Charge Form Factor Research Articles

Charge form factors of two-neutron halo nuclei in halo EFT

We set up a formalism to calculate the charge form factors of two-neutron halo nuclei with S-wave neutron-core interactions in the framework of the halo effective field theory. The method is applied to some known and suspected halo nuclei. In particular, we calculate the form factors and charge radii relative to the core to leading order in the halo EFT and compare to experiments where they are available. Moreover, we investigate the general dependence of the charge radius on the core mass and the one- and two-neutron separation energies.

Precision measurement of thee+e−→K+K−(γ)cross section with the initial-state radiation method atBABAR

A precise measurement of the cross section for the process e+e- --> K+K-(gamma) from threshold to an energy of 5 GeV is obtained with the initial-state radiation (ISR) method using 232 fb^{-1} of data collected with the BaBar detector at e+e- center-of-mass energies near 10.6 GeV. The measurement uses the effective ISR luminosity determined from the e+e- --> mu+mu-(gamma)gamma_ISR process with the same data set. The corresponding lowest-order contribution to the hadronic vacuum polarization term in the muon magnetic anomaly is found to be a_mu^{KK, LO}=(22.93 +- 0.18_{stat} +- 0.22_{syst}) * 10^{-10}. The charged kaon form factor is extracted and compared to previous results. Its magnitude at large energy significantly exceeds the asymptotic QCD prediction, while the measured slope is consistent with the prediction.

Dispersive representation of the pion vector form factor in τ→ππν τ decays

We propose a dispersive representation of the charged pion vector form factor that is consistent with chiral symmetry and fulfills the constraints imposed by analyticity and unitarity. Unknown parameters are fitted to the very precise data on $\tau^-\to\pi^-\pi^0\nu_\tau$ decays obtained by Belle, leading to a good description of the corresponding spectral function up to a $\pi\pi$ squared invariant mass $s\simeq 1.5$ GeV$^2$. We discuss the effect of isospin corrections, and obtain the values of low energy observables. For larger values of $s$, this representation is complemented with a phenomenological description to allow its implementation in the new TAUOLA hadronic currents.

Nuclear monopole charge form factor calculation for relativistic models including center-of-mass corrections

Relativistic models for finite nuclei contain spurious center-of-mass motion in most applications for the nuclear many-body problem, where the nuclear wave function is taken as a single Slater determinant within a space-fixed frame description. We use the Peierls-Yoccoz projection method, previously developed for relativistic approaches together with a reparametrization of the coupling constants that fits binding energies and charge radius and apply our results to calculate elastic electron scattering monopole charge form factors for light nuclei.

Baryon Structure and Electromagnetic Properties

We seek dynamical consequences of the assumption that the baryon is composed of slowly moving heavy objects (quarks). It is found that the hyperfine structure of hydrogen is relativity sensitive to structure, and the effect tends to reduce the present discrepancy between theory and experiment. It is also pointed out that all neutral baryons will have vanishing charge form factors according to the present model.

Electron scattering in isotonic chains as a probe of the proton shell structure of unstable nuclei

Electron scattering on unstable nuclei is planned in future facilities of the GSI and RIKEN upgrades. Motivated by this fact, we study theoretical predictions for elastic electron scattering in the $N=82$, $N=50$, and $N=14$ isotonic chains from very proton-deficient to very proton-rich isotones. We compute the scattering observables by performing Dirac partial-wave calculations. The charge density of the nucleus is obtained with a covariant nuclear mean-field model that accounts for the low-energy electromagnetic structure of the nucleon. For the discussion of the dependence of scattering observables at low-momentum transfer on the gross properties of the charge density, we fit Helm model distributions to the self-consistent mean-field densities. We find that the changes shown by the electric charge form factor along each isotonic chain are strongly correlated with the underlying proton shell structure of the isotones. We conclude that elastic electron scattering experiments on isotones can provide valuable information about the filling order and occupation of the single-particle levels of protons.

Photoproduction of bound states with hidden charm

The photo-production of $J/\Psi$-$^3He$ bound state ($[^3He]_{J/\Psi}$) on a $^4He$ target has been investigated using the impulse approximation. The calculations have been performed using several $\gamma+N \rightarrow J/\Psi +N$ models based on the Pomeron-exchange and accounting for the pion-exchange mechanism at low energies. The $J/\Psi$ wavefunctions in $[^3He]_{J/\Psi}$ are generated from various $J/\Psi$-nucleus potentials which are constructed by either using a procedure based on the Pomeron-quark coupling mechanism or folding a $J/\Psi$-N potential ($v_{J/\Psi,N}$) into the nuclear densities. We consider $v_{J/\Psi,N}$ derived from the effective field theory approach, Lattice QCD, and Pomeron-quark coupling mechanism. The upper bound of the predicted total cross sections is about $0.1 - 0.3$ pico-barn. We also consider the possibility of photo-production of a six quark-$J/\Psi$ bound state ($[q^6]_{J/\Psi})$ on the $^3He$ target. The Compound Bag Model of $NN$ scattering and the quark cluster model of nuclei are used to estimate the $[q^6]$-N wavefunction in $^3He$ by imposing the condition that the calculated $^3He$ charge form factor must be consistent with what is predicted by the conventional nuclear model. The upper bound of the predicted total cross sections of $\gamma + ^3He \rightarrow [q^6]_{J/\Psi} +N$ is about 2 - 4 pico-barn, depending on the model of $\gamma+N \rightarrow J/\Psi +N$ used in the calculations. Our results call for the need of precise measurements of $\gamma+p \rightarrow J/\Psi +p$ and also the $\gamma+^2H\rightarrow J/\Psi +n + p $ reactions near the threshold.

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.

Structure properties of medium and heavy exotic nuclei

Investigations of important characteristics of the structure of nuclei near drip-lines in coordinate and momentum space have been performed. The charge form factors, charge and matter densities and the corresponding rms radii for even-even isotopes of Ni, Kr, and Sn are calculated in the framework of deformed self-consistent mean field Skyrme DDHF+BCS method. The resulting charge radii and neutron skin thicknesses of these nuclei are compared with available experimental data, as well as with other theoretical predictions. The formation of a neutron skin is analyzed in terms of various definitions. Its correlation with the nuclear symmetry energy is studied within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The nucleon momentum distributions for the same isotopic chains of neutron-rich nuclei are studied in the framework of the same mean-field method, as well as of theoretical correlation methods based on light-front dynamics and local density approximation. The isotopic sensitivities of the calculated neutron and proton momentum distributions are investigated together with the effects of nucleon correlations and deformation of nuclei.

Theoretical Study of the Nuclear Charge Distributions of Tin Isotopes

Nuclear binding energies, charge radii and the charge distributions of even-even tin (Sn) isotopes are calculated using relativistic mean field theory, and the theoretical results are found to be in accordance with the experimental data. The nuclear charge form factors for Sn isotopes are calculated using the phase-shift analysis method. It is shown that the minima of the charge form factors shift upward and inward with an increase in the neutron number of the Sn isotopes.

Weak charge form factor and radius of208Pb through parity violation in electron scattering

We use distorted wave electron scattering calculations to extract the weak charge form factor F_W(q), the weak charge radius R_W, and the point neutron radius R_n, of 208Pb from the PREX parity violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer q=0.475 fm$^{-1}$. We find F_W(q) =0.204 \pm 0.028 (exp) \pm 0.001 (model). We use the Helm model to infer the weak radius from F_W(q). We find R_W= 5.826 \pm 0.181 (exp) \pm 0.027 (model) fm. Here the exp error includes PREX statistical and systematic errors, while the model error describes the uncertainty in R_W from uncertainties in the surface thickness \sigma of the weak charge density. The weak radius is larger than the charge radius, implying a "weak charge skin" where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius R_n=5.751 \pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm$, from R_W. Here there is only a very small error (strange) from possible strange quark contributions. We find R_n to be slightly smaller than R_W because of the nucleon's size. Finally, we find a neutron skin thickness of R_n-R_p=0.302\pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm, where R_p is the point proton radius.

Theoretical study of the central depression of nuclear charge density distribution by electron scattering

The charge form factors of elastic electron scattering for isotones with N = 20 and N = 28 are calculated using the phase-shift analysis method, with corresponding charge density distributions from relativistic mean-field theory. The results show that there are sharp variations at the inner parts of charge distributions with the proton number decreasing. The corresponding charge form factors are divided into two groups because of the unique properties of the s-states wave functions, though the proton numbers change uniformly in two isotonic chains. Meanwhile, the shift regularities of the minima are also discussed, and we give a clear relation between the minima of the charge form factors and the corresponding charge radii. This relation is caused by the diffraction effect of the electron. Under this conclusion, we calculate the charge density distributions and the charge form factors of the A = 44 nuclei chain. The results are also useful for studying the central depression in light exotic nuclei.

Analysis of the G0 Backward Angle experiment

We have measured parity-violating asymmetries in elastic electron-proton and quasi-elastic electron-deuteron scattering at Q 2 = 0.22 and 0.63 GeV 2 .T hey are sensitive to strange quark contributions to currents in the nucleon, and to the nucleon axial current. The results indicate strange quark contributions of ≤10% of the charge and magnetic nucleon form factors at these four-momentum transfers. Analysis of the data is summarized.

Magnetic moments of the ground-stateJP=32+baryon decuplet

The magnetic moment - a function of the electric charge form factor $F_{1}(q^{2})$ and the magnetic dipole form factor $F_{2}(q^{2})$ at zero four-momentum transfer $q^{2}$-of the ground-state $J^{P}=(3/2)^{+}$ baryon decuplet magnetic moments have been studied for many years with limited success. At present, only the magnetic moment of the $\Omega^{-}$ has been accurately determined. We calculate nonperturbatively the magnetic moments of the \emph{physical baryon decuplet $J^{P}=(3/2)^{+}$} members and in particular, we obtain $\mu_{\Delta^{++}}= (+3.67 \pm 0.07) \mu_{N}$, $\mu_{\Delta^{+}}= (+1.83 \pm 0.04) \mu_{N}$, $\mu_{\Delta^{0}}= (0) \mu_{N}$, and the magnetic moments of their $U$-Spin partners in terms of $\Omega^{-}$ magnetic moment data.

Exclusive production of lepton, quark and meson pairs in peripheral ultrarelativistic heavy ion collisions

We discuss exclusive production of lepton-antilepton, quark-antiquark, $\pi \pi$ and $\rho^0 \rho^0$ pairs in ultraperipheral, ultrarelativistic heavy-ion collisions. The cross sections for exclusive production of pairs of particles is calculated in Equivalent Photon Approximation (EPA). Realistic (Fourier transform of charge density) charge form factors of nuclei are used and the corresponding results are compared with the cross sections calculated with monopole form factor used in the literature. Absorption effects are discussed and quantified. The cross sections obtained with realistic form factors are significantly smaller than those obtained with the monopole form factors.

Exclusive production of large invariant mass pion pairs in ultraperipheral ultrarelativistic heavy ion collisions

The cross section for exclusive production of π+π− and π0π0 meson pairs in ultrarelativistic heavy ion collisions is calculated for LHC energy sNN=3.5 TeV taking into account photon–photon mechanism. We concentrate on the production of large two-pion invariant masses where the mechanism of the elementary γγ→ππ process is not fully understood. In order to include a size of nuclei we perform calculation in the impact-parameter equivalent photon approximation (EPA). Realistic charge densities are used to calculate charged form factor of 208Pb nucleus and to generate photon fluxes associated with ultrarelativistic heavy ions. Sizeable cross sections are obtained that can be measured at LHC. The cross section for elementary γγ→ππ process is calculated in the framework of pQCD Brodsky–Lepage (BL) mechanism with the distribution amplitude used to describe recent data of the BaBar Collaboration on pion transition form factor, using hand-bag mechanism advocated to describe recent Belle data as well as t- and u-channel meson/reggeon exchanges. We present distributions in two-pion invariant mass as well as the pion pair rapidity for the nuclear process.

Exclusive [formula omitted] meson pair production in peripheral ultrarelativistic heavy-ion collisions

The cross sections for exclusive D+D− and D0D¯0 meson pair production in peripheral nucleus–nucleus collisions are calculated and several differential distributions are presented. The calculation of the elementary γγ→DD¯ cross section is done within the heavy-quark approximation and in the Brodsky–Lapage formalism with distribution amplitudes describing recent CLEO data on leptonic D+ decay. Realistic (Fourier transform of charge density) charge form factors of nuclei are used to generate photon flux factors. Absorption effects are discussed and quantified. The cross sections of a few nb are predicted for RHIC and of a few hundreds of nb for LHC with details depending on the approximation made in calculating elementary γγ→DD¯ cross sections.

EXCLUSIVE D+D- PAIR PRODUCTION IN THE AA → AAD+D- REACTION

The cross sections for exclusive D+D- meson pair production in nucleus - nucleus collisions are calculated and differential distributions are shown. Realistic (Fourier transform of the charge density) charge form factors of nuclei are used. Absorption effects are included. Predictions for the STAR and PHENIX collaboration measurements at RHIC are presented.

Radiative corrections to electron–pion scattering revisited

We calculate in closed analytical form the one-loop radiative corrections to electron–pion scattering e−π− → e−π−. Concise expressions (in terms of dimensionless Mandelstam variables) are given for the pertinent interference terms between the tree diagram and the one-loop diagrams related to photonic vertex correction, vacuum polarization and two-photon exchange. Infrared finiteness of these virtual radiative corrections is achieved (in the standard way) by including soft-photon radiation below an energy cutoff λ. We evaluate the finite part of the soft-photon correction factor in the center-of-mass frame. For all contributions we keep the full dependence on the electron mass. The results for the loop amplitudes can also be applied to pion-pair production e−e+ → π+π−. The radiative corrections to the corresponding total cross section are calculated with consideration of the pion structure via a vector meson dominance form factor. We find that such an additional charge form factor (inserted into the photonic vertex correction of the pion) changes the radiative corrections to the total cross section by about −0.2%.

RQM description of PS meson form factors, constraints from space-time translations and underlying dynamics

The role of Poincar\'e covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for in all relativistic quantum mechanics calculations. It implies constraints that have been largely ignored until now but should be fulfilled to ensure the full Poincar\'e covariance. The violation of these constraints, which is more or less important depending on the form of relativistic quantum mechanics that is employed, points to the validity of using a single-particle current, which is generally assumed in calculations of form factors. In short, these constraints concern the relation of the momentum transferred to the constituents to the one transferred to the system. How to account for the related constraints, as well as restoring the equivalence of different relativistic quantum mechanics approaches in estimating form factors, is discussed. Some conclusions relative to the underlying dynamics are given in the pion case.