Microscopic particle-rotor model for the low-lying spectrum of $\Lambda$ hypernuclei

We propose a novel method for low-lying states of hypernuclei based on the particle-rotor model, in which hypernuclear states are constructed by coupling the hyperon to low-lying states of the core nucleus. In contrast to the conventional particle-rotor model, we employ a microscopic approach for the core states; that is, the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this microscopic particle-rotor model to ${}_{\Lambda }^9\mathrm{Be}$ as an example employing a point-coupling version of the relativistic mean-field Lagrangian. A reasonable agreement with the experimental data for the low-spin spectrum is achieved using the $\Lambda N$ coupling strengths determined to reproduce the binding energy of the $\Lambda$ particle.

Figure 1

The low-energy excitation spectra of ${}^8\mathrm{Be}$ [columns (a) and (b)] and ${}_{\Lambda }^9\mathrm{Be}$ [columns (c)–(i)]. For ${}^8\mathrm{Be}$, the full GCM+PN1DAMP calculations shown in column (a) are compared with the experimental data taken from Ref. [40]. For ${}_{\Lambda }^9\mathrm{Be}$, columns (c), (d), and (e) show the results of the single-channel calculations for the $\Lambda$ particle in the $s_{1/2}$, $p_{1/2}$, and $p_{3/2}$ channels, respectively. Columns (f), (g), and (h) show the results of the coupled-channels calculations, which are compared with the experimental data [1, 42, 43] shown in column (i).