# Test the accuracy of the Dubna phenomenological model of the masses of the atomic nuclei

## TL;DR

This paper evaluates the Dubna phenomenological model's accuracy in predicting atomic nuclei masses, confirming known magic numbers and demonstrating high reliability across a broad range of nuclei with minimal residual errors.

## Contribution

The study provides a reliability test of a generalized Bethe-Weizsacker mass formula, incorporating corrections for magic numbers, and confirms the existence of specific proton and neutron magic numbers.

## Key findings

- Model describes 2654 nuclei with accuracy between -1.90 and 1.80 MeV.
- Confirmed 10 proton and 11 neutron magic numbers.
- Only 14 nuclei have residuals exceeding 1.90 MeV.

## Abstract

In this paper is presented the reliability test the numerical generalization of Bethe-Weizsacker mass formula which describes the values of measured 2654 nuclei masses in AME2012 nuclear database: https://www-nds.iaea.org/amdc/, with accuracy in the interval (-1.90,1.80) MeV, for the nulear with mass number A=2(1,1) to 294(117,177). In the analyzed generalization of the Bethe-Weizsacker formula the little correction of proton and neutron magic numbers and boundaries of their influence was derived as a solution of nonlinear inverce problem (Ivanenko shell model!). There was confirmed the existence of ten proton (2,8,14,20,28,50,82,96,108,126) and eleven neutron (2,8,14,20,28,50,82,126,142,152,184) magic numbers. The test was performed analyzing the new data from Nuclide ground states: https://www-nds.iaea.org/relnsd/NdsEnsdf/QueryForm.html, containing 3182 data for A=2(1,1) to 294(118,176) and confirmed the above values of proton and neutron magic numbers. The accuracy of masses description is in the interval (-2.80,1.80) MeV. Only fourteen nuclear masses have bigger than 1.90 MeV residual.

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Source: https://tomesphere.com/paper/1704.04748