A new relation for nuclear masses based on the nuclide chain with the same number of neutrons

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. In this work, we analyze the relationship among the four neighboring nuclei based on the OES of nuclide chain with the same number of neutrons in atomic mass evaluation database (AME2016 database). Our purpose in this paper is to describe an empirical formula with one constant for OES of nuclear masses that can be useful in describing and predicting nuclear masses with mass number $A\ge 100$. With the empirical formula and AME2016 database, the root-mean-square deviation (RMSD) of the nuclei that we have successfully obtained 172$$keV for $A\ge 100$ (the RMSD is 140$$keV for $A\ge 158$). This paper also uses Levenberg–Marquart (L-M) neural network approach to study the OES of nuclear masses ($A\ge 100$, RMSD $\simeq 143$$$keV; $A\ge 158$, RMSD $\simeq 119$$$keV). The results show that the RMSD of nuclear masses for $A\ge 100$ based on neural network approach 30$$keV decreases than that based on empirical formula (the accuracy is increased by about 17%). In addition, the predicted values based on the empirical formula and L-M neural network approach are consistent with the values in AME2020 database, and the difference between our predicted values based on AME2016 database and experimental values measured in recent years is small. These results show that the new relation for nuclear masses has good simplicity, accuracy and reliability. Accurate nuclear mass is helpful to the research of nuclear physics, nuclear technology and astrophysics.