Collectivity at $N=50$: ${}^{82}\mathrm{Ge}$ and ${}^{84}\mathrm{Se}$

The neutron-rich $N=50$ isotones ${}^{82}\mathrm{Ge}$ and ${}^{84}\mathrm{Se}$ were investigated using intermediate-energy Coulomb excitation on a ${}^{197}\mathrm{Au}$ target and inelastic scattering on ${}^9\mathrm{Be}$. As typical for intermediate-energy Coulomb excitation with projectile energies exceeding 70 MeV/nucleon, only the first $2^{+}$ states were excited in ${}^{82}\mathrm{Ge}$ and ${}^{84}\mathrm{Se}$. However, in the inelastic scattering on a ${}^9\mathrm{Be}$ target, a strong population of the first $4^{+}$ state was observed for ${}^{84}\mathrm{Se}$, while there is no indication of a similarly strong excitation of the corresponding state in the neighboring even-even isotone ${}^{82}\mathrm{Ge}$. The results are discussed in the framework of systematics and shell-model calculations using three different effective interactions.

Figure 1

Particle identification for the cocktail beam optimized on ${}^{82}\mathrm{Ge}$ after interaction with the gold target. Plotted is the energy loss measured with the S800 ionization chamber versus the time of flight measured between the plastic trigger scintillator at the back of the S800 focal plane and a timing scintillator at the spectrograph’s object position.

Figure 2

Projectile Coulomb excitation of ${}^{82}\mathrm{Ge}$ (top panel) and ${}^{84}\mathrm{Se}$ (bottom panel). The $\gamma$-ray energies are event-by-event Doppler reconstructed into the rest frame of the projectile using the angle information obtained from the segmentation of the SeGA detectors. Only one $\gamma$-ray transition, the de-excitation of the $2_1^{+}$ state, was observed in each nucleus. The inset shows a wider range of the ${}^{84}\mathrm{Se}$ $\gamma$-ray spectrum on a logarithmic scale; no other transitions were observed.

Figure 3

Coulomb excitation of ${}^{197}\mathrm{Au}$ induced by the ${}^{84}\mathrm{Se}$ projectile beam passing through the gold target (laboratory frame, $v/c=0$). The $\gamma$-ray transition corresponds to the de-excitation of the 547.5 keV $7/2^{+}$ state to the $3/2^{+}$ ground state.

Figure 4

$B(E2;0^{+}\to 2_1^{+})$ systematics of the $N=50$ isotones. The evolution of quadrupole collectivity along $N=50$ is compared to shell-model calculations with the jj4b [14] ($e_p=2.12$), jj4pna [14] ($e_p=2.03$), and the JUN45 [20] ($e_p=2.00$) effective interactions. The effective proton charge, $e_p$, was chosen for each interaction to get closest to the experimental data. The need for fairly high effective charges of $e_p\approx 2$ illustrates the importance of core excitations across the $N=50$ shell gap which are outside of the employed model space. The experimental data stems from the present work and references [6, 7, 17, 33, 35, 36].

Figure 5

$B(E2;0^{+}\to 2_1^{+})$ systematics of the selenium and germanium isotopic chains compared to calculations with the constrained Hartree-Fock Bogoliubov with mapping on the five-dimensional collective Hamiltonian [37] approach (top panel) and HFB calculations using the HFB-17 parametrization [38] (bottom panel). Experimental values are taken from [6, 7, 13, 33, 35] and the present work.

Figure 6

Event-by-event Doppler-reconstructed $\gamma$-ray spectra from ${}^{82}\mathrm{Ge}+{}^9\mathrm{Be}$ (top panel) and ${}^{84}\mathrm{Se}+{}^9\mathrm{Be}$ (bottom panel) inelastic scattering. The only $\gamma$-ray transition in ${}^{82}\mathrm{Ge}$ is the $2_1^{+}\to 0^{+}$ transition. An in-beam background spectrum, obtained from an off-prompt SeGA time gate, is overlayed. In the ${}^{84}\mathrm{Se}$ spectrum, an intense $\gamma$-ray transition at 667(4) keV is observed in addition to the decay of the $2_1^{+}$ state at 1454 keV.

Figure 7

Systematics of the $3_1^{-}$ states in the chain of Se isotopes (top panel) and the $N=50$ isotones (bottom panel). From both systematics one would expect the first $3^{-}$ state in ${}^{84}\mathrm{Se}$ to lie above or around 3-MeV excitation energy.