Pygmy dipole resonances in the tin region

The evolution of the low-energy electromagnetic dipole response with the neutron excess is investigated along the Sn isotopic chain within an approach incorporating Hartree-Fock-Bogoljubov (HFB) and multiphonon quasiparticle-phonon model (QPM) theory. General aspects of the relationship of nuclear skins and dipole sum rules are discussed. Neutron and proton transition densities serve to identify the pygmy dipole resonance (PDR) as a generic mode of excitation. The PDR is distinct from the GDR by its own characteristic pattern given by a mixture of isoscalar and isovector components. Results for the ${}^{100}\mathrm{Sn}$-${}^{132}\mathrm{Sn}$ isotopes and the several $N=82$ isotones are presented. In the heavy Sn isotopes the PDR excitations are closely related to the thickness of the neutron skin. Approaching ${}^{100}\mathrm{Sn}$ a gradual change from a neutron to a proton skin is found and the character of the PDR is changed correspondingly. A delicate balance between Coulomb and strong interaction effects is found. The fragmentation of the PDR strength in ${}^{124}\mathrm{Sn}$ is investigated by multiphonon calculations. Recent measurements of the dipole response in ${}^{130,132}\mathrm{Sn}$ are well reproduced.

Figure 1

Ground state properties of the Sn isotopes. The nuclear binding energies per particle calculated with the DFT approach, discussed in the text, are compared to data from the Audi-Wapstra compilation [12].

Figure 2

BCS ground-state densities of Sn isotopes obtained by the phenomenological DFT approach and used in the QPM calculations.

Figure 3

QPM results for the total PDR strengths in the ${}^{100-132}\mathrm{Sn}$ isotopes (upper panel) are displayed for comparison together with the nuclear skin thickness $\delta r$, Eq. (2.10) (lower panel). Experimental data on the total PDR strengths in ${}^{116}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$ [36] and ${}^{112}\mathrm{Sn}$ [37] are also shown. In the lower panel, the skin thickness derived from charge exchange reactions by Krasznahorkay et al. [16, 17] are indicated.

Figure 4

QRPA results for the one-phonon dipole transition densities in $N=82$ nuclei.

Figure 5

QRPA results for the one-phonon dipole transition densities in ${}^{112,122,132}\mathrm{Sn}$ nuclei.

Figure 6

QRPA results for the one-phonon dipole transition densities in ${}^{100}\mathrm{Sn}$.

Figure 7

QRPA results for the PDR and GDR strength distributions in ${}^{100,116,122,124,132}\mathrm{Sn}$ isotopes.

Figure 8

Electromagnetic dipole response in ${}^{124}\mathrm{Sn}$ from (a) QRPA calculations; (b) Distributions of the PDR QRPA phonons over the $1^{-}$ excited states in terms of one-phonon amplitudes $R^2$ defined with Eq. (4.9); (c) QPM with up to three-phonon configuration space, including 250 components; (d) experimental data from Ref. [36] up to excitation energies $E^{*}=7.5$ MeV.

Figure 9

Electromagnetic QRPA dipole response function and LAND-FRS data [5] for ${}^{130}\mathrm{Sn}$. The QRPA results (left) were obtained by solving the Dyson equation and include the decay widths from particle emission. In the right panel the theoretical response function has been folded with the experimental acceptance filter [47] (dashed line) and is compared to the data (symbols).

Figure 10

Electromagnetic QRPA dipole response function and LAND-FRS data [5] for ${}^{132}\mathrm{Sn}$. As in Fig. 9 the QRPA results (left) include the decay widths from particle emission. In the right panel the theoretical response function has been folded with the experimental acceptance filter [47] (dashed line) and is compared to the data (symbols).