In order to find the selection rules that can be applied to the electromagnetic transitions when the chiral geometry is achieved, a model for a special configuration in triaxial odd-odd nuclei is constructed which exhibits degenerate chiral bands with a sizable rotation. A quantum number obtained from the invariance of the Hamiltonian is given and the selection rule for electromagnetic transition probabilities in chiral bands is derived in terms of this quantum number. Among the available candidates for chiral bands of odd-odd nuclei, in which the near degeneracy of two $ΔI = 1$ bands is observed, the measured electromagnetic properties of the two bands in $^{128}_{55}$Cs$_{73}$ and $^{126}_{55}$Cs$_{71}$ are consistent with the rules, while those of $^{134}_{59}$Pr$_{75}$ and $^{132}_{57}$La$_{75}$ are not.
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.
We derive the leading two-pion exchange contributions to the two-nucleon electromagnetic current operator in the framework of chiral effective field theory using the method of unitary transformation. Explicit results for the current and charge densities are given in momentum and coordinate space.
We derive the leading one-loop contribution to the one-pion exchange and short-range two-nucleon electromagnetic current operator in the framework of chiral effective field theory. The derivation is carried out using the method of unitary transformation. Explicit results for the current and charge densities are given in momentum and coordinate space.
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 calculate the deuteron electromagnetic form factors in a modified version of Weinberg's chiral effective field theory approach to the two-nucleon system. We derive renormalizable integral equations for the deuteron without partial wave decomposition. Deuteron form factors are extracted by applying the Lehmann-Symanzik-Zimmermann reduction formalism to the three-point correlation function of deuteron interpolating fields and the electromagnetic current operator. Numerical results of a leading-order calculation with removed cutoff regularization agree well with experimental data.
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.
I summarize three recent calculations of electromagnetic reactions on deuterium in chiral perturbation theory. All of these calculations were carried out to O(Q^4), i.e. next-to-next-to-leading order. The reactions discussed here are: elastic electron-deuteron scattering, Compton scattering on deuterium, and the photoproduction of neutral pions from deuterium at threshold.
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.
It is shown that the rotating mean field of triaxial nuclei can break the chiral symmetry. Two nearly degenerate $ΔI =1 $ rotational bands originate from the left-handed and right-handed solution.
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.
A relativistic interpretation for why the proton's $G_E/G_M$ falls and $QF_2/F_1$ is approximately constant is presented. Reproducing the observed $G_E^n$ mandates the inclusion of the effects of the pion cloud. The full relativistic model with a pion cloud provides a good reproduction of all of the nucleon electromagnetic form factors.
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.
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.
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.
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…
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 present a calculation of the three complex form factors parametrizing the nucleon to Delta transition matrix element in the framework of chiral effective field theory with explicit Delta degrees of freedom. The interplay between short and long range physics is discussed and estimates for systematic uncertainties due to higher order effect are given.
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…
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 intrinsic electromagnetic nuclear meson exchange charge and current operators arising from a separation of the center-of-mass motion are derived for a one-boson-exchange model for the nuclear interaction with scalar, pseudoscalar and vector meson exchange including leading order relativistic terms. Explicit expressions for the meson exchange operators corresponding to the different meson types are given in detail for a two-nucleon system. These intrinsic operators are to be evaluated between intrinsic wave functions in their center-of-mass frame.
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.
The relativistic version of finite-range-regularisation is proposed. The covariant regulator is generated from the nonlocal Lagrangian. This nonlocal interaction is gauge invariant and is applied to study the nucleon electromagnetic form factors at momentum transfer up to 2 GeV$^2$. Both octet and decuplet intermediate states are included in the one loop calculation. Using a dipole regulator with $Λ$ around 0.85 GeV, the obtained form factors, electromagnetic radii as well as the ratios of the form factors are all comparable with the experimental data. This successful application of chiral eff…
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.
Electromagnetic mean squared radii of Lambda(1405) are evaluated in chiral unitary approach. In this approach we regard Lambda(1405) as dynamically generated resonances in the octet meson and octet baryon scattering, and also as KbarN bound state. Especially for the Lambda(1405) as KbarN bound state we obtain negative electric mean squared radius. With the small binding energy of Lambda(1405) in the chiral unitary approach, our results imply that Lambda(1405) has structure that K^- is widely spread around p.
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 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 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.
We calculate the electromagnetic form factors of a bound proton. The Chiral Quark-Soliton model provides the quark and antiquark substructure of the proton, which is embedded in nuclear matter. This procedure yields significant modifications of the form factors in the nuclear environment. The sea quarks are almost completely unaffected, and serve to mitigate the valence quark effect. In particular, the ratio of the isoscalar electric to the isovector magnetic form factor decreases by 20% at Q^2=1 GeV^2 at nuclear density, and we do not see a strong enhancement of the magnetic moment.
