Dispersion relation formalism for virtual Compton scattering off the proton

We present in detail a dispersion relation formalism for virtual Compton scattering (VCS) off the proton from threshold into the Δ(1232)-resonance region. Such a formalism can be used as a tool to extract the generalized polarizabilities of the proton from both unpolarized and polarized VCS observables over a larger energy range. We present calculations for existing and forthcoming VCS experiments and demonstrate that the VCS observables in the energy region between pion production threshold and the Δ(1232)-resonance show an enhanced sensitivity to the generalized polarizabilities. Received: 14 March 2001 / Accepted: 18 June 2001     

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities γ₁,,γ₄ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at . In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.     

Compton scattering from deuterium and the polarizabilities of the neutron

A new program of Compton scattering on deuterium is under way at the tagged-photon facility at MAX-Lab in Lund, Sweden. We will measure differential cross sections between 60° and 150° over the photon energy range 60–115?MeV in 5?MeV steps, with the ultimate goal of obtaining new precision information on the electric and magnetic polarizabilities of the neutron.     

Generalized polarizabilities of the nucleon studied in the linear sigma model (II)

In a previous paper virtual Compton scattering off the nucleon has been investigated in the one-loop approximation of the linear sigma model in order to determine the 3 scalar generalized polarizabilities. We have now extended this work and calculated the 7 vector polarizabilities showing up in the spin-dependent amplitude of virtual Compton scattering. The results fulfill 3 model-independent constraints recently derived. Compared to the constituent quark model there exist enormous differences for some of the vector polarizabilities. At vanishing three-momentum of the virtual photon, the analytical results of the sigma model and of chiral perturbation theory can be related. The influence of the π⁰ exchange in the t channel has been discussed in some detail. Besides, the vector polarizabilities determine 2 linear combinations of the third order spin-polarizabilities appearing in real Compton scattering.     

Manifestly-covariant <Emphasis Type="Italic">p</Emphasis><Superscript>3</Superscript> calculation of nucleon Compton scattering

We compute the Compton scattering off the nucleons in the framework of manifestly covariant baryon chiral perturbation theory (BχPT). The results for observables differ substantially from the corresponding calculations in heavy-baryon chiral perturbation theory (HBχPT), most appreciably in the forward kinematics. We verify that the covariant p ³ result fulfills the forward-Compton-scattering sum rules. We also explore the effect of the Δ(1232) resonance at order p ⁴/Δ, with Δ ≈ 300 MeV, the resonance excitation energy. We find that the substantial effect of the Δ-excitation on the nucleon polarizabilities can naturally be accommodated in the manifestly covariant calculation. The article is published in the original.     

Spin polarizabilities of the nucleon from polarized low-energy Compton scattering

As a guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross-sections in low-energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low-energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the -resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.Received: 19 August 2003, Revised: 30 October 2003, Published online: 27 April 2004PACS: 13.40.-f Electromagnetic processes and properties - 13.60.Fz Elastic and Compton scattering - 14.20.Dh Protons and neutronsH.W. Grießhammer: Permanent address: Technische Universität MünchenT.R. Hemmert: Permanent address: Technische Universität München     

Compton scattering from chiral dynamics with unitarity and causality

Proton Compton scattering is analyzed with the chiral Lagrangian. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. We present and discuss predictions for various spin observables and polarizabilities of the proton. While for the transition polarizabilities γE1M2, γM1E2 we recover the results of strict chiral perturbation theory, for the diagonal γE1E1, γM1M1 elements we find significant effects from rescattering.     

Study of Electric Polarizabilities of Nucleon with a Constituent Quark Model and Pion Meson Cloud

In this work, a subtle role of the pion meson cloud effect on the electric polarizabilities of the proton and neutron is stressed. It is shown that the electric polarizabilities of the proton and neutron, and the difference between the electric polarizabilities of the proton and neutron can be explained by including the pion meson cloud explicitly. However, the magnitude of the estimated mean-square charge radius of the neutron is still far from the measurement.     

Observation of complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches

We consider the nonequilibrium evolution in the spin-1/2 XXZ Heisenberg chain for fixed magnetization after a local quantum quench. This model is equivalent to interacting spinless fermions. Initially an infinite magnetic field is applied to n consecutive sites and the ground state is calculated. At time t=0 the field is switched off and the time evolution of observables such as the z component of spin is computed using the time evolving block decimation algorithm. We find that the observables exhibit strong signatures of linearly propagating spinon and bound state excitations. These persist even when integrability-breaking perturbations are included. Since bound states ("strings") are notoriously difficult to observe using conventional probes such as inelastic neutron scattering, we conclude that local quantum quenches are an ideal setting for studying their properties. We comment on implications of our results for cold atom experiments.     

Nucleon polarizabilities in real and virtual Compton scattering: Recent theoretical issues

We review recent developments in the theoretical investigation of the nucleon polarizabilities. We first report on the static polarizabilities as measured in real Compton scattering, comparing and interpreting the results from various theoretical approaches. In a second step, we extend the discussion to the generalized polarizabilities which can be accessed in virtual Compton scattering, showing how the information encoded in these quantities can provide a spatial interpretation of the induced polarization densities in the nucleon.     

入射质子的能量对质子与晕核弹性散射观测量的影响

用相对论脉冲近似(RIA)对不同的中能质子(200MeV, 400MeV和800MeV)与¹⁴Be, ¹⁶O和¹²C的弹性散射进行了研究, 讨论了不同的入射能量对3种观测量, 即微分散射截面、分析本领和自旋转动函数的影响. 研究发现在小散射角的区域晕中子对观察量的影响趋势保持一致, 不随入射质子能量的改变而改变.     

Compton scattering from the deuteron and extracted neutron polarizabilities

Differential cross sections for Compton scattering from the deuteron were measured at MAX-Lab for incident photon energies of 55 and 66 MeV at nominal laboratory angles of 45 degrees, 125 degrees, and 135 degrees. Tagged photons were scattered from liquid deuterium and detected in three NaI spectrometers. By comparing the data with theoretical calculations in the framework of a one-boson-exchange potential model, the sum and the difference of the isospin-averaged nucleon polarizabilities, alpha(N)+beta(N)=17.4+/-3.7 and alpha(N)-beta(N)=6.4+/-2.4 (in units of 10(-4) fm(3)), have been determined. By combining the latter with the global-averaged value for alpha(p)-beta(p) and using the predictions of the Baldin sum rule for the sum of the nucleon polarizabilities, we have obtained values for the neutron electric and magnetic polarizabilities of alpha(n)=8.8+/-2.4(total)+/-3.0(model) and beta(n)=6.5-/+2.4(total)-/+3.0(model), respectively.     

Spin observables in neutron-proton elastic scattering

The analyzing power, , and the polarization transfer observables , and have been measured in neutron-proton elastic scattering at 260, 318, 386, 472 and 538 MeV for c.m. scattering angles between 64° and 160°. The data were obtained at PSI with a polarized neutron beam and a polarimeter analyzing the transverse polarization of the outgoing proton. They make a significant impact on the knowledge of the Isospin I = 0 nucleon-nucleon scattering. Received: 27 January 1998 / Published online: 30 March 1998     

Calculations of Three-Nucleon Reactions

Faddeev calculations using the chiral three-nucleon force in next-to-next-to-next-to-leading-order show that this force is too weak to provide an explanation for the low-energy A _y puzzle. The large discrepancy between data and theory for the neutron–neutron quasi-free-scattering cross section in low energy neutron–deuteron breakup requires a modification of the ${^{1}S_0}$ neutron–neutron force. We discuss the consequences that a bound ${^{1}S_0}$ state of two neutrons has on neutron–deuteron scattering observables. At higher energies we compare the solutions of the non-relativistic three-nucleon Faddeev equations with three-nucleon force included to the solutions of its Poincaré invariant version.     

COULOMB CORRECTION OF THE p-4He LOW ENERGY SCATTERING PHASE SHIFTS

A simple approach of Coulomb correction to the p-⁴He low energy scattering phase shifts is proposed,in which the channel radius of each partial wave is taken as an adjustable parameter.By using the Coulomb correction the n-⁴He scattering observables predicted from p-⁴He scattering phase shifts are in excllent agreement with experiment.Our calculations show that the neutron polarization depends sensitively on the channel radius of p waves and the obtained channel radius are adeguate to the different sets of phase shifts.     

Coulomb effects on single-particle exchange singularities

We consider the singularity in the scattering amplitude arising from the exchange of a massive neutral particle. It is shown that the presence of Coulomb distortion in the entrance or exit channel modifies the exchange pole residue. Within the framework of the Coulomb wave Born approximation the exchange pole residue is modified by an energy-dependent factor that is independent of the orbital angular momentum of the bound states involved in the exchange process. The implications of this result on the polarization observables and on recent determinations of the deuteron asymptotic D- to S-state ratio, by analytic continuation in cos θ to the neutron exchange pole, are discussed.     

Transport of quantum noise through random media

We present an experimental study of the propagation of quantum noise in a multiple scattering random medium. Both static and dynamic scattering measurements are performed: the total transmission of noise is related to the mean free path for scattering, while the noise frequency correlation function determines the diffusion constant. The quantum noise observables are found to scale markedly differently with scattering parameters compared to classical noise observables. The measurements are explained with a full quantum model of multiple scattering.     

QCD sum rules and electromagnetic polarizabilities of a nucleon

We investigate the electromagnetic polarizabilities of a nucleon using the method of QCD sum rules. The diagrams in the operator product expansion are taken into account up to dimension 6. We find that the polarizabilities of a nucleon can be expressed by means of three new kinds of susceptibilities of quark condensates which represent the response under weak external electromagnetic fields. Estimating the susceptibilities with the QCD sum rules itself based on the formalism by Balitsky et al., we see that good agreement is obtained for the neutron electric polarizability.