Structure functions of bound nucleons: From the EMC effect to nuclear shadowing

We describe the nuclear structure functions in the whole range of the Bjorken variablex, by combining various effects in a many-step procedure. First, we present a QCD motivated model of nucleons, treated, in the limit of vanishingQ ², as bound states of three relativistic constituent quarks. Gluons and sea quarks are generated radiatively from the input valence quarks. All parton distributions are described in terms of the confinement (or nucleon's) radius. The results for free nucleons are in agreement with the experimental determinations. The structure functions of bound nucleons are calculated by assuming that the main effect of nucleon binding is stretching of nucleons. The larger size of bound nucleons lowers the valence momentum and enhances the radiatively generated glue and sea densities. In the small-x region the competitive mechanism of nuclear shadowing takes place. It also depends on the size of the nucleons. By combining stretching, shadowing and Fermi motion effects (the latter confined to very largex), the structure function ratio is well reproduced. Results are also presented for theA-dependence of the momentum integral of charged partons, the nuclear gluon distribution and the hadron-nuclei cross sections.     

The interaction of K mesons with nuclei

The experimental data for K⁻ capture by nuclei is interpreted in terms of K⁻ nucleon scattering amplitudes in a region of negative relative kinetic energy. It is shown that constant scattering length solutions which represent the data in the region of positive relative kinetic energy up to 100 MeV do not satisfactorily describe the interaction with bound nucleons and a modified scattering length solution is proposed. Measured values of the widths of K-mesic X-ray lines which require a strongly attractive K⁻ nucleons optical potential are successfully interpreted in terms of K⁻N scattering lengths appropriate for bound nucleons. The information obtainable about relative neutron and proton density distributions in the nuclear periphery from studies of this kind is discussed. The need for more data on interaction of K⁻ in hydrogen at low kinetic energies and at rest and in other elements at rest is emphasised.     

Neutrino quasielastic scattering on nuclear targets Parametrizing transverse enhancement (meson exchange currents)

We present a parametrization of the observed enhancement in the transverse electron quasielastic (QE) response function for nucleons bound in carbon as a function of the square of the four momentum transfer (Q ²) in terms of a correction to the magnetic form factors of bound nucleons. The parametrization should also be applicable to the transverse cross section in neutrino scattering. If the transverse enhancement originates from meson exchange currents (MEC), then it is theoretically expected that any enhancement in the longitudinal or axial contributions is small. We present the predictions of the “Transverse Enhancement” model (which is based on electron scattering data only) for the ν _μ , [`(n)]_m\bar{\nu}_{\mu} differential and total QE cross sections for nucleons bound in carbon. The Q ² dependence of the transverse enhancement is observed to resolve much of the long standing discrepancy in the QE total cross sections and differential distributions between low energy and high energy neutrino experiments on nuclear targets.     

The reactionpd → ppn and the narrow dibaryon resonances

The effective mass spectra of two nucleons from the reactionpd →ppn were studied at four incident proton energies in the range 800–1000 MeV, one of nucleons being backward emitted. After selecting the events either with large nucleon momenta or with large opening angles between the nucleons several narrow peaks are observed in the effective mass spectra (M=1.95, 2.03, 2.08 and 2.14 GeV/c²) which can be considered as probable dibaryon resonances.     

Simulation of the Pauli-principle effects in the description of light ion scattering and bound states

A simple model which takes care phenomenologically of the effects of the Pauli principle is proposed to calculate, in the framework of the resonating group method, bound and scattering states of nuclear systems comprised of two light nuclei (n, t and α-particles) without performing a complete antisymmetrization of the wave functions. Retaining only the antisymmetrization between the nucleons belonging to a given cluster, the contributions of the terms corresponding to the exchange of two nucleons belonging to two different clusters are simulated by the matrix elements of an effective central, local, l-dependent, energy-independent nucleon-nucleon potential. The lowenergy levels of ⁸Be and ⁷Li as well as the phase shifts for l = 0 to 4 for energies below 10 MeV (c.m.) have been calculated with this effective potential (added to the regular nucleon-nucleon potential). Good agreement between exact and model calculations is achieved.     

NN correlations measured in <Superscript>3</Superscript>He(e,e'pp)n

We have measured the ³He (e, e'pp)n reaction in the Jefferson Lab CLAS with 2.2 and 4.4 GeV electrons. We looked at the energy distribution of events with all three nucleons at high momentum (p > 250 MeV/c). This distribution has peaks where two nucleons each have 20% or less of the energy transfer (i.e., the third or ?leading? nucleon carries most of the kinetic energy). The angular distribution of these two ?fast? nucleons shows a very large back-to-back peak, indicating the effect of correlations. While there is some theoretical disagreement, experimental evidence, plus calculations at lower energy by W. Glöckle, indicates that these events are primarily sensitive to NN correlations.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.45.+v Few-body systems - 25.30.Dh Inelastic electron scattering to specific statesL.B. Weinstein: For the CLAS Collaboration     

K − absorption in nuclei by two and three nucleons

It will be shown that the peaks in the (Λp) and (Λd) invariant mass distributions, observed in recent FINUDA experiments and claimed to be signals of deeply bound kaonic states, are naturally explained in terms of K ^? absorption by two or three nucleons leaving the rest of the original nuclei as spectator. For reactions on heavy nuclei, the subsequent interactions of the particles produced in the primary absorption process with the residual nucleus play an important role. Our analyses leads to the conclusion that at present there is no experimental evidence of deeply bound K ^? state in nuclei. Although the FINUDA experiments have been done for reasons which are not supported a posteriori, some new physics can be extracted from the data.     

Solutions of the integral equations for four identical particles

Using the separable representation of the scattering amplitudes for the subsystems 3 + 1 and 2 + 2, the integral equations for four identical particles with a separable two-particle interaction are reduced to a set of single variable integral equations. By solving the equations obtained, the binding energies and wave functions of the low-lying 0⁺ states of the system of four identical bosons, as well as the scattering length of a particle scattered by three bound particles, are calculated. The solution of the set of integral equations, describing the bound state of four nucleons, is performed, approximating the space wave function by a symmetric one, and the binding energy and wave function of the nucleus ⁴He are calculated.     

Many-body terms in the folded diagram expansion

The folded diagram expansion for the effective hamiltonian to be used in shell-model calculations for a system with A valence nucleons yields folded diagrams connecting up to A nucleons. The importance of such effective many-nucleon forces is investigated for the example of 4 valence nucleons in the 1s0d shell (²⁰Ne). The folded diagram terms turn out to reduce the binding energy for the low-lying states. The effects of the folded diagrams involving three nucleons are of the same importance as those of the two-body terms. The four-nucleon forces originating from folded diagrams are considerably weaker. This suggests that three-body operators have to be considered in a microscopic calculation of an effective energy-independent shell-model hamiltonian, whereas terms involving four nucleons may be ignored.     

Polarized quark distributions in bound nucleon and polarized EMC effect in Thermodynamical Bag Model

The polarized parton distribution functions (PDFs) and nuclear structure functions are evaluated by the phenomenological Thermodynamical Bag Model for nuclear media ⁷Li and ²⁷Al. The Fermi statistical distribution function which includes the spin degree of freedom is used in this statistical model. We predict a sizeable polarized EMC effect. The results of quark spin sum and axial coupling constant of bound nucleons are compared with theoretical predictions of modified Nambu–Jona-Lasinio (NJL) model by Bentz et al.     

Nichtlokale Potentiale im Einteilchen-Modell des Atomkerns

In the nonlocal part of the single particle potential of bound nucleons the Gaussian nonlocality, which was used in earlier papers, is replaced by a Yukawa- and an exponential potential. The nonlocal parameters are fitted to the nucleon scattering experiments and the results are used for a calculation of single particle levels of Pb²⁰⁹ and Pb²⁰⁷. The nonlocality required by the Pauli-exclusion-principle is compared with the phenomenological approach. It turns out that the form of this nonlocality is essentially given by the supposed nucleon-nucleon potential. The range of this potential is determined by the experimentally known energy-dependence of the single particle potential.     

Kinematically complete measurement of the absorption of stopped pions in 3He

The reactions π^?3He → nnp and π^?3He → nd have been measured in a kinematically complete experiment with stopped pions. The results show strong preference for collinear events. About three quarters of all absorption processes occur as quasi-free absorption on np- or pp-pairs with a ratio of R = 10.1 ± 1.5. The remaining quarter shows energy sharing among all three nucleons and is located in the final-state interaction regions. Branching ratios for all observed final states are given.     

Production of hypernuclei with the reaction

We present results on the production of bound states of Θ⁺ in nuclei using the (K⁺,π⁺) reaction. By taking into account the states obtained within a wide range of strength of the Θ⁺ nucleus optical potential, plus the possibility to replace different nucleons of the nucleus, we obtain an excitation spectra with clearly differentiated peaks. The magnitude of the calculated cross sections is well within reachable range.     

Analysis of α-7Li elastic and inelastic scattering at low energy with a simple model of the pauli principle effects

The elastic and inelastic scattering of α on ⁷Li are calculated at different low energies in the framework of the resonating group method in which the ⁷Li is supposed to be comprised of two clusters, α and t. To reduce the time of calculation, the effects of the Pauli principle due to the exchange of two nucleons belonging to two different clusters are approximated with an effective nucleon-nucleon potential which has been determined previously in order to reproduce correctly the scattering and bound states of the nuclear systems comprised of two particles, 2α or α + t. This calculation takes into account the exchange of the incoming a with the a belonging to ⁷Li as well as the coupling with the ⁸Be + t channel. Without any free parameter, the model calculation reproduces correctly the main features of the experimental data when the projectile energy is less than 5 MeV (lab). It appears that the coupling with the ⁸Be + t channel cannot be neglected.     

Structural properties of the 10Be and 10C four-cluster nuclei

The structure functions for the ¹⁰Be and ¹⁰C nuclei are studied in a four-particle approximation (two alpha-particle clusters plus two nucleons). New versions of the αα interaction potential are constructed. Together with the nα, pα, and NN potentials proposed previously, they make it possible to describe the binding energies and radii of the nuclei being considered, along with the S-wave twocluster phase shifts at low energies. General properties of four-particle wave functions are studied, and two basic configurations of the cross and tetrahedron types are revealed in the ¹⁰Be and ¹⁰C nuclei. A detailed analysis of the behavior of the structure functions is performed for these nuclei. The density distributions, form factors, and pair correlation functions are considered. The momentum distributions are obtained for the alpha particles and extra nucleons. The structure functions for the ¹⁰Be and ¹⁰C four-cluster nuclei are compared with those for the ⁶He three-cluster nucleus. The bound states of the nuclei are studied within a high-precision variational approach by using Gaussian bases.     

Quasi-elastic and deep-inelastic dissipative processes

Quasi-elastic and deep inelastic rates are calculated assuming that the colliding nuclei move on classical trajectories and that the excitations and the particle or energy exchanges are due to the shell-model wells interacting with the nucleons. (One-body collisions). This allows a microscopic, parameter free, calculation of the optical potential, as well as the energy and the angular momentum losses, and is a good approximation as long as the collision is peripheral. The correction due to two-body collisions between individual nucleons is also evaluated. The focus will be on the evolution of the various reaction rates as a function of energy. The system chosen for the discussion is ¹⁶O + ¹⁶O from 3 MeV/A to 60 MeV/A.     

Brink model with tetrahedral alpha-particle clusters for three-particle forces

Three-particle interaction is introduced in the Brink model modification that takes into account an arbitrary localization of nucleons within alpha-particle clusters. Simultaneously, the class of single-particle variational functions is substantially extended by replacing the traditionally employed Gaussian function by the sum of Gaussian functions. In the case of the Bonche-Koonin-Negele (BKN) interaction, three Gaussian functions provide a good upper bound on the results of solving the Hartree-Fock equation for the ⁴He nucleus. It is shown that the BKN three-particle interaction simulates to some extent the effect of short-range correlations in the multiparticle wave function.     

Self-consistent description of finite nuclei based on a relativistic quark model

Relativistic Hartree equations for spherical nuclei have been derived from a relativistic quark model of the structure of bound nucleons which interact through the (self-consistent) exchange of scalar (σ) and vector (ω and ϱ) mesons. The coupling constants and the mass of the σ-meson are determined from the properties of symmetric nuclear matter and the rms charge radius in ⁴⁰Ca. Calculated properties of static, closed-shell nuclei from ¹⁶O to ²⁰⁸Pb are compared with experimental data and with results of Quantum Hadrodynamics (QHD). The dependence of the results on the nucleon size and the quark mass is investigated. Several possible extensions of the model are also discussed.