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We review recent progress and motivate the need for further developments in nuclear optical potentials that are widely used in the theoretical analysis of nucleon elastic scattering and reaction cross sections. In regions of the nuclear chart away from stability, which represent a frontier in nuclear science over the coming decade and which will be probed at new rare-isotope beam facilities worldwide, there is a targeted need to quantify and reduce theoretical reaction model uncertainties, especially with respect to nuclear optical potentials. We first describe the primary physics motivations for an improved description of nuclear reactions involving short-lived isotopes, focusing on its benefits for fundamental science discoveries and applications to medicine, energy, and security. We then outline the various methods in use today to build optical potentials starting from phenomenological, microscopic, and ab initio methods, highlighting in particular the strengths and weaknesses of each approach. We then discuss publicly-available tools and resources facilitating the propagation of recent progresses in the field to practitioners. Finally, we provide a set of open challenges and recommendations for the field to advance the fundamental science goals of nuclear reaction studies in the rare-isotope beam era., Comment: This paper is the outcome of the Facility for Rare Isotope Beams Theory Alliance (FRIB - TA) topical program "Optical Potentials in Nuclear Physics" held in March 2022 at FRIB. Its content is non-exhaustive, was chosen by the participants and reflects their efforts related to optical potentials

This chapter presents an overview of the optical model description of nucleon-nucleus scattering and reactions based on fundamental nuclear two-body and many-body forces. The chapter begins with a historical review followed by a discussion of several commonly used theoretical techniques for deriving nucleon-nucleus optical model potentials that account for antisymmetry, Pauli blocking, and multiple scattering. This is followed by a summary of current efforts to derive microscopic nuclear forces consistent with the fundamental theory of strong interactions, quantum chromodynamics, and the use of such interactions in the construction of microscopic optical potentials. The chapter will also outline the dispersive optical potential approach, which despite being primarily phenomenological, has its origins in formal Green's function theory. Finally, the results from modern optical potentials will be benchmarked to experimental data., Comment: 29 pages, 9 figures. Contribution to the "Handbook of Nuclear Physics", Springer, 2022, edited by I. Tanihata, H. Toki and T. Kajino. Comments welcome

Born in the aftermath of core collapse supernovae, neutron stars contain matter under extraordinary conditions of density and temperature that are difficult to reproduce in the laboratory. In recent years, neutron star observations have begun to yield novel insights into the nature of strongly interacting matter in the high-density regime where current theoretical models are challenged. At the same time, chiral effective field theory has developed into a powerful framework to study nuclear matter properties with quantified uncertainties in the moderate-density regime for modeling neutron stars. In this article, we review recent developments in chiral effective field theory and focus on many-body perturbation theory as a computationally efficient tool for calculating the properties of hot and dense nuclear matter. We also demonstrate how effective field theory enables statistically meaningful comparisons between nuclear theory predictions, nuclear experiments, and observational constraints on the nuclear equation of state., Comment: additional references and minor improvements; 31 pages, 8 figures; invited review prepared for Annu. Rev. Nucl. Part. Sci. (2021)

We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range 12 $\leq$ A $\leq$ 242 for energies between 0 MeV $<$ E $\lesssim$ 150 MeV. We then parameterize a global optical potential for each chiral force that depends smoothly on the projectile energy as well as the target nucleus mass number and isospin asymmetry. Uncertainty bands for elastic scattering observables are generated from a full covariance analysis of the parameters entering in the description of our global optical potential and benchmarked against existing experimental data for stable target nuclei. Since our approach is purely microscopic, we anticipate a similar quality of the model for nucleon scattering on unstable isotopes.

We formulate microscopic neutron-nucleus optical potentials from many-body perturbation theory based on chiral two- and three-body forces. The neutron self energy is first calculated in homogeneous matter to second order in perturbation theory, which gives the central real and imaginary terms of the optical potential. The real spin-orbit term is calculated separately from the density matrix expansion using the same chiral interaction as in the self energy. Finally, the full neutron-nucleus optical potential is derived within the improved local density approximation utilizing mean field models consistent with the chiral nuclear force employed. We compare the results of the microscopic calculations to phenomenological models and experimental data up to projectile energies of $E = 200$ MeV. Experimental elastic differential scattering cross sections and vector analyzing powers are generally well reproduced by the chiral optical potential, but we find that total cross sections are overestimated at high energies.

We formulate a microscopic optical potential from chiral two- and three-body forces. The real and imaginary central terms of the optical potential are obtained from the nucleon self-energy in infinite matter, while the real spin-orbit term is extracted from a nuclear energy density functional constructed from the density matrix expansion using the same chiral potential. The density-dependent optical potential is then folded with the nuclear density distributions for selected Calcium isotopes resulting in energy-dependent nucleon-nucleus optical potentials from which we study proton-nucleus elastic scattering cross sections calculated using the TALYS reaction code. We compare the results of the microscopic calculations to phenomenological models and experimental data., Comment: Submitted to CNR*18 conference proceedings

We present predictions for neutron star tidal deformabilities obtained from a Bayesian analysis of the nuclear equation of state, assuming a minimal model at high-density that neglects the possibility of phase transitions. The Bayesian posterior probability distribution is constructed from priors obtained from microscopic many-body theory based on realistic two- and three-body nuclear forces, while the likelihood functions incorporate empirical information about the equation of state from nuclear experiments. The neutron star crust equation of state is constructed from the liquid drop model, and the core-crust transition density is found by comparing the energy per baryon in inhomogeneous matter and uniform nuclear matter. From the cold $\beta$-equilibrated neutron star equation of state, we then compute neutron star tidal deformabilities as well as the mass-radius relationship. Finally, we investigate correlations between the neutron star tidal deformability and properties of finite nuclei., Comment: 15 pages, 17 figures. Invited contribution to the EPJA Topical Issue "First joint gravitational wave and electromagnetic observations: Implications for nuclear and particle physics"

We formulate microscopic optical potentials for nucleon-nucleus scattering from chiral two- and three-nucleon forces. The real and imaginary central terms of the optical potentials are obtained from the nucleon self energy in infinite nuclear matter at a given density and isospin asymmetry, calculated self-consistently to second order in many-body perturbation theory. The real spin-orbit term is extracted from the same chiral potential using an improved density matrix expansion. The density-dependent optical potential is then folded with the nuclear density distributions of 40Ca, 42Ca, 44Ca, and 48Ca from which we study proton-nucleus elastic scattering and total reaction cross sections using the reaction code TALYS. We compare the results of the microscopic calculations to those of phenomenological models and experimental data up to projectile energies of E = 180 MeV. While overall satisfactory agreement with the available experimental data is obtained, we find that the elastic scattering and total reaction cross sections can be significantly improved with a weaker imaginary optical potential, particularly for larger projectile energies., Comment: 12 pages, 10 figures

We present predictions for the equation of state of symmetric nuclear and pure neutron matter based on recent high-quality nucleon-nucleon potentials from leading order to fifth order in the chiral expansion. We include as well the next-to-next-to-leading order (N2LO) chiral three-nucleon force whose low-energy constants cD and cE are fitted to the binding energies of 3H and 3He as well as the \b{eta}-decay lifetime of 3H. The ground state energy per particle is computed in the particle- particle ladder approximation up to a few times saturation density. Due to the soft character of the interactions, uncertainties due to the convergence in many-body perturbation theory are small. We find that nuclear matter saturation is reproduced quantitatively at N3LO and N4LO, and therefore we encourage the application of these interactions in finite nuclei, where the description of ground- state energies and charge radii of medium-mass nuclei may be improved., Comment: 11 pages, 12 figures

We compute from chiral two- and three-body forces the complete quasiparticle interaction in symmetric nuclear matter up to twice nuclear matter saturation density. Second-order perturbative contributions that account for Pauli-blocking and medium polarization are included, allowing for an exploration of the full set of central and noncentral operator structures permitted by symmetries and the long-wavelength limit. At the Hartree-Fock level, the next-to-next-to-leading order three-nucleon force contributes to all noncentral interactions, and their strengths grow approximately linearly with the nucleon density up that of saturated nuclear matter. Three-body forces are shown to enhance the already strong proton-neutron effective tensor interaction, while the corresponding like-particle tensor force remains small. We also find a large isovector cross-vector interaction but small center-of-mass tensor interactions in the isoscalar and isovector channels. The convergence of the expansion of the noncentral quasiparticle interaction in Landau parameters and Legendre polynomials is studied in detail., Comment: 15 pages, 14 figures

We compute from chiral two- and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-order convergence in both many-body perturbation theory and the chiral expansion. Including also variations in the resolution scale at which nuclear forces are resolved, we provide new error bands on the equation of state, the isospin-asymmetry energy, and its slope parameter. We find in particular that the inclusion of third-order diagrams reduces the theoretical uncertainty at low densities, while in general the largest error arises from omitted higher-order terms in the chiral expansion of the nuclear forces., Comment: 10 pages, 10 figures

Realistic nuclear potentials, derived within chiral perturbation theory, are a major breakthrough in modern nuclear structure theory, since they provide a direct link between nuclear physics and its underlying theory, namely the QCD. As a matter of fact, chiral potentials are tailored on the low-energy regime of nuclear structure physics, and chiral perturbation theory provides on the same footing two-nucleon forces as well as many-body ones. This feature fits well with modern advances in ab-initio methods and realistic shell-model. Here, we will review recent nuclear structure calculations, based on realistic chiral potentials, for both finite nuclei and infinite nuclear matter., Comment: 10 pages, 8 figures, plenary talk presented at "Nucleus-Nucleus 2015" Conference, 21-26 June 2015, Catania, to be published in the "Conference Proceedings" Series of the Italian Physical Society

Model-space effective interactions $V_{eff}$ derived from free-space nucleon-nucleon interactions $V_{NN}$ are reviewed. We employ a double decimation approach: first we extract a low-momentum interaction $V_{low-k}$ from $V_{NN}$ using a $T$-matrix equivalence decimation method. Then $V_{eff}$ is obtained from $V_{low-k}$ by way of a folded-diagram effective interaction method. For decimation momentum $\Lambda \simeq 2 fm^{-1}$, the $V_{low-k}$ interactions derived from different realistic $V_{NN}$ models are nearly model independent, and so are the resulting shell-model effective interactions. For nucleons in a low-density nuclear medium like valence nucleons near the nuclear surface, such effective interactions derived from free-space $V_{NN}$ are satisfactory in reproducing experimental nuclear properties. But it is not so for nucleons in a nuclear medium with density near or beyond nuclear matter saturation density. In this case it may be necessary to include the effects from Brown-Rho (BR) scaling of hadrons and/or three-nucleon forces $V_{3N}$, effectively changing the free-space $V_{NN}$ into a density-dependent one. The density-dependent effects from BR scaling and $V_{3N}$ are compared with those from empirical Skyrme effective interactions., Comment: 20 pages, 19 figures, Submitted to Physica Scripta Special Edition: Celebrating the 1975 Nobel Prize

We compute the isospin-asymmetry dependence of microscopic optical model potentials from realistic chiral two- and three-body interactions over a range of resolution scales $\Lambda \simeq 400-500$\,MeV. We show that at moderate projectile energies, $E_{\rm inv} = 110 - 200$\,MeV, the real isovector part of the optical potential changes sign, a phenomenon referred to as isospin inversion. We also extract the strength and energy dependence of the imaginary isovector optical potential and find no evidence for an analogous phenomenon over the range of energies, $E \leq 200$\,MeV, considered in the present work. Finally, we compute for the first time the leading corrections to the Lane parametrization for the isospin-asymmetry dependence of the optical potential and observe an enhanced importance at low scattering energies., Comment: 8 pages, 7 figures

In a recent paper we studied the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations employed realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. In this contribution, after a detailed description of the numerical method we employed in the solution of the BCS equations, we will show a preliminary analysis of the Cooper pair wavefunctions., Comment: 9 pages, 4 figures, contribution to the Proceedings of ICNFP2014 and PANIC14

We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.

We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically we study the equations of state using consistent NLO and N2LO (next-to-next-to-leading order) chiral potentials where the low-energy constants cD and cE associated with contact vertices in the N2LO chiral three-nucleon force are fitted to reproduce the binding energies of 3H and 3He as well as the beta-decay lifetime of 3H. At these low orders in the chiral expansion there is little sign of convergence, while an exploratory study employing the N3LO two-nucleon force together with the N2LO three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and N2LO potentials described in the present work provide the basis for estimating theoretical uncertainties associated with the order-by-order convergence of nuclear many-body calculations in chiral effective field theory., Comment: 9 pages, 6 figures. Accepted for publication in Physical Review C

Core-polarization (CP) and Brown-Rho (BR) scaling were among Gerry's most favorite topics. In this contribution, we will discuss some of the early history as well as more recent work associated with these two fascinating phenomena. I (TTSK) will begin with some recollections of Princeton, where I met Gerry for the first time in 1964 and worked as his postdoc. Core polarization was in fact the first topic he assigned to me. JWH started working with Gerry at Stony Brook from 2003 and was Gerry's last student in nuclear physics. We three had teamed up well, working closely on both CP and BR scaling, particularly on the latter's connection to the anomalously-long beta-decay lifetime of carbon-14. We shall here briefly review these topics, including a recently developed new Brown-Rho scaling based on a Skyrmion half-Skyrmion two-phase model., Comment: 8 pages, 7 figures, published in Nuclear Physics A special issue in memory of Gerry Brown

Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $\chi(p)$ defined by $\Delta(p) = \Delta_F \chi(p)$ and a non-linear algebraic equation for the gap magnitude $\Delta_F = \Delta(p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled $^3PF_2$ partial wave. Results: We have successfully applied Khodel's method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems., Comment: 18 pages and 9 figures

We calculate neutrino absorption rates due to charged-current reactions $\nu_e+n \rightarrow e^- + p $ and $\bar{\nu}_e+p \rightarrow e^+ + n $ in the outer regions of a newly born neutron star called the neutrino-sphere. To improve on recent work which has shown that nuclear mean fields enhance the $\nu_e$ cross-section and suppress the $\bar{\nu}_e$ cross-section, we employ realistic nucleon-nucleon interactions that fit measured scattering phase shifts. Using these interactions we calculate the momentum-, density-, and temperature-dependent nucleon self-energies in the Hartree-Fock approximation. A potential derived from chiral effective field theory and a pseudo-potential constructed to reproduce nucleon-nucleon phase shifts at the mean-field level are used to study the equilibrium proton fraction and the charged-current rates are studied in detail. We compare our results to earlier calculations obtained using phenomenological mean-field models and to those obtained in the virial expansion valid at low density. We find that for typical ambient conditions in the neutrino-sphere, $T=5-10$ MeV and $\rho =10^{11}-10^{13}$ g/cm$^3$, the difference between the $\nu_{e}$ and $\bar{\nu}_e$ absorption rates is much larger than predicted earlier. Our results have important implications for heavy-element nucleosynthesis in supernovae and for supernova neutrino detection.

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wavefunction of neutron matter, containing non-perturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10^3 discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin-independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Lambda = 414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Lambda = 414 MeV) are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations which employed chiral two-body forces at next-to-next-to-leading order (N2LO). In addition we include the effects of three-body forces at N2LO, which provide important repulsion at densities higher than 0.02 fm^-3, as well as two-body forces at N3LO.

We compute the energy per particle of infinite symmetric nuclear matter from chiral N3LO (next-to-next-to-next-to-leading order) two-body potentials plus N2LO three-body forces. The low-energy constants of the chiral three-nucleon force that cannot be constrained by two-body observables are fitted to reproduce the triton binding energy and the 3H-3He Gamow-Teller transition matrix element. In this way, the saturation properties of nuclear matter are reproduced in a parameter-free approach. The equation of state is computed up to third order in many-body perturbation theory, with special emphasis on the role of the third-order particle-hole diagram. The dependence of these results on the cutoff scale and regulator function is studied. We find that the inclusion of three-nucleon forces consistent with the applied two-nucleon interaction leads to a reduced dependence on the choice of the regulator only for lower values of the cutoff., Comment: 9 pages, 12 figures, 3 tables, to be published in Physical Review C. arXiv admin note: text overlap with arXiv:1209.5537

We calculate perturbatively the energy per nucleon in infinite nuclear matter with a chiral N3LO (next-to-next-to-next-to-leading order) two-body potential plus a N2LO three-body force (3BF). The 3BF low-energy constants which cannot be constrained by two-body observables are chosen such as to reproduce the A=3 binding energies and the triton Gamow-Teller matrix element. This enables to study the nuclear matter equation of state in a parameter-free approach., Comment: 7 pages, 5 figures, talk presented at "XIV Convegno su Problemi di Fisica Nucleare Teorica", Cortona October 29-31, 2013. Submitted to Journal of Physics: Conferences Series

This presentation reviews an approach to nuclear many-body systems based on the spontaneously broken chiral symmetry of low-energy QCD. In the low-energy limit, for energies and momenta small compared to a characteristic symmetry breaking scale of order 1 GeV, QCD is realized as an effective field theory of Goldstone bosons (pions) coupled to heavy fermionic sources (nucleons). Nuclear forces at long and intermediate distance scales result from a systematic hierarchy of one- and two-pion exchange processes in combination with Pauli blocking effects in the nuclear medium. Short distance dynamics, not resolved at the wavelengths corresponding to typical nuclear Fermi momenta, are introduced as contact interactions between nucleons. Apart from a set of low-energy constants associated with these contact terms, the parameters of this theory are entirely determined by pion properties and low-energy pion-nucleon scattering observables. This framework (in-medium chiral perturbation theory) can provide a realistic description of both isospin-symmetric nuclear matter and neutron matter. The importance of three-body forces is emphasized, and the role of explicit Delta(1232)-isobar degrees of freedom is investigated in detail. Nuclear chiral thermodynamics is developed and a calculation of the nuclear phase diagram is performed. This includes a successful description of the first-order phase transition from a nuclear Fermi liquid to an interacting Fermi gas and the coexistence of these phases below a critical temperature T_c. Density functional methods for finite nuclei based on this approach are also discussed. Effective interactions, their density dependence and connections to Landau Fermi liquid theory are outlined. Finally, the density and temperature dependence of the chiral (quark) condensate is investigated., Comment: 63 pages, 45 figures

The energy- and density-dependent single-particle potential for nucleons is constructed in a medium of infinite isospin-symmetric nuclear matter starting from realistic nuclear interactions derived within the framework of chiral effective field theory. The leading-order terms from both two- and three-nucleon forces give rise to real, energy-independent contributions to the nucleon self-energy. The Hartree-Fock contribution from the two-nucleon force is attractive and strongly momentum dependent, in contrast to the contribution from the three-nucleon force which provides a nearly constant repulsive mean field that grows approximately linearly with the nuclear density. Together, the leading-order perturbative contributions yield an attractive single-particle potential that is however too weak compared to phenomenology. Second-order contributions from two- and three-body forces then provide the additional attraction required to reach the phenomenological depth. The imaginary part of the optical potential, which is positive (negative) for momenta below (above) the Fermi momentum, arises at second-order and is nearly inversion-symmetric about the Fermi surface when two-nucleon interactions alone are present. The imaginary part is strongly absorptive and requires the inclusion of an effective mass correction as well as self-consistent single-particle energies to attain qualitative agreement with phenomenology., Comment: 12 pages, 7 figures, added references, corrected typos

We calculate the energy per particle in infinite neutron matter perturbatively using chiral N3LO two-body potentials plus N2LO three-body forces. The cutoff dependence of the predictions is investigated by employing chiral interactions with different regulators. We find that the inclusion of three-nucleon forces, which are consistent with the applied two-nucleon interaction, leads to a strongly reduced regulator dependence of the results., Comment: 7 pages, 8 figures, 1 table, to be published in Physical Review C

We present a microscopic calculation of the complete quasiparticle interaction, including central as well as noncentral components, in neutron matter from high-precision two- and three-body forces derived within the framework of chiral effective field theory. The contributions from two-nucleon forces are computed in many-body perturbation theory to first and second order (without any simplifying approximations). In addition we include the leading-order one-loop diagrams from the N2LO chiral three-nucleon force, which contribute to all Fermi liquid parameters except those associated with the center-of-mass tensor interaction. The relative-momentum dependence of the quasiparticle interaction is expanded in Legendre polynomials up to L=2. Second-order Pauli blocking and medium polarization effects act coherently in specific channels, namely for the Landau parameters f_1, h_0 and g_0, which results in a dramatic increase in the quasiparticle effective mass as well as a decrease in both the effective tensor force and the neutron matter spin susceptibility. For densities greater than about half nuclear matter saturation density \rho_0, the contributions to the Fermi liquid parameters from the leading-order chiral three-nucleon force scale in all cases approximately linearly with the nucleon density. The largest effect of the three-nucleon force is to generate a strongly repulsive effective interaction in the isotropic spin-independent channel. We show that the leading-order chiral three-nucleon force leads to an increase in the spin susceptibility of neutron matter, but we observe no evidence for a ferromagnetic spin instability in the vicinity of the saturation density \rho_0. This work sets the foundation for future studies of neutron matter response to weak and electromagnetic probes with applications to neutron star structure and evolution., Comment: 21 pages, 6 figures, 5 tables

We review recent progress in implementing high-precision chiral two- and three-body forces in nuclear many-body systems beyond light nuclei. We begin with applications to finite nuclei, which we study through the nuclear shell model and self-consistent mean field theory. We then turn our attention to infinite nuclear matter treated within the framework of Landau's theory of normal Fermi liquids., Comment: 7 pages, 5 figures. Talk presented at the International School of Nuclear Physics: "From Quarks and Gluons to Hadrons and Nuclei", 16-24 Sept 2011, Erice-Sicily, Italy

We derive the effective interaction between two quasiparticles in symmetric nuclear matter resulting from the leading-order chiral three-nucleon force. We restrict our study to the L=0,1 Landau parameters of the central quasiparticle interaction computed to first order. We find that the three-nucleon force provides substantial repulsion in the isotropic spin- and isospin-independent component F_0 of the interaction. This repulsion acts to stabilize nuclear matter against isoscalar density oscillations, a feature which is absent in calculations employing low-momentum two-nucleon interactions only. We find a rather large uncertainty for the nuclear compression modulus due to a sensitive dependence on the low-energy constant c_3. The effective nucleon mass on the Fermi surface, as well as the nuclear symmetry energy, receive only small corrections from the leading-order chiral three-body force. Both the anomalous orbital g-factor and the Landau-Migdal parameter g'_{NN} (characterizing the spin-isospin response of nuclear matter) decrease with the addition of three-nucleon correlations. In fact, the anomalous orbital g-factor remains significantly smaller than its value extracted from experimental data, whereas g'_{NN} still compares well with empirical values. The inclusion of the three-nucleon force results in relatively small p-wave (L=1) components of the central quasiparticle interaction, thus suggesting an effective interaction of short range., Comment: 20 pages, 6 figures

An improved density-matrix expansion is used to calculate the nuclear energy density functional from chiral two- and three-nucleon interactions. The two-body interaction comprises long-range one- and two-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition we employ the leading order chiral three-nucleon interaction with its parameters $c_E, c_D$ and $c_{1,3,4}$ fixed in calculations of nuclear few-body systems. With this input the nuclear energy density functional is derived to first order in the two- and three-nucleon interaction. We find that the strength functions $F_\nabla(\rho)$ and $F_{so}(\rho)$ of the surface and spin-orbit terms compare in the relevant density range reasonably with results of phenomenological Skyrme forces. However, an improved description requires (at least) the treatment of the two-body interaction to second order. This observation is in line with the deficiencies in the nuclear matter equation of state $\bar E(\rho)$ that remain in the Hartree-Fock approximation with low-momentum two- and three-nucleon interactions., Comment: 16 pages, 12 figures, submitted to Eur. Phys. J. A

We employ Landau's theory of normal Fermi liquids to study the quasiparticle interaction in nuclear matter in the vicinity of saturation density. Realistic low-momentum nucleon-nucleon interactions evolved from the Idaho N3LO chiral two-body potential are used as input potentials. We derive for the first time exact results for the central part of the quasiparticle interaction computed to second order in perturbation theory, from which we extract the L=0 and L=1 Landau parameters as well as some relevant bulk equilibrium properties of nuclear matter. The accuracy of the intricate numerical calculations is tested with analytical results derived for scalar-isoscalar boson exchange and (modified) pion exchange at second order. The explicit dependence of the Fermi liquid parameters on the low-momentum cutoff scale is studied, which provides important insight into the scale variation of phase-shift equivalent two-body potentials. This leads naturally to explore the role that three-nucleon forces must play in the effective interaction between two quasiparticles., Comment: 25 pages, 5 figures

Shell-model calculations for several mass 16-19 nuclei are performed using the N$^3$LO two-nucleon potential $V_{2N}$ with and without the addition of an in-medium three-nucleon potential $V_{3N}^{med}$, which is a density-dependent effective two-nucleon potential recently derived from the leading-order chiral three-nucleon force $V_{3N}$ by Holt, Kaiser, and Weise. We first calculate the $V_{low-k}$ low-momentum interactions from $V_{2N}$ and $V_{3N}^{med}$. The shell-model effective interactions for both the $sd$ one-shell and $sdpf$ two-shell model spaces are then obtained from these low-momentum interactions using respectively the Lee-Suzuki and the recently developed Okamoto and Suzuki iteration methods. The effects of $V_{3N}^{med}$ to the low-lying states of $^{18}O$, $^{18}F$, $^{19}O$ and $^{19}F$ are generally small and attractive, mainly lowering the ground-state energies of these nuclei and making them in better agreements with experiments than those calculated with $V_{2N}$ alone. The excitation spectra of these nuclei are not significantly affected by $V_{3N}^{med}$. The low-lying spectra of these nuclei calculated with the $sd$ and $sdpf$ model spaces are closely similar to each other. Our shell-model calculations for $^{16}O$ indicate that the $V_{3N}^{med}$ interaction is important and desirable for the binding energy of this nucleus., Comment: 9 pages, 11 figures

We study the role of density-dependent low-momentum nucleon-nucleon interactions in describing the anomalously long beta decay lifetime of 14C. We approach this problem both from the perspective of chiral effective field theory, in which genuine three-body forces generate an effective density-dependent two-body interaction, as well as from the perspective of Brown-Rho scaling, in which the masses and form factor cutoffs in one-boson-exchange interactions are modified in a dense nuclear medium due to the partial restoration of chiral symmetry. The beta decay transition of 14C to the ground state of 14N is calculated within the shell model using a model space consisting of two 0p-shell holes within a closed 16O core. The effective 0p-shell interaction is calculated up to second order in perturbation theory with single-particle energies extracted from experiment. We find that both three-nucleon forces and Brown-Rho scaling medium modifications give qualitatively similar results not only for the ground state to ground state Gamow-Teller transition but also for Gamow-Teller transitions from excited states of 14C to the ground state of 14N. In this way, it is observed that at a low-momentum scale of V_(low-k) = 2.1 fm-1, medium-modifications of the nuclear force play an essential role in increasing the lifetime of 14C from a few minutes to an archaeologically long one of 5730 years., Comment: Submitted to Gerry Brown's 85th birthday Festschrift

We present calculations of shell-model effective interactions for both degenerate and non-degenerate model spaces using the Krenciglowa-Kuo (KK) and the extended Krenciglowa-Kuo iteration method recently developed by Okamoto, Suzuki {\it et al.} (EKKO). The starting point is the low-momentum nucleon-nucleon interaction $V_{low-k}$ obtained from the N$^3$LO chiral two-nucleon interaction. The model spaces spanned by the $sd$ and $sdpf$ shells are both considered. With a solvable model, we show that both the KK and EKKO methods are convenient for deriving the effective interactions for non-degenerate model spaces. The EKKO method is especially desirable in this situation since the vertex function $\hat Z$-box employed therein is well behaved while the corresponding vertex function $\hat Q$-box employed in the Lee-Suzuki (LS) and KK methods may have singularities. The converged shell-model effective interactions given by the EKKO and KK methods are equivalent, although the former method is considerably more efficient. The degenerate $sd$-shell effective interactions given by the LS method are practically identical to those from the EKKO and KK methods. Results of the $sd$ one-shell and $sdpf$ two-shell calculations for $^{18}$O, $^{18}$F, $^{19}$O and $^{19}$F using the EKKO effective interactions are compared, and the importance of the shell-model three-nucleon forces is discussed., Comment: 10 pages, 12 figures

We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon scattering T-matrix. Analytic expressions are presented for each of these in both isospin-symmetric nuclear matter as well as nuclear matter with a small isospin asymmetry. The results are combined with the low-momentum nucleon-nucleon potential V(low-k) to obtain an effective density-dependent interaction suitable for nuclear structure calculations. The in-medium interaction is decomposed into partial waves up to orbital angular momentum L = 2. Our results should be particularly useful in calculations where an exact treatment of the chiral three-nucleon force would otherwise be computationally prohibitive., Comment: 25 pages, 15 figures

We study the equation of state for symmetric nuclear matter using a ring-diagram approach in which the particle-particle hole-hole ($pphh$) ring diagrams within a momentum model space of decimation scale $\Lambda$ are summed to all orders. The calculation is carried out using the renormalized low-momentum nucleon-nucleon (NN) interaction $V_{low-k}$, which is obtained from a bare NN potential by integrating out the high-momentum components beyond $\Lambda$. The bare NN potentials of CD-Bonn, Nijmegen and Idaho have been employed. The choice of $\Lambda$ and its influence on the single particle spectrum are discussed. Ring-diagram correlations at intermediate momenta ($k\simeq$ 2 fm$^{-1}$) are found to be particularly important for nuclear saturation, suggesting the necessity of using a sufficiently large decimation scale so that the above momentum region is not integrated out. Using $V_{low-k}$ with $\Lambda \sim 3$ fm$^{-1}$, we perform a ring-diagram computation with the above potentials, which all yield saturation energies $E/A$ and Fermi momenta $k_F^{(0)}$ considerably larger than the empirical values. On the other hand, similar computations with the medium-dependent Brown-Rho scaled NN potentials give satisfactory results of $E/A \simeq -15$ MeV and $k_F^{(0)}\simeq 1.4$ fm$^{-1}$. The effect of this medium dependence is well reproduced by an empirical 3-body force of the Skyrme type., Comment: 8 pages, 7 figures

We present a shell model calculation for the beta decay of 14-C to the 14-N ground-state, treating the relevant nuclear states as two 0p-holes in an 16-O core. Employing the universal low-momentum nucleon-nucleon potential V(low-k) only, one finds that the Gamow-Teller matrix element is too large to describe the known (very long) lifetime of 14-C. As a novel approach to the problem, we invoke the chiral three-nucleon force (3NF) at leading order and derive from it a density-dependent in-medium NN interaction. Including this effective in-medium NN interaction, the Gamow-Teller matrix element vanishes for a nuclear density close to that of saturated nuclear matter. The genuine short-range part of the three-nucleon interaction plays a particularly important role in this context, since the medium modifications to the pion propagator and pion-nucleon vertex (due to the long-range 3NF) tend to cancel out in the relevant observable. We discuss also uncertainties related to the off-shell extrapolation of the in-medium NN interaction. Using the off-shell behavior of V(low-k) as a guide, we find that these uncertainties are rather small., Comment: 22 pages, 11 figures

We present shell model calculations for the beta-decay of the 14C ground state to the 14N ground state, treating the states of the A=14 multiplet as two 0p holes in an 16O core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller matrix element is too large to describe the known lifetime. By using a modified version of this potential that incorporates the effects of Brown-Rho scaling medium modifications, we find that the GT matrix element vanishes for a nuclear density around 85% that of nuclear matter. We find that the splitting between the (J,T)=(1+,0) and (J,T)=(0+,1) states in 14N is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of 14C to the 14N ground state are compatible with recent experiments., Comment: 4 pages, 5 figures Updated to include referee comments/suggestions

Starting from the microscopic low-momentum nucleon-nucleon interaction V{low k}, we present the first systematic shell model study of magnetic moments and magnetic dipole transition strengths of the basic low-energy one-quadrupole phonon excitations in nearly-spherical nuclei. Studying in particular the even-even N=52 isotones from 92Zr to 100Cd, we find the predicted evolution of the predominantly proton-neutron non-symmetric state reveals a restoration of collective proton-neutron mixed-symmetry structure near mid-shell. This provides the first explanation for the existence of pronounced collective mixed-symmetry structures in weakly-collective nuclei., Comment: 5 Pages, 3 figures

The low-spin structure of 93Nb has been studied using the (n,n' gamma) reaction at neutron energies ranging from 1.5 to 3.0 MeV and the 94Zr(p,2n gamma)93Nb reaction at bombarding energies from 11.5 to 19 MeV. States at 1779.7 and 1840.6 keV, respectively, are proposed as mixed-symmetry states associated with the coupling of a proton hole in the p_1/2 orbit to the 2+_1,ms state in 94Mo. These assignments are derived from the observed M1 and E2 transition strengths to the symmetric one-phonon states, energy systematics, spins and parities, and comparison with shell model calculations., Comment: 5 pages, 3 figures

We compare the momentum-space decimation procedure used to construct the low momentum nucleon-nucleon interaction V(low-k) with the configuration-space separation method of Moszkowski and Scott. Each procedure defines a separation of scales in the nuclear many-body problem, and the extent to which these two scales coincide is studied. By studying the effects of the separation method on the relative S-state Kallio-Kolltveit potential, it is found that close agreement with V(low-k) is obtained as the configuration-space cutoff is lowered to ~ 1.0 fm., Comment: 5 pages, 6 figures