Two-nucleon emitters within a pseudostate method: The case of ${}^6\mathrm{Be}$ and ${}^{16}\mathrm{Be}$

Background: Since the first experimental observation, two-nucleon radioactivity has gained renewed attention since the early 2000s. The ${}^6\mathrm{Be}$ system is the lightest two-proton ground-state emitter, while ${}^{16}\mathrm{Be}$ was recently proposed to be the first two-neutron ground-state emitter ever observed. A proper understanding of their properties and decay modes requires a reasonable description of the three-body continuum.

Purpose: Study the ground-state properties of ${}^6\mathrm{Be}$ and ${}^{16}\mathrm{Be}$ within a general three-body model and investigate their nucleon-nucleon correlations in the continuum.

Method: The pseudostate (PS) method in hyperspherical coordinates, using the analytical transformed harmonic oscillator (THO) basis for three-body systems, is used to construct the ${}^6\mathrm{Be}$ and ${}^{16}\mathrm{Be}$ ground-state wave functions. These resonances are approximated as a stable PS around the known two-nucleon separation energy. Effective core-$N$ potentials, constrained by the available experimental information on the binary subsystems ${}^5\mathrm{Li}$ and ${}^{15}\mathrm{Be}$, are employed in the calculations.

Results: The ground state of ${}^{16}\mathrm{Be}$ is found to present a strong dineutron configuration, with the valence neutrons occupying mostly an $l=2$ state relative to the core. The results are consistent with previous $R$-matrix calculations for the actual continuum. The case of ${}^6\mathrm{Be}$ shows a clear symmetry with respect to its mirror partner, the two-neutron halo ${}^6\mathrm{He}$: The diproton configuration is dominant, and the valence protons occupy an $l=1$ orbit.

Conclusions: The PS method is found to be a suitable tool in describing the properties of unbound $\text{core}+N+N$ ground states. For both ${}^{16}\mathrm{Be}$ and ${}^6\mathrm{Be}$, the results are consistent with previous theoretical studies and confirm the dominant dinucleon configuration. This favors the picture of a correlated two-nucleon emission.

Figure 1

The three sets of scaled Jacobi coordinates.

Figure 2

Two-nucleon decay paths for (a) ${}^{16}\mathrm{Be}$ and (b) ${}^6\mathrm{Be}$.

Figure 3

Upper panel: $n\text{−}{}^{14}\mathrm{Be}$ phase shifts for $5/2^{+}$ states. Lower panel: Overlaps between ${}^{15}\mathrm{Be}$ continuum states and the ${}^{16}\mathrm{Be}$ ground state, with the maximum representing the resonance position. The shaded area corresponds to the experimental value [36].

Figure 4

The same as Fig. 3 but corresponding to the $p\text{−}{}^4\mathrm{He}$ (solid) and $n\text{−}{}^4\mathrm{He}$ (dashed) $3/2^{-}$ continuum, together with the experimental data on ${}^5\mathrm{Li}$ and ${}^5\mathrm{He}$ ground-state energies [37].

Figure 5

${}^{16}\mathrm{Be}$ spectra as a function of the THO parameter $\gamma$, which controls the level density after diagonalization. Calculations are provided for $b=0.7$ fm, $K_{\max }=30$, and $i_{\max }=15$. A stable PS around 1.3 MeV can be clearly identified.

Figure 6

As in Fig. 5 but changing the parameter $b$ while keeping $\gamma =2$ ${\mathrm{fm}}^{1/2}$.

Figure 7

Convergence of the ${}^{16}\mathrm{Be}$ ground-state energy as a function of (a) $K_{\max }$ and (b) $i_{\max }$. Calculations correspond to $\gamma =2.0$ ${\mathrm{fm}}^{1/2}$.

Figure 8

Ground-state probability of ${}^{16}\mathrm{Be}$, with the scale given in ${\mathrm{fm}}^{-2}$, as a function of $r_x\equiv r_{n\text{−}n}$ and $r_y\equiv r_{\left(nn\right)\text{−}{}^{14}\mathrm{Be}}$. The maximum corresponds to the dineutron configuration.

Figure 9

The same as Fig. 8 but without $n\text{−}n$ interaction. The dineutron configuration no longer dominates.

Figure 10

Convergence of the ${}^6\mathrm{He}$ ground-state (upper panel) and ${}^6\mathrm{Be}$ (lower panel) as a function of the maximum hypermomentum $K_{\max }$.

Figure 11

Ground-state probability of ${}^6\mathrm{He}$ as a function of $r_x\equiv r_{n\text{−}n}$ and $r_y\equiv r_{\left(nn\right)\text{−}{}^4\mathrm{He}}$.

Figure 12

Ground-state probability of ${}^6\mathrm{Be}$ as a function of $r_x\equiv r_{p\text{−}p}$ and $r_y\equiv r_{\left(pp\right)\text{−}{}^4\mathrm{He}}$.