Decay of quadrupole-octupole $1^{-}$ states in ${}^{40}\mathrm{Ca}$ and ${}^{140}\mathrm{Ce}$

Background: Two-phonon excitations originating from the coupling of two collective one-phonon states are of great interest in nuclear structure physics. One possibility to generate low-lying $E1$ excitations is the coupling of quadrupole and octupole phonons.

Purpose: In this work, the $\gamma$-decay behavior of candidates for the ${(2_1^{+}\otimes 3_1^{-})}_{1^{-}}$ state in the doubly magic nucleus ${}^{40}\mathrm{Ca}$ and in the heavier and semimagic nucleus ${}^{140}\mathrm{Ce}$ is investigated.

Methods: $(\vec{\gamma },{\gamma }^{\prime })$ experiments have been carried out at the High Intensity $\gamma$-ray Source $\left(\mathrm{HI}\gamma \mathrm{S}\right)$ facility in combination with the high-efficiency $\gamma$-ray spectroscopy setup ${\gamma }^3$ consisting of HPGe and ${\mathrm{LaBr}}_3$ detectors. The setup enables the acquisition of $\gamma \text{−}\gamma$ coincidence data and, hence, the detection of direct decay paths.

Results: In addition to the known ground-state decays, for ${}^{40}\mathrm{Ca}$ the decay into the $3_1^{-}$ state was observed, while for ${}^{140}\mathrm{Ce}$ the direct decays into the $2_1^{+}$ and the $0_2^{+}$ state were detected. The experimentally deduced transition strengths and excitation energies are compared to theoretical calculations in the framework of EDF theory plus QPM approach and systematically analyzed for $N=82$ isotones. In addition, negative parities for two $J=1$ states in ${}^{44}\mathrm{Ca}$ were deduced simultaneously.

Conclusions: The experimental findings together with the theoretical calculations support the two-phonon character of the $1_1^{-}$ excitation in the light-to-medium-mass nucleus ${}^{40}\mathrm{Ca}$ as well as in the stable even-even $N=82$ nuclei.

Figure 1

Projected $\gamma$-ray spectra of (a) the HPGe detectors with HPGe-${\mathrm{LaBr}}_3$ coincidence condition, (b) the ${\mathrm{LaBr}}_3$ detectors with HPGe-${\mathrm{LaBr}}_3$ coincidence condition, (c) the HPGe detectors with HPGe-${\mathrm{LaBr}}_3$ coincidence condition and energy gate on the $2_1^{+}\to 0_1^{+}$ transition in the ${\mathrm{LaBr}}_3$ detectors, and (d) the ${\mathrm{LaBr}}_3$ detectors with HPGe-${\mathrm{LaBr}}_3$ coincidence condition and energy gate on the $2_1^{+}\to 0_1^{+}$ transition in the HPGe detectors after background subtraction. Arrows indicate a hypothetical $1_1^{-}\to 3_1^{-}$ transition. The data was taken in the measurement on ${}^{140}\mathrm{Ce}$ with a $\gamma$-beam energy of 3.6 MeV.

Figure 2

Singles $\gamma$-ray spectra of (a) HPGe detectors and (b) ${\mathrm{LaBr}}_3$ detectors. The data were taken in the measurement on ${}^{140}\mathrm{Ce}$ with a $\gamma$-beam energy of 3.6 MeV.

Figure 3

Experimental (left) and theoretical (right) decay pattern of the $1_1^{-}$ state in ${}^{140}\mathrm{Ce}$. The numbers indicate the transition strengths in mW.u. for $E1$ transitions (blue and green) and W.u. for $E2$ transitions (black).

Figure 4

Compilation of experimental (markers) and QPM (lines) data in $N=82$ isotones: (a) Excitation energies, (b) $E1$ transition strengths of $1^{-}\to J_f^{{\pi }_f}$ transitions, (c) $E2$ transition strengths.

Figure 5

Singles $\gamma$-ray spectrum of the HPGe detectors for the measurement on ${}^{40}\mathrm{Ca}$. The transitions within the excitation window defined by the beam profile (dashed curve) are labeled. Single (SE) and double (DE) escape peaks are visible at lower energies.

Figure 6

Low-energy part of the singles $\gamma$-ray spectrum obtained with the HPGe detectors. The insets show the energy regions where the $1_1^{-}\to 3_1^{-}$ (left) and $3_1^{-}\to 0_1^{+}$ (right) transitions are located.