New model of binding energies of heavy nuclei with Z≥90

A new form of the binding energy formula of heavy nuclei with Z≥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≥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≥90 and N≥140 with an average deviation 0.118 MeV. This is the first time that the binding energies of heavy nuclei with Z≥90 and N≥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≥90 with nine parameters and good agreement with experimental binding energies is also reached for all nuclei with Z≥90.