Bethe–Weizsa ¨cker semiempirical mass formula coefficients 2019 update based on AME2016 Djelloul Benzaid 1 • Salaheddine Bentridi 1 • Abdelkader Kerraci 1 • Naima Amrani 2 Received: 26 September 2019 / Revised: 13 November 2019 / Accepted: 18 November 2019 Ó China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, Chinese Nuclear Society and Springer Nature Singapore Pte Ltd. 2020 Abstract In the present work, the classical Bethe–Weiz- sa ¨cker (BW) mass formula with five energy terms is revisited and updated. We use the least-squares adjust- ments on the binding energy of 2497 different nuclides from the last update of the atomic mass evaluation, AME2016 published in March 2017, to provide a new set of energy coefficients of the mass formula. The obtained set of formula coefficients allowed us to reproduce most of the experimental values of the binding energies for each nucleus with A  50. The comparison between the binding energies provided with updated mass formula and those of AME2016 on the one hand, and those of previous works, on the other hand, yields relative errors that oscillate between less than 0:05% and 1:5%. The revisited BW formula is in very good agreement with the experimental data. Keywords Binding energy of atomic nuclei  Mass formula coefficients  AME2016  Least-squares adjustments 1 Introduction The semiempirical mass formula (SEMF), usually known as Bethe–Weizsa ¨cker formula, has been developed to most effectively describe the binding energy of any given nucleus at the ground level. In the classical expres- sion, the binding energy is represented as a function of atomic number Z, neutron number N and mass number A ¼ Z þ N, using five energy coefficients. Each energy coefficient represents an aspect of the binding energy in the liquid-drop model of the nucleus. Considered to be a spherical-like volume with a radius defined as R ¼ r 0 A 1 3 , the stability of the nucleus is based mainly on its volume energy term as a contribution of each nucleon to nuclei cohesion. According to the adopted model, negative con- tributions should be considered and therefore subtracted from the cohesion component, namely surface tension term, electrical repulsion term (Coulombian term) and asymmetrical term. The contribution of the parity term is given as a delta function of the parity values of both Z and N, and it may be a negative, null or positive contribution. Except for the Coulombian coefficient which may be obtained by analytical calculations (a c  0:7 MeV), the remaining energy coefficients are obtained via experi- mental data from nuclear reactions, resulting in updated nuclear mass data. Using these data, one may deduce a set of the energy coefficients of the Bethe–Weizsa ¨cker (BW) mass formula using numerical methods. The aim of the present work is to obtain a new set of energy coefficients (including the Coulombian coefficient used as the coher- ence referring term) based on an update of the nuclear masses table (AME2016), which was processed using numerical code that we developed based on the least- squares adjustments method. & Djelloul Benzaid d.benzaid@univ-dbkm.dz 1 Laboratory of Energy and Smart Systems, University of Khemis Miliana, Route de Theniet El Had, 44225 Ain Defla, Algeria 2 Dosing, Analysis and Characterization in High Resolution Laboratory, Physics Department, Faculty of Sciences, Ferhat ABBAS University, 19000 Se ´tif-1, Algeria 123 NUCL SCI TECH (2020) 31:9 https://doi.org/10.1007/s41365-019-0718-8