Properties of ${}^{15}\mathrm{Be}\left(5/2^{+}\right)$

A simple ${\left(sd\right)}^3$ shell-model calculation has previously worked extremely well in predicting absolute energies of the lowest $5/2^{+}$ state in ${}^{19}\mathrm{O},{}^{17}\mathrm{C}$, and ${}^{13}\mathrm{Be}$. Here, I apply the same model to ${}^{15}\mathrm{Be}$. When combined with a recent experimental result, the analysis produces tight constraints on the $s$ and $d$ single-particle energies in ${}^{13}\mathrm{Be}$.

Figure 1

Relationship (with an uncertainty band) between the single-particle energies $E_s$ and $E_d$ to reproduce the absolute energy $[E_n=1.8\left(1\right),E_{3n}=0.53\left(16\right)\mathrm{MeV}]$ of the lowest $5/2^{+}$ state in ${}^{15}\mathrm{Be}$.