Excitations of the magic $N=50$ neutron-core revealed in ${}^{81}\mathrm{Ga}$

The high-spin states of the neutron-rich ${}^{81}\mathrm{Ga}$, with three valence protons outside a ${}^{78}\mathrm{Ni}$ core, were measured. The measurement involved prompt $\gamma$-ray spectroscopy of fission fragments isotopically identified using the combination of the variable mode spectrometer ($\mathrm{VAMOS}++$) and the advanced gamma tracking array (AGATA). The new $\gamma$-ray transitions, observed in coincidence with ${}^{81}\mathrm{Ga}$ ions, and the corresponding level scheme do not confirm the high-spin levels reported earlier. The newly observed high-spin states in ${}^{81}\mathrm{Ga}$ are interpreted using the results of state-of-the-art large-scale shell model (LSSM) calculations. The lower excitation energy levels are understood as resulting from the recoupling of three valence protons to the closed doubly magic core, while the highest excitation energy levels correspond to excitations of the magic $N=50$ neutron core. These results support the doubly magic character of ${}^{78}\mathrm{Ni}$ and the persistence of the $N=50$ shell closure but also highlight the presence of strong proton-neutron correlations associated with the promotion of neutrons across the magic $N=50$ shell gap, only few nucleons away from ${}^{78}\mathrm{Ni}$.

Figure 1

(Top) Normalized atomic number distribution for $A=81$ isotopes. (Bottom) Normalized mass distribution for $Z=31$ isotopes. The continuous red and dotted blue lines represent, respectively, the fit of the total distributions and individual mass and atomic charge contributions.

Figure 2

Tracked Doppler corrected $\gamma$-ray spectrum measured in coincidence with the isotopically identified ${}^{81}\mathrm{Ga}$. Known $\gamma$-ray transition energies are labeled and newly reported transitions are marked with star symbols. The inset shows the $\gamma \text{−}\gamma$ coincidence gated on the 813.6 keV transition in ${}^{81}\mathrm{Ga}$.

Figure 3

Experimental level scheme observed in the present work (left) and theoretical level scheme (right) of ${}^{81}\mathrm{Ga}$. Levels marked with red (blue) correspond to dominant contributions from 0 p-h (1 p-h) excitations of the ${}^{78}\mathrm{Ni}$ core.

Figure 4

Comparison between the ${\mathrm{\Delta }}_{\text{n}}$ shell gap at $N=50$ and the energy of core-excited states in $N=50$ isotones. Solid line: ${\mathrm{\Delta }}_{\text{n}}$ from binding energies [29, 49, 50]. Dashed-dotted line: ${\mathrm{\Delta }}_{\text{n}}$ from LSSM calculations. Symbols: excitation energy of core-excited states [48]. The dotted line represents ${\mathrm{\Delta }}_{\text{n}}$ using extrapolated mass for ${}^{80}\mathrm{Cu}$ (see text).

Figure 5

Theoretical predictions for excitation energies and decomposition of the wave functions for states in ${}^{78}\mathrm{Ni}$ [11] and ${}^{81}\mathrm{Ga}$ (this work). For ${}^{78}\mathrm{Ni}$ the spherical (left) and collective (right) states are shown. The histograms represent the distribution of total number of particle-hole excitations of the inert core ($n_{\text{p-h}}^{\nu }+n_{\text{p-h}}^{\pi }$) contributing to the state. The contribution of the excitations of the inert core due to the protons (red) and neutrons (blue) is represented in color in terms of probability in each level (the length of the color bar is normalized to 100% for each state), the white area corresponds to a closed inert core configuration. The relevant single-particle proton and neutron states are also shown.