New model of binding energies of heavy nuclei with $Z\ge 90$

A new form of the binding energy formula of heavy nuclei with $Z\ge 90$ is proposed where new terms beyond the standard Bethe and Weizsäcker formula are introduced by analytical expressions. This can be considered an interesting development of the Bethe and Weizsäcker mass formula for heavy nuclei with $Z\ge 90$. Two versions of the formulae are presented. The first version of the formula can reproduce the 117 known binding energies of nuclei with $Z\ge 90$ and $N\ge 140$ with an average deviation $0.118$ MeV. This is the first time that the binding energies of heavy nuclei with $Z\ge 90$ and $N\ge 140$ can be calculated very accurately by a formula with only seven parameters. The binding energies, α-decay energies, and α-decay half-lives of unknown superheavy nuclei are predicted. The second version of the formula is obtained by fitting the 181 data of nuclei with $Z\ge 90$ with nine parameters and good agreement with experimental binding energies is also reached for all nuclei with $Z\ge 90$.

Figure 1

The variation of the deviations between experimental binding energies and calculated ones for the cases with shell influence and without shell influence in the formula of binding energies of the 117 heavy nuclei with $Z\ge 90$ and $N\ge 140$.

Figure 2

The variation of the experimental and calculated α-decay energies with neutron number for even-even heavy nuclei with $Z\ge 92$.

Figure 3

The variation of the experimental and calculated two-neutron separation energies with neutron number for even-even nuclei with $Z\ge 90$.

Figure 4

The variation of the experimental (or estimated) and calculated one-proton separation energies with proton number for $N=152$ isotonic chain.

Figure 5

The variation of the experimental and calculated one-neutron separation energies with neutron number for $Z=94$ isotopic chain.

Figure 6

The variation of the deviations between experimental binding energies and calculated ones from the formula of binding energies of the 181 heavy nuclei.

Figure 7

The variation of the experimental and calculated average binding energies of even-even nuclei with $Z=90\text{−}94$ where the second version of the formula is used.

Figure 8

The variation of the experimental and calculated average binding energies of even-even nuclei with $Z=96\text{−}100$ where the second version of the formula is used.

Figure 9

The upper part of this figure is the variation of the experimental (or estimated) and calculated two-neutron separation energies of the uranium isotopes where the second version of the formula is used. The hollow circles with an arrow are estimated values from Audi et al. when experimental data are not available. The middle one of this figure is the variation of two-proton separation energies and the low one is that of α-decay energies of the uranium isotopes.