Bethe–Weizsäcker semiempirical mass formula coefficients 2019 update based on AME2016

Variational Inference with Vine Copulas: An efficient Approach for Bayesian Computer Model Calibration

“…Bayesian calibration has been especially popular because it enhances the understanding of nuclear model's structure through parameter estimation and potentially advances the quality of nuclear modeling by accounting for systematic errors. In this context, we use our variational Algorithm 2 to calibrate the 4-parameter Liquid Drop Model (LDM) (Myers and Swiatecki, 1966;Kirson, 2008;Benzaid et al, 2020) which is a global (across the whole nuclear chart) model of nuclear binding energies; the minimum energy needed to disassemble the nucleus of an atom into unbound protons and neutrons.…”

“…We use 2000 experimental binding energies randomly selected from the AME2003 dataset (Audi et al, 2003) (publicly available at http://amdc.impcas.ac.cn/web/masstab.html) for calibration, see Figure 4, and an additional set of 10 4 model evaluations. These were generated with the Latin hypercube design for the calibration inputs so that all the reasonable values of (a vol , a surf , a sym , a C ) given by the literature are covered (Weizsäcker, 1935 Bacher, 1936;Myers and Swiatecki, 1966;Kirson, 2008;Benzaid et al, 2020). The model inputs (Z, N ) were selected from the set of 2000 experimental binding energies, duplicated five-fold, and randomly permuted among the generated calibration inputs to span only the set of relevant nuclei.…”

“…First, we consider the independent Gaussian distributions centered at the LS estimates θL 2 (in Table 3) with standard deviations 7.5 × SE( θL 2 ) so that the calibration parameters used for generating the model runs are covered roughly within two standard deviations of the priors. Namely, The prior distributions for hyperparameters of the GP 's were selected as Gamma(α, β) with the scale parameter α and rate parameter β, so that they represent a vague knowledge about the scale of these parameters given by the literature on nuclear mass models (Weizsäcker, 1935;Bethe and Bacher, 1936;Myers and Swiatecki, 1966;Fayans, 1998;Kirson, 2008;McDonnell et al, 2015;Kortelainen et al, 2010Kortelainen et al, , 2012Kortelainen et al, , 2014Benzaid et al, 2020;Kejzlar et al, 2020).…”

“…C.2 Experimental design Kennedy and O'Hagan (2001) recommend to select the calibration inputs for the model runs so that the plausible value θ of the true calibration parameter is covered. In this context, we consider the space of calibration parameters to be centered at the values of least squares estimates θL 2 and broad enough to contain the majority of values provided by the nuclear physics literature (Weizsäcker, 1935;Bethe and Bacher, 1936;Myers and Swiatecki, 1966;Kirson, 2008;Benzaid et al, 2020). Table 4 gives the lower and upper bounds for the parameter space so that Lower bound = θL 2 − 15 × SE( θL 2 ) and Upper bound = θL 2 + 15 × SE( θL 2 ).…”

Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field: An investigation of propagating uncertainties for independent model parameters

“…For a defined mathematical model, the sampling (selection) and the quality of the experimental data will determine the resulting optimal parameter set and its quality. In principle, this can be done through the standard statistical fitting procedures, such as the least squares and χ 2 fitting [10][11][12][13]. Then the physical quantity can be computed using the 'optimal paremeters'.…”