$E1$ strength in ${}^{208}\mathrm{Pb}$ within the shell model

The dipole response of the doubly magic nuclide ${}^{208}\mathrm{Pb}$ was studied in photon-scattering experiments at the electron linear accelerator ELBE with bremsstrahlung produced at kinetic electron energies of 9.0 and 15.0 MeV. The present $(\gamma ,{\gamma }^{\prime })$ data combined with $(\gamma ,n)$ data from the literature are compared with results of shell-model calculations and calculations using a quasiparticle random-phase approximation. The shell-model calculations including (2p-2h) excitations describe the experimental $E1$ strength well and reproduce the spreading of the giant dipole resonance by applying a small smearing width only.

Figure 1

Part of a spectrum of photons scattered from ${}^{208}\mathrm{Pb}$ combined with ${}^{11}\mathrm{B}$, measured during the irradiation with bremsstrahlung produced by electrons of $E_e^{\mathrm{kin}}=15.0$ MeV. This spectrum is the sum of the spectra measured with the two detectors placed at ${127}^{°}$ relative to the beam. The most prominent peaks assigned to ground-state transitions from states in ${}^{208}\mathrm{Pb}$ are marked with their energies in keV.

Figure 2

Reduced $E1$ strengths for $0^{+}\to 1^{-}$ transitions in ${}^{208}\mathrm{Pb}$ resulting from the present shell-model calculations. (a, b) Pure (unmixed) (1p-1h) strengths for protons and neutrons, respectively. (c, d) Mixed (1p-1h) strength in different scales. Note that the dominating bars at about 11 and 12 MeV are cut in (d). (e) The (0p-0h) to $(1\mathrm{p}\text{−}1\mathrm{h})+(2\mathrm{p}\text{−}2\mathrm{h})$ strengths. (f) Includes (2p-2h) admixtures to the ground state.

Figure 3

Reduced $E1$ strengths for $0^{+}\to 1^{-}$ transitions in ${}^{208}\mathrm{Pb}$ resulting from the present QRPA calculations. (a, b) Strengths in different scales. Note that the dominating bars between 10 and 15 MeV are cut in (b).

Figure 4

Experimental integrated scattering cross sections deduced from the present $(\gamma ,{\gamma }^{\prime })$ experiments (red circles) compared with the ones deduced from the calculated $E1$ strengths shown in Fig. 2f (black bars).

Figure 5

Experimental photoabsorption cross sections deduced from the present $(\gamma ,{\gamma }^{\prime })$ experiments (red circles) and from $(\gamma ,n)$ experiments [67] (green squares) compared with the solutions of the shell-model calculations (black) and the QRPA calculations (blue), as shown in Figs. 2f and 3, respectively, but folded with Lorentz curves with a width of $\Gamma =0.5$ MeV. (a) Energy region up to 22 MeV. (b) Zooms in on the low-energy part below 10 MeV. The neutron-separation energy of 7.4 MeV is marked $S_n$.