Reduced transition strengths of low-lying yrast states in chromium isotopes in the vicinity of $N=40$

Background: In neutron-rich nuclei around $N=40$ rapid changes in nuclear structure can be observed. While ${}^{68}\mathrm{Ni}$ exhibits signatures of a doubly magic nucleus, experimental data along the isotopic chains in even more exotic Fe and Cr isotopes—such as excitation energies and transition strengths—suggest a sudden rise in collectivity toward $N=40$.

Purpose: Reduced quadrupole transition strengths for low-lying transitions in neutron-rich ${}^{58,60,62}\mathrm{Cr}$ are investigated. This gives quantitative new insights into the evolution of quadrupole collectivity in the neutron-rich region close to $N=40$.

Method: The recoil distance Doppler-shift (RDDS) technique was applied to measure lifetimes of low-lying states in ${}^{58,60,62}\mathrm{Cr}$. The experiment was carried out at the National Superconducting Cyclotron Laboratory (NSCL) with the SeGA array in a plunger configuration coupled to the S800 magnetic spectrograph. The states of interest were populated by means of one-proton knockout reactions.

Results: Data reveal a rapid increase in quadrupole collectivity for ${}^{58,60,62}\mathrm{Cr}$ toward $N=40$ and point to stronger quadrupole deformations compared to neighboring Fe isotopes. The experimental $B(E2$) values are reproduced well with state-of-the-art shell-model calculations using the LNPS effective interaction. A consideration of intrinsic quadrupole moments and ${\mathrm{B}}_{42}$ ratios suggest an evolution toward a rotational nature of the collective structures in ${}^{60,62}\mathrm{Cr}$. Compared to ${}^{58}\mathrm{Cr}$, experimental ${\mathrm{B}}_{42}$ and ${\mathrm{B}}_{62}$ values for ${}^{60}\mathrm{Cr}$ are in better agreement with the $E\left(5\right)$ limit.

Conclusion: Our results indicate that collective excitations in neutron-rich Cr isotopes saturate at $N=38$, which is in agreement with theoretical predictions. More detailed experimental data of excited structures and interband transitions are needed for a comprehensive understanding of quadrupole collectivity close to $N=40$. This calls for additional measurements in neutron-rich Cr and neighboring Ti and Fe nuclei.

Figure 1

Particle identification for the ${}^{58}\mathrm{Cr}$ setting. (a) Particles of the secondary beams are identified by means of a time-of-flight measurement. (b) Reacted beam particles are identified by their energy loss $\mathrm{\Delta }E$ in the ionization chamber and their time-of-flight through S800 (incoming particle gate is set on ${}^{59}\mathrm{Mn}$).

Figure 2

${}^{58}\mathrm{Cr}$, target-only $\gamma$-ray spectrum. The Doppler-shift-corrected experimental data for all detectors is shown in red (light gray; with errors), while the simulation is shown with a solid blue (dark gray) line. The feeding scheme as used in the simulation is depicted on the right side.

Figure 3

${}^{58}\mathrm{Cr}$, lifetime of the $6_1{}^{+}$ and $5_1^{-}$ states. The experimental spectrum (black dots with error bars) and the best simulated spectrum (red [light gray] solid line) are shown for the detector ring at $\theta \approx {30}^{\circ }$. Here, T (D) denotes the decay component behind the target (degrader).

Figure 4

${}^{58}\mathrm{Cr}$, plunger data. Comparison of experimental data (red [light gray] dots with error bars) and best simulation with $\tau \left({2_1}^{+}\right)=6.8$ ps and $\tau \left(4_1{}^{+}\right)=2.8$ ps (blue [dark gray] solid line) for (a) detectors at $\theta \approx {30}^{\circ }$ and (b) detectors at $\theta \approx {140}^{\circ }$. The spectra denoted with “short distances” are the sum of $0,25$, and 50 $\mu \mathrm{m}$.

Figure 5

${}^{60}\mathrm{Cr}$, target-only $\gamma$-ray spectrum. The experimental data (red [light gray] dots with errors) and the best simulation (blue [dark gray] solid line) are shown for the statistics of all detectors. The feeding scheme as used in the simulation is depicted on the right side.

Figure 6

${}^{60}\mathrm{Cr}$, lifetime of the $6_1{}^{+}$ state. The experimental spectrum (red [light gray] dots with errors) and the best simulation for a lifetime of 2 ps (black solid line) are shown for (a) detectors at $\theta \approx {30}^{\circ }$ and (b) detectors at $\theta \approx {140}^{\circ }$.

Figure 7

${}^{60}\mathrm{Cr}$, plunger data. Comparison of experimental data (red [light gray] dots with error bars) and best simulation with $\tau \left({2_1}^{+}\right)=26.5$ ps and $\tau \left(4_1{}^{+}\right)=5.2$ ps (blue [dark gray] solid line) for (a) detectors at $\theta \approx {30}^{\circ }$ and (b) detectors at $\theta \approx {140}^{\circ }$.

Figure 8

${}^{62}\mathrm{Cr}$, plunger data. Comparison of experimental data (red [light gray] dots with error bars) and best simulation with $\tau \left(2_1{}^{+}\right)=125$ ps and $\tau \left(4_1{}^{+}\right)=6.8$ ps (blue [dark gray] solid line) for (a) detectors at $\theta \approx {30}^{\circ }$ and (b) detectors at $\theta \approx {140}^{\circ }$. In the simulation a level scheme as depicted in the upper right spectrum is assumed.

Figure 9

Lifetimes of the $2_1^{+}$ and $4_1^{+}$ states in (a) ${}^{58}\mathrm{Cr}$, (b) ${}^{60}\mathrm{Cr}$, and (c) ${}^{62}\mathrm{Cr}$ as deduced from the decay curves. The experimental data are depicted in red (light gray) and the fitted decay curves are depicted in blue (dark gray). See text for further details.

Figure 10

The error analysis applied to the $2_1{}^{+}\to 0_1^{+}$ transition in ${}^{62}\mathrm{Cr}$. (a) Analysis of the statistical error $\mathrm{\Delta }{\tau }_{\text{t}}$. (b) Influence of degrader excitation on the deduced lifetime. Simulated data is shown in red (light gray) while fits are shown in blue (dark gray).

Figure 11

The evolution of first $2^{+}$ state energies for $N=26–52$ is shown in panel (a) and corresponding $B\left(E2\right)$ values are shown in panel (b). In panel (c) $B(E2$) values of Fe and Cr are compared to the scaled $B\left(E2\right)$ values of their VPS partner Se and Kr, respectively. The scaling factor is given by $Z={(Z_L/Z_H)}^2(A_L/A_H)$, where $Z_H$ and $A_H$ ($Z_L$ and $A_L$) denote the atomic and mass numbers of the the heavier (lighter) partner. See Ref. [55] for details.

Figure 12

Comparison of excitation energies (in MeV) and $B(E2$) values in ${}^{58,60,62}\mathrm{Cr}$ with SM calculations using the interaction LNPS [27], realistic SM calculations [31], and IBM-2 calculations [27]. Values on arrows indicate the $B(E2$) values in units of $e^2{\mathrm{fm}}^4$. The thickness of the arrows is proportional to the corresponding $B\left(E2\right)$ value. See text for details.

Figure 13

Occupation numbers in the wave functions of the ground states in ${}^{58,60,62}\mathrm{Cr}$ as calculated with the LNPS interaction. (a) Results for the proton $p_{3/2}$ and $f_{7/2}$ orbitals. (b) Results for the neutron $d_{5/2}$ and $g_{9/2}$ orbitals.