Nuclear Hamiltonians: the question of their spectral predictive power and the associated inverse problem

Abstract

In this article we introduce a subjective notion of the predictive power of nuclear Hamiltonians (an objective one does not exist) and examine it in the particular context of the single-nucleon energy spectra. We consider various types of uncertainties originating both from the experiment and theory stressing the dominating character of the theoretical errors. The latter originate from the complexity of the nuclear many body systems that is not matched adequately by the formalism behind the present day nuclear Hamiltonians. The related inverse problem is formulated and the presence of errors (ignorance, lack of knowledge) is parametrized in terms of the associated probability distributions. Various hypotheses concerning the input uncertainties ('numerical noise') are formulated and the impact of the input-uncertainties in the adjustment procedures down to the final parameter values and theoretical spectra is illustrated and discussed. A number of Open Problems are formulated and listed at the end of the article.

Dynamics of nuclear single-particle structure in covariant theory of particle-vibration coupling: From light to superheavy nuclei

“…In the second procedure, the center of gravity of the fragmented levels with a given quantum number j π (j is the total angular momentum and π is a parity) and energies ε ν k is obtained via weighted-average [32,33] procedure…”

“…[33] for a number of levels. However, even in this case the accuracy of the definition of ε grav k is not known because of the number of the reasons listed below.…”

“…However, even in this case the accuracy of the definition of ε grav k is not known because of the number of the reasons listed below. The absolute values of spectroscopic factors are characterized by large ambiguities and depend strongly on the reaction employed in experiment and the reaction model used in the analysis [33,34] [38] and Table III in the current manuscript). In addition, the spins and parities of many high-lying fragments are uncertain (see, for example, Table 1 in Ref.…”

Propagation of uncertainties in the Skyrme energy-density-functional model

“…New experimental data on nuclei with a large neutron or proton excess will put predictions of the current and future EDF models to the test. Therefore, it is important to assess the uncertainties and predictive power of models [1][2][3][4].…”

Spectroscopic Properties of Nuclear Skyrme Energy Density Functionals

“…They are usually associated with masses and spectra of odd nuclei by considering the socalled spectroscopic factors related to probabilities of one-nucleon transfer reactions. Different analyses of this type exist in the literature, and for the purpose of the present study, we use those of Grawe et al [31][32][33] (data set A), Schwierz et al [34] (data set B), and Porquet et al [35][36][37] (data set C). In addition, we also compare our results to two derived or reduced data sets: (i) data set M, which contains average values of SPEs simultaneously listed in data sets A, B, and C, provided the three energies agree with the average values within 200 keV, and (ii) data set S, which contains a subset of data set B for spectroscopic factors larger than 0.8.…”