Nucleus density based new relationship of nuclear charge radius

Abstract

This paper we obtained the description and evaluation value of the nuclear charge radii by analyzes the relationship between nuclear masses and nuclear charge radii. We got 884 nuclei (<i>Z</i>, <i>N</i> ≥ 8) with known mass and charge radii by combining AME2020 database with CR2013 database, and then obtained the quality density <i>ρ<sub>m</sub></i> of 884 nuclear. Our purpose is to describe an empirical formula with one constant for <i>ρ<sub>m</sub></i> of nuclear masses that can be useful in describing and predicting nuclear charge radius with <i>Z</i> ≥ 8 and <i>N</i> ≥ 8. With the empirical formula and AME2020 database, the root-mean-square deviation (RMSD) of the nuclear charge radius that we have successfully obtained <i>σ</i> = 0.093 fm. Considering the impact of neutron numbers on <i>ρ<sub>m</sub></i>, we use the neutron factor 1/<i>N</i> to correct the empirical formula, and then the RMSD is reduced to <i>σ</i> = 0.047 fm (the accuracy is increased by about 50%). The second correction is shell effect of neutrons, results show that the RMSD of nuclear charge radius was reduced about 0.013 fm based on shell effect of neutrons. We used the empirical formula with corrections to predict nuclear charge radius (1573 nuclear charge radius with <i>Z</i>, <i>N</i> ≥ 8) that is difficult to measure experimentally. The difference between our predicted values based on AME2020 database and experimental values measured in recent years is in the allowable range of deviation. The result shows that the new relation for nuclear charge radius has simplicity and reliability. In addition, we deleted some nuclei with special shell effect and isotope chains, which the RMSD of the calculation value for 791 nuclei is reduced to <i>σ</i> = 0.032 fm. These results show that the new relation proposed in this paper can be comparable to <i>A</i><sup>1/3</sup> and <i>Z</i><sup>1/3</sup> formulas with corrections. Moreover, we study the 884 and 791 nuclear quality density by using L-M neural network method to build description and prediction models. Then obtained the calculated values and predicted values of nuclear charge radius. Comparing with CR2013, the RMSDs of nuclear charge radius are <i>σ</i> = 0.018 fm and <i>σ</i> = 0.014 fm, respectively. The RMSDs are reduced by about 50% than the empirical formula with corrections, and the predicted values are closer to the experimental values measured in recent years.