Nonrotational states in isotonic chains of heavy nuclei

The ground-state deformations of heavy nuclei are explored with the microscopic-macroscopic approach using the single-particle Woods-Saxon potential of the quasiparticle-phonon model. The calculations of the energies of low-lying nonrotational states take into account the residual pairing and phonon-quasiparticle interactions. The spectra of these states are presented for the $N=147–161$ isotones. The sensitivity of the calculated results to the parameters of the model is studied. A rather good description of the available experimental data is demonstrated.

Figure 1

Comparison of the calculated energies of single-particle levels in ${}^{251}\mathrm{Es}$ for the Woods-Saxon potential (closed symbols) and the TCSM potential (open symbols). The results for protons and neutrons are shown by circles and squares, respectively. The energies are counted from the corresponding Fermi energies $E_F$.

Figure 2

Contour plot of the potential energy of ${}^{253}\mathrm{Fm}$ as a function of ${\beta }_2$ and ${\beta }_4$. The energies are counted from the potential energy of spherical nucleus. The potential minimum is at ${\beta }_2=0.277$ and ${\beta }_4=0.037$.

Figure 3

Contour plot of the potential energy of ${}^{251}\mathrm{No}$ as a function of ${\beta }_2$ and ${\beta }_4$. The energies are counted from the potential energy of spherical nucleus. The potential minimum is at ${\beta }_2=0.266$ and ${\beta }_4=0.033$.

Figure 4

Contour plot of the potential energy of ${}^{286}\mathrm{Fl}$ as a function of ${\beta }_2$ and ${\beta }_4$. The energies are counted from the potential energy of spherical nucleus. There are two potential minimum at ${\beta }_2=-0.136,{\beta }_4=0.009$ and ${\beta }_2=0.161,{\beta }_4=-0.074$.

Figure 5

Nuclear shapes $R\left(\theta \right)$ of ${}^{286}\mathrm{Fl}$ in two potential minima shown in Fig. 4. The nuclear shapes for positive and negative values of ${\beta }_2$ are shown by solid and dashed lines, respectively. The nuclear shape shown by solid line is transformed into that shown by dotted line at ${\beta }_4=0$. The shape of spherical nucleus is shown by thin red line.

Figure 6

The spectra of low-lying nonrotational states in ${}^{249}\mathrm{Cm}$. The calculated results are obtained with various parameters of the WS potential and compared with the experimental data (exp) [57]. The second column presents the results obtained with the parameters from Table 2. In other columns, the results are obtained with indicated parameter for neutrons different from those given in Table 2. The depth of the WS potential is taken to be $V_0=54.25\pm 39.6(N-Z)/A$.

Figure 7

Calculated spectra of low-lying states are compared with the available experimental data [57] for $N=147$ isotones. The solid lines denote the states with one-quasiparticle component contributing more than $70\%$ of the norm. The dotted lines correspond to the states with the quasiparticle $\otimes$ phonon component exceeding $70\%$. Other states are denoted by the dashed lines. The value of $K$ in brackets means the tentative assignment.

Figure 8

The same as in Fig. 7, but for the $N=149$ isotones.

Figure 9

The same as in Fig. 7, but for the $N=151$ isotones.

Figure 10

The same as in Fig. 7, but for the $N=153$ isotones.

Figure 11

The same as in Fig. 7, but for the $N=155$ isotones.

Figure 12

The same as in Fig. 7, but for the $N=157$ isotones.

Figure 13

The same as in Fig. 7, but for the $N=159$ isotones.

Figure 14

The same as in Fig. 7, but for ${}^{269}\mathrm{Hs}$ as an example of nucleus with $N=161$.