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Register a new userModification of the Nuclear Landscape in the Inverse Problem Framework using the Generalized Bethe-Weizs{a}cker Mass Formula
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The dependence on the structure functions and Z, N numbers of the nuclear binding energy is investigated within the inverse problem(IP) approach. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The IP was formulated for the numerical generalization of the semi-empirical mass formula of BW. It was solved in 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 MeV, starting from the number of protons and number of neutrons equal to 1. The set of parameters ${a_{i}}$, $i=1,dots, {mathcal{N}}_{rm{param}}$ of our fit represent the solution of an overdetermined system of nonlinear equations, which represent equalities between the binding energy $E_{B,j}^{rm{Expt}}(A,Z)$ and its model $E_{B,j}^{rm{Th}}(A,Z,{a_{i}})$, where $j$ is the index of the given isotope. The solution of the overdetermined system of nonlinear equations has been obtained with the help of the Aleksandrovs auto-regularization method of Gauss-Newton(GN) type for ill-posed problems. The efficiency of the above methods was checked by comparing relevant results with the results obtained independently. The explicit form of unknown functions was discovered in a step-by-step way using the modified least $chi^{2}$ procedure, that realized in the algorithms which were developed by Aleksandrov to solve nonlinear systems of equations via the GN method, lets us to choose between two functions with same $chi^{2}$ the better one. 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.
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The von Weizs{a}cker theorem states that every sequence of nonnegative random variables has a subsequence which is Ces`{a}ro convergent to a nonnegative random variable which might be infinite. The goal of this note is to provide a description of the set where the limit is finite. For this purpose, we use a decomposition result due to Brannath and Schachermayer.
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 numericaly generalized the semi-empirical mass formula of Bethe and von Weizs{a}cker. It was solved in step by step way based on the AME2012 nuclear database. The solution of the overdetermined system of nonlinear equations has been obtained with the help of the Aleksandrovs auto-regularization method of Gauss-Newton type for ill-posed problems. 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. These results help us to evaluate the borders of the nuclear landscape and show their limit. The efficiency of the applied approach was checked by comparing relevant results with the results obtained independently.
Nuclear Density Functional Theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the existence of a nuclear Energy Density Functional (EDF), yet its form is unknown. Current efforts to build a nuclear EDF are hindered by the lack of a strategy for systematic improvement. In this context, alternative approaches should be pursued and, so far, an unexplored avenue is that related to the inverse DFT problem. DFT is based on the one-to-one correspondence between Kohn-Sham (KS) potentials and densities. The exact EDF produces the exact density, so that from the knowledge of experimental or {it ab initio} densities one may deduce useful information through reverse engineering. The idea has already been proven to be useful in the case of electronic systems. The general problem should be dealt with in steps, and the objective of the present work is to focus on testing algorithms to extract the Kohn-Sham potential within the simplest ansatz from the knowledge of the experimental neutron and proton densities. We conclude that while robust algorithms exist, the experimental densities present some critical aspects. Finally, we provide some perspectives for future works.
The coupled-cluster wave function factorizes to a very good approximation into a product of an intrinsic wave function and a Gaussian for the center-of-mass coordinate. The width of the Gaussian is in general not identical to the oscillator length of the underlying single-particle basis. The quality of the separation can be verified by a simple procedure.
In this work, we propose a method to show the correspondence between hadron and its quark component nuclear modification factors. A parton and hadron cascade model PACIAE based on the PYTHIA6.4 is employed to calculate the hadron and its quark component nuclear modification factors in the 0-5% most central $Pb+Pb$ collisions at $sqrt{s_{NN}}$=2.76 TeV. It turns out that the hadron nuclear modification factor is usually smaller than that of its quark component. On the other hand, it is shown in our study that the dead cone effect is more likely to be identified with the quarks and mesons but not with the baryon states obviously.
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