Modification of the nuclear landscape in the inverse problem framework using the generalized Bethe–Weizsäcker mass formula

Abstract

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6[Formula: see text]MeV, starting from the number of protons and number of neutrons equal to 1. The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least [Formula: see text] procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss–Newton method, lets us to choose the better one between two functions with same [Formula: see text]. In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models.

Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120

“…The like linear dependences discovered in Z, N plane for all elements in Mendeleev table are illustrated. Recent published [3,[8][9][10][11][12][13][14][16][17][18][19][20] and presented herein results allow the suggestion that the resonant interaction of the electron shell and the nuclei causes the existence of the magic numbers.…”

“…In this paper we use the connections between atomic masses, nuclear masses, and mass excess as follows: [3,[16][17][18][19][20] , , = , , − , ,…”

“…The method of discovering the explicit form of the functions , , , , , , ℎ , , , , , , ! "# , , , , , 6 , & ' , , , 7 8 , , , 7 , , , 7 9 , , , 7 : , , , 7 ; , , and the calculated values of a set of unknown digital parameters is described in papers [3,[5][6][7][16][17][18][19][20] using the 3 overdetermined algebraic system of the equality of experimental values of equations (1,2,3) and their model, calculated from equation (4). The number of the experimental data from the data base [21,22] is M = 2536.…”

Computation of the Binding Energies in the Inverse Problem Framework

“…This in turn allows us to make a prediction for the binding energy, nuclear and atomic mass, and mass excess of the recently discovery nuclei at the DGFRS separator 39 , see Ref. 23 . Moreover, this finding together with the asymptotic behavior, and accurate predictions of the binding energies of all known isotopes allows us to obtain quite precise predictions for the location of the proton and neutron drip lines, and claim the exact number of bound nuclei in the nuclear landscape, see Fig.1.…”

“…(3) is beyond the focus of the current note, therefore for a curious reader we recommend this Ref. 23 for more detailed examination. However, note, that totally in our parametrization we use 17 linearly independent variables and 241 free parameters.…”