two sets of resonance states are also shown. $V_b$ is the height of the Coulomb barrier between $p$ and ${}^{15}\mathrm{O}$.

Figure 2

The density distribution for the ground state of ${}^{17}\mathrm{Ne}$ (the upper panel) and of ${}^{16}\mathrm{C}$ (the lower panel). It is plotted as a function of $r=r_1=r_2$ and the opening angle between the valence nucleons ${\theta }_{12}$. A weight factor of $4\pi r^2·2\pi r^2\hspace{0.5em}\sin \hspace{0.5em}{\theta }_{12}$ has been multiplied.

Figure 3

The same as the upper panel of Fig. 2, but for the pure $[d_{5/2}]{}^2$ configuration.

Figure 4

The distribution of the second nucleon when the first nucleon is located at $(z_1,x_1)=(\sqrt{\langle r_{\mathrm{C}-2\mathrm{N}}^2\rangle },0)$. The upper and lower panels are for ${}^{17}\mathrm{Ne}$ and ${}^{16}\mathrm{C}$, respectively.