Borromean structures in medium-heavy nuclei

Borromean nuclear cluster structures are expected at the corresponding drip lines. We locate the regions in the nuclear chart with the most promising constituents, it being protons and $\alpha$ particles and investigate in details the properties of the possible Borromean two-$\alpha$ systems in medium-heavy nuclei. We find in all cases that the $\alpha$ particles are located at the surface of the core nucleus as dictated by Coulomb and centrifugal barriers. The two lowest three-body bound states resemble a slightly contracted ${}^8\text{Be}$ nucleus outside the core. The next two excited states have more complex structures but with strong components of linear configurations with the core in the middle. $\alpha$-removal cross sections would be enhanced with specific signatures for these two different types of structures. The even-even Borromean two-$\alpha$ nucleus, ${}^{142}\mathrm{Ba}$, is specifically investigated and predicted to have ${}^{134}\text{Te}\text{−}\alpha \text{−}\alpha$ structure in its ground state and low-lying spectrum.

Figure 1

The theoretical $\alpha$, neutron, and proton drip lines in the chart of nuclei, where nuclei with a negative separation energy have been marked in a corresponding color. Marked in green are ${}^{140}\text{Ba}$, ${}^{144}\text{Ce}$, and ${}^{148}\text{Nd}$, which represents nuclei of interest in the $\alpha$-drip-line region.

Figure 2

The two-body potentials for three different angular momenta (and corresponding potential depths). The potential depths are adjusted to give roughly the same energy as reflected by very similar minima. The depth of the interaction potential can be found in Table 1.

Figure 3

The two-body radial wave functions, $u$, for three different angular momenta (and corresponding potential depths).

Figure 4

Effective potentials [Eq. (8)] calculated from the five lowest ${\lambda }_n\left(\rho \right)$, for the case where $V_0=28.8\mathrm{MeV}$ and $J^{+}=0^{+}$. The horizontal lines correspond to the lowest, and first excited state of the lowest ${\lambda }_n\left(\rho \right)$, when it is approximated by a harmonic oscillator. It is noteworthy how similar the effective potentials are for the different ${\lambda }_n$ functions.

Figure 5

The probability distribution for the $0^{+}$ ground-state wave with the $\alpha$-core potential specified in Table 2. Projected contour curves are shown at the bottom of each figure. The distance variables correspond to the two different Jacobi sets, where top and bottom panels are for the first and second Jacobi sets, respectively.

Figure 6

The same as top panel of Fig. 5 for the three excited $0^{+}$ states.

Figure 7

The same as the top panel of Fig. 5 for the second and third excited $2^{+}$ states.

Figure 8

The same as the top panel of Fig. 5 for the second and third excited $4^{+}$ states.

Figure 9

The same as top panel of Fig. 5 for the lowest $0^{+}$, $2^{+}$, $4^{+}$, and $6^{+}$ ${}^{142}\mathrm{Ba}$ states.

Figure 10

The same as top panel of Fig. 5 for the first excited $0^{+}$ (top) and $2^{+}$ (bottom) states of ${}^{142}\mathrm{Ba}$.

Figure 11

The same as top panel of Fig. 5 for the lowest $1^{-}$ and $3^{-}$ states of ${}^{142}\mathrm{Ba}$.