Light nuclei with semilocal momentum-space regularized chiral interactions up to third order
P. Maris, E. Epelbaum, R. J. Furnstahl, J. Golak, K. Hebeler, T. Hüther, H. Kamada, H. Krebs, Ulf-G. Meißner, J. A. Melendez, A. Nogga, P. Reinert, R. Roth, R. … 展开作者
P. Maris, E. Epelbaum, R. J. Furnstahl, J. Golak, K. Hebeler, T. Hüther, H. Kamada, H. Krebs, Ulf-G. Meißner, J. A. Melendez, A. Nogga, P. Reinert, R. Roth, R. Skibiński, V. Soloviov, K. Topolnicki, J. P. Vary, Yu. Volkotrub, H. Witała, T. Wolfgruber
We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$.
We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of …
We present a complete calculation of nucleon-deuteron scattering as well as ground and low-lying excited states of light nuclei in the mass range A=3-16 up through next-to-next-to-leading order in chiral effective field theory using semilocal coordinate-space regularized two- and three-nucleon forces. It is shown that both of the low-energy constants entering the three-nucleon force at this order can be reliably determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. The inclusion of the three-nucleon force is found to improv…
We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to $A=48$ using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N$^2$LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A \sim 10$ found in our earlier study utilizing the N$^2$LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. The resulting Hamiltonian can …
We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the…
We present results of the Hartree-Fock-Bogolyubov calculations performed using nuclear energy density functionals based on regularized functional generators at next-to-leading and next-to-next-to-leading order. We discuss properties of binding energies and pairing gaps determined in semi-magic spherical nuclei. The results are compared with benchmark calculations performed for the functional generator SLyMR0 and functional UNEDF0.
We developed new parameterizations of local regularized finite-range pseudopotentials up to next-to-next-to-next-to-leading order (N3LO), used as generators of nuclear density functionals. When supplemented with zero-range spin-orbit and density-dependent terms, they provide a correct single-reference description of binding energies and radii of spherical and deformed nuclei. We compared the obtained results to experimental data and discussed benchmarks against the standard well-established Gogny D1S functional.
[Background] Symmetry restoration and configuration mixing in the spirit of the generator coordinate method based on energy density functionals have become widely used techniques in low-energy nuclear structure physics. Recently, it has been pointed out that these techniques are ill-defined for standard Skyrme functionals, and a regularization procedure has been proposed to remove the resulting spuriosities from such calculations. This procedure imposes an integer power of the density for the density dependent terms of the functional. At present, only dated parameterizations of the Skyrme inte…
Ab initio charge form factors and radii of light isoscalar nuclei: Role of the two-body charge density
Forschungszentrum Jülich（于利希研究中心）；Ruhr-Universität Bochum（波鸿鲁尔大学）；Universität Bonn（波恩大学）；Helmholtz-Institut für Strahlen- und Kernphysik（亥姆霍兹射线与核物理研究所）；Bethe Center for Theoretical Physics（贝特理论物理中心）；Peng Huanwu Collaborative Center for Research and Education, International Institute for Interdisciplinary and Frontiers, Beihang University（北京航空航天大学国际交叉前沿研究院彭桓武教研协同中心）
We present preliminary results obtained with a finite-range two-body pseudopotential complemented with zero-range spin-orbit and density-dependent terms. After discussing the penalty function used to adjust parameters, we discuss predictions for binding energies of spherical nuclei calculated at the mean-field level, and we compare them with those obtained using the standard Gogny D1S finite-range effective interaction.
We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon-deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon-deuteron scattering data below pion production thresh…
The problem of the divergences which arise in beyond mean-field calculations, when a zero-range effective interaction is employed, has not been much considered so far. Some of us have proposed, quite recently, a scheme to regularize a zero-range Skyrme-type force when it is employed to calculate the total energy, at second-order perturbation theory level, in uniform matter. Although this scheme looked promising, the extension for finite nuclei is not straightforward. We introduce such procedure in the current paper, by proposing a regularization procedure that is similar, in spirit, to the one…
We apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation of state of nuclear matter with a zero-range effective interaction. The unphysical ultraviolet divergence that is generated at second order by the zero range of the interaction is removed by the regularization technique and the regularized equation of state (mean-field + second-order contributions) is adjusted to a reference equation of state. The main prac…
While ab initio many-body techniques have been able to successfully describe the properties of light and intermediate mass nuclei based on chiral effective field theory interactions, neutron-rich nuclei still remain out of reach for these methods. Conversely, energy density functional approaches can be used to calculate properties of heavy nuclei but rely mostly on phenomenological interactions. A usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces was presented recently. The first component of this new set of functionals corresponds to th…
In Landau theory of Fermi liquids, the particle-hole interaction near the Fermi energy in different spin-isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to constrain properties of nuclear energy density functionals in symmetric nuclear matter and finite nuclei. In this study, we present general expressions for Landau parameters corresponding to a two-body central local regularized pseudopotential. We also show results obtained for two recently adjusted NLO and N$^2$LO parametrizations. Such pseudopotentials will be use…
We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate suffici…
Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their effi…
Classes of two-nucleon ($2N$) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet $np$ scattering length and deuteron binding energy at LO, and $np$ and $pp$ scattering data in the laboratory-energy range 0--15 MeV at NLO and 0--25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for $T\,$=$\,0$ and the other for $T\,$=$\,1$ channels. The cutoffs are taken to vary in the ranges $R_0\,$=$(1.5$--2.3) fm and $R_1\,$=$(…
The complex scaling method (CSM) is a useful similarity transformation of the Schrödinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the $L^2$ basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lin…
We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology to low-energy phenomena in nuclei. They allow for defining the order of expansion in terms of the order of derivatives acting on the finite-range potential. Numerical calculations show a rapid convergence of the expansion and independence of results of the regularization scale.
We present a new two-body finite-range and momentum-dependent but density-independent effective interaction, which can be interpreted as a regularized zero-range force. We show that no three-body or density-dependent terms are needed for a correct description of saturation properties in infinite matter, that is, on the level of low-energy density functional, the physical three-body effects can be efficiently absorbed in effective two-body terms. The new interaction gives a very satisfying equation of state of nuclear matter and opens up extremely interesting perspectives for the mean-field and…
We investigate the influence of phenomenological three-nucleon interactions on the systematics of ground-state energies and charge radii throughout the whole nuclear mass range from 4-He to 208-Pb. The three-nucleon interactions supplement unitarily transformed two-body interactions constructed within the Unitary Correlation Operator Method or the Similarity Renormalization Group approach. To be able to address heavy nuclei as well, we treat the many-body problem in Hartree-Fock plus many-body perturbation theory, which is sufficient to assess the systematics of energies and radii, and limit o…
We present a high-accuracy calculation of the deuteron structure radius in chiral effective field theory. Our analysis employs the state-of-the-art semilocal two-nucleon potentials and takes into account two-body contributions to the charge density operators up to fifth order in the chiral expansion. The strength of the fifth-order short-range two-body contribution to the charge density operator is adjusted to the experimental data on the deuteron charge form factor. A detailed error analysis is performed by propagating the statistical uncertainties of the low-energy constants entering the two…
Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of ${A}$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the AGS form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coul…
