Neutron number dependence of the energies of the $\gamma$-vibrational states in nuclei with $Z\sim 100$ and the manifestation of pseudospin symmetry

Background: The symmetry-guided methods have shown their power over many years of nuclear physics research. It was found that the concept of the pseudospin symmetry is very helpful in providing a simple explanation of many features of heavy nuclei.

Purpose: To show, based on the results of calculations of the energies of the $\gamma$-vibrational states in nuclei with $Z\sim 100$, that the experimental data on these energies will give us information indicating how well the pseudospin symmetry is realized in these exotic nuclei.

Method: The quasiparticle-phonon model is used to calculate the energies of the $\gamma$-vibrational states.

Results: It is shown that the energies of the $\gamma$-vibrational states in the Cm, Cf, Fm, No, and Rf isotopes considered as the functions of the number of neutrons $N$ have a minimum at $N=156$ when the neutron Fermi level lies just between the following neutron single particle levels: 3/2[622] and 1/2[620] which belong to the pseudospin doublet. It is shown that the corresponding two-quasiparticle component gives the main contribution to the structure of the $\gamma$ phonon.

Conclusion: The experimental information on the energies of the $\gamma$-vibrational states in nuclei with $Z\sim 100$ can be used to determine a splitting of the $\widetilde{\left[521\right]}$ pseudospin doublet.

Figure 1

The neutron single particle level scheme of the Woods-Saxon potential calculated with the parameters given in Table .

Figure 2

The proton single particle level scheme of the Woods-Saxon potential calculated with the parameters given in Table .