Nuclear Field Theory Research Articles

Dyson treatment of NFT medium polarization processes in superfluid nuclei

We discuss the solution of the Dyson equation (also known as the Nambu-Gor'kov equation) for the case of medium polarization Nuclear Field Theory (NFT) processes in nuclei, and apply it to the nucleus 120Sn. Starting from a mean field obtained with the Sly4 effective nucleon-nucleon force, (mk = 0.7), we renormalize the single-particle states and the pairing interaction through the coupling to collective vibrations of the system, obtaining a detailed description of the fragmentation of the quasiparticle strength and of the state-dependent pairing gap. These quantities are calculated in term of one- and two-particle spectroscopic amplitudes, amplitudes which can be used to calculate both one- and two-nucleon absolute transfer reaction cross sections to be directly confronted with the experimental findings.

Effects which will not blur the message of the 1H (11Li, 9Li) 3H reaction: observation of phonon–exchange pairing correlations in nuclei

The results of the 1H (11Li, 9Li) 3H experiment carried out recently at TRIUMF have given detailed information concerning the structure and the reaction mechanism at work in the case of halo, exotic nuclei, providing important stepping stones for an eventual quantitative description of superfluidity in finite nuclei. In fact, the central role played by renormalization processes as testified by the excitation of the 1/2– (2.69 MeV) member of the 9Li (2+ ⊗p3/2(π))j− multiplet (nuclear structure) together with the post-prior symmetry (reaction), testify to the fact that a detailed knowledge of the "bare" quantities, like e.g. the NN-interaction is likely to be less important, in a unified Nuclear Field Theory description of the structure and the reaction aspects of the experiment, than previously thought.

Lattice EFT calculation of thermal properties of low-density neutron matter

Thermal properties of low-density neutron matter are investigated by lattice calculation with nuclear effective field theory without pions up to the next-to-leading order. The 1S0 pairing gap is extracted near zero temperature at low densities. We find that the pairing gap is smaller than the BCS approximation with the conventional NN potentials, but not as small as those by various many-body calculations beyond BCS approximation. Our result is consistent with the recent Green's Function Monte Carlo calculation within the statistical errors. The critical temperature of the normal-to-superfluid phase transition and the pairing temperature scale are also extracted at low densities, and the phase diagram is given. We find that the physics of low-density neutron matter is clearly identified as being BCS-BEC crossover.

Neutral pion photoproduction off 3H and 3He in chiral perturbation theory

We calculate electromagnetic neutral pion production off three-nucleon bound states (3H, 3He) at threshold to leading one-loop order in the framework of chiral nuclear effective field theory. In addition, we analyze the dependence of the nuclear S-wave amplitude E0+ on the elementary neutron amplitude E0+π0n which in the case of 3He provides a stringent test of the prediction based on chiral perturbation theory. Uncertainties from higher order corrections are estimated.

Pions are neither perturbative nor nonperturbative: Wilsonian renormalization-group analysis of nuclear effective field theory including pions

Pionful nuclear effective field theory (NEFT) in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, $\Lambda$, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space including up to $\mathcal{O}(p^2)$ and find the nontrivial fixed points in the $^1S_0$ and $^3S_1$--$^3D_1$ channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative.

Perturbative Renormalization of Chiral Two Pion Exchange in Nuclear Effective Field Theory

We consider the perturbative renormalization of chiral two pion exchange in effective field theory when one pion exchange is treated non-perturbatively at leading order. This particular prescription, which is able to reconcile the requirements of power counting and renormalizability, implements the modified Weinberg counting proposal made by Nogga, Timmermans and van Kolck up to next-to-next-to-leading order. We show how the renormalizability of the scattering amplitude is able to determine the power counting of the contact operators.

Hamiltonian light-front field theory within an AdS/QCD basis

Non-perturbative Hamiltonian light-front quantum field theory presents opportunities and challenges that bridge particle physics and nuclear physics. Fundamental theories, such as Quantum Chromodynmamics (QCD) and Quantum Electrodynamics (QED) offer the promise of great predictive power spanning phenomena on all scales from the microscopic to cosmic scales, but new tools that do not rely exclusively on perturbation theory are required to make connection from one scale to the next. We outline recent theoretical and computational progress to build these bridges and provide illustrative results for nuclear structure and quantum field theory. As our framework we choose light-front gauge and a basis function representation with two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography.

MORE ABOUT THE WILSONIAN ANALYSIS ON THE PIONLESS NEFT

We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective field theory in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of [Formula: see text] in the S waves, and, on the other hand, (2) we consider the RG flows in higher partial waves (P and D waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two "fixed lines" and a "fixed surface" which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the S waves, but there are two relevant directions in the P waves at the nontrivial fixed points and three in the D waves. We explain the physical meaning of the P-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern and Richardson, and possible implementation of power divergence subtraction in higher partial waves.

Lattice calculation of thermal properties of low-density neutron matter with pionlessNNeffective field theory

Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the ${}^{1}{S}_{0}$ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined in the vanishing lattice filling limit. The ${}^{1}{S}_{0}$ pairing gap at $T\ensuremath{\approx}0$ is computed directly from the off-diagonal long-range order of the spin pair-pair correlation function and is found to be approximately 30% smaller than BCS calculations with the conventional nucleon-nucleon potentials. The critical temperature ${T}_{c}$ of the normal-to-superfluid phase transition and the pairing temperature scale ${T}^{*}$ are determined, and the temperature-density phase diagram is constructed. The physics of low-density neutron matter is clearly identified as being a BCS-Bose-Einstein condensation crossover.

Pion-less effective field theory on low-energy deuteron electrodisintegration

In view of its relation to Big Bang nucleosynthesis and a reported discrepancy between nuclear models and data taken at S-DALINAC, electro-induced deuteron breakup {sup 2}H(e,e{sup '}p)n is studied at momentum transfer q<100 MeV and close to threshold in the low-energy nuclear effective field theory without dynamical pions, EFT({pi} /). The result at next-to-next-to-leading order (N{sup 2}LO) for electric dipole currents and at next-to-leading order (NLO) for magnetic ones converges order-by-order better than quantitatively predicted and contains no free parameter. It is at this order determined by simple, well-known observables. Decomposing the triple differential cross section into the longitudinal-plus-transverse (L+T), transverse-transverse (TT), and longitudinal-transverse interference (LT) terms, we find excellent agreement with a potential-model calculation by Arenhoevel and co-workers, based on the Bonn potential. Theory and data also agree well on {sigma}{sub L+T}. There is however no space on the theory side for the discrepancy of up to 30%(3{sigma}) between theory and experiment in {sigma}{sub LT}. From universality of EFT({pi} /), we conclude that no theoretical approach with the correct deuteron asymptotic wave function can explain the data. Undetermined short-distance contributions that could affect {sigma}{sub LT} enter only at high orders (i.e., at the few-percent level). We notice some issuesmore » with the kinematics and normalization of the data reported.« less

Measurement of the ReactionH2(e,e′)at 180° Close to the Deuteron Breakup Threshold

Inclusive inelastic electron scattering off the deuteron under 180 degrees has been studied at the S-DALINAC close to the breakup threshold at momentum transfers q=0.27 fm;{-1} and 0.74 fm;{-1} with good energy resolution sufficient to map in detail the spin flip M1 response, which governs the starting reaction pn-->dgamma of big-bang nucleosynthesis over most of the relevant temperature region. Results from potential model calculations and (for q=0.27 fm;{-1}) from pionless nuclear effective field theory are in excellent agreement with the data.

Two-pion-exchange contributions to the [formula omitted] reaction

Our previous study of the near-threshold pp→ppπ0 reaction based on a hybrid nuclear effective field theory is further elaborated by examining the momentum dependence of the relevant transition operators. We show that the two-pion-exchange diagrams give much larger contributions than the one-pion-exchange diagram, even though the former is of higher order in the Weinberg counting scheme. The relation between our results and an alternative counting scheme, the momentum counting scheme, is also discussed.

Power counting for nuclear effective field theory and Wilsonian renormalization group

We consider an application of Wilsonian Renormalization Group (RG) to the power counting issue in Nuclear Effective Field Theory(NEFT). After reviewing the relevance of scaling dimensions in determining the power counting, we consider the pionless NEFT as the simplest example. The inclusion of the so-called “redundant operators” in a Wilsonian analysis is emphasized.

Renormalization group analysis of nuclear force

We study a relation between nuclear forces based on phenomenological approach ( V ph ) and nuclear effective field theory ( V EFT ) from a viewpoint of renormalization group. We find the relation between these two types of nuclear force using Wilsonian renormalization group equation. Considering the fact that V EFT is defined in a certain small model space, we show that a simple contact interaction accurately simulates short-distance physics, and that V EFT is free from dependence on modelling the details of the short-distance physics. Based on our result, we discuss some features of nuclear effective field theory.

Nuclear effective field theory with pions

Nuclear effective field theory with pions

Modern theory of nuclear forces: status and perspectives

I present and discuss recent results on nuclear forces and few-nucleon systems obtained in the framework of chiral effective nuclear field theory.

Modern theory of nuclear forces A.D. 2006

I present and discuss recent results on nuclear forces and few-nucleon systems obtained in the framework of chiral effective nuclear field theory.

Sigma exchange in the nuclear force and effective field theory

In the phenomenological description of the nuclear interaction a crucial role is traditionally played by the exchange of a scalar I=0 meson, the sigma, of mass 500-600 MeV, which however is not seen clearly in the particle spectrum and which has a very ambiguous status in QCD. I show that a remarkably simple and reasonably controlled combination of ingredients can reproduce the features of this part of the nuclear force. The use of chiral perturbation theory calculations for two pion exchange supplemented by the Omnes function for pion rescattering suffices to reproduce the magnitude and shape of the exchange of a supposed $\sigma$ particle, even though no such particle is present in this calculation. I also show how these ingredients can describe the contact interaction that enters more modern descriptions of the internucleon interaction.

Anomalous dimensions determine the power counting: Wilsonian RG analysis of nuclear EFT

The Legendre flow equation, a version of exact Wilsonian renormalization group (WRG) equation, is employed to consider the power counting issues in nuclear effective field theory. A WRG approach is an ideal framework because it is nonperturbative and does not require any prescribed power counting rule. The power counting is determined systematically from the scaling dimensions of the operators at the nontrivial fixed point. The phase structure is emphasized and the inverse of the scattering length, which is identified as a relevant coupling, is shown to play a role of the order parameter. The relations to the work done by Birse, McGovern, and Richardson and to the Kaplan–Savage–Wise scheme are explained.

Wilsonian RG and redundant operators in nonrelativistic effective field theory

In a Wilsonian renormalization group (RG) analysis, redundant operators, which may be eliminated by using field redefinitions, emerge naturally. It is therefore important to include them. We consider a nonrelativistic effective theory (the so-called “pionless” nuclear effective field theory) as a concrete example and show that the off-shell amplitudes cannot be renormalized if the redundant operators are not included. The relation between the theories with and without such redundant operators is established in the low-energy expansion. We perform a Wilsonian RG analysis for the off-shell scattering amplitude in the theory with the redundant operator.