Low-energy theorem for virtual compton scattering and generalized sum rules of the nucleon

We formulate the low-energy theorem for virtual Compton scattering off a nucleon and examine its consequences for generalized nucleon polarizabilites. As a result of a new, model-independent definition of the low-energy limit for doubly virtual Compton scattering, all generalized sum rules of the nucleon have a continuous limit for real photons and obtain contributions from the t channel that were not included previously.     

The low-energy compton scattering and polarizability of spin-0 Hadrons in a Gaugeinvariant approach

In this work, the amplitude of the interaction of an electromagnetic field with π-mesons has been determined in the context of a relativistic gauge-invariant approach by solving electrodynamic equations with the use of the covariant Green’s function method. Based on this approach, the effective Lagrangian of the two-photon interaction with spin-0 hadrons taking into account the electric and magnetic polarizabilities has been obtained.     

Low-energy theorems for nuclear compton and raman scattering and 0+ → 0+ two-photon decays in nuclei

Low-energy theorems for elastic photon scattering (nuclear Compton scattering) from a nucleus of arbitrary spin are derived in the nonrelativistic approximation through terms quadratic in the photon frequency. The same derivation is made for the special case of 0⁺ → 0⁺ nuclear excitation by inelastic photon scattering (nuclear Raman scattering). Use is made of the general principle of gauge invariance, which bypasses the need to specify the form of the current operator explicitly. A general discussion of the contribution of mesonic exchanges is made and their effect is isolated. The center-of-mass correction to the nuclear diamagnetic susceptibility is calculated. The 0⁺ → 0⁺ two-photon decay amplitude is obtained from the nuclear Raman amplitude and the transition rate is calculated.     

Deeply virtual compton scattering from the neutron with CLAS and CLAS12

Generalised Parton Distributions (GPDs) offer an insight into the three-dimensional structure of the nucleon and its internal dynamics, relating the longitudinal momentum of quarks to their transverse position. A very effective means of accessing GPDs is via measurements of cross-sections and polarisation-asymmetries in Deeply Virtual Compton Scattering (DVCS). In particular, the beam-spin asymmetry (BSA) in DVCS from the neutron is especially sensitive to angular momentum of the up- and down-quarks, and its measurement therefore has potential to shed important light on the puzzle of nucleon spin. We present a preliminary extraction of BSA from a recent experiment using a 6 GeV electron beam and the CLAS detector at Jefferson Laboratory and introduce the Central Neutron Detector to be integrated with CLAS12 for the exclusive measurement of neutron DVCS at 11 GeV, made possible by the Jefferson Lab upgrade.     

Polarized electron scattering on spin zero and polarized spin-1/2 targets: Deep inelastic scattering,elastic electron-muon scattering,and elastic electron-nucleon scattering

A covariant formulation is developed and used to derive cross sections for the analysis of experiments in which polarized electrons (muons) are scattered from spin-zero and from polarized spin-1/2 targets. The analysis is based upon the single virtual photon representation of the electromagnetic interaction, initially, neither high-energy nor low-energy approximations are made so that one may derive results in which the orientation of the polarization vectors of the interacting particles changes as a result of the scattering. The general formulation is valid for all polarization configurations for the electron and nucleon in deep inelastic scattering, and for all polarization configurations for the initial and final state particles in elastic scattering. From the general covariant results, specific cross sections are derived for deep inelastic scattering as well as elastic scattering of electrons on muons, nucleons, and spin zero targets. In the latter case, the actual polarization vector for the scattered electron is determined. In the other cases discussed, this vector may be obtained from the cross sections. In addition, a method is presented for defining covariant cross sections, and this method is used to obtain results in the center-of-mass system as well as the laboratory system. Furthermore, explicit cross sections for virtual photon absorption are derived. Finally, in the appendices, an alternative method for the evaluation of traces is given as well as a discussion of the relativistic limit.     

Energy dependence of heavy ion collisions 4He + 12C and 12C + 12C elastic scattering

We have studied the transparency of heavy ion collisions at high energies by using Glauber's multiple scattering theory. The good agreement between our calculation and the existing data available strongly emphasizes the dominance of the nucleon-nucleon interaction in nucleus-nucleus collisions at high energies.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

Duality,scaling and fixed poles in virtual compton scattering

J-plane fixed poles are considered in the lepton-hadron scattering amplitudes. A relation between the scale-invariant behaviour of the virtual Compton scattering structure W₂ and the J = 1 pole is established using the wrong signature FESR. A dual mechanism for the generation of fixed poles, leading to a number of interesting implications for a singular behaviour of the pole residue in the variable q² (photon mass square), is indicated.     

Radiative photoproduction of pions and pion compton scattering

The cross section for the radiative photoproduction of ⁺ mesons on hydrogenp ⁺ n in dependence on the momentum transfer squared has been measured at the 1·2 GeV electron synchrotron PACHRA. Using extrapolation of the data to pion pole the differential cross section for the pion Compton scattering ^{+ +} has been obtained, and the electric polarizability of the ⁺ meson has been estimated to be =(20±12) x 10^-43cm³.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The authors thank P. A. Cherenkov for his constant attention to this work and helpful discussions at all stages of the work.     

Monopole excitation of 4He in α-particle scattering from 12C, 13C,and 16O

The excitation of the O⁺ state in ⁴He at 20.1 MeV has been studied in α-scattering from ¹²C, ¹³C, and ¹⁶O at E_α=65MeV by measuring the decay $\text{α}{}^1\text{→}\text{p}\text{+}\text{t}$ with a coincidence method. DWBA calculations of this monopole transition using both microscopic and collective model transition densities are presented.     

Elastic scattering of intermediate energy protons on4He and12C

The elastic angular distribution and polarization of ～1 GeV protons on⁴He and¹²C have been analysed using the recently proposed correlation expansion for the Glauber amplitude by retaining terms up to three-body density only. The calculations include Coulomb and spin effects. Using realistic form factors for target nuclei it is found that we need to consider only up to the second-order density term to provide a satisfactory explanation of both kinds of experimental data in the available momentum transfer region. The contribution of the three-body density term is only marginal except in⁴He differential cross-section in the cm angular range 45°<θ _cm<65°.     

One-arm12 C(e,p) cross section

The information content of one-arm (e, p) cross sections and the connection with coincidence (e, e′ p) cross sections is discussed. Results for the¹² C(e,p) cross section based on continuum shell model wavefunctions are given.     

C, P, and T invariance of noncommutative gauge theories

In this paper we study the invariance of the noncommutative gauge theories under C, P, and T transformations. For the noncommutative space (when only the spatial part of straight theta is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R(4)(straight theta) is transformed to the theory on R(4)(-straight theta), so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change straight theta by -straight theta. Hence altogether NCQED is CPT invariant. Moreover, we show that the CPT invariance holds for general noncommutative space-time.     

Angular dependence of intensity,chemical shift,and fine structure of the discontinuous compton scattering

The angular dependence of the intensity, the chemical shift, and the fini structure of discontinuous Compton radiation scattered by the K-electrons of Be, BeO, Li, and LiF were studied. Discrete lines resulting from scattering by L-electrons were observed in the case of Na, Al, and Si.     

Low-energy γp scattering and determination of proton polarizabilities

For the first time, an analysis of all experimental data on the differential cross section for elastic γp scattering at photon energies below 150 MeV is performed in order to determine the electric (α _p) and magnetic (β _p) polarizabilities of the proton. A fit to these data with two free parameters α p and β _p embedded into the theoretical cross section obtained on the basis of finite-energy s-channel dispersion relations gives the following world-average values of the proton polarizabilities: α _p=11.7±0.8 (stat.+syst.)±0.7 (model), β _p=2.3±0.9 (stat.+syst.)±0.7 (model) in units of 10^?4 fm³. The first error is combined—it takes into account the statistical and systematic errors in the experimental cross sections—while the second error comes from the theoretical uncertainties in the dispersion-theory cross sections.     

Low-energy Compton scattering and the polarizabilities of the proton

Differential cross-sections for Compton scattering from the proton have been measured at the MAMI tagged photon facility using the TAPS setup. The data cover an angular range of θ^lab _γ = 59^°-155^° and photon energies ranging from 55 MeV to 165 MeV. Our results are in good agreement with those from previous experiments, but yield higher precision. Using dispersion relations the proton polarizabilities have been determined to be = [11.9±0.5_stat.±1.3_syst.±0.3_mod.] ^. 10^-4 fm ³ and = [1.2±0.7_stat.±0.3_syst.±0.4_mod.)] ^. 10^-4 fm ³. These results confirm the Baldin sum rule which was re-evaluated to be + = [13.8±0.4] ^. 10^-4 fm ³. We can also conclude that there is no significant additional asymptotic contribution to the backward spin polarizability γ_π beyond the t-channel π⁰-exchange. Received: 9 January 2001 / Accepted: 13 February 2001     

Comparison of predictions for alignment in inelastic scattering of 12C + 12C

The predictions for the spin alignment in the single 2⁺ excitation in ${}^{12}\text{C +}{}^{12}\text{C}$ scattering in four typical models, i.e., the Austern-Blair diffraction model, the Band Crossing Model, the DWBA model and the strong-coupling model, are compared among themselves and with experiment.     

Electron scattering and charged pion photoproduction on12C and13C

Electron scattering and charged pion photoproduction at 200 MeV on¹²C and¹³C have been studied by the nuclear shell model to investigateM1 andE2 nuclear form factors of the isovector type. Starting with the Op-shell model of Hauge-Maripuu, the effects of core polarization by theM 3Y force and the one-pion-exchange current are taken into account. The effect of core polarization is found to be essential in both electron scattering and pion photoproduction, while the meson-exchange current, which also improves the calculated results, gives contributions of about 10%–15%.     

On spectral temperatures of negative pions produced in d 12C, 4He12C, and 12C12C collisions at 4.2 A GeV/c

The experimental transverse momentum distributions of negative pions produced in d ¹²C, ⁴He¹²C, and ¹²C¹²C collisions at 4.2 A GeV/c were analyzed in the framework of Hagedorn Thermodynamic Model. The spectral temperatures of π ^? mesons as well as their relative contributions to the total multiplicity of π ^? mesons were extracted from fitting the p _t spectra by two-temperature Hagedorn function. The results were compared systematically with the earlier results obtained from analysis of non-invariant center-of-mass energy spectra of negative pions produced in the analyzed collisions.