Three-body model for the two-neutron emission of ${}^{16}\mathrm{Be}$

Background: While diproton emission was first theorized in 1960 and first measured in 2002, it was first observed only in 2012. The measurement of ${}^{14}\mathrm{Be}$ in coincidence with two neutrons suggests that ${}^{16}\mathrm{Be}$ does decay through the simultaneous emission of two strongly correlated neutrons.

Purpose: In this work, we construct a full three-body model of ${}^{16}\mathrm{Be}$ (as ${}^{14}\mathrm{Be}+n+n$) in order to investigate its configuration in the continuum and, in particular, the structure of its ground state.

Method: In order to describe the three-body system, effective $n-{}^{14}\mathrm{Be}$ potentials were constructed, constrained by the experimental information on ${}^{15}\mathrm{Be}$. The hyperspherical $R$-matrix method was used to solve the three-body scattering problem, and the resonance energy of ${}^{16}\mathrm{Be}$ was extracted from a phase-shift analysis.

Results: In order to reproduce the experimental resonance energy of ${}^{16}\mathrm{Be}$ within this three-body model, a three-body interaction was needed. For extracting the width of the ground state of ${}^{16}\mathrm{Be}$, we use the full width at half maximum of the derivative of the three-body eigenphase shifts and the width of the three-body elastic scattering cross section.

Conclusions: Our results confirm a dineutron structure for ${}^{16}\mathrm{Be}$, dependent on the internal structure of the subsystem ${}^{15}\mathrm{Be}$.

Figure 1

Three Jacobi coordinate systems, (a) Jacobi $X$ system, (b) Jacobi $Y$ system, and (c) Jacobi $T$ system. Because the two neutrons are identical, the $X$ and $Y$ coordinate systems are identical.

Figure 2

Level scheme for ${}^{15}\mathrm{Be}$. The first column shows the shell-model calculation provided by [23], while the second column shows the ${}^{15}\mathrm{Be}$ levels that we used in this work; here, the shell model levels are lower by 1 MeV so the $1d_{5/2}$ state in the shell-model calculation reproduces the experimental $l=2$ energy from Ref. [17], as shown in the third column.

Figure 3

Convergence of the three-body energy as a function of the maximum $K$ value included in the model space.

Figure 4

Eigenphases as a function of three-body energy for ${}^{16}\mathrm{Be}$ models D (solid, black), D3B (dashed, red), DNN (dotted, green), and S (double-dash dotted, blue).

Figure 5

Three-body cross section as a function of three-body energy for ${}^{16}\mathrm{Be}$ models D (solid, black), D3B (dashed, red), DNN (dotted, green), and S (double-dash dotted, blue).

Figure 6

Three-body configurations: (a) dineutron (two neutrons close together and far from the core), (b) helicopter (two neutrons are close to the core and far from each other), and (c) three-body (the three bodies are equally spaced).

Figure 7

Three-body density as a function of the distance between the two neutrons ($r$) and the distance between the $nn$ pair and the core ($s$) for D3B. The scale on the right is given in ${\mathrm{fm}}^{-5}$.

Figure 8

Same as Fig. 7 for the model DNN.

Figure 9

Same as Fig. 7 for a plane wave solution of ${}^{16}\mathrm{Be}$, at $E_{3B}=1.35$ MeV, for comparison.