Collectivity of light Ge and As isotopes

Background: The self-conjugate nuclei of the $A\sim 70$ mass region display rapid shape evolution over isotopic or isotonic chains. Shape coexistence has been observed in Se and Kr isotopes reflecting the existence of deformed subshell gaps corresponding to different shell configurations. As and Ge isotopes are located halfway between such deformed nuclei and the $Z=28$ shell closure.

Purpose: The present work aims at clarifying the low-lying spectroscopy of ${}^{66}$Ge and ${}^{67}$As, and providing a better insight into the evolution of collectivity in light even-even Ge and even-odd As isotopes.

Methods: We investigate the low-lying levels and collectivity of the neutron deficient ${}^{67}$As and ${}^{66}$Ge through intermediate-energy Coulomb excitation, inelastic scattering, and proton knockout measurements. The experiment was performed using a cocktail beam of ${}^{68}$Se, ${}^{67}$As, and ${}^{66}$Ge nuclei at an energy of 70–80 MeV/nucleon. Spectroscopic properties of the low-lying states are compared to those calculated via shell model with the JUN45 interaction and beyond-mean-field calculations with the five-dimensional collective Hamiltonian method implemented using the Gogny D1S interaction. The structure evolution of the lower-mass Ge and As isotopes is discussed.

Results: Reduced electric quadrupole transition probabilities $B\left(E2\right)$ have been extracted from the Coulomb-excitation cross sections measured in ${}^{66}$Ge and ${}^{67}$As. The value obtained for the $B(E2;0_1^{+}\to 2_1^{+})$ in ${}^{66}$Ge is in agreement with a recent measurement, ruling out the existence of a minimum at $N=34$ in the $B\left(E2\right)$ systematics as previously observed. New transitions have been found in ${}^{67}$As and were assigned to the decay of low-lying negative-parity states.

Figure 1

Identification of the isotopes produced in reaction from the ${}^{66}$Ge beam (a) and the ${}^{67}$As beam (b) impinging on a ${}^9$Be target. The atomic number is given by the energy loss $\Delta E$ in the ionization chamber at the S800 focal plane and $A/q$ by a time-of-flight measurement.

Figure 2

$\gamma$-ray spectra of ${}^{66}$Ge. The spectra correspond to the decay of excited states populated in the inelastic (red), Coulomb excitation (blue), and one-proton knockout channels (black), respectively. The level scheme deduced from the observed transitions is plotted in the inset. Transition energies are given in keV.

Figure 3

$B(E2\uparrow )$ transition probabilities for the 0${}_1^{+}$ $\to$ 2${}_1^{+}$ transition in ${}^{66}$Ge. The red and blue points corresponds to the results obtained for the 37${}^{\circ }$ and 90${}^{\circ }$ ring with their statistical error. The black line corresponds to the average obtained considering the results up to 2.5${}^{\circ }$, and the shaded area represents the error on the average.

Figure 4

Experimental [11, 48] and calculated $B(E2\uparrow )$'s for Ge isotopes from $N=32$ to $N=40$. The value for ${}^{66}$Ge from Ref. [28] is presented together with the one obtained with the RDDS technique [30] and our result. The measured values are compared with those calculated with shell model using the JUN45 [29] and the GXPF1A [43] interactions, and with 5DCH calculations based on the Gogny D1S force [45]. The 5DCH predictions are displayed without (continuous blue curve) and with (dotted blue curve) renormalized collective masses. For more details, see Sec. 4e.

Figure 5

$\gamma$-ray spectra of ${}^{67}$As. The red and blue lines correspond to the decay of excited states populated in the inelastic scattering and Coulomb excitation, respectively. Transition energies are given in keV and are between square brackets when no spin-parity assignment is can be argued based on the present data.

Figure 6

Proposed level scheme for ${}^{67}$As. The new transitions observed in this measurement and the corresponding transitions obtained via a shell-model calculation with the JUN45 interaction are presented.

Figure 7

$B(E2\uparrow )$ transition probabilities for the 5/2${}_1^{-}$ $\to$ $7/2_1^{-}$ and 5/2${}_1^{-}$ $\to$ $9/2_1^{-}$ transitions in ${}^{67}$As. The red and blue points correspond to the results obtained for the 37${}^{\circ }$ and 90${}^{\circ }$ ring with their statistical error. The black line corresponds to the average obtained considering the results up to 2.5${}^{\circ }$, and the shaded area represents the error on the average.

Figure 8

As isotopes with $32\le N\le 36$. Experimental (symbols) and shell-model (lines) energies (a), and spectroscopic quadrupole moments (b) of the first low-lying negative-parity states. Shell model calculations are performed in the f${}_{5/2}$pg${}_{9/2}$ model space with the JUN45 interaction.

Figure 9

Potential energy surfaces from ${}^{64}$Ge to ${}^{72}$Ge calculated with the HFB model using the Gogny D1S interaction. Red stars mark mean $\beta$ and $\gamma$ deformations of the ground states.

Figure 10

Comparison between experimental data and model predictions for ${}^{64–72}$Ge isotopes. (a) Spectroscopic quadrupole moments $Q_s$ for the 2${}_1^{+}$ and 2${}_2^{+}$ levels, (b) staggering parameter $S\left(4\right)$, and (c) branching ratio $R=B(E2;2_2^{+}\to 2_1^{+})/B(E2;2_2^{+}\to 0_1^{+})$. Shell-model (5DCH) calculations are shown as green (blue) curves. In panel (c) the shell-model predictions are scaled by 0.05 for ease of comparison with data. For references to measurements see text. The dashed line in panel (c) is for 5DCH calculations using renormalized masses.