Least-squares fitting applied to nuclear mass formulas. Solution by the Gauss–Seidel method

In this paper, a numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear system which is solved by iterations according to the Gauss–Seidel scheme. The steps of the algorithm are given in detail. In practice, the method is very simple to implement and is able to treat large data in a very fast way. In fact, although this method has been illustrated here by specific examples, it can be applied without difficulty to any experimental or statistical data of the same type, i.e. those leading to linear system characterized by symmetric and positive-definite matrices.

A neural network approach based on more input neurons to predict nuclear mass

The study of nuclear mass is very important, and the neural network(NN) approach can be used to improve the prediction of nuclear mass for various models. Considering the number of valence nucleons of protons and neutrons separately in the input quantity of the NN model, the root-mean-square deviation of binding energy between data from AME2016 and liquid drop model calculations for 2314 nuclei was reduced from 2.385 MeV to 0.203 MeV. In addition, some defects in the Weizs\"{a}cker-Skyrme(WS)-type model were repaired, which well reproduced the two neutron separation energy of the nucleus synthesized recently by RIKEN RI Beam Factory [Phys. Rev. Lett 125 (2020) 122501]. The masses of some of the new nucleus appearing in the latest atomic mass evaluation(AME2020) are also well reproduced. However, the results of neural network methods for predicting the description of regions far from known atomic nuclei need to be further improved The study shows that such a statistical model can be a possible tool for searching in systematic of nuclei beyond existing experimental data.

The Nuclear Matter Density Functional under the Nucleonic Hypothesis

A Bayesian analysis of the possible behaviors of the dense matter equation of state informed by recent LIGO-Virgo as well as NICER measurements reveals that all the present observations are compatible with a fully nucleonic hypothesis for the composition of dense matter, even in the core of the most massive pulsar PSR J0740+6620. Under the hypothesis of a nucleonic composition, we extract the most general behavior of the energy per particle of symmetric matter and density dependence of the symmetry energy, compatible with the astrophysical observations as well as our present knowledge of low-energy nuclear physics from effective field theory predictions and experimental nuclear mass data. These results can be used as a null hypothesis to be confronted with future constraints on dense matter to search for possible exotic degrees of freedom.

The mass-charge binding energy as an explanation for the superfine adjustment of the hadron and baryon masses

Quantum chromodynamics (QCD) describes how mass is created at the quark level. This mechanism is special, because the binding of quarks does not result in a mass loss or a release of energy, as in the case of the nuclear mass defect. Rather, mass is created by the binding of quarks. To achieve this binding, energy must be expended. At the same time, however, quarks are firmly bound to each other. Several authors have shown that the masses of the elementary particles as determined by means of QCD agree quite well with the experimentally determined values. In the following, superfine adjustment of the masses of the charged elementary particles is shown to be possible by considering the mass defect in terms of the mass-charge binding energy.