Empirical mass formula with proton-neutron interaction

Takahiro Tachibana*, Masahiro Uno, Masami Yamada, So Yamada

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

76 Citations (Scopus)


An atomic mass formula consisting of a gross part, an average even-odd part, and an empirical shell part is presented. The gross part is, apart from a small atomic term, taken to be the sum of nucleon rest masses, Coulomb energies, and a polynomial in A 1 3 and |N - Z| A. The Coulomb term includes several parameters, which are determined mainly from comparison with the Coulomb displacement energies. The shell part includes, in addition to proton and neutron shell terms, a proton-neutron interaction term which represents the mutual support of nuclear magicities and the cooperative deformation effect. The average even-odd part, also including several parameters, is constructed so as to represent smoothed even-odd energies. Six coefficients in the polynomial in the gross part are fixed somewhat arbitrarily in order to avoid their drift to unreasonable values in the optimization procedure, while the remaining six coefficients, treated as adjustable parameters, and 269 shell parameters are determined from simultaneous considerations of fit to experimental data, charge symmetry, and reasonableness of the behavior of the shell parameters as functions of Z and N. The root-mean-square deviation of the calculated masses from the 1986 Wapstra et al. masses is 538 keV.

Original languageEnglish
Pages (from-to)251-258
Number of pages8
JournalAtomic Data and Nuclear Data Tables
Issue number2
Publication statusPublished - 1988 Jul

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics


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