Photoabsorption Sum Rule Research Articles

Quark correlations in the ground and excited nucleon states via the photo-absorption sum rules

The account of the dynamical correlations of quarks composing the nucleons is necessary for relevant description of nucleon and nuclear interactions. The present work is devoted to the use of the technique of known integral sum rules for the cross-sections and amplitude of the photo-hadron processes. In particular, a kind of the visual representation and quantification of the valence quark correlation characteristics referring to the photo-excitation of the nucleon resonances can be presented.

The role of charge-symmetry invariance in the σ−1 “bremsstrahlung-weighted” photo-absorption sum rules for the non-relativistic and relativistic few-body systems

Within the non-relativistic approach to photo-absorption sum rules for the 3N(4N)-nuclei the new σ−1 sum rules proposed which are based on general charge-symmetry (CS) consequences for a pair of the “CS-conjugated” triton and 3He nuclei and for the “self-conjugated” nucleus 4He. The numerical deviations from the less general “charge-independent” approach leading to the long-known Foldy-Khokhlow sum rules are estimated. In the relativistic domain the functional inapplicability is demonstrated of the “charge independence” approximation in the derivation of the σ−1 - type sum rules in the case of nucleons. With application of the relevant “charge symmetry” approach, the general system of the sum rules is derived and the inevitable isospin-dependent dynamics of the constituent quarks is underlined.

Photo-absorption sum rules σ–1 in different environments (Atoms, nuclei, nucleons)

Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ–1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the “CS-conjugated” triton and 3He.

Photo-absorption sum rulesσ−1and further questions about correlations of constituents inside bound hadrons

Within the non-relativistic approach to photo-absorption sum rules for the 3N(4N)-nuclei the new σ −1 sum rules are proposed which are based on general chargesymmetry (CS) consequences for the “CS-conjugated” triton and 3 He and the CS-self-conjugated 4 He . Combining the relativistic constituent quark model of the nucleon and the known spin-,isospin- and the dipole-moment fluctuation sum rules, the relevant moments of the quark coordinate distribution and correlation functions in the ground state of the nucleon are derived and discussed.

Photo-absorption sum rules σ−1 in different environments

Combining the spin-dependent dispersion GDH-sum rule, the iso-vector, photo-excitation states projecting Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (or generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector.

Compton scattering from nuclei and photo-absorption sum rules

We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new "constituent quark model" sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition we extract the $\alpha=0$ pole contribution for both proton and nuclei. Using the modern high energy proton data we find that the $\alpha=0$ pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman.

Classical sum rules and spin correlations in photoabsorption and photoproduction processes

In this paper we study the possibility of generalizing the classical photoabsorption ($\gamma a \to b c$) sum rules, to processes $b c \to \gamma a$ and crossed helicity amplitudes. In the first case, using detailed balance, the sum rule is written as $\int_{\nu_{th}}^\infty {\frac{{d\nu}}{\nu}} K\Delta \sigma_{Born} (\nu)=0$ where $K$ is a kinematical constant which depends only on the mass of the particles and the center of mass energy. For other crossed helicity amplitudes, we show that there is a range of values of $s$ and $t$ for which the differential cross section for the process $\gamma b \to a c$ or $a c \to \gamma b$ in which the helicities of the photon and particle $a$ have specific values, is equal to the differential cross section for the process in which one of these two helicities is reversed (parallel-antiparallel spin correlation).

PYGMY RESONANCES IN ARTIFICIAL NUCLEI: FAR-INFRARED ABSORPTION BY ELECTRON–HOLE DROPLETS

The structure of E1 resonances has been examined in a microscopic random phase approximation calculation for neutral, symmetric, closed shell and electron–hole systems in a quantum dot. The number of electron–hole pairs, N, is varied from 6 to 42. The occurrence of small, but distinct, E1 peaks in the far-infrared spectra located in the low energy tail of the giant dipole resonance consisting of highly coherent electron–hole excitations is predicted. These pygmy resonances account for about 2% of the dipole energy-weighted photoabsorption sum rule. A very weak dependence of the average pygmy resonance energy on the number of electron–hole pairs is found.

Far-infrared giant dipole resonances in neutral quantum dots

A resonance behaviour of the far-infrared absorption probability at a frequency ∼ N 1/4 is predicted for clusters of N electron–hole pairs (2⩽ N⩽110) confined in disk-shaped quantum dots. For radially symmetric dots, the absorption is dominated by a giant dipole resonance, which accounts for more than 98% of the energy-weighted photoabsorption sum rule.

Chiral restoration and the extended photoabsorption sum rule in nuclei

The Bethe-Levinger sum rule is extended beyond the potential model. The pion degrees of freedom are taken into account and the modifications of the potential theory are analysed within a dispersion relation on the Compton amplitude. Our aim is to extract from the photon data experimental information on the expectation value of the square of the pion field, a quantity which enters also in the restoration of chiral symmetry in nuclei. We are led to incorporate in the description the Δ resonance, which is strongly excited by the pion degrees of freedom.

Generalized photonuclear sum rule, resonance broadening and shadowing effects

The consistency of resonance broadening and shadowing effects in nuclear photoabsorption processes is investigated within a generalized photoabsorption sum rule. To check this consistency we show that a region exists where the impulse approximation is valid and the real Compton amplitude for free and bound nucleons is the same. The new data in the resonance region and the shadowing effect with α = 0.9 in the high-energy region are compatible with this generalized photoabsorption sum rule. The important role of correlations is also discussed.

Relativistic and retardation corrections to photon-nucleon absorption sum rules in the constituent-quark model

A general method is given for studying photoabsorption sum rules in the constituent-quark model with relativistic corrections. Kinematic or recoil contributions are properly taken into account. The model gives the standard expression for theσ−2 sum rule. Numerically relevant corrections are obtained for theσ0E1 (TRK) sum rule.

Classical photoabsorption sum rules

We use a quantum loop expansion to derive sum rule constraints on polarized photoabsorption cross sections in the Standard Model, generalizing earlier results obtained by Altarelli, Cabibbo, and Maiani. We show that the logarithmic integral of the spin-dependent photoabsorption cross section ∫ v th ∞ dv v δωBonn(v) vanishes foror any 2 → 2 process γa → bc in the classical, tree-graph approximation in the Standard Model, supersymmetric gauge theories, and other quantum field theories where the Drell-Hearn-Gerasimov sum rule is valid. Here ν = p · q M and Δσ( ν) = σ P ( ν) f- σ A ( ν) is the difference between the photoabsorption cross section for parallel and antiparallel photon and target helicities. Tests of the sum rule for the reactions γe → Wν and γγ → W + W f- can provide new tests of the canonical magnetic and quadrupole couplings of the Standard Model. We also extend the sum rule to certain virtual photon processes.

Relativistic effects in deuteron photoabsorption sum rules

The effect of the relativistic one-body ( Delta rho 1) and two-body ( rho 2) charge density is considered in the Thomas-Reiche-Kuhn deuteron photoabsorption sum rule sigma 0 and in the E1 bremsstrahlung-weighted cross section for different NN potential models. rho 2 includes all the terms, local and non-local, deriving from the one-pion exchange processes, calculated both in pseudoscalar and in pseudovector pi N coupling. Delta rho 1 also includes the kinematical corrections to the wavefunctions. The results are compared with those obtained in the exact calculation of the total cross section for the deuteron photodisintegration process. The remarkable sensitivity of the Delta rho 1 contributions of sigma 0 on the NN potentials is shown to come from the different short-range behaviour of these potentials.

Integrated photoabsorption strength and sum rules for a bound Dirac particle

Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a few percent. Whereas the total M1-strength is strongly underestimated by the lowest order M1-sum rule, the total E2-strength is reasonably well reproduced up to about 10% by the lowest order E2-sum rule.

Bremsstrahlung sum rule and nuclear charge distribution

We derive a model-independent relation between the nuclear charge radius R c , the bremsstrahlung-weighted photoabsorption sum rule σ −1 and the mean proton distance. Such a relation allows the mean proton distance to be determined from available experimental data. We also discuss the Foldy sum rule in the light of our result.

Deuteron photoabsorption sum rule: Two-body effects

In deuteron photoabsorption, the effect of mesonic exchange currents is considered in detail. Related to the electric dipole operator D1 (Siegert form) and to the nuclear interactions, a factor k appears in the integrated cross-section σ0, previously obtained by the Thomas–Reiche–Kuhn dipole sum rule. The introduction of the two-body density [Formula: see text] modifies the form of D1 and increases κ which becomes κ + Δκ. The influence of several NN potentials is clearly shown on the factor Δκ, some 25% difference occurring between a super soft core potential and the Paris potential. In this last case the value of Δκ is about 50% of the initial κ value.

Two-body effects in deuteron photoabsorption sum rules

The effect of the two-body charge and current densities is considered in the deuteron photoabsorption sum rules. The modifications induced in the Siegert form of the $E1$ operator give rise to an enhancement factor ${k}_{2}\ensuremath{\simeq}0.2$ over the Thomas-Reiche-Kuhn value of the integrated cross section ${\ensuremath{\sigma}}_{0}$. The bremsstrahlung-weighted cross section ${\ensuremath{\sigma}}_{\ensuremath{-}1}(E1)$ is found practically unchanged with respect to its value in impulse approximation, while ${\ensuremath{\sigma}}_{\ensuremath{-}1}(M1)$ shows a 30% increase. The calculations are performed with hard-core, soft-core, and super-soft-core potentials. The dependence on the potential model is small for ${\ensuremath{\sigma}}_{0}$ and quite negligible for ${\ensuremath{\sigma}}_{\ensuremath{-}1}$.NUCLEAR REACTIONS Two-body charge and current densities, deuteron photoabsorption sum rules.

Skyrme interactions and the total muon capture rate in 16O

A sum rule technique which systematically improves the usual closure approximation has been used to study the total muon capture rate in oxygen. To apply this method the energy-weighted moments m 0, m 1, m 2, m 3 for vector, axial vector and pseudoscalar excitations are calculated with different density-dependent effective interactions. These include standard Skyrme forces as well as new parametrizations developed recently for self-consistent RPA calculations. The v/ c corrections to the capture rate are evaluated consistently by calculating the corresponding moments m' 0, m' 1. Although the velocity dependence of the Skyrme interactions leads to a considerable reduction of total rates compared to the rates of the independent particle model, the results are still 10–60% higher than the experimental value. Similar discrepancies in photoabsorption sum rules indicate the need for ground-state correlations.

A new sum rule from the parton model

We present a photoabsorption sum rule, derived in the framework of the parton model. The sum rule agrees with the experimental data.