Self-consistent calculations of quadrupole moments of the first 2${}^{+}$ states in Sn and Pb isotopes

A method of describing static moments of excited states and transitions between excited states is formulated for nonmagic nuclei within the Green's function formalism. Quadrupole moments of the first 2${}^{+}$ states in tin and lead isotope chains are calculated self-consistently using the energy density functional by Fayans et al. [Nucl. Phys. A 676, 49 (2000)]. Reasonable agreement with available experimental data is obtained. Quadrupole moments of unstable nuclei including ${}^{100}$Sn and ${}^{132}$Sn are predicted. A nontrivial dependence of the quadrupole moments on the neutron excess is found which can be traced to the negative proton contributions.

Figure 1

$g^2$ order corrections to the mass operator in magic nuclei. The circles with one wavy line in the first term are the phonon creation amplitudes $g$. The second term is the phonon tadpole.

Figure 2

Matrix element $M_{LL}$ in the form of Eq. (5).

Figure 3

Matrix elements for $M_{LL}^{\left(1\right)}$ and $M_{LL}^{\left(5\right)}$ for nonmagic nuclei.

Figure 4

Quadrupole moments of the first 2${}^{+}$ excited states in even Sn isotopes.

Figure 5

Same as in Fig. 4 but for Pb isotopes.