  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.
