The study of Nuclear binding energy for $A\geq100$ based on Odd-Even staggering of nuclear masses
The existing nuclear masses formula and nuclear masses model has undoubtedly achieved very good results, but it is still not satisfactory for some nuclear masses. Although there are many studies in Odd-Even staggering (OES) of nuclear masses, but the research on nuclear masses by using the systematicness of OES is indeed very few. Our purpose in this paper is to describe an empirical formula for Odd-Even staggering of nuclear masses that can be useful in describing and predicting nuclear masses. We empirically obtained the formula of odd-Z (odd-N) nuclei and even-Z (even-N) nuclei based on studying the OES of nuclear masses (AME2012). With the proton (neutron) empirical pairing gap from the OES of the binding energies and AME2012 database, the root-mean-square deviation of even-Z nuclei and odd-Z nuclei that we have successfully obtained 208 keV and 238 keV, respectively. The RMSD of even-N nuclei and odd-N nuclei is 222 keV and 240 keV. The result shows that our predicted values are compared well with values in AME2016, and some predicted values agree better with the experimental values. These results demonstrate that our empirical formulas have good accuracy and reliability. Another advantage of these formulas is that they use less known nuclear masses to predict unknown nuclear masses. In addition, this paper also uses BP neural network to study proton Odd-Even staggering of nuclear masses (even-Z and odd-Z nuclei) and neutron Odd-Even staggering of nuclear masses (even-N and odd-N nuclei). The RMSD of even-Z and odd-Z nuclei is 141 keV and 159 keV; the RMSD of even-N and odd-N nuclei is 150 keV and 160 keV. The results show that the RMSD of nuclear masses based on neural network 60-80 keV decrease than that based on empirical formula (the accuracy is increased by about 32%). Accurate nuclear mass is helpful to the research of nuclear physics, nuclear technology and astrophysics.