Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper,the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles.For axially deformed nuclei,two different types of density profiles are used to describe their charge distributions.For the same charge distributions expanded with different basis functions,the corresponding longitudinal form factors are derived and compared with each other.Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions.Further numerical calculations of longitudinal form factors of~(12)C indicates that the C_0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions.For deformed nuclei,their charge RMS radii can also be determined accurately by the C_0 measurement.The studies in this paper examine the model-independent properties of electron scattering,which are useful for interpreting electron scattering experiments on exotic deformed nuclei.     

Pole and quark-counting model for form factors of light nuclei

The dispersion relation approach is applied to form factors of light nuclei. The form factor is approximated by a sum of poles. The asymptotic behaviour of form factor is assumed to be determined by quark-counting rule. Examples of³He,⁴He and⁶Li are considered. Data on form factors of these nuclei have been fitted with smaller number of parameters than usual, and corresponding charge distributions have been found which differ from conventional ones in central regions of nuclei.     

Relation between nuclear matter and nuclear potential in inelastic alpha—nucleus scattering

Inelastic transition form factors for alpha—nucleus collective excitations are derived from deformed matter distributions by averaging an effective alpha nucleus interaction over the nucleons in the nucleus. The method is an extension of the procedure of calculating the real part of elastic alpha—nucleus potentials from nuclear matter distributions. Numerical examples for the nuclei of ⁴²Ca and ¹⁴²Nd are given. The resulting inelastic form factors depend on the multipolarity of the inelastic excitation and differ from those conventionally derived from a deformed optical potential.     

Nucleon momentum distributions in doubly closed shell nuclei

The momentum distributions in nuclei like⁴He,¹⁶O and⁴⁰Ca are explicitly calculated within a phenomenological model which includes dynamical short range and tensor correlation effects. The common behaviour of such distributions in the high momentum region, already established in light nuclei, is extended to the medium weight region. Comparison with existing calculations is discussed and, for completeness, also form factors are evaluated within the same framework.     

Analysis of elastic and inelastic α-12C data (Eα = 1.37 GeV) with a multiple diffraction model

High-energy inelastic α-¹²C distributions are analyzed with an eikonalized DWIA. Using an elastic phase function parametrized to fit the elastic α-¹²C distribution and further inelastic form factors from electron scattering data, we obtained reasonable agreement for the 2⁺ and 0⁺ distributions. We observe and discuss the anomalous absence of a predicted diffraction minimum in the 3^? distribution as is also the case for the 1 GeV p-¹²C data.     

Pion production in two-body pd collisions

The reactions d(p, π⁺)t and d(p, π^o)³ He are analyzed in terms of the pp → π⁺d sub-process. The exclusion principle induces an additional exchange contribution involving the πd scattering amplitude. Acceptable deuteron and tritron (³H) wave functions which reproduce the charge form factors yield results consistent with experimental angular distributions at 470, 590, 754 and 1192 proton lab. energies. The forward peak is not sensitive to details of the wave functions. Both the direct and exchange form factors develop a zero which is imposed by the dip in the ³He charge form factor. The associated interference pattern governs the backward cross section.     

Instabilities of the Conventional Nucleus-Nucleus Interactions for (<Superscript>3</Superscript>H<Superscript>4</Superscript>He) Proton Pickup Cross-Sections

The angular distributions of the ²⁶Mg, ²⁸Si, ³⁰Si(³H, ⁴He) reactions have been analyzed using the exact finite-range DWBA calculations. The optical model potential is assumed to have the conventional spin-orbit potential. The obtained cross-sections with the spin-orbit potential are not significantly different from those calculated using the phenomenological Woods–Saxon form factors in the forward angle regions. The inclusion of the spin-orbit potential gives the best fit to the data and greatly improves the large angle cross-sections. Different reasonable spectroscopic factors are found to account well for the cross-section magnitudes.     

Nucleon form factors, <Emphasis Type="Bold">B</Emphasis>-meson factories and the radiative return

The feasibility of a measurement of the electric and magnetic nucleon form factors at B-meson factories through the radiative return is studied. Angular distributions allow for a separation of the contributions from the two form factors. The distributions are presented for the laboratory and the hadronic rest frame, and the advantages of different coordinate systems are investigated. It is demonstrated that Q ² values up to 8 or even 9 GeV² are within reach. The Monte Carlo event generator PHOKHARA is extended to nucleon final states, and results are presented which include next-to-leading order radiative corrections from initial-state radiation. The impact of angular cuts on rates and distributions is investigated and the relative importance of radiative corrections is analyzed.Received: 8 March 2004, Revised: 12 April 2004, Published online: 9 June 2004Work supported in part by BMBF under grant number 05HT9VKB0, EC 5th Framework Programme under contract HPRN-CT-2002-00311 (EURIDICE network), Polish State Committee for Scientific Research (KBN) under contract 2 P03B 017 24, BFM2002-00568, Generalitat Valenciana under grant GRUPOS03/013, and MCyT under grant FPA-2001-3031.     

Nucleon momentum distributions and elastic electron scattering form factors for some 1p-shell nuclei

The nucleon momentum distributions (NMD) and elastic electron scattering form factors of the ground state for 1p-shell nuclei with Z?=?N (such as ⁶Li, ¹⁰B, ¹²C and ¹⁴N nuclei) have been calculated in the framework of the coherent density fluctuation model (CDFM) and expressed in terms of the weight function $\left| {f( x )} \right|^2$ . The weight function has been expressed in terms of nucleon density distribution (NDD) of the nuclei and determined from the theory and the experiment. The feature of the long-tail behaviour at high-momentum region of the NMDs has been obtained by both the theoretical and experimental weight functions. The experimental form factors F(q) of all the considered nuclei are very well reproduced by the present calculations for all values of momentum transfer q. It is found that the contributions of the quadrupole form factors F _C2(q) in ¹⁰B and ¹⁴N nuclei, which are described by the undeformed p-shell model, are essential for obtaining a remarkable agreement between the theoretical and experimental form factors.     

The 27Al(t,p)29Al reaction at Et = 15 MeV

The ²⁷Al(t, p)²⁹Al reaction was studied at an incident energy of E_t = 15 MeV. Proton angular distributions were measured for the first 23 low-lying states. Comparisons of the data to DWBA calculations based on cluster-model and pure-configuration form factors were made which provided decompositions of the angular distributions into contributing L-values. Comparisons were also made to DWBA predictions based on microscopic amplitudes from a complete, sd-basis shell-model calculation.     

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei (⁴He and ¹⁶O). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own “Tassie-Barker” factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of ⁴He and ¹⁶O evaluated by using the well-known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.     

Inelastic processes and form factor effects in the 162, 164Dy(3He,d) reactions at 46.5 MeV

The 162, 164Dy(³He, d) reactions at E_3He = 46.5 MeV are analyzed using the coupled channels Born approximation (CCBA) and improved form factors derived from a deformed Woods-Saxon potential. The latter are generated using the coupled channels procedure of Rost. The transitions considered populate the $\text{7}\text{2}$^?[523], $\text{1}\text{2}$⁺[411], $\text{3}\text{2}$⁺[411], $\text{1}\text{2}$^?[541] and $\text{5}\text{2}$⁺ orbitals in ^{163, 165}Ho. Indirect processes induced by inelastic scattering are found to have an influence on the cross sections comparable to that deduced for neutron transfer reactions on rare earth nuclei at lower energies. Considered alone, these can alter the cross sections even of strong transitions by a factor of two and of weaker ones by an order of magnitude. For the weaker transitions equally large changes can result when the improved form factors, rather than conventional spherical Woods-Saxon functions, are used in the calculations. In the examples considered these two effects tend to cancel, often, but not always, resulting in predicted cross sections similar in magnitude to the results of conventional DWBA calculations made with spherical Woods-Saxon form factors. The CCBA angular distributions are generally similar in shape to DWBA predictions, which usually give good fits to the experimental angular distributions over the 0–35° range of the data. Compared with DWBA predictions which use (he same optical parameters, but spherical Woods-Saxon form factors, the CCBA with deformed Woods-Saxon form factors is in better overall agreement with the experimental cross-section magnitudes. However there are a number of cases in which the CCBA, although usually predicting larger cross sections than the DWBA, still underestimates the experimental cross sections by nearly factor of two. These cases all occur in the $\text{71}\text{2}$^?[541] band or in the strongly Coriolis mixed $\text{1}\text{2}$⁺[411] and $\text{3}\text{2}$⁺[411] bands, and include the majority of transitions populating these orbitals. Since both nuclear structure and reaction mechanism effects are interwoven m the calculations, further data would be most useful in probing the origin of the discrepancy.     

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.     

Transfer reactions induced by 16O on 29, 30Si

Angular distributions for one- and two-nucleon transfer reactions induced by ¹⁶O on ^{29, 30}Si and for the elastic scattering of ¹⁶O on ^{28, 29, 30}Si have been measured at 73.5 MeV bombarding energy. The results are analyzed with the DWBA code BRUNHILD that includes recoil effects. Spectroscopic factors extracted for all observed transitions in one-nucleon transfer reactions agree well with those derived from light panicle reactions. The effects of recoil on the Spectroscopic factors for transitions to final states with different spins are discussed. The transitions from smooth to oscillating angular distributions are examined. It is found that the shape of the angular distributions depends on both the matching conditions of the reaction and the localization of the S-matrix amplitudes in L-spacef.     

Parametrization of nuclear parton distributions

Optimum nuclear parton distributions are obtained by analysing available experimental data on electron and muon deep inelastic scattering (DIS). The distributions are given at Q ²=1 GeV² with a number of parameters, which are determined by a X ² analysis of the data. Valencequark distributions are relatively well determined at medium x, but they are slightly dependent on the assumed parametrization form particularly at small x. Although antiquark distributions are shadowed at small x, their behavior is not obvious at medium x from the F ₂ data. The gluon distributions could not be restricted well by the inclusive DIS data; however, the analysis tends to support the gluon shadowing at small x. We provide analytical expressions and computer subroutines for calculating the nuclear parton distributions, so that other researchers could use them for applications to other high-energy nuclear reactions.     

Parton distributions in the small-x region within LLX approximation

The solutions of Lipatov-Fadin-Kuraev equation (LFK) within LLX approximation for gluon distributions are studied. The results are based on the semiphenomenological boundary conditions taken from LLQ² analysis. We find, that pure theoretical LLX approach can reproduce the form of singular small-x behaviour of gluon and sea-quark distributions obtained within LLQ²A with singular input parametrizations. Some remarks about shadowing corrections are presented.     

Dipole resonances in the electroexcitation of the <Superscript>24</Superscript>Mg nucleus

The wave functions and form factors of E1 excited states of the deformed nucleus ²⁴Mg are obtained within the particle-core coupling version of the shell model by using spectroscopic data on direct nucleon-pickup reactions. A comparison of the calculated E1-strength distributions with experimental cross sections shows the validity of the theoretical approach used, which is based on connections between direct and resonance nuclear reactions.     

Study on Charge Form Factors of the Exotic Nuclei 6,8He

Charge radius and charge form factors of different charge density distributions for ^6,8He are calculated with the relativistic Eikonal approximation. Detailed comparisons and discussions are presented. It is found that the charge form factors curves of ^6,8He are much lower than the experimental ones of ⁴He. This is, in principle, consistent with the experimental fact. Whereas detailed comparison among the charge form factors which correspond to different charge distributions show significant deviations. This indicates that the effects of the correlations between the halo neutrons and the α-core in ^6,8He with different charge density distributions are quite different. This result would provide a useful reference for the possible experiments on the next-generation electron-nucleus collider and for the tests of different theoretical models for the exotic nuclei ^6,8He.     

Near-barrier transfer and fusion of the systems33S +90,91,92Zr

Double differential cross sections of all prominent transfer channels have been measured in the systems³³S +^99,91,92Zr at two energies close to the nominal Coulomb barrier. In addition the fusion excitation functions of these systems have been measured below and around the barrier. The angular- andQ-distributions of the most important transfer reactions have been analysed in the framework of a simple semiclassical formalism. Particularly the two-nucleon transfer angular distributions exhibit strong multi step coupling effects which manifest themselves in reduced cross sections at large angles corresponding to close distances. From the angular distributions at forward angles, where a single step character of the transfer reaction can be assumed, approximate form factors have been extracted employing a first order perturbation theory. Within the uncertainties of a schematic coupled channels calculation the isotopic differences of the sub-barrier fusion enhancement can be understood on the basis of the isotopic differences of the transfer form factors andQ-values.