We investigate the thermodynamic equation of state of isospin-symmetric nuclear matter with microscopic nuclear forces derived within the framework of chiral effective field theory. Two- and three-body nuclear interactions constructed at low resolution scales form the basis for a perturbative calculation of the finite-temperature equation of state. The nuclear force models and many-body methods are benchmarked against bulk properties of isospin-symmetric nuclear matter at zero temperature, which are found to be well reproduced when chiral nuclear interactions constructed at the lowest resolution scales are employed. The calculations are then extended to finite temperatures, where we focus on the liquid-gas phase transition and the associated critical point. The Maxwell construction is applied to construct the physical equation of state, and the value of the critical temperature is determined to be T_c =17.2-19.1 MeV, in good agreement with the value extracted from multifragmentation reactions of heavy ions.
These are personal recollections of how Gerry Brown's work and thinking influenced the development of the chiral effective Lagrangian based theory of nuclear forces.
It is shown that an enhancement in the spectral function near 2$m_π$ threshold in the I=J=0 channel is a good signal of the partial restoration of chiral symmetry in nuclear medium. Several experiments are discussed to detect the enhancement, which uses hadron-nucleus and photo-nucleus reactions.
A survey is given on selected topics concerning the role of spontaneous chiral symmetry breaking in low-energy QCD, and its dynamical implications for nuclear systems. This includes aspects of chiral thermodynamics (the temperature and density dependence of the chiral condensate). It also includes an update on the theory of low-energy (s-wave) pion-nuclear interactions relevant for deeply-bound states of pionic atoms and the quest for possible fingerprints of chiral symmetry restoration in nuclear systems.
In these proceedings, we discuss the current status of nuclear bound state predictions based on chiral nuclear interactions. Results of ordinary $s$- and $p$-shell nuclei and light hypernuclei are shown.
We investigate nuclear matter, i.e. the nuclear equation-of-state (EOS) as well as the relativistic mean fields in the chiral limit. The investigations are based on a chiral nucleon-nucleon EFT interaction where the explicit and implicit pion mass dependence is known up to next-to-leading order. The nuclear bulk properties are found to remain fairly stable in the chiral limit. Based on the same interaction the in-medium scalar condensate is derived, both in Hartree-Fock approximation as well as from the Brueckner G-matrix, making thereby use of the Hellman-Feynman theorem. Short distance physi…
In spite of the great progress we have seen in recent years in the derivation of nuclear forces from chiral effective field theory (EFT), some important issues are still unresolved. In this contribution, we discuss the open problems which have particular relevance for microscopic nuclear structure, namely, the proper renormalization of chiral nuclear potentials and sub-leading many-body forces.
We present a relativistic chiral theory of nuclear matter which includes the effect of confinement. Nuclear binding is obtained with a chiral invariant scalar background field associated with the radial fluctuations of the chiral condensate Nuclear matter stability is ensured once the scalar response of the nucleon depending on the quark confinement mechanism is properly incorporated. All the parameters are fixed or constrained by hadron phenomenology and lattice data. A good description of nuclear saturation is reached, which includes the effect of in-medium pion loops. Asymmetry properties o…
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, b…
We review the main achievements of the research programme for the study of nuclear forces in the framework of chiral symmetry and discuss some problems which are still open.
The present note summarizes the discourse on power counting issues of chiral nuclear forces, with an emphasis on renormalization-group invariance. Given its introductory nature, I will lean toward narrating a coherent point of view on the concepts, rather than covering comprehensively the development of chiral nuclear forces in different approaches.
Two recent experiments have demonstrated that the effective $ρ$-mass in nuclear medium, as extracted from the $^3He(γ, π^+ π^-)$ reaction, is substantially reduced. This has been advocated as an indication of partial restoration of chiral symmetry in nuclear matter. We show that even in the absence of chiral symmetry, effective mean field nuclear matter models can explain these findings quantitatively.
We present a new chiral power expansion scheme for the nuclear equation of state. The scheme is effective in the sense that it is constructed to work around nuclear saturation density. The leading and subleading terms are evaluated and are shown to provide an excellent equation of state. As a further application we considered the chiral quark condensate in nuclear matter. Already at nuclear saturation density we predict a substantially smaller reduction of the condensate as compared to conventional approaches.
We substantiate our statement that the deuteron remains bound in the chiral limit. We critically discuss recent claims that effective field theory cannot give a definite answer to this question.
We discuss partial restoration of chiral symmetry in nuclear medium, which is realized as an effective reduction of the quark condensate in nuclear medium. We derive the in-medium Weinberg-Tomozawa relation. We also give a brief calculation of the in-medium quark condensate based on chiral perturbation theory. We conclude that the density dependence of the quark condensate beyond the linear density comes from the vertex correction of the chiral field insertion and nucleon correlations.
After giving brief discussions on the chiral condensate in hot and/or dense hadronic matter and the significance of the $σ$ meson in QCD, we discuss the importance of experiments using nuclear targets including ones with electro-magnetic probes for obtaining clearer confirmation of the existence of the $σ$ meson and for exploring the possible restoration of chiral symmetry in nuclear medium.
This paper is a write-up of introductory lectures on the modern approach to the nuclear force problem based on chiral effective field theory given at the 2009 Joliot-Curie School, Lacanau, France, 27 September - 3 October 2009.
We study a chiral relativistic theory of nuclear matter aimed at the desciption of both the binding and saturation properties and the QCD properties, quark condensate and QCD susceptibilities. For this purpose the nucleon scalar response of the quark-meson coupling model is introduced in the linear sigma model. The consequences for the nuclear and the QCD scalar susceptibilities are discussed.
A self-consistent approach based on finite temperature Green's functions is used to investigate thermodynamic properties of nuclear matter. The internal energy is derived from the diagrams associated to the interaction energy. Pressure and entropy up to T=20 MeV are obtained from the generating functional form of the thermodynamic potential.
The constraints imposed by chiral symmetry on hadron correlation functions in nuclear medium are discussed. It is shown that these constraints imply a certain structure for the in-medium hadron correlators and lead to the cancelation of the order $ρm_π$ term in the in-medium nucleon correlator. We also consider the effect of mixing of the chiral partners correlation functions arising from the interaction of nuclear pions with corresponding interpolating currents. It reflects the phenomena of partial restoration of chiral symmetry. The different scenarios of such restoration are briefly discuss…
We discuss the relevance of the scalar modes appearing in chiral theories with spontaneous symmetry breaking such as the NJL model for nuclear matter studies. We show that it depends on the relative role of chiral symmetry breaking and confinement in the nucleon mass origin. It is only in the case of a mixed origin that nuclear matter can be stable and reach saturation. We describe models of nucleon structure where this balance is achieved. We show how chiral constarints and confinement modify the QCD sum rules for the mass evolution in nuclear matter.
A new Fermionic Molecular Dynamics (FMD) model based on a Skyrme functional is proposed in this paper. After introducing the basic formalism, some first applications to nuclear structure and nuclear thermodynamics are presented
We investigate single-particle properties in infinite nuclear matter using a variety of interactions. One of the focal points is to study the impact of chiral three-nucleon forces on the nucleon self-energy and related quantities, such as spectral function and momentum distribution. We also present results for pairing correlations in nuclear matter. We find characteristic and systematic differences between the predictions obtained with the (softer) chiral interactions and those based on one-boson-exchange or phenomenology.
We study nuclear physics in the chiral limit ($m_u$, $m_d=0$) in which the pion mass vanishes. We find that the deuteron mass is changed little, but that P--wave nucleon--nucleon scattering volumes are infinite. This motivates an investigation of the possibilities that there could be a two--nucleon $^3P_0$ bound state, and that the nuclear matter ground state is likely to be a condensed state of nucleons paired to those quantum numbers. However, the short distance repulsion in the nucleon--nucleon potential is not affected by the chiral limit and prevents such new chiral possibilities. Thus th…
We study here the equation of state of symmetric nuclear matter at finite temperatures using a modified SU(2) Chiral Sigma model. The effect of temperature on effective mass, pressure, entropy and binding energy is discussed. The liquid-gas phase transition is investigated and the critical values of temperature, density and pressure are calculated.
A nonlinear realization of SU(2) chiral symmetry spontaneous breaking approach is developed in the composite operator formalism. A Lagrangian including quark, gluon and Goldstone boson degrees of freedom of the chiral quark model is obtained from the QCD Lagrangian. A way to link the chiral symmetry spontaneous breaking formalism at hadron level and that at quark level is predicted. too. The application to nuclear matter shows that the approach is quite successful in describing the properties of nuclear matter and the quark condensate in it.
We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at N3LO and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.
We systematically investigate the vacuum stability and nuclear properties in the effective chiral model with higher order terms in $σ$. We evaluate the model parameters by considering the saturation properties of nuclear matter as well as the normal vacuum to be globally stable at zero and finite baryon densities. We can find parameter sets giving moderate equations of state, and apply these models to finite nuclei.
We have attempted to apply the CJT formalism to study the nuclear matter. The thermodynamic potential is calculated in Hartree-Fock approximation in the CJT formalism. After neglecting the medium effects to the mesons, the numerical results are found very consistent with those obtained from the mean field calculation. In our calculation the thermodynamical consistency is also preserved.
This presentation reviews recent developments in the understanding of low-energy kaon-nucleon interactions as they relate to the possible existence of antikaon-nuclear quasibound states. A state-of-the-art discussion of low-energy \bar{K}N interactions is given, with special emphasis on the subthreshold region relevant to the proposed kaon-nuclear systems.
The temperature dependence of the chiral condensate in isospin-symmetric nuclear matter at varying baryon density is investigated using thermal in-medium chiral effective field theory. This framework provides a realistic approach to the thermodynamics of the correlated nuclear many-body system and permits calculating systematically the pion-mass dependence of the free energy per particle. One- and two-pion exchange processes, $Δ(1232)$-isobar excitations, Pauli blocking corrections and three-body correlations are treated up to and including three loops in the expansion of the free energy densi…
We show that the Q-box expansion of nuclear many-body physics can be applied in nuclear effective field theory with explicit pions and external sources. We establish the corresponding power counting and give an algorithm for the construction of a hermitean and energy-independent potential for arbitrary scattering processes on nucleons and nuclei to a given order in the chiral expansion. Various examples are discussed in some detail.
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.
The properties of nuclear matter are studied using state-of-the-art nucleon-nucleon forces up to fifth order in chiral effective field theory. The equations of state of symmetric nuclear matter and pure neutron matter are calculated in the framework of the Brueckner-Hartree-Fock theory. We discuss in detail the convergence pattern of the chiral expansion and the regulator dependence of the calculated equations of state and provide an estimation of the truncation uncertainty. For all employed values of the regulator, the fifth-order chiral two-nucleon potential is found to generate nuclear satu…
The description of nuclear matter bulk properties in the framework of quark-based hadron models in curved unit cells is extended to finite temperature. We discuss the analogy and interplay of density and temperature effects in this formulation and study, as an application, the temperature and density dependence of chiral vacuum properties in the Nambu-Jona-Lasinio (NJL) model.
After a brief review on the status of few--nucleon studies based on conventional nuclear forces, we sketch the concepts of the effective field theory approach constrained by chiral symmetry and its application to nuclear forces. Then first results for few--nucleon observables are discussed.
We report on the recent developments of a new effective field theory for nuclear matter [1,2,3]. We present first the nuclear matter chiral power counting that takes into account both short-- and long--range inter-nucleon interactions. It also identifies non-perturbative strings of diagrams, related to the iteration of nucleon-nucleon interactions, which have to be re-summed. The methods of unitary chiral perturbation theory has been shown to be a useful tool in order to perform those resummations. Results up to next-to-leading order for the ground state energy per particle of nuclear matter, …
We report on shell-model calculations employing effective interactions derived from a new realistic nucleon-nucleon (NN) potential based on chiral effective field theory. We present results for 18O, 134Te, and 210Po. Our results are in excellent agreement with experiment indicating a remarkable predictive power of the chiral NN potential for low-energy microscopic nuclear structure.
The 1S0 pairing gap in isospin-symmetric nuclear matter and finite nuclei is investigated using the chiral nucleon-nucleon potential at the N3LO order in the two-body sector, and the N2LO order in the three-body sector. To include realistic nuclear forces in RHB (Relativistic Hartree Bolgoliubov) calculations we rely on a separable form of the pairing interaction adjusted to the bare nuclear force. The separable pairing force is applied to the analysis of pairing properties for several isotopic and isotonic chains of spherical nuclei.
The equation of state of a family of alternative linear chiral models in the mean field approximation is discussed. We investigate the analogy between some of these models with current models in the literature, and we show that it is possible to reproduce very well the saturation properties of nuclear matter.
Brueckner theory is used to investigate the properties of hyperons in nuclear matter. The hyperon-nucleon interaction is taken from chiral effective field theory at next-to-leading order with SU(3) symmetric low-energy constants. Furthermore, the underlying nucleon-nucleon interaction is also derived within chiral effective field theory. We present the single-particle potentials of Lambda and Sigma hyperons in symmetric and asymmetric nuclear matter computed with the continuous choice for intermediate spectra. The results are in good agreement with the empirical information. In particular, our…
Chiral effective field theory is being developed into a precision tool for low-energy nuclear physics. I review the state of the art in the two-nucleon sector, discuss applications to few-nucleon systems and address challenges that will have to be faced over the coming years.
This paper is devoted to the interplay between p-wave, s-wave pion-nucleon/ nucleus interaction and in-medium pion-pion interaction with special emphasis on the role of the nuclear pionic scalar density driving a large amount of chiral symmetry restoration. In particular we show that the $πNN$ coupling constant and the Goldberger-Treiman relation are preserved in the nuclear medium within certain conditions. We also discuss the related problem of the in-medium pion-pion strength function.
The in-medium mass of the $η^{\prime}$ meson is discussed in a context of partial restoration of chiral symmetry in nuclear medium. The $η^{\prime}$ mass is expected to be reduced by order of 100 MeV at the saturation density. The reduction is a consequence of the suppression of the anomaly effect on the $η^{\prime}$ mass induced by partial restoration of chiral symmetry. This strong attraction in $η^{\prime}$ nuclear systems does not accompany large absorption of $η^{\prime}$ into nuclear matter. This leads to the possibility of so narrow bound states of the $η^{\prime}$ meson in nuclei to be…
We present a novel description of nuclear many-body systems, both for nuclear matter and finite nuclei, emphasizing the connection with the condensate structure of the QCD ground state and spontaneous chiral symmetry breaking. Lorentz scalar and vector mean-fields are introduced in accordance with QCD sum rules. Nuclear binding arises from pionic fluctuations, using in-medium chiral perturbation theory up to three-loop order. Ground state properties of $^{16}$O and $^{40}$Ca are calculated. The built-in QCD constraints reduce the number of input parameters significantly in comparison with pure…
The nuclear thermodynamic observables like the temperature, volume and the specific heat as obtained from isotopic ratios in hot disassembled nuclear matter are examined in the light of the S-matrix approach to the nuclear equation of state. The values of the observables, as extracted without inclusion of scattering effects are found to be modified appreciably in some cases when scattering between the fragment species is taken care of.
The role of chiral (pion) dynamics in nuclear matter is reviewed. Contributions to the energy per particle from one- and two-pion exchange are calculated systematically, and it is demonstrated that already at order $k^4_f$ in the Fermi momentum, two-pion exchange produces realistic nuclear binding together with very reasonable values for the compressibility and the asymmetry energy. Further implications of these results are discussed.
We present recent results on lattice simulations using chiral effective field theory. In particular we discuss lattice simulations for dilute neutron matter at next-to-leading order and three-body forces in light nuclei at next-to-next-to-leading order.
After outlining the basic ideas of nuclear chiral perturbation theory, I discuss its application, presenting three examples which I believe are of great current interest: (1) Exchange currents in those cases where the leading chiral-order terms dominate; (2) The near-threshold $p+p\ra p+p+π^0$ reaction, for which the leading order terms are suppressed and consequently higher-order corrections play a prominent role; (3) Radiative $μ$-capture on the proton.
We investigate the relation between the binding energy and the Fermi energy and between different expressions for the pressure in cold nuclear matter. For a self-consistent calculation based on a $Φ$ derivable $T-$matrix approximation with off-shell propagators the thermodynamic relations are well satisfied unlike for a $G-$matrix or a $T-$matrix approach using quasi-particle propagators in the ladder diagrams.
We present new nuclear matter calculations based on low-momentum interactions derived from chiral effective field theory potentials. The current calculations use an improved treatment of the three-nucleon force contribution that includes a corrected combinatorial factor beyond Hartree-Fock that was omitted in previous nuclear matter calculations. We find realistic saturation properties using parameters fit only to few-body data, but with larger uncertainty estimates from cutoff dependence and the 3NF parametrization than in previous calculations.
The density and temperature dependence of the nuclear symmetry free energy is investigated using microscopic two- and three-body nuclear potentials constructed from chiral effective field theory. The nuclear force models and many-body methods are benchmarked to properties of isospin-symmetric nuclear matter in the vicinity of the saturation density as well as the virial expansion of the neutron matter equation of state at low fugacities. The free energy per particle of isospin-asymmetric nuclear matter is calculated assuming a quadratic dependence of the interaction contributions on the isospi…
Recently, we have shown that the continuity equation for the nuclear vector and axial current operators acquires additional terms if the latter depend on the energy transfer. We analyze in detail the electromagnetic single-nucleon four-current operators and verify the validity of the modified continuity equation for all one- and two-nucleon contributions up to fourth order in the chiral expansion. We also derive, for the first time, the leading contribution to the three-nucleon charge operator which appears at this order. Our study completes the derivation of the electroweak nuclear currents t…
The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.
We develop a chiral SU(3) RMF model for octet baryons, as an extension of the recently developed chiral SU(2) RMF model with logarithmic sigma potential. For Sigma-meson coupling, strong repulsion(SR) and weak repulsion(WR) cases are examined in existing atomic shift data of Sigma^-. In both of these cases, we need an attractive pocket of a few MeV depth around nuclear surface.
Chiral symmetry serves as a guiding principle in low-energy hadron dynamics. An effective lagrangian, which explicitly breaks chiral symmetry via a small mass term, allows for a systematic method of calculating higher order corrections to tree-level results. This is applied to radiative muon capture on hydrogen, %to extract the weak pseudoscalar form factor, and to proton-proton $π^0$ production near threshold. Both processes pose theoretical challenges in light of recent experimental results.
Nucleus-nucleus optical potentials are constructed from an energy density functional approach first outlined by Brueckner et al. The interaction term of the energy density functional comes from the complex nucleon self-energy computed in nuclear matter with two- and three-body chiral nuclear forces. Nuclear density distributions are calculated from Skyrme functionals constrained to the equations of state calculated from the same chiral forces used for the self-energy. Predictions for elastic scattering cross sections and fusion cross sections are compared to experimental data. Very good agreem…
A survey is given of the evolution from Yukawa's early work, via the understanding of the pion as a Nambu-Goldstone boson of spontaneously broken chiral symmetry in QCD, to modern developments in the theory of the nucleus based on the chiral effective field theory representing QCD in its low-energy limit.
Within the cranked Skyrme-Hartree-Fock approach the self-consistent solutions have been obtained for planar and chiral rotational bands in 132La. It turns out that the chiral band cannot exist below some critical rotational frequency which in the present case equals omega=0.6MeV. The appearance of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.
