Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schrödinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chiral effective field theory.
We compare nuclear forces derived from chiral effective field theory (EFT) with those obtained from traditional (phenomenological and meson) models. By means of a careful analysis of paralleles and differences, we show that chiral EFT is superior to all earlier approaches in terms of both formal aspects and successful applications in ab initio calculations. However, in spite of the considerable progress made possible by chiral EFT, complete satisfaction cannot be claimed until outstanding problems---the renormalization issue being the most important one---are finally settled.
We set up a formalism to calculate the charge form factors of two-neutron halo nuclei with S-wave neutron-core interactions in the framework of the halo effective field theory. The method is applied to some known and suspected halo nuclei. In particular, we calculate the form factors and charge radii relative to the core to leading order in the halo EFT and compare to experiments where they are available. Moreover, we investigate the general dependence of the charge radius on the core mass and the one- and two-neutron separation energies.
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 are celebrating thirty-years from the seminal papers from Weinberg proposing to use the rules of Chiral Perturbation Theory to nucleon systems. His proposal was to build an Effective Field Theory (EFT) with Chiral symmetry as a key property. A big effort on this line have been made during these three decades, however the issue of renormalization of the theory is not settled. I will briefly review my path on this issue and give my personal view.
We exploit the separation of scales in weakly-bound nuclei to compute E2 transitions and electric form factors in a Halo EFT framework. The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of $R_{core}/R_{halo}$, where $R_{core}$ and $R_{halo}$ denote the length scales of the core and halo, respectively. We include the strong $s$-wave and $d$-wave interactions by introducing dimer fields. The dimer propagators are regulated by employing the power divergence subtraction scheme and matched to the effective range expansion in the respective…
I report on recent progress in the description of baryon-baryon systems within chiral effective field theory. In particular, I discuss results for the strangeness S=-3 to -4 baryon-baryon systems, obtained to leading order.
Recent developments in nuclear theory allow us to make a connection between quantum chromodynamics (QCD) and low-energy nuclear physics. First, chiral effective field theory (chiEFT) provides a natural hierarchy to define two-nucleon (NN), three-nucleon (NNN), and even four-nucleon interactions. Second, ab initio methods have been developed capable to test these interactions for light nuclei. In this contribution, we discuss ab initio no-core shell model (NCSM) calculations for s-shell and p-shell nuclei with NN and NNN interactions derived within chiEFT.
In recent years, the combination of advanced quantum Monte Carlo (QMC) methods and local interactions derived from chiral effective field theory (EFT) has been shown to provide a versatile and systematic approach to nuclear systems. Calculations at next-to-next-to-leading order in chiral EFT have lead to fascinating results for nuclei and nucleonic matter. On the one hand, ground-state properties of nuclei are well reproduced up to $A\leq16$, even though these potentials have been fit to nucleon-nucleon scattering and few-body observables only. On the other hand, a reasonable description of ne…
Recently we succeeded to make a reliable EFT prediction in a totally parameter-free manner for the $S$ factors for the solar $pp$ and $hep$ processes, $p+p\to d + e^+ +ν_e$ and $\He3+p \to \He4 + e^+ + ν_e$. The strategy used in there is to embed a highly sophisticated standard nuclear physics approach (SNPA) exploiting realistic potentials into an EFT framework, that we refer to as EFT*. Up to next-next-to-leading order in chiral expansion, it turnes out that there is effectively only one counter-term relevant to this process, the coefficient of which -- ($\hat d^R$) -- has been renormalized …
Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-20th century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field theories (EFTs) in the 1990s promised a solution to this problem but unexpected obstacles were encountered. The response of the nuclear community has been to focus on "chiral potentials" with regulators chosen to produce a good description of data. Meanwhile, a successful EFT without explicit pion exchange --- Pionless EFT --- has been formulated where renorma…
The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($χ$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is the electric charge. The specific form of the N3LO and N4LO corrections from, respectively, one-pion-exchange and two-pion-exchange depends on the off-the-energy-shell prescriptions adopted for the non-static terms in the corresponding potentials. We show that different prescriptions lead to unitarily equivalent potentials and accompanying charge operators. Thus, provided a consistent set is adopted, …
We recently developed an Effective Field Theory (EFT) for rotational bands in odd-mass nuclei. Here we use EFT expressions to perform a Bayesian analysis of data on the rotational energy levels of $^{99}$Tc, ${}^{155,157}$Gd, ${}^{159}$Dy, ${}^{167, 169}$Er, ${}^{167, 169}$Tm, ${}^{183}$W, ${}^{235}$U and ${}^{239}$Pu. The error model in our Bayesian analysis includes both experimental and EFT truncation uncertainties. It also accounts for the fact that low-energy constants (LECs) at even and odd orders are expected to have different sizes. We use Markov Chain Monte Carlo (MCMC) sampling to ex…
Since the pioneering work of Weinberg, Chiral Effective Field Theory ($χ$EFT) has been widely and successfully utilized in nuclear physics to study many-nucleon interactions and associated electroweak currents. Nuclear $χ$EFT has now developed into an intense field of research and is applied to study light to medium mass nuclei. In this contribution, we focus on the development of electroweak currents from $χ$EFT and present applications to selected nuclear electroweak observables.
The effective field theory (EFT) for triaxially deformed even-even nuclei is generalized to include the vibrational degrees of freedom. The pertinent Hamiltonian is constructed up to next-to-leading order. The leading order part describes the vibrational motion, and the NLO part couples rotations to vibrations. The applicability of the EFT Hamiltonian is examined through the description of the energy spectra of the ground state bands, $γ$-bands, and $K=4$ bands in the $^{108, 110, 112}$Ru isotopes. It is found that by taking into account the vibrational degrees of freedom, the deviations for h…
We solve the ab initio no-core shell model (NCSM) in the complete Nmax = 8 basis for A = 7 and A = 8 nuclei with two-nucleon and three-nucleon interactions derived within chiral effective field theory (EFT). We find that including the chiral EFT three-nucleon interaction in the Hamiltonian improves overall good agreement with experimental binding energies, excitation spectra, transitions and electromagnetic moments. We predict states that exhibit sensitivity to including the chiral EFT three-nucleon interaction but are not yet known experimentally.
We analyze the longest-range two-pion exchange contributions to the three-nucleon force at leading-loop order in the framework of heavy-baryon chiral effective field theory with explicit $Δ(1232)$ degrees of freedom. All relevant low-energy constants which appear in the calculation are determined from pion-nucleon scattering. Comparing our results with the ones obtained in the $Δ$-less theory at N4LO, we find effects of the $Δ$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $Δ$-less approach.
The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for Effective Field Theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantage there is to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-str…
We present a determination of optical potentials using the double-folding method based on chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with dispersion relations to constrain the imaginary part. This approach is benchmarked on $^{16}$O--$^{16}$O collisions, and extended to the $^{12}$C--$^{12}$C and $^{12}$C--$^{16}$O cases. Predictions derived from these potentials are compared to data for elastic scattering at energies up to 1000 MeV, as well as for fusion at low energy. Without adjusting parameters, excellent agreement with experiment i…
Neutron matter presents a unique system in chiral effective field theory (EFT), because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We discuss perturbative and first Quantum Monte Carlo (QMC) calculations of neutron matter with chiral EFT interactions and their astrophysical impact for the equation of state and neutron stars.
Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Errat…
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband $E2$ transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
A compressible liquid-drop approach adjusted to uniform matter many-body calculations based on chiral EFT interactions and to the experimental nuclear masses is used to investigate the neutron star crust properties. Eight chiral EFT hamiltonians and a representative phenomenological force (SLy4) are confronted. We show that some properties of the crust, e.g. clusters mass, charge, and asymmetry, are mostly determined by symmetric matter properties close to saturation density and are therefore mainly constrained by experimental nuclear masses, while other properties, e.g., energy per particle, …
Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT formalism. Its applicability is examined by comparing with a five-dimensional collective Hamiltonian (5DCH) for the description of the energy spectra of the ground state and $γ$ band in Ru isotopes. It is found that by taking into account the NLO corrections, the ground state band in the whole spin region and the $γ$ band in the low spin region are well describ…
We review the nuclear forces currently in use, i.e., the high-precision NN potentials of the 1990's and the nuclear two- and many-body forces based upon chiral effective field theory (EFT). We argue that the EFT approach is superior to any of the older schemes. Since accurate chiral forces are available now, the stage is set for microscopic nuclear structure to move into a new exciting era.
We have studied electroweak (EW) interactions in quantum hadrodynamics (QHD) effective field theory (EFT). The Lorentz-covariant EFT contains nucleon, pion, $Δ$, isoscalar scalar ($σ$) and vector ($ω$) fields, and isovector vector ($ρ$) fields. The lagrangian exhibits a nonlinear realization of (approximate) $SU(2)_L \otimes SU(2)_R$ chiral symmetry and incorporates vector meson dominance. First, we discuss the EW interactions at the quark level. Then we include EW interactions in QHD EFT by using the background-field technique. The completed QHD EFT has a nonlinear realization of $SU(2)_L \ot…
The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($χ$EFT) up to one loop are determined by a simultaneous fit to the $A\,$=$\,2$--3 nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the $^3$He/$^3$H magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to $\approx 0.8$ GeV/c, beyond the expected regime of validity of t…
Recent chiral EFT calculations of nucleon polarizabilities reveal a problem in the current empirical determination of proton's electromagnetic polarizabilities. We also report on the progress in the empirical determination of the $Δ$(1232)-resonance magnetic moment in the process of $γp \to p π^0 γ'$ measured at MAMI.
Effective Field Theory (EFT) provides a powerful framework to exploit a separation of scales in order to perform systematically improvable, model-independent calculations. We apply this method to strongly interacting quantum systems with short-range interactions and large scattering length. Such systems display remarkable universal properties which include a geometric spectrum of shallow three-body states called "Efimov states" and log-periodic dependence of scattering observables on the scattering length. We review the EFT for large scattering length and some of its applications in the physic…
Heavy even-even nuclei exhibit low-energy collective excitations that are separated in scale from the microscopic (fermion) degrees of freedom. This separation of scale allows us to approach nuclear vibrations within an effective field theory (EFT). In odd-mass nuclei collective and single-particle properties compete at low energies, and this makes their description more challenging. In this article we describe odd-mass nuclei with ground-state spin $I=\sfrac{1}{2}$ by means of an EFT that couples a fermion to the collective degrees of freedom of an even-even core. The EFT relates observables …
Recent calculations of EDMs of light nuclei in the framework of chiral effective field theory are presented. We argue that they can be written in terms of the leading six low-energy constants encoding CP-violating physics. EDMs of the deuteron, triton, and helion are explicitly given in order to corroborate our claim. An eventual non-zero measurement of these EDMs can be used to disentangle the different sources and strengths of CP-violation.
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-ord…
We develop an effective field theory (EFT) for deformed odd-mass nuclei. These are described as an axially symmetric core to which a nucleon is coupled. In the coordinate system fixed to the core the nucleon is subject to an axially symmetric potential. Power counting is based on the separation of scales between low-lying rotations and higher-lying states of the core. In leading order, core and nucleon are coupled by universal derivative terms. These comprise a covariant derivative and gauge potentials which account for Coriolis forces and relate to Berry-phase phenomena. At leading order, the…
M. Smoluchowski Institute of Physics, Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University（雅盖隆大学物理、天文学与应用科学学院 M.Smoluchowski 物理研究所）；Doctoral School of Exact and Natural Sciences, Jagiellonian University（雅盖隆大学精确与自然科学研究生院）；Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Institut für Theoretische Physik II（波鸿鲁尔大学物理与天文学院理论物理第二研究所）
We study neutrinoless double-beta decay in an effective field theory (EFT) for heavy nuclei, which are treated as a spherical core coupled to additional neutrons and/or protons. Since the low-energy constants of the EFT cannot be fitted to data for this unobserved decay, we follow an alternative strategy to constrain these through a correlation with double Gamow-Teller transitions. This correlation was recently found to hold for shell-model calculations, energy-density functionals, and other nuclear structure models. We therefore first calculate the nuclear matrix elements for double Gamow-Tel…
We present a fit of the spin-independent electromagnetic polarisabilities of the proton to low-energy Compton scattering data in the framework of covariant baryon chiral effective field theory. Using the Baldin sum rule to constrain their sum, we obtain $α=[10.6\pm0.25$(stat)$\pm0.2$(Baldin)$\pm0.4$(theory)$]\times10^{-4}$fm$^3$ and $β=[3.2\mp0.25$(stat)$\pm0.2$(Baldin)$\mp0.4$(theory)$]\times10^{-4}$fm$^3$, in excellent agreement with other chiral extractions of the same quantities.
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in recent LQCD simulations carried out at pion masses much heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron and triton LQCD ener…
We present a study of two-nucleon scattering in chiral effective field theory with a finite cutoff to next-to-leading order in the chiral expansion. In the proposed scheme, the contributions of the lowest-order interaction to the scattering amplitude are summed up to an arbitrary order, while the corrections beyond leading order are iterated only once. We consider a general form of the regulator for the leading-order potential including local and non-local structures. The main objective of the paper is to address formal aspects of renormalizability within the considered scheme. In particular, …
Recently, a new generation of nuclear forces has been developed in the framework of chiral EFT. An important feature of these potentials is a novel semi-local regularization approach that combines the advantages of a local regulator for long-range interactions with the convenience of an angle-independent nonlocal regulator for contact interactions. The authors discuss the key features of the semi-local two-nucleon potentials and demonstrate their outstanding performance in the two-nucleon sector by showing selected results up to fifth order in the EFT expansion. Also reviewed are applications …
Halo nuclei are a promising new arena for studies based on effective field theory (EFT). We develop an EFT for shallow p-wave states and discuss the application to elastic n-alpha scattering. In contrast to the s-wave case, both the scattering length and effective range enter at leading order. We also discuss the prospects of using EFT in the description of other halos, such as the three-body halo nucleus 6He.
We discuss the application of an effective field theory (EFT) which incorporates the chiral symmetry of QCD to Compton scattering from the proton and deuteron. We describe the chiral EFT analysis of the proton Compton scattering database presented in our recent review (arXiv:1203.6834), which gives: alpha^{(p)}=10.5 +/- 0.5(stat) +/- 0.8(theory); beta^{(p)}= 2.7 +/- 0.5(stat) +/- 0.8(theory), for the electric and magnetic dipole polarizability of the proton. We also summarize the chiral EFT analysis of the world data on coherent Compton scattering from deuterium presented in arXiv:1203.6834. T…
The reaction $NN \to NN π$ offers a good testing ground for chiral effective field theory at intermediate energies. It challenges our understanding of the first inelastic channel in nucleon-nucleon scattering and of the charge-symmetry breaking pattern in hadronic reactions. In our previous studies, we presented a complete calculation of the pion-production operator for s-wave pions up-to-and-including next-to-next-to-leading order (NNLO) in the formulation of chiral effective field theory, which includes pions, nucleons and $Δ(1232)$ degrees of freedom. In this paper we calculate the near thr…
We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N$^2$LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the nonlocal HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermo…
We compare the predictions of different variants of chiral effective field theory for the gamma-p elastic scattering differential cross section. We pay particular attention to the role of pion loops, and the impact that a heavy-baryon expansion has on the behavior of those loops. We also correct erroneous results for these loops that were published in Phys. Rev. C 67, 055202 (2003) [ arXiv:nucl-th/0212024 ].
We compute the medium-mass nuclei $^{16}$O and $^{40}$Ca using pionless effective field theory (EFT) at next-to-leading order (NLO). The low-energy coefficients of the EFT Hamiltonian are adjusted to experimantal data for nuclei with mass numbers $A=2$ and $3$, or alternatively to results from lattice quantum chromodynamics (QCD) at an unphysical pion mass of 806 MeV. The EFT is implemented through a discrete variable representation in the harmonic oscillator basis. This approach ensures rapid convergence with respect to the size of the model space and facilitates the computation of medium-mas…
We outline the modified formulation of baryon chiral effective field theory for nucleon-nucleon scattering and discuss the issue of a possible power counting violation by the nucleon mass. We also present the results for the quark mass dependence of the $^1S_0$ and $^3S_1$ scattering lengths and the deuteron binding energy at leading order.
Chiral effective field theory has established itself as the method of choice to study nuclear forces and low-energy nuclear dynamics. I review the status and prospects of this approach and discuss ongoing efforts to advance the precision frontier for ab initio description of few-nucleon systems. Special emphasis is put on the precise determination of the two-nucleon force at fifth order in the chiral expansion, role of the chiral symmetry, the convergence pattern of the chiral expansion and the quantification of the theoretical uncertainties. The discussed topics are essential for ongoing stud…
We review a new generation of nuclear forces derived in chiral effective field theory using the recently proposed semilocal regularization method. We outline the conceptual foundations of nuclear chiral effective field theory, discuss all steps needed to compute nuclear observables starting from the effective chiral Lagrangian and consider selected applications in the two- and few-nucleon sectors. We highlight key challenges in developing high-precision tree-body forces, such as the need to maintain consistency between two- and many-body interactions and constraints placed by the chiral and ga…
Chiral effective field theory (EFT) provides a systematic and controlled approach to low-energy nuclear physics. Here, we use chiral EFT to calculate low-energy weak Gamow-Teller transitions. We put special emphasis on the role of two-body (2b) weak currents within the nucleus, and discuss their applications in predicting physical observables.
We use chiral effective field theory (EFT) to make predictions for the longitudinal electromagnetic response function of the deuteron, f_L, which is measured in d(e,e'N) reactions. In this case the impulse approximation gives the full chiral EFT result up to corrections that are of O(P^4) relative to leading. By varying the cutoff in the chiral EFT calculations between 0.6 and 1 GeV we conclude that the calculation is accurate to better than 10 % for values of q^2 within 4 fm^{-2} of the quasi-free peak, up to final-state energies E_{np}=60 MeV. In these regions chiral EFT is in reasonable agr…
This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and then the varied frontiers of EFT for finite nuclei and nuclear matter are surveyed.
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective…
