Lowest excited $2^{+}$ and $3^{-}$ states in even-$A N=82$ and $N=126$ isotones from relativistic quasiparticle random-phase approximation

Excitation energy, reduced transition rates, and $g$ factors of the lowest $2^{+}$ and $3^{-}$ states of even-even $N=82$ and $N=126$ isotones are studied in relativistic QRPA formalism. These values are compared to available experimental data and some of the recent theoretical results. In the following the obtained results are presented first for $N=82$ isotones with $Z=36–72$, that is very neutron-rich to neutron-deficient nuclei with $N/Z$ varying from 2.28 to 1.14 and then for $N=126$ isotones with $Z=76–92$. These calculations are performed employing NL3, as well as its recently revised version $\mathrm{NL}{3}^{*}$ set of the RMF Lagrangian parameters. It is found that both the interaction sets produce almost similar results. The agreement with available data is rather satisfactory in view of such a wide range of nuclei considered here, though there are serious disagreements like in the case of ${}^{140}\mathrm{Ce}$ and properties of $3^{-}$ states of $N=126$ isotones.

Figure 1

Variation of $B\left(E2\right)\uparrow$ of tin isotopes with mass number $A$. Experimental data “Expt-a” represent the adopted values taken from [13] for $A=112–124$ and from Ref. [16] for $A=126–134$ (as reported in Ref. [11]). Expt-b indicates the latest values taken from Refs. [15, 16, 17, 18, 19]. The label NL3 indicates the RQRPA results [11] using the corresponding force parameters listed in Table 1. The shell model (SM) numbers are taken from Ref. [14].

Figure 2

Variation of binding energy per nucleon ($B/A$) with mass number $A$ for $N=82$ isotones. Experimental data are taken from Ref. [24].

Figure 3

Variation of $E_2, B(E2;0\to 2)$ and $g$ factor $g_2$ as a function of mass number for $N=82$ isotones. The labels Holt [2] and SMc [29] for $B\left(E2\right)$ and SMa [28], SMb [31] for $g_2$ represent shell model values and “expt” is the experimental data from Refs. [25, 30].

Figure 4

Variation of the neutron contribution $I_n$ to the total overlap $I$ normalized to unity as a function of the mass number for $N=82$ isotones. The upper panel (a) corresponds to the NL3 set of the parameters and the lower one to $\mathrm{NL}{3}^{*}$.

Figure 5

Variation of $E_{3^{-}}, B(E3;0\to 3^{-})$ and $g$ factor $g_3$ as a function of mass number for $N=82$ isotones. Experimental data taken from Ref. [33]. The label “Holt” indicates QRPA values of Holt et al. [2].

Figure 6

Same as Fig. 2 for $N=126$ isotones. Experimental data taken from Ref. [24].

Figure 7

Same as Fig. 3 for $N=126$ isotones. Experimental data taken from Ref. [25].

Figure 8

Same as Fig. 4 for $N=126$ isotones.

Figure 9

Same as Fig. 5 for $N=126$ isotones.