Chiral perturbation theory in heavy-fermion formalism is developed for mesonexchange currents in nuclei and applied to nuclear axial-charge transitions. Calculation is performed to the next-to-leading order in chiral expansion which involves graphs up to one loop. The result turns out to be very simple. The previously conjectured notion of "chiral filter mechanism" in the time component of the nuclear axial current and the space component of the nuclear electromagnetic current is verified to that order. As a consequence, the phenomenologically observed soft-pion dominance in the nuclear process is given a simple interpretation in terms of chiral symmetry in nuclei. In this paper we focus on the axial current, relegating the electromagnetic current which can be treated in a similar way to a separate paper. We discuss the implication of our result on the enhanced axial-charge transitions observed in heavy nuclei and clarify the relationship between the phenomenological meson-exchange description and the chiral Lagrangian description.

Exchange vector currents are calculated up to one-loop order (corresponding to next-to-next-to-leading order) in chiral perturbation theory. As an illustration of the power of the approach, we apply the formalism to the classic nuclear process n + p → d + γ at thermal energy. The exchange current correction comes out to be (4.5 ± 0.3) % in amplitude giving a predicted cross section σ = (334 ± 3) mb in excellent agreement with the experimental value (334.2 ± 0.5) mb. Together with the axial charge transitions computed previously, this result provides a strong support for the power of chiral Lagrangians in nuclear physics. As a byproduct of our results, we suggest an open problem in the application of chiral Lagrangian approach to nuclear processes that has to do with giving a physical meaning to the short-range correlations that play an important role in nuclei.(a) Permanent address :

We calculate the cross-section for the thermal n + p → d + γ process in chiral perturbation theory to next-to-next-to-leading order using heavy-fermion formalism. The exchange current correction is found to be (4.5 ± 0.3) % in amplitude and the chiral perturbation at one-loop order gives the cross section σ np th = (334 ± 2) mb which is in agreement with the experimental value (334.2 ± 0.5) mb. Together with the axial charge transitions, this provides a strong support for the power of chiral Lagrangians for nuclear physics. PACS: 12.39.Fe 21.30.+y 21.10.Ky 25.40.Lw Typeset using REVT E X 1 One of the corner-stones of nuclear physics is the successful explanation in terms of exchange currents given two decades ago by Riska and Brown [1] of the ∼ 10% discrepancy between the experimental cross-section and the theoretical impulse approximation prediction for the processat threshold. Riska and Brown computed, using a realistic hard-core wave function for the deuteron, the two one-pion-exchange diagrams initially suggested in 1947 by Villars [2] plus the ω and ∆ resonance diagrams. That the dominant contributions to electroweak exchange currents could be gotten from current-algebra low-energy theorems was suggested by Chemtob and Rho [3] who gave a systematic rule for organizing the leading exchangecurrent diagrams effective at low energy and momentum. Although suspected since the Yukawa force was introduced, the work of Riska and Brown was the first unequivocal evidence for the role of mesons, in particular that of pions, in nuclear interactions. In this Letter, we show that the terms considered by Riska and Brown are a (main) part of the terms that figure in chiral perturbation theory to next-to-next-to-leading (N 2 L) order and that when completed by the rest of the N 2 L order terms, chiral perturbation theory scores an impressive success in nuclei.In the modern understanding of QCD, it is the spontaneous breaking of chiral symmetry associated with the light quarks that predominantly governs the structure of low-energy hadrons as well as the forces mediating between them. In fact, the full content of the gauge theory of strong interactions, QCD, can be expressed at low energy by a systematic chiral expansion starting with effective chiral Lagrangians [4]. Stated more strongly, such an approach, known as chiral perturbation theory (χP T ), while reproducing the current algebra, is now considered to be exactly equivalent to QCD in long wavelength regime [5]. Our paper reports the first quantitative chiral perturbation calculation of the fundamental nuclear process (1) and shows that chiral symmetry is indeed a powerful guiding principle in nuclear dynamics, confirming the work of Riska and Brown [1] and the conjecture of Kubodera, Delorme and Rho [6].Two recent developments provide a strong motivation for this work. The first is the work of Weinberg [7] and Ordóñez, Ray and van Kolck [8] on understanding nuclear forces from chiral Lagrangians. The second is the explanation by the present authors [9] of...

Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-density functional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferrably small fractional power of the density ρ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parameterisations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power. Purpose: Beginning with the observation that the Fermi momentum kF , i.e., the cubic root of the density, is a key variable in the description of Fermi systems, we first wish to examine if a power hierarchy in a kF expansion can be inferred from the properties of homogeneous matter in a domain of densities which is relevant for nuclear structure and neutron stars. For subsequent applications we want to determine a functional that is of good quality but not overtrained. Method: For the EDF, we fit systematically polynomial and other functions of ρ 1/3 to existing microscopic, variational calculations of the energy of symmetric and pure neutron matter (pseudodata) and analyze the behavior of the fits. We select a form and a set of parameters which we found robust and examine the parameters' naturalness and the quality of resulting extrapolations. Results: A statistical analysis confirms that low-order terms such as ρ 1/3 and ρ 2/3 are the most relevant ones in the nuclear EDF beyond lowest order. It also hints at a different power hierarchy for symmetric vs. pure nutron matter, supporting the need for more than one density-dependent terms in non-relativistic EDFs. The functional we propose easily accommodates known or adopted properties of nuclear matter near saturation. More importantly, upon extrapolation to dilute or asymmetric matter, it reproduces a range of existing microscopic results, to which it has not been fitted. It also predicts a neutron-star mass-radius relation consistent with observations. The coefficients display naturalness. Prospects: Having been already determined for homogeneous matter, a functional of the present form can be mapped onto extended Skyrme-type functionals in a straightforward manner, as we outline here, for applications to finite nuclei. At the same time, the statistical analysis can be extended to higher orders and for different microscopic (ab initio) calculations with sufficient pseudodata points and for polarized matter.

The proton burning process important for the stellar evolution of main-sequence, stars of mass equal to or less than that of the Sun, is computed in e †ective Ðeld theory by means of chiral perturbation expansion to the next to next to leading chiral order. This represents a modelindependent calculation consistent with low-energy e †ective theory of QCD comparable in accuracy to the radiative np capture at thermal energy previously calculated by Ðrst using very accurate two-nucleon wave functions backed up by an e †ective Ðeld theory technique with a Ðnite cuto †. The result obtained thereby is found to support within theoretical uncertainties the previous calculation of the same process by Bahcall and his coworkers.