arXiv subjects

M. Kortelainen

Publications and source records attributed to M. Kortelainen.

46 records · Page 3Linked to original sources

arXiv2010

Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization

In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test $χ^2$ function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.

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arXiv2010

Natural Units For Nuclear Energy Density Functional Theory

Naive dimensional analysis based on chiral effective theory, when adapted to nuclear energy density functionals, prescribes natural units and a hierarchy of contributions that could be used to constrain fits of generalized functionals. By applying these units, a large sample of Skyrme parametrizations is examined for naturalness, which is signaled by dimensionless coupling constants of order one. The bulk of the parameters are found to be natural, with an underlying scale consistent with other determinations. Significant deviations from unity are associated with deficiencies in the corresponding terms of particular functionals or with an incomplete optimization procedure.

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arXiv2010

Nuclear Energy Density Optimization

We carry out state-of-the-art optimization of a nuclear energy density of Skyrme type in the framework of the Hartree-Fock-Bogoliubov (HFB) theory. The particle-hole and particle-particle channels are optimized simultaneously, and the experimental data set includes both spherical and deformed nuclei. The new model-based, derivative-free optimization algorithm used in this work has been found to be significantly better than standard optimization methods in terms of reliability, speed, accuracy, and precision. The resulting parameter set UNEDFpre results in good agreement with experimental masses, radii, and deformations and seems to be free of finite-size instabilities. An estimate of the reliability of the obtained parameterization is given, based on standard statistical methods. We discuss new physics insights offered by the advanced covariance analysis.

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arXiv2010

The Negele-Vautherin density matrix expansion applied to the Gogny force

We use the Negele-Vautherin density matrix expansion to derive a quasi-local density functional for the description of systems of fermions interacting with short-ranged interactions composed of arbitrary finite-range central, spin-orbit, and tensor components. Terms that are absent in the original Negele-Vautherin approach owing to the angle averaging of the density matrix are fixed by employing a gauge invariance condition. We obtain the Kohn-Sham interaction energies in all spin-isospin channels, including the exchange terms, expressed as functions of the local densities and their derivatives up to second (next to leading) order. We illustrate the method by determining the coupling constants of the Skyrme functional or Skyrme force that correspond to the finite-range Gogny central force. The resulting self-consistent solutions reproduce the Gogny-force binding energies and radii within the precision of 1-2%.

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arXiv2010

Instabilities in the Nuclear Energy Density Functional

In the field of Energy Density Functionals (EDF) used in nuclear structure and dynamics, one of the unsolved issues is the stability of the functional. Numerical issues aside, some EDFs are unstable with respect to particular perturbations of the nuclear ground-state density. The aim of this contribution is to raise questions about the origin and nature of these instabilities, the techniques used to diagnose and prevent them, and the domain of density functions in which one should expect a nuclear EDF to be stable.

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arXiv2008

Local nuclear energy density functional at next-to-next-to-next-to-leading order

We construct nuclear energy density functionals in terms of derivatives of densities up to sixth, next-to-next-to-next-to-leading order (N3LO). A phenomenological functional built in this way conforms to the ideas of the density matrix expansion and is rooted in the expansions characteristic to effective theories. It builds on the standard functionals related to the contact and Skyrme forces, which constitute the zero-order (LO) and second-order (NLO) expansions, respectively. At N3LO, the full functional with density-independent coupling constants, and with the isospin degree of freedom taken into account, contains 376 terms, while the functionals restricted by the Galilean and gauge symmetries contain 100 and 42 terms, respectively. For functionals additionally restricted by the spherical, space-inversion, and time-reversal symmetries, the corresponding numbers of terms are equal to 100, 60, and 22, respectively.

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arXiv2008

Error analysis of nuclear mass fits

We discuss the least-square and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models' parameters, and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number dependent weights on uncertainties of liquid-drop global parameters.

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arXiv2008

Dependence of single-particle energies on coupling constants of the nuclear energy density functional

We show that single-particle energies in doubly magic nuclei depend almost linearly on the coupling constants of the nuclear energy density functional. Therefore, they can be very well characterized by the linear regression coefficients, which we calculate for the coupling constants of the standard Skyrme functional. We then use these regression coefficients to refit the coupling constants to experimental values of single-particle energies. We show that the obtained rms deviations from experimental data are still quite large, of the order of 1.1 MeV. This suggests that the current standard form of the Skyrme functional cannot ensure spectroscopic-quality description of single-particle energies, and that extensions of this form are very much required.

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arXiv2007

Short-range correlations and neutrinoless double beta decay

In this work we report on the effects of short-range correlations upon the matrix elements of neutrinoless double beta decay. We focus on the calculation of the matrix elements of the neutrino-mass mode of neutrinoless double beta decays of 48Ca and 76Ge. The nuclear-structure components of the calculation, that is the participant nuclear wave functions, have been calculated in the shell-model scheme for 48Ca and in the proton-neutron quasiparticle random-phase approximation (pnQRPA) scheme for 76Ge. We compare the traditional approach of using the Jastrow correlation function with the more complete scheme of the unitary correlation operator method (UCOM). Our results indicate that the Jastrow method vastly exaggerates the effects of short-range correlations on the neutrinoless double beta decay nuclear matrix elements.

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arXiv2002

Ordinary muon capture as a probe of virtual transitions of $ββ$ decay

A reliable theoretical description of double-beta-decay processes needs a possibility to test the involved virtual transitions against experimental data. Unfortunately, only the lowest virtual transition can be probed by the traditional electron-capture or $β^-$-decay experiments. In this article we propose that calculated amplitudes for many virtual transitions can be probed by experiments measuring rates of ordinary muon capture (OMC) to the relevant intermediate states. The first results from such experiments are expected to appear soon. As an example we discuss the $ββ$ decays of $^{76}$Ge and $^{106}$Cd and the corresponding OMC for the $^{76}$Se and $^{106}$Cd nuclei in the framework of the proton-neutron QRPA with realistic interactions. It is found that the OMC observables, just like the $2νββ$-decay amplitudes, strongly depend on the strength of the particle-particle part of the proton-neutron interaction.

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