Coulomb Sum Rule Research Articles

Light-front sum rules.

Sum rules for inelastic electron scattering from a composite system are derived within the framework of light-front dynamics. The underlying assumptions are similar in spirit to those used to derive the nonrelativistic Coulomb sum rule. The light-front sum rule yields parton model sum rules in the limit that the constituents are structureless Dirac particles. The connection to the Coulomb sum rule is discussed.

Nuclear medium modification of nucleons via a Bethe ansatz model.

The modification of the internal structure of nucleons inside the nucleus is investigated within the context of a constituent quark model, in which quarks interact forming bound clusters that act as nucleons. The elastic form factor, the momentum distribution, the correlation function, and the Coulomb sum rule are calculated. The contribution to these structure functions arising from nucleon degrees of freedom is identified by means of an impulse approximation, in which the quark structure of nucleons is assumed to be unaffected by other nucleons, and the dynamics of nucleons is given by an effective theory, extracted from our quark model. The effect of the modification of the nucleon is found to be noticeable on the elastic form factor at large momentum transfer, and on the Coulomb sum rule. A cluster approximation is also used to study the extent to which these effects are due to exchange of quarks.

Many-body correlation effects on the longitudinal response in the quasielastic (e,e') reaction.

A study is made of the influence of many-body corrections on the longitudinal response function for the inclusive quasielastic (e, e') reaction. This response function is well known to be suppressed, by about a factor of two, when compared with theoretical predictions based on the concept of single nucleon ejection. This is a characteristic of the data that persists through a wide range of different nuclei and suggests a violation of the Coulomb sum rule. It is here shown how an estimation of the effect of many-body correlations, including a consistent treatment of inelastic final state interactions, can be computed through a relationship to the nuclear optical model. The approximations are such that the Coulomb sum rule in guaranteed to remain satisfied providing the optical potential is hermitian analytic. Calculations of the longitudinal response are carried out within the Fermi Gas Model using phenomenological parameterizations of the nuclear optical potential. The reductions

Non-energy-weighted sum rule in the response function method: One- and two-body density matrices

Two expressions for the non-energy-weighted sum rules are studied in detail. One of them contains the information of one- and two-body density matrices of the ground state of a nucleus. The other summarizes the elastic and inelastic processes which determine the nuclear response to an external probe. These processes are well described by the response function method. In this paper, we establish the relation of these two expressions; namely, we show which processes of the response have the information of the one- and two-body density matrices. To make the physical points clear, we use the Coulomb sum rule as an example.

The Coulomb sum rule in the extended RPA theory

We investigate in detail the Coulomb sum rule of 40Ca with momentum transfer q = 2.0 fm −1, in the framework of traditional nuclear many-body theory, i.e. by using the G-matrix and the extended RPA theory. We have separately evaluated the one-body part (total charge Z) and the two-body part (two-body correlation function) of the sum rule. A considerable part of the missing charge in the existing experimental data is shown to be explained by the ground-state correlations induced by the tensor force. It is also found that the one-body part is not fully observed in the existing experimental data. Problems left to be discussed are pointed out.

Pionic effects in quasielastic electron scattering

Quasielastic electron scattering from nuclei at high momentum transfer and energy loss is approached using a model which incorporates specific classes of effects arising from the exchange of pions between nucléons in the nucleus. Building on the (purely nucleonic) relativistic Fermi gas responses, pionic effects in 1p1h correlation and meson exchange current contributions to the total responses are studied. The extent to which current conservation is satisfied when such effects are included is examined. In applying the model to predictions for a typical nucleus, consequences for the Coulomb sum rule and y-scaling are also discussed.

Pionic effects in quasielastic electron scattering

Quasielastic electron scattering from nuclei at high momentum transfer and energy loss is approached using a model which incorporates specific classes of effects arising from the exchange of pions between nucléons in the nucleus. Building on the (purely nucleonic) relativistic Fermi gas responses, pionic effects in 1p1h correlation and meson exchange current contributions to the total responses are studied. The extent to which current conservation is satisfied when such effects are included is examined. In applying the model to predictions for a typical nucleus, consequences for the Coulomb sum rule and y-scaling are also discussed.

Green's function Monte Carlo calculations of light nuclei

Recently, Green's Function Monte Carlo methods have been developed which enable one to perform exact calculations for the ground states of three and four body nuclei. These methods allow the alpha particle to be used as a testing ground for a variety of two- and three-nucleon interaction models, both in terms of their ground state energies and a variety of other ground state expectation values. We present a brief review of GFMC methods as applied to light nuclei, including recent improvements of the algorithm and a discussion of the prospects for the inclusion of momentum-dependent terms. We then discuss results for the ground state energy, one- and two-body density distributions, D-state probability, coulomb sum rule, and momentum distributions. The GFMC results are compared to experimental results and to variational Monte Carlo calculations.

Two-body nuclear density determined from quasielastic electron scattering in the three-nucleon system.

The proton-proton two-body density in the three-nucleon system is extracted from quasielastic-electron-scattering data. The two-body density is determined in momentum space using the integrated longitudinal response functions and assuming that the nonrelativistic Coulomb sum rule is valid. The range of the measurement is for momenta between 200 and 550 MeV/c. The data are compared to a proton-proton density calculated using Faddeev wave functions. The data and the calculation both show a ``second maximum'' but the data exceed the calculation by about an order of magnitude.

The Coulomb sum rule of 40Ca

We investigate the Coulomb sum rule of40Ca for the momentum transfer q=2.0 fm−1 in the framework of traditional nuclear many-body theory, namely, by using the G-matrix and the extended RPA theory. We have evaluated the one-body part (total chargeZ and the two-body part (two-body correlation function) of the Coulomb sum rule separately. A considerable part of the missing charge in the existing experimental data is found to be explained maily by the ground state correlations induced by the tensor force. It was also found that the one-body part (charge Z) is not in the existing experimental data.

Quasielastic (e,e') sum rule saturation.

A microscopic Green's function doorway formalism is used to study Coulomb sum rule saturation in inclusive quasielastic electron scattering as a function of momentum transfer. Form factor, kinematical restriction, and final-state interaction effects on the approach to saturation are examined in detail, as are the roles of nonhermiticity, energy dependence, and the analytic behavior of the final-state interactions. The implications of relativistic kinematics and dynamics for the approach to saturation at not-too-high values of the momentum transfer are assessed. Because the pair production of relativistic treatments destroys the asymptotic nature of the nonrelativistic Coulomb sum rule, the degree to which a regime of validity can be expected for this sum rule, and its location, is considered. The breakdown of the sum rule as the momentum transfer increases is also examined. Similar theoretical studies of an analogous nonrelativistic transverse sum in its saturation region are developed as well. Theoretical predictions are compared with the experimental data for $^{40}\mathrm{Ca}$ both directly and using a variety of theoretical prescriptions and limits. Neutron knockout contributions and associated uncertainties due to ambiguity in the free neutron form factors are examined.

Causality and the Coulomb sum rule in nuclei.

The spectral function in the Jost-Lehmann-Dyson representation of causal commutators is determined for the nonrelativistic limit of inclusive lepton scattering from nuclei. From this an extrapolation of the Coulomb sum rule to higher-momentum transfers is performed which is consistent with the requirement of causality.

Coulomb sum rule in the relativistic sigma omega rho model.

The Coulomb sum rule is studied using the random-phase approximation to the relativistic \ensuremath{\sigma}\ensuremath{\omega}\ensuremath{\rho} model. The addition of the \ensuremath{\rho} meson to the \ensuremath{\sigma}\ensuremath{\omega} model has a large effect on the quenching of the sum rule because of its random-phase approximation correlation and its coupling with the isovector anomalous magnetic moment of the nucleon. The low-density surfaces of finite nuclei have a larger response than their interior so that the quenching of the Coulomb sum rule is not as significant as in the nuclear matter ground state. Calculations for finite nuclei using the local density approximation agree with existing experimental data on $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{56}\mathrm{Fe}$.

Models for relativistic coulomb sum rules: Expansions in moments of the nuclear momentum density

Relativistic Coulomb sum rules for quasielastic electron scattering from nuclei are developed using a class of relativistic models for the nuclear ground-state momentum distribution. Approximate sum rules at constant 3- or 4-momentum transfer are expressed as expansions in moments of the momentum distribution. New sum-rule functions are derived which, even for very large values of energy and momentum where relativistic effects become dominant, approach simple asymptotic values; in doing so they approximately retain the flavor of the nonrelativistic Coulomb sum rule which approaches Z. Specific ways of achieving an optimum separation of effects relating to the electromagnetic response of a single nucleon and of a many-body system of structureless particles are discussed, including a study of sensitivities to alternative parameterizations of G En. Comparisons of results using different momentum distributions for the case of 16O are presented.

Proton-neutron correlations and the longitudinal nuclear response

We study the influence of the proton-neutron correlations, in particular of the tensor ones, on the longitudinal nuclear response. They generate a high-energy tail that we evaluate. We show that this tail produces an apparent quenching of the Coulomb sum rule. The amount of quenching found is significant, although insufficient to explain the totality of the missing strength.

Longitudinal response functions and sum rules for quasielastic electron scattering from 3H and 3He.

Longitudinal response functions for /sup 3/H and /sup 3/He have been obtained from inclusive electron scattering cross sections, for 200less than or equal toqless than or equal to550 MeV/c. The response functions are compared with several theoretical calculations, all of which use exact three-body ground-state wave functions. The response functions are found to be more similar than the calculations predict. When a direct calculation of the Coulomb sum rule is compared with our data, the agreement is good and evidence for two-proton correlations in /sup 3/He is clear.

DWBA (e,e′) cross section and coulomb sum rule

The Coulomb sum rule is studied in 12C, 40Ca and 208Pb in impulse approximation including the distortion of the electron wave. The effects are sizeable even in medium weight nuclei. Transverse responses are also discussed.

Delta electroproduction and inelastic charge scattering from carbon and iron.

Electroproduction of the $\ensuremath{\Delta}$ isobar in C and Fe has been studied for incident electrons with energies between 0.6 and 1.6 GeV. A longitudinal-transverse decomposition of the inclusive cross section has been made for ${q}_{\ensuremath{\mu}}^{2}=0.1$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. The residual longitudinal cross sections measured do not provide the additional strength needed above the quasifree region to satisfy the Coulomb sum rule. The transverse cross sections are in good agreement with data from photoabsorption.

Vacuum polarization and the Coulomb sum rule

Abstract The longitudinal response function for quasielastic electron scattering from nuclear matter is calculated in a relativistic random phase approximation to the Walecka model including vacuum polarization effects. The Walecka model has nucleons interacting with isoscalar sigma and omega meson fields. The change in the vacuum polarization response of the Dirac sea because of the decrease in the relativistic effective mass of the nucleons leads to a thirty percent decrease in the energy integrated longitudinal response function (Coulomb sum rule). This change is isoscalar. Therefore, the transverse response, which is dominated by the isovector anomalous moment, is largely unchanged.

On the interpretation of the Coulomb sum rule in electron scattering by nuclei

Abstract The validity of the assumptions underlying the interpretation of the integrated longitudinal response of (e, e′) processes in terms of proton-proton correlation function is analysed. The results of realistic many-body calculations of the Coulomb sum in nuclear matter and complex nuclei indicate that, even within a conventional nuclear physics approach, a highly accurate description of the free nucleon form factors is required to extract quantitative information on dynamical correlation effects.