Search results for "sum rule"
showing 10 items of 186 documents
The Drell-Hearn-Gerasimov Sum Rule
1994
The Drell-Hearn-Gerasimov (DHG) sum rule relates the helicity structure of the photoabsorption cross section to the anomalous magnetic moment of the nucleon. It is based on Lorentz and gauge invariance, crossing symmetry, causality and unitarity. A generalized DHG sum rule my be derived for virtual photons. At low momentum transfer this generalized sum rule is saturated by the resonance region, at high momentum transfer it may be expressed by the parton spin distributions measured in deep inelastic scattering. The longitudinal-transverse interference determines the Cottingham sum rule, which is related to the electric and magnetic form factors over the whole range of momentum transfer.
Gerasimov-Drell-Hearn sum rule and related integrals
2001
The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.
Partial-wave analysis of proton Compton scattering data below the pion-production threshold
2018
Low-energy Compton scattering off the proton is used for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The most recent determinations are based on either the fixed-$t$ dispersion relations (DR) or chiral perturbation theory in the single-baryon sector ($\chi$PT). The two approaches obtain rather different results for proton polarizabilities, most notably for $\beta_{M1}$ (magnetic dipole polarizability). We attempt to resolve this discrepancy by performing a partial-wave analysis of the world data on proton Compton scattering below thr…
A model study on the nuclear photoeffect
1977
In a simple model of a spinless particle moving in a finite square well potential influences of final state Born approximation and of various approximations in the electromagnetic operators on photoabsorption differential, total and integrated cross sections are investigated. While the Born approximation is very poor in all respects, the long wave length approximation turns out to be the best and reproduces the total cross section quite well. However, appreciable deviations occur in the differential cross section at intermediate energies. The integrated cross section slightly exceeds the classical sum rule resulting from nonanalyticity of the forward compton scattering amplitude, as is disc…
Dipole excitations of neutron-proton asymmetric nuclei
2004
Dipole excitations of unstable short-lived nuclei has been investigated experimentally by utilizing the electromagnetic-excitation process with high-energy secondary beams. From an exclusive measurement of the neutron-decay channels, differential cross sections with respect to excitation energy, which are directly related to the photo-absorption cross section and accordingly to the dipole-strength function, have been derived. Light neutron-rich nuclei in the mass range fromA = 11 toA = 23 with mass-over-charge ratios up toA/Z≈ 2.8 have been investigated systematically. Much in contrast to stable nuclei, low-lying dipole excitations well below the giant dipole resonance region have been obse…
Measurement of the dipole response of neutron-rich nuclei in the A∼20 region
2002
Abstract Coulomb break up of the neutron-rich 15,17 C and 17–22 O isotopes has been studied experimentally using secondary beams at energies of 500–600 MeV/u. A comparison between differential cross sections, d σ/ d E ∗ , with that obtained from a binary model shows that the main ground-state configuration of 15 C is 14 C(0 + )⊗ ν S 1/2 as expected. For 17 C, our preliminary data analysis reveals that the predominant (∼64%) configuration of the ground state is 16 C(2 + )⊗ ν s , d . For 17–22 O, the low-lying E1 strength amounts up to about 12% of the energy weighted sum rule strength depending on neutron number. The energy weighted E1 strength (integrated up to 15 MeV excitation energy) inc…
Ground state correlations and the nuclear charge distribution
1979
Combining a sum rule approach and the generator coordinate model we evaluate the influence of ground state correlations on the moments of the radial charge distribution. The isotopic and isotonic differences of the moments come out to be particularly sensitive to fluctuations of the ground state correlations due to changes in the low energy spectrum. A comparison with the experimental results for the isotopes of Ca, Fe, Ni and Zn shows a fair agreement and confirms the importance of the ground state correlations for isotopic and isotonic differences of radial moments.
One-loop calculation of the oblique S parameter in higgsless electroweak models
2012
We present a one-loop calculation of the oblique S parameter within Higgsless models of electroweak symmetry breaking and analyze the phenomenological implications of the available electroweak precision data. We use the most general effective Lagrangian with at most two derivatives, implementing the chiral symmetry breaking SU(2)_L x SU(2)_R -> SU(2)_{L+R} with Goldstones, gauge bosons and one multiplet of vector and axial-vector massive resonance states. Using the dispersive representation of Peskin and Takeuchi and imposing the short-distance constraints dictated by the operator product expansion, we obtain S at the NLO in terms of a few resonance parameters. In asymptotically-free gauge …
Set of sum rules for anomalous gauge boson couplings
1999
The dependence of the differential cross-section for on-shell W-pair production on the anomalous trilinear gauge couplings invariant under C and P is examined. It is shown that the contributions of the anomalous magnetic moments of the W boson due to the photon and the Z can be individually projected out by means of two appropriately constructed polynomials. The remaining four anomalous couplings are shown to satisfy a set of model-independent sum rules. Specific models which predict special relations among the anomalous couplings are then studied; in particular, the composite model of Brodsky and Hiller, and the linear and non-linear effective Lagrangian approaches. The relations predicted…
Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves
2012
In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for $s$-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg's compositeness condition, which was only valid for weakly bound states in one channel and $s$-wave. An example, requiring only experimental data, is shown for the $\ensuremath{\rho}$ meson indicating that i…