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![Hierarchy of nuclear degrees of freedom and associated energy scales [2] (courtesy of Oak Ridge National Laboratory, US Department of Energy).](profile/Kai-Hebeler/publication/258282471/figure/fig2/AS:11431281207412170@1701181948278/Hierarchy-of-nuclear-degrees-of-freedom-and-associated-energy-scales-2-courtesy-of-Oak.jpg)
Hierarchy of nuclear degrees of freedom and associated energy scales [2] (courtesy of Oak Ridge National Laboratory, US Department of Energy).
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We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to...
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Citations
... The use of interactions based on chiral effective field theory (EFT) [14][15][16][17] and polynomially scaling many-body methods [18][19][20][21] has allowed for a rapid extension of the reach of ab initio methods both in terms of mass number A and of observables of interest. For applications across the nuclear chart, low-resolution interactions, either fit with a low-momentum cutoff Λ or obtained from a similarity renormalization group (SRG) evolution [22,23] have proven especially successful [24][25][26][27][28]. In particular, they offer good convergence properties with respect to both model space size and expansion order of the many-body ...
... The use of interactions based on chiral effective field theory (EFT) [14][15][16][17] and polynomially scaling many-body methods [18][19][20][21] has allowed for a rapid extension of the reach of ab initio methods both in terms of mass number A and of observables of interest. For applications across the nuclear chart, low-resolution interactions, either fit with a low-momentum cutoff Λ or obtained from a similarity renormalization group (SRG) evolution [22,23] have proven especially successful [24][25][26][27][28]. In particular, they offer good convergence properties with respect to both model space size and expansion order of the many-body method. ...
Neutron-rich nuclei provide important insights to nuclear forces and to the nuclear equation of state. Advances in ab initio methods combined with new opportunities with rare isotope beams enable unique explorations of their properties based on nuclear forces applicable over the entire nuclear chart. In this Letter, we develop novel chiral low-resolution interactions that accurately describe bulk properties from 16 O to 208 Pb. With these, we investigate density distributions and neutron skins of neutron-rich nuclei. Our results show that neutron skins are narrowly predicted over all nuclei with interesting sensitivities for the most extreme, experimentally unexplored cases.
... The hypernuclear Hamiltonian, required as input for the NCSM, consists of a term for the kinetic energy and a nucleonnucleon (NN) and three-nucleon (3N) part accompanied by a YN interaction. We further employ a similarity renormalization group (SRG) transformation of the Hamiltonian in order to accelerate the convergence of the NCSM calculation [40][41][42][43]. This unitary transformation induces additional terms up to the A-body level. ...
Ab initio structure calculations for p-shell hypernuclei have recently become accessible through extensions of nuclear many-body methods, such as the no-core shell model, in combination with hyperon-nucleon interactions from chiral effective field theory. However, the low-energy constants in these hyperon-nucleon interactions are poorly constraint due to the very limited amount of experimental scattering data available. We present a hyperon-nucleon interaction that is additionally constrained by experimental ground-state and spectroscopic data for selected p-shell hypernuclei and, thus, optimized for hypernuclear structure calculations. We show that the previous overestimation of the hyperon separation energies in the p-shell is remedied and discuss the significantly improved description of the $_\Lambda$He isotopic chain. We further discuss the uncertainty quantification for hypernuclear observables on the many-body level, obtained through a novel machine-learning tool.
... There are several review articles detailing both the free-space SRG [21,22] and the in-medium SRG [15,[23][24][25][26], and so here I will review only what is needed for our present purposes. ...
... [57,58], these currents were normal ordered with respect to uniform nuclear matter to obtain an in-medium quenching factor for the one-body operator. In Ref. [59], the full two-body current was constructed, consistently (in [59], the relationship between the two-body currents and three-body force contained an erroneous factor of −1/4 [55]) with the NN + 3N force, and the normal-ordered one-body operator (with respect to a Hartree-Fock reference) was used to compute Gamow-Teller decays of 14 C, 22 O, and 24 O with the coupled-cluster method. (I also note that while the decay of 14 C is interesting due to the anomalously long half-life [60,61], the small matrix element makes it difficult to draw conclusions regarding systematic quenching effects.) ...
We review the status of ab initio calculations of allowed beta decays (both Fermi and Gamow–Teller), within the framework of the valence-space in-medium similarity renormalization group approach.
... There are several review articles detailing both the free-space SRG [21,22] and the inmedium SRG [15,[23][24][25][26], and so here I will review only what is needed for our present purposes. ...
... [48] and [49], these currents were normal ordered with respect to uniform nuclear matter to obtain an in-medium quenching factor for the one-body operator. In Ref. [51], the full two-body current was constructed, consistently 2 with the NN+3N force, and Gamow-Teller decays of 14 C, 22 O and 24 O were computed using the coupled cluster method 3 . In all three of these cases, a quenching of about the right size was obtained. ...
We review the status of ab initio calculations of allowed beta decays (both Fermi and Gamow-Teller), within the framework of the valence-space in-medium similarity renormalization group approach.
... Priorities include exploring alternatives to Weinberg power counting for χ EFT and pushing pionless EFT to higher A, which can help establish universal features in nuclei. Similarity renormalization group (SRG) methods have played an important role softening χ EFT Hamiltonians [64,65], but the SRG has yet to be applied to pionless EFT. Also on the wishlist is to explore more matching calculations between different EFTs, e.g., ab initio based on χ EFT to halo EFT or EFTs with collective DOFs. ...
Steven Weinberg’s seminal papers from 1990–92 initiated the use of effective field theories (EFTs) for nuclei. We summarize progress, priorities, and open questions for nuclear EFT developments based on the 2019 INT program “Nuclear Structure at the Crossroads.”
... Priorities include exploring alternatives to Weinberg power counting for χEFTand pushing pionless EFT to higher A, which can help establish universal features in nuclei. Similarity renormalization group (SRG) methods have played an important role softening χEFT Hamiltonians [64,65], but the SRG has yet to be applied to pionless EFT. Also on the wishlist is to explore more matching calculations between different EFTs, e.g., ab initio based on chiral EFT to halo EFT or EFTs with collective DOFs. ...
Steven Weinberg's seminal papers from 1990-92 initiated the use of effective field theories (EFTs) for nuclei. We summarize progress, priorities, and open questions for nuclear EFT developments based on the 2019 INT program "Nuclear Structure at the Crossroads."
... The cut-off Λ is taken above 300 MeV in the laboratory, corresponding to relative momentum q ≈ 2.1 fm −1 , that is the largest energy where the experimental data are established. The fact that V low k is soft has the advantage to be much more manageable than a hard-core interaction, in particular it can be used in perturbation expansion and in nuclear structure calculations in a more efficient way [61,62]. ...
We review the current status and recent progress of microscopic many-body approaches and phenomenological models, which are employed to construct the equation of state of neutron stars. The equation of state is relevant for the description of their structure and dynamical properties, and it rules also the dynamics of core-collapse supernovae and binary neutron star mergers. We describe neutron star matter assuming that the main degrees of freedom are nucleons and hyperons, disregarding the appearance of quark matter. We compare the theoretical predictions of the different equation-of-state models with the currently available data coming from both terrestrial laboratory experiments and recent astrophysical observations. We also analyse the importance of the nuclear strong interaction and equation of state for the cooling properties of neutron stars. We discuss the main open challenges in the description of the equation of state, mainly focusing on the limits of the different many-body techniques, the so-called "hyperon puzzle," and the dependence of the direct URCA processes on the equation of state.
... Although considerable progress for fully correlated many-body calculations has been made over the last two decades (for reviews see e.g. [1][2][3][4]), the method of choice, especially for heavy nuclei, remains for the time being a description through mean-field models. Empirical shell model potentials delivered first microscopic models for nuclear structure [5] which were since used extensively with great success [6]. ...
... SkyAx is presented in Sec. 3. In Sections 4 and 5 we describe the input and output of the code and in Sec. ...
... ξ q (r) = α∈q s w α u α v α ψ α (r, s)ψ α (r, s) pairing density (3) where w α stands for a soft cutoff of pairing space (explained below) and q labels the nucleon species, q = p for protons and q = n for neutrons. The variable s ∈ ±1 indicates the spinor component of the wave functions. ...
The nuclear mean-field model based on Skyrme forces can predict a variety of properties of nuclear ground states. We present the Code SkyAx solving the Hartree–Fock equations in two spatial dimensions assuming axial symmetry. Pairing can be included in the BCS approximation. The code is implemented with a view on computational speed.
Program summary
Program title: SkyAx
CPC Library link to program files: http://dx.doi.org/10.17632/fd453hc4jb.1
Licensing provisions: GPLv3
Programming language: Fortran 90 and parallel version with OpenMP.
External routines/libraries: BLAS, LAPACK.
Nature of problem: The Hartree–Fock equations can be used to determine static properties of nuclei all over the nuclear chart, e.g., nuclear masses, charge radii and deformations. This code implements the widely used Skyrme forces as interaction model and offers in addition to include the pairing interaction through the BCS theory. Due to its two-dimensional nature, the code allows only for axial deformations, which is suitable for most nuclei in the chart of nuclides.
Solution method: The nucleonic wave functions are represented on a two-dimensional mesh assuming axial symmetry. The Coulomb potential is calculated for an isolated charge distribution by splitting the problem into a short-range and a long-range part. All spatial derivatives are evaluated using the finite Fourier transform method. The code solves the static Hartree–Fock equations with a damped gradient iteration method. It also allows for constraint iterations, where the monopole, quadrupole, octupole and hexadecapole moments can be fixed.
Additional comments including restrictions and unusual features: The current implementation is restricted to even–even nuclei. Furthermore the Hartree–Fock + BCS model is valid only for well-bound nuclei. For nuclei near the neutron and proton drip lines, a full Hartree–Fock–Bogolyubov treatment would be more suitable.
The code allows for multipole constraints up to l=4. Furthermore the code can be used to calculate fission paths or landscapes of deformations (potential energy surfaces) in one single run.
... With the development of chiral EFT interactions at low cutoff scales [1,2] and renormalization group (RG) methods that allow to evolve interactions to lower resolution [39,40], many-body perturbation theory (MBPT) becomes a viable and systematic approach to the nuclear many-body problem [39,41]. Here, in Sec. ...
We study the equation of state of neutron matter at finite temperature based on two- and three-nucleon interactions derived within chiral effective field theory to next-to-next-to-next-to-leading order. The free energy, pressure, entropy, and internal energy are calculated using many-body perturbation theory including terms up to third order around the self-consistent Hartree-Fock solution. We include contributions from three-nucleon interactions without employing the normal-ordering approximation and provide theoretical uncertainty estimates based on an order-by-order analysis in the chiral expansion. Our results demonstrate that thermal effects can be captured remarkably well via a thermal index and a density-dependent effective mass. The presented framework provides the basis for studying the dense matter equation of state at general temperatures and proton fractions relevant for core-collapse supernovae and neutron star mergers.
... A flourishing of new or reimplemented formalisms [13][14][15][16][17][18][19][20][21][22][23][24][25] associated with new numerical approaches [26][27][28] have allowed ab initio methods to finally leave the realm of light nuclei and access midmass isotopes up to A ∼ 100 [29,30] over the past few decades. But all of those approaches seem to have reached a new ceiling with the Sn isotopic line. ...
We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLOsat chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for 100Sn. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.
