Dipole excitations via isoscalar probes: The splitting of the pygmy dipole resonance in ${}^{124}\mathrm{Sn}$

Inelastic $\alpha$-scattering excitation cross sections are calculated for electric-dipole excitations in ${}^{124}\mathrm{Sn}$ based on the transition densities obtained from the relativistic quasiparticle time-blocking approximation (RQTBA) in the framework of a semiclassical model. The calculation provides the missing link to directly compare the results from the microscopic RQTBA calculations to recent experimental data measured via the $(\alpha ,{\alpha }^{\prime }\gamma )$ reaction, which show a structural splitting of the low-lying $E1$ strength often denoted as pygmy dipole resonance (PDR). The experimentally observed splitting is reproduced by the cross-section calculations, which allows us to draw conclusion on the structure of the PDR.

Figure 1

(a) Bunching procedure for the strength distribution calculated within RQTBA, and (b) the obtained isoscalar and (c) electromagnetic reduced transition probabilities of the bunched states.

Figure 2

Inelastic cross sections as function of the excitation energy for the systems $\alpha +{}^{124}\text{Sn}$ at $E_{\alpha }=136$ MeV. The calculations are performed when only (a) the nuclear and (b) the Coulomb interaction is switched on. (c) The results when both interactions are working.

Figure 3

Ratios between the inelastic cross sections, calculated by putting to zero the energies of the states, to their corresponding $B\left(EL\right)$. The two panels show the results for (a) the nuclear and (b) the Coulomb excitations. The four black lines correspond to the four dipole states in Fig. 1 with the bigger response to the isoscalar probe.

Figure 4

Deflection function for the system $\alpha +{}^{124}\text{Sn}$ at $E_{\alpha }=136$ MeV. The horizontal dashed lines delimit the experimental $\alpha$-scattering-angle range. The vertical solid line determine the corresponding impact-parameter ranges.

Figure 5

Same as Fig. 2, in this case only the impact parameters intervals whose corresponding trajectories terminate to the measured scattering-angle range are taken into account.

Figure 6

Comparison of experimental and RQTBA-based cross section for the (upper row) $(\alpha ,{\alpha }^{\prime }\gamma )$ reaction and (lower row) $B_{em}\left(E1\right)$ values for ${}^{124}\mathrm{Sn}$. Experimental values are taken from Refs. [20, 38].

Figure 7

Comparison of experimental and RQTBA $(\alpha ,{\alpha }^{\prime }\gamma )$ cross sections for ${}^{124}\mathrm{Sn}$ in terms of their cumulative sums.