Quadrupole Collectivity in Neutron-Rich Fe and Cr Isotopes

Intermediate-energy Coulomb excitation measurements are performed on the $N\ge 40$ neutron-rich nuclei ${}^{66,68}\mathrm{Fe}$ and ${}^{64}\mathrm{Cr}$. The reduced transition matrix elements providing a direct measure of the quadrupole collectivity $B(E2;2_1^{+}\to 0_1^{+})$ are determined for the first time in ${}^{68}\mathrm{Fe}_{42}$ and ${}^{64}\mathrm{Cr}_{40}$ and confirm a previous recoil distance method lifetime measurement in ${}^{66}\mathrm{Fe}_{40}$. The results are compared to state-of-the-art large-scale shell-model calculations within the full $fpgd$ neutron orbital model space using the Lenzi-Nowacki-Poves-Sieja effective interaction and confirm the results of the calculations that show these nuclei are well deformed.

Figure 1

Doppler-corrected $\gamma$-ray spectra collected in coincidence with (a) ${}^{66}\mathrm{Fe}$, following Coulomb excitation on the thin $245\mathrm{mg}/{\mathrm{cm}}^2$ ${}^{209}\mathrm{Bi}$ target (b) ${}^{68}\mathrm{Fe}$, and (c) ${}^{64}\mathrm{Cr}$. In each case, the spectra include $\gamma$ rays in coincidence only with events detected in the S800 focal plane and scattering angles below the cutoff determined for safe impact parameters as described in the text. The fit of the GEANT simulation output (dot-dashed blue line) plus double exponential background (dashed green line) is shown in each case by the solid red line.

Figure 2

Systematics of $E(2_1^{+})$ (upper panels) and quadrupole collectivity (lower panels) along the Fe (left panels) and Cr (right panels) isotopic chains. Shell-model calculations using the state-of-the-art LNPS [7] effective interaction are shown by the solid red lines, using the effective charges of Dufour and Zuker [30] and the nucleon valence spaces as described in the text for $N=34$ through $N=42$. For the calculations at $N=32$, the neutron valence space excluded the $1g_{9/2}$ and $2d_{5/2}$ orbitals, but included the entire $pf$ shell required for description of the lighter isotopes. Available experimental data are shown in hollow black symbols, including results deduced, with an optical model dependence, from (p,p’) measurements [16]. The present results are shown as filled blue circles.

Figure 3

Calculated proton and neutron electric quadrupole ($2_1^{+}\to 0_1^{+}$) transition amplitudes in $e{\mathrm{fm}}^2$.