Search results for "Sum rule in quantum mechanics"

Electromagnetic sum rules for light nuclei

2008

Electromagnetic sum rules describe gross features of the electromagnetic structure of nuclei 1). A well known example is the Thomas-Reiche-Kuhn (TRK) sum rule, which relates the integrated total El-absorption cross section to the ground state expectation value of the double commutator of the dipole operator D with the nuclear Hamiltonian. While the k inet ic energy gives a model independent contr ibut ion, i . e . , the classical sum rule ~cl = 60 NZ/A MeV mb, the nuclear twobody potential gives an additional contr ibution in the presence of exchange and/or momentum dependent (or nonlocal) forces. In this case, I

Electromagnetic sum rules in nuclei

2005

Ab Initio Computation of the Longitudinal Response Function in Ca40

2021

We present a consistent ab initio computation of the longitudinal response function ${R}_{L}$ in $^{40}\mathrm{Ca}$ using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for ${R}_{L}$ in $^{4}\mathrm{He}$ and the Coulomb sum rule in $^{40}\mathrm{Ca}$ against experimental data and other calculations. For ${R}_{L}$ in $^{40}\mathrm{Ca}$ we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a m…

Electric polarizability of nuclei from a longitudinal sum rule

1998

The nuclear electric polarizability is theoretically analyzed using a sum rule derived from the longitudinal part of the forward Compton amplitude. Beyond the leading dipole contribution, this approach leads to the presence of potential-dependent terms that do not show up in previous analyses. The significance of these new contributions is illustrated by performing an explicit calculation for a proton-neutron system interacting via a separable potential.

enhancement and the Glashow-Schnitzer-Weinberg sum rule

2000

Abstract In 1967 Glashow, Schnitzer and Weinberg derived a sum rule in the soft-pion and soft kaon limit relating the ΔI= 1 2 non-leptonic K→2π amplitude to integrals over strange and non-strange spectral functions. Using the recent ALEPH data from τ-decay, we show that the sum rule, slightly modified to reduce contributions near the cut, yields the correct magnitude decay amplitude corresponding to the ΔI= 1 2 rule.

Unsubtracted dispersion-relation for longitudinal compton amplitude

1975

Abstract It is shown that there is a simple connection between the slope, at q2 = 0, of the longitudinal Compton amplitude and the electric polarizability of the nucleon. The longitudinal subtraction function is thus known to order q2. The assumption of an unsubtracted dispersion relation for the longitudinal amplitude leads to a sum rule for the electric polarizability. This is a model independent test of the high-energy behaviour of the forward virtual Compton amplitude.

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…