Structural evolution in transitional nuclei of mass $82\le A\le 132$

In this theoretical study, we report an investigation on the behavior of two-neutron separation energy, a differential variation of the nucleon separation energy, the nuclear charge radii, and the single-particle energy levels along the isotopic chains of transitional nuclei. We have used the relativistic mean-field formalism with NL3 and NL3* forces for this present analysis. The study refers to the even-even nuclei such as Zr, Mo, Ru, and Pd for $N=42-86$, where a rich collective phenomena such as proton radioactivity, cluster or nucleus radioactivity, exotic shapes, island of inversion, etc. are observed. We found that there are few nonmonotonic aspects over the isotopic chain, which are correlated with the structural properties such as shell/subshell closures, the shape transition, clustering, magicity, etc. In addition to these, we have shown the internal configuration of these nuclei to get a further insight into the reason for these discrepancies.

Figure 1

The obtained results for nuclear relative binding energy difference ${\left(\mathrm{\Delta }E\right)}_B=E_B(N_F=18)-E_B(N_F=10–22)$, charge radius $r_{ch}$ and the quadruple deformation ${\beta }_2$ for ${}^{100,126}\mathrm{Zr}, {}^{102,128}\mathrm{Mo}, {}^{104,130}\mathrm{Ru}$, and ${}^{106,132}\mathrm{Pd}$ isotopes from NL3 and NL3* force parameter. See text for more details.

Figure 2

The potential energy surface of ${}^{82,90,110,120}\mathrm{Zr}$ as a function of quadrupole deformation parameter ${\beta }_2$ for both NL3 and NL3* forces in axially deformed relativistic mean field calculations.

Figure 3

The two-neutron separation energy as a function of neutron number from RMF theory with NL3 and NL3* force parameter for ${}^{82-126}\mathrm{Zr}, {}^{84-128}\mathrm{Mo}, {}^{86-130}\mathrm{Ru}$, and ${}^{88-132}\mathrm{Pd}$ nuclei are compared with the experimental data [82].

Figure 4

The differential variation of the two-neutron separation energy $d{S}_{2n}$ as a function of neutron number from RMF theory with NL3 and NL3* force parameter for ${}^{82-126}\mathrm{Zr}, {}^{84-128}\mathrm{Mo}, {}^{86-130}\mathrm{Ru}$, and ${}^{88-132}\mathrm{Pd}$ nuclei are compared with the experimental data [82].

Figure 5

The root-mean-square charge distribution $r_{ch}$ of ${}^{82-126}\mathrm{Zr}, {}^{84-128}\mathrm{Mo}, {}^{86-130}\mathrm{Ru}$, and ${}^{88-132}\mathrm{Pd}$ nuclei from RMF theory with NL3 and NL3* force parameter are compared with the experimental data [89].

Figure 6

The single-particle energy levels ${\epsilon }_i$ for ${}^{90}\mathrm{Zr}, {}^{104}\mathrm{Zr}, {}^{114}\mathrm{Zr}$, and ${}^{122}\mathrm{Zr}$ from RMF model with NL3 force parameter

Figure 7

The contour plot of the axially deformed ground-state density distribution of proton and neutron for ${}^{82}\mathrm{Zr}$ and ${}^{90}\mathrm{Zr}$.

Figure 8

The contour plot of the axially deformed ground-state density distribution of proton and neutron for ${}^{100}\mathrm{Zr}$ and ${}^{126}\mathrm{Zr}$.