Two-pion Exchange Research Articles

Signatures of the chiral two-pion exchange electromagnetic currents in theH2andHe3photodisintegration reactions

The recently derived long-range two-pion exchange (TPE) contributions to the nuclear current operator which appear at next-to-leading order (NLO) of the chiral expansion are used to describe electromagnetic processes. We study their role in the photodisintegration of 2H and 3He and compare our predictions with experimental data. The bound and scattering states are calculated using five different parametrizations of the chiral next-to-next-to-leading order (N2LO) nucleon-nucleon (NN) potential which allows us to estimate the theoretical uncertainty at a given order in the chiral expansion. For some observables the results are very close to the predictions based on the AV18 NN potential and the current operator (partly) consistent with this force. In the most cases, the addition of long-range TPE currents improved the description of the experimental data.

Renormalization of chiral two-pion exchangeNNinteractions withΔexcitations: Correlations in the partial-wave expansion

In this work we consider the renormalization of the chiral two-pion exchange potential with explicit delta-excitations for nucleon-nucleon scattering at next-to-leading (NLO) and next-to-next-to-leading order (N2LO). Due to the singular nature of the chiral potentials, correlations between different partial waves are generated. In particular we show that two-body scattering by a short distance power like singular attractive interaction can be renormalized in all partial waves with a single counterterm, provided the singularities are identical. A parallel statement holds in the presence of tensor interactions when the eigenpotentials in the coupled channel problem also coincide. While this construction reduces the total number of counterterms to eleven in the case of nucleon-nucleon scattering with chiral two-pion exchange interactions with delta degrees of freedom, the differences in the scattering phases as compared to the case with the uncorrelated partial wave renormalization become smaller as the angular momentum is increased in the elastic scattering region.

Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering

We study the perturbative renormalizability of chiral two-pion exchange for singlet and triplet channels within effective field theory, provided that the one-pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed to obtain finite results when the cutoff is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that perturbative chiral two-pion exchange reproduce the data up to a center-of-mass momentum of $k~200--300$ MeV in the singlet channel and $k~300--400$ MeV in the triplet.

Effective short-range interaction for spin-singletP-wave nucleon-nucleon scattering

Distorted-wave methods are used to remove the effects of one- and two-pion exchange up to order Q^3 from the empirical 1P1 phase shift. The one divergence that arises can be renormalised using an order-Q^2 counterterm which is provided by the (Weinberg) power counting appropriate to the effective field theory for this channel. The residual interaction is used to estimate the scale of the underlying physics.

The ab initio No-Core Shell Model and Light Nuclei

The ab initio no-core shell model (NCSM) is a well-established theoretical framework aimed at an exact description of nuclear structure starting from high-precision interactions between the nucleons. In the NCSM we consider a system of A point-like, non-relativistic nucleons that interact by realistic inter-nucleon interactions. We consider two-nucleon interactions that reproduce nucleon-nucleon phase shifts with high precision, typically up to 350 MeV lab energy. We can also include three-nucleon interactions with terms, e.g., related to two-pion exchanges with an intermediate delta excitation. Both semi-phenomenological potentials, based on meson-exchange models, as well as modern chiral interactions can be considered. The performance of the NCSM within nuclear physics will be exemplified by showing results from studies of light nuclei. Major challenges in the future development of the method will be outlined.

Deconstructing 1S0 nucleon-nucleon scattering

A distorted-wave method is used to analyse nucleon-nucleon scattering in the 1S0 channel. Effects of one-pion exchange are removed from the empirical phase shift to all orders by using a modified effective-range expansion. Two-pion exchange is then subtracted in the distorted-wave Born approximation, with matrix elements taken between scattering waves for the one-pion exchange potential. The residual short-range interaction shows a very rapid energy dependence for kinetic energies above about 100 MeV, suggesting that the breakdown scale of the corresponding effective theory is only 270MeV. This may signal the need to include the Delta resonance as an explicit degree of freedom in order to describe scattering at these energies. An alternative strategy of keeping the cutoff finite to reduce large, but finite, contributions from the long-range forces is also discussed.

Low energy electromagnetic processes based on the chiral effective field theory approach

Chiral effective field theory describes the interaction of nucleons and pions in the low-energy regime of QCD. This theory offers a consistent picture of nuclear forces and nuclear current operators. We study the electromagnetic processes based on ChEFT dynamical picture and compare our predictions to results obtained in the conventional framework. In particular, we consider low energy photo-disintegration of the deuteron at different orders of the chiral expansion. We investigate a role of different ingredients in the two-nucleon current operator. For the first time calculations involve consistent contributions from long-range two-pion exchange currents which appear at next-to-leading order of the chiral expansion. We present novel results for cross sections and various polarization observables.

Renormalizing the NN interaction with multiple subtractions

The aim of this work is to show how to renormalize the nucleon-nucleon interaction at next-to-next-to-leading order using a systematic subtractive renormalization approach with multiple subtractions. As an example, we calculate the phase shifts for the partial waves with total angular momentum J = 2 . The intermediate driving terms at each recursive step as well as the renormalized T-matrix are also shown. We conclude that our method is reliable for singular potentials such as the two-pion exchange and derivative contact interactions.

Modified effective range expansion for nucleon-nucleon scattering

The standard effective range expansion is commonly used in nucleon-nucleon scattering to encode the properties of the nuclear force model-independently in a small set of parameters. However, its applicability is limited by the longest-range part of the nuclear potential, i.e. by the one pion exchange, to the domain of momenta below half the pion mass. Therefore, it is not useful to study shorter-range parts of the interaction, e.g. two-pion exchange. To this aim a modification that explicitly takes a given long-range part of the interaction into account is required. This is known as modified effective range expansion. Here, we apply this approach to the nucleonnucleon interaction to separate the known long-range interactions from the rest. To show the effectiveness of this technique, we consider a toy model with a two-range potential. We study the scaling behaviour of the parameters of the standard and modified effective range expansion in this two-scale problem and compare their convergence behaviour.

Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation

Using the method of unitary transformation in combination with chiral effective field theory we derive the two-pion exchange contributions to the two-nucleon electromagnetic current. A formal definition of the current operator in this scheme and the power counting is presented. We discuss the implications of additional unitary transformations that have to be present to ensure the renormalizability of the one-pion exchange current. Further, we give explicit and compact results for the current in coordinate-space.

Three-nucleon force effects in proton-deuteron scattering

Possible three-nucleon forces that may be considered in addition to a widely accepted two-pion exchange three-nucleon force are studied to improve the fit to experimental data of proton-deuteron scattering. Calculations are performed with including effects of long-range Coulomb force by a recently developed method to solve the Faddeev equation in coordinate space. Two different kinds of three-nucleon potentials: a phenomenological potential and one due to the exchange of pion and sigma bosons, are presented and compared with experimental data of elastic differential cross sections, a tensor analyzing power, and a nucleon-to-nucleon polarization transfer coefficient.

Renormalization of Proton-Proton Scattering and Proton-Proton Fusion with Chiral Two Pion Exchange: Regulator Independent Results.

The renormalization of the s -wave proton-proton scattering amplitude with chiral two-pion exchange is considered up to next-to-next-to-leading order in the chiral expansion. The resulting phase shifts accurately describe the s -wave phases up to k cm ≃ 200 MeV. The effect and possible improvements coming from finite cut-offs or spectral function regularization are considered. Proton-proton fusion is calculated with the resulting renormalized wave functions in a regulator independent way at next-to-next-to-leading order (N 2 LO).

Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation

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.

Subtractive renormalization of theNNinteraction in chiral effective theory up to next-to-next-to-leading order:Swaves

We extend our subtractive-renormalization method to evaluate the ${}^{1}{\mathrm{S}}_{0}$ and ${}^{3}{\mathrm{S}}_{1}\text{\ensuremath{-}}{}^{3}{\mathrm{D}}_{1} \mathit{NN}$-scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the $\mathit{NN}$ potential, the ${}^{1}{\mathrm{S}}_{0}$ phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the ${}^{1}{\mathrm{S}}_{0}$ phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the $J=1$ coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the ${}^{3}{\mathrm{S}}_{1}$scattering length, the ${}^{3}{\mathrm{S}}_{1}$ phase shift at a specific energy, and the ${}^{3}{\mathrm{S}}_{1}\text{\ensuremath{-}}{}^{3}{\mathrm{D}}_{1}$ generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO $S$-wave phase shifts for cutoffs as large as $19$ GeV and show that the presence of linear energy dependence in the $\mathit{NN}$ potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the $\mathit{NN}$ potential.

Hypernuclear single particle spectra based on in-medium chiral [formula omitted] dynamics

A previously derived relativistic energy density functional for nuclei, based on low-energy in-medium chiral dynamics, is generalized to implement constraints from chiral SU ( 3 ) effective field theory and applied to Λ hypernuclei. Density-dependent central and spin–orbit mean fields are calculated for a Λ hyperon using the SU ( 3 ) extension of in-medium chiral perturbation theory to two-loop order. Long range ΛN interactions arise from kaon-exchange and from two-pion-exchange with a Σ hyperon in the intermediate state. Short-distance dynamics is encoded in contact interactions. They include scalar and vector mean fields reflecting in-medium changes of quark condensates, constrained by QCD sum rules. The Λ single particle orbitals are computed for a series of hypernuclei from 13 Λ C to 208 Λ Pb. The role of a surface (derivative) term is studied. Its strength is found to be compatible with a corresponding estimate from in-medium chiral perturbation theory. Very good agreement with hypernuclear spectroscopic data is achieved. The smallness of the Λ-nuclear spin–orbit interaction finds a natural explanation in terms of an almost complete cancellation between short-range scalar/vector contributions and longer range terms generated by two-pion exchange.

Renormalization of the off-shell chiral two-pion exchangeNNinteractions

The renormalization, finiteness and off-shellness of short distance power like singular interactions is discussed. We show analytically that the renormalizability of the off-shell scattering amplitude relies completely on the corresponding on-shell amplitude without proliferation of new counterterms. We illustrate the result by complementary calculations both in coordinate as well as in momentum space in the simplest 1S0 channel for chiral np interactions including Two Pion Exchange.

Energy of the ground and2+excited states ofΛΛ10Be: A partial ten-body model

The energies of the ground and excited 2{sup +} states of {sub {lambda}}{sub {lambda}}{sup 10}Be have been calculated variationally in the Monte Carlo framework. The hypernucleus is treated as a partial ten-body problem in the {lambda}{lambda}+{alpha}{alpha} model where nucleonic degrees of freedom of {alpha}'s are taken into consideration ignoring the antisymmetrization between two {alpha}'s. The central two-body {lambda}N and {lambda}{lambda} and the three-body dispersive and two-pion exchange {lambda}NN forces, constrained by the {lambda}p scattering data and the observed ground state energies of {sub {lambda}}{sup 5}He and {sub {lambda}}{sub {lambda}}{sup 6}He, are employed. The product-type trial wave function predicts binding energy for the ground state considerably less than for the event reported by Danysz et al.; however, it is consistent with the value deduced assuming a {gamma} ray of 3.04 MeV must have escaped undetected in the decay of the product {sub {lambda}}{sup 9}Be* {yields} {sub {lambda}}{sup 9}Be+{gamma} of the emulsion event {sub {lambda}}{sub {lambda}}{sup 10}Be{yields} {pi}{sup -}+p+{sub {lambda}}{sup 9}Be* and for the excited 2{sup +} state closer to the value measured in the Demachi-Yanagi event. The hypernucleus {sub {lambda}}{sub {lambda}}{sup 10}Be has an oblate shape in the excited state. These results are consistent with the earlier four-body {alpha} cluster modelmore » approach where {alpha}'s are assumed to be structureless entities.« less

Two-potential formula and its application to proton-proton scattering

Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range Coulomb forces as well as short distance singular potentials. As an example illustrating the use of the formula we analyze the determination of the strong proton-proton scattering s-wave phase shift from the experimentally determined Coulomb phase when the one-pion exchange and two-pion exchange chiral potentials are taken into account and analyze the relevant scales of the problem.

A relativistic structure of one-meson and one-gluon exchange forces and a lower excitation spectrum of the nucleon and Δ

A lower excitation spectrum of the nucleon and Δ is calculated in a relativistic chiral quark model. Corrections to the baryon mass spectrum from the second-order self-energy and exchange diagrams induced by pion and gluon fields are estimated in the field-theoretical framework. Convergent results for the self-energy terms are obtained when including the intermediate quark and antiquark states with a total momentum up to j = 25/2. Relativistic one-meson and color-magnetic one-gluon exchange forces are shown to generate spin 0, 1, 2, etc operators, which couple the lower and the upper components of the two interacting valence quarks and yield reasonable matrix elements for the lower excitation spectrum of the nucleon and Δ. The only contribution to the ground-state nucleon and Δ comes from the spin-1 operators, which correspond to the exchanged pion or gluon in the l = 1 orbit, thus indicating that both pion exchange and color-magnetic gluon exchange forces can contribute to the spin of baryons. Is is shown also that the contribution of the color-electric component of the gluon fields to the baryon spectrum is enormously large (more than 500 MeV with a value of αs = 0.65) and one needs to restrict to very small values of the strong coupling constant or to exclude completely the gluon-loop corrections to the baryon spectrum. With this restriction, the calculated spectrum reproduces the main properties of the data; however it needs further contribution from the two-pion exchange and instanton-induced exchange (for the nucleon sector) forces in consistence with the realistic NN-interaction models.

The degenerate spin-flip doublet (3+/2,5+/2) ofΛ9Be

The energy of the degenerate doublet $({3}^{+}/2,{5}^{+}/2)$ of ${}_{\ensuremath{\Lambda}}^{9}\mathrm{Be}$, treating it as a partially nine-body system in the $\ensuremath{\Lambda}\ensuremath{\alpha}\ensuremath{\alpha}$ cluster model, has been calculated in the variational Monte Carlo framework. A simplified treatment, with the central two-body Urbana type $\ensuremath{\Lambda}N$ and the three-body dispersive and two-pion exchange $\ensuremath{\Lambda}\mathit{NN}$ forces along with the central two- and three-body correlations, is found to be adequate in explaining the energy of observed $\ensuremath{\gamma}$-ray transition from the excited degenerate doublet to the ground state. The hypernucleus ${}_{\ensuremath{\Lambda}}^{9}\mathrm{Be}$ is highly deformed and has an oblate shape in the excited state. The results of the present work are consistent with the earlier three-body cluster model analyzes of ${}_{\ensuremath{\Lambda}}^{9}\mathrm{Be}$.