Nuclear Mean-Field Hamiltonians and Factors Limiting Their Predictive Power

Dudek, J.; Rybak, K.; Szpak, B.; Porquet, M. G.; Molique, H.; Fornal, B.

doi:10.1142/s0218301310015060

Cited by 6 publications

(4 citation statements)

References 4 publications

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“…and observing the valley-patterns, seee.g.figure 2 in [20] and figures 2 and 3 below. With the help of this projection technique, we will determine the form of the parametric correlations between the four coupling constants, l l l l pp pn np nn { } , , , , see equations ( 27), (28).…”

Section: Parametric Correlations: Detection and Illustrationsmentioning

confidence: 94%

Predictive power of theoretical modelling of the nuclear mean field: examples of improving predictive capacities

Dedes

Dudek

2018

Phys. Scr.

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We examine the effects of the parametric correlations on the predictive capacities of the theoretical modelling keeping in mind the nuclear structure applications. The main purpose of this work is to illustrate the method of establishing the presence and determining the form of parametric correlations within a model as well as an algorithm of elimination by substitution (see text) of parametric correlations. We examine the effects of the elimination of the parametric correlations on the stabilisation of the model predictions further and further away from the fitting zone. It follows that the choice of the physics case and the selection of the associated model are of secondary importance in this case. Under these circumstances we give priority to the relative simplicity of the underlying mathematical algorithm, provided the model is realistic. Following such criteria, we focus specifically on an important but relatively simple case of doubly magic spherical nuclei. To profit from the algorithmic simplicity we chose working with the phenomenological spherically symmetric Woods-Saxon mean-field. We employ two variants of the underlying Hamiltonian, the traditional one involving both the central and the spin orbit potential in the Woods-Saxon form and the more advanced version with the self-consistent density-dependent spin-orbit interaction. We compare the effects of eliminating of various types of correlations and discuss the improvement of the quality of predictions ('predictive power') under realistic parameter adjustment conditions.

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Section: Parametric Correlations: Detection and Illustrationsmentioning

confidence: 94%

Predictive power of theoretical modelling of the nuclear mean field: examples of improving predictive capacities

Dedes

Dudek

2018

Phys. Scr.

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“…With a sample of N =20 000 sets η i , cf. the comments around equations (10)(11)(12), the parametric histograms resembling those in figure 2 have been obtained (using 11 level simulation); the noise width σ=0.1MeV. With each of the so obtained N =20 000 sets of parameters the results for the neutrons in 132 Sn nucleus have been obtained.…”

Section: Predictive Power: Examples Of Neutron Spectra In 132 Sn Nucleusmentioning

confidence: 99%

“…For that reason we refer to them as dynamical transforms of the input uncertainty distributions of the inverse problem. In the detailed illustrations, we distinguish among the variants such as the rms transforms represented by (10), induced parameter-transforms by (11), energy transforms by (12), etc. It will be instructive to illustrate the above notions using a simple but realistic phenomenological model.…”

Section: Uncertainty Distributions and Their Dynamical Transformsmentioning

confidence: 99%

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

Dudek¹,

Szpak²,

Porquet³

et al. 2010

J. Phys. G: Nucl. Part. Phys.

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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.

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Predictive power and theoretical uncertainties of mathematical modelling for nuclear physics

et al. 2013

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Nuclear Mean-Field Hamiltonians and Factors Limiting Their Predictive Power

Cited by 6 publications

References 4 publications

Predictive power of theoretical modelling of the nuclear mean field: examples of improving predictive capacities

Predictive power of theoretical modelling of the nuclear mean field: examples of improving predictive capacities

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

Predictive power and theoretical uncertainties of mathematical modelling for nuclear physics

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