Instantaneous-shape sampling for calculation of the electromagnetic dipole strength in transitional nuclei

Electromagnetic dipole absorption cross sections of transitional nuclei with large-amplitude shape fluctuations are calculated in a microscopic way by introducing the concept of instantaneous-shape sampling, which is based on slow shape dynamics as compared with fast dipole vibrations. The dipole strength is calculated by means of the quasiparticle random-phase approximation (QRPA) for the instantaneous shapes, the probability of which is obtained by means of the interacting boson approximation. The calculations agree well with the experimental photoabsorption cross sections near the nucleon emission threshold, but they underestimate it at low energies. The cumulative cross sections for the region below the threshold are a factor of 2 too low.

Figure 1

Probability distributions of the instantaneous nuclear shapes over the $\beta \text{−}\gamma$ plane. Coexisting distributions are distinguished by their color.

Figure 2

Photoabsorption cross sections of ${}^{94}\mathrm{Mo}$. (a) Cross sections as calculated in QRPA with a narrow width of 0.1 MeV. MM: for the equilibrium deformation; ISS: QRPA averaged over the probability distributions for the shapes in Fig. 1. (b) Corresponding cross sections MM-CD and ISS-CD, respectively, as obtained in QRPA by folding with an energy-dependent Lorentzian (see text). The experimental data (black dots) are from Ref. [17] in both figures.

Figure 3

Same as Fig. 2, but for the energy range around the neutron emission threshold, where $S_n=9.68,9.15,8.64,8.29$ MeV for $N=52,54,56,58$, respectively. Data from Refs. [16, 17].

Figure 4

Same as Fig. 3, but the mean of the proton and neutron thresholds are $(S_p+S_n)/2=10.86,10.16,10.06$ MeV for $Z=38,40,42$, respectively. Data from Refs. [17, 18, 19].