Delta Excitation Research Articles

Empirical Transverse Charge Densities in the Nucleon and the Nucleon-to-ΔTransition

Using only the current empirical information on the nucleon electromagnetic form factors we map out the transverse charge density in proton and neutron as viewed from a light front moving towards a transversely polarized nucleon. These charge densities are characterized by a dipole pattern, in addition to the monopole field corresponding with the unpolarized density. Furthermore, we use the latest empirical information on the N-->Delta transition form factors to map out the transition charge density which induces the N-->Delta excitation. This transition charge density in a transversely polarized N and Delta contains both monopole, dipole and quadrupole patterns, the latter corresponding with a deformation of the N and Delta charge distribution.

Finite-width effects on Delta baryons in QCD sum rules

The quantum chromodynamics (QCD) sum rules for the Delta baryons are analyzed by taking into account the finite-width effects, through explicit utilization of the Breit–Wigner shape. We apply a Monte Carlo based analysis to the ‘traditional’ and the parity-projected sum rules. The first Delta excitation state is also considered as a sub-continuum resonance and the widths are calculated using the mass values as input.

Investigation of Proton-Proton Short-Range Correlations via theC12(e,e′pp)Reaction

We investigated simultaneously the 12C(e,e'p) and 12C(e,e'pp) reactions at Q2=2 (GeV/c)2, xB=1.2, and in an (e, e'p) missing-momentum range from 300 to 600 MeV/c. At these kinematics, with a missing momentum greater than the Fermi momentum of nucleons in a nucleus and far from the delta excitation, short-range nucleon-nucleon correlations are predicted to dominate the reaction. For (9.5+/-2)% of the 12C(e,e'p) events, a recoiling partner proton was observed back-to-back to the 12C(e,e'p) missing-momentum vector, an experimental signature of correlations.

Superscaling analysis of inclusive electron scattering and its extension to charge-changing neutrino-nucleus cross sections beyond the relativistic Fermi gas approach

Superscaling analyses of inclusive electron scattering from nuclei are extended from the quasielastic processes to the delta excitation region. The calculations of $(e,{e}^{'})$ cross sections for the target nucleus $^{12}\mathrm{C}$ at various incident electron energies are performed using scaling functions $f({\ensuremath{\psi}}^{'})$ obtained in approaches going beyond the mean-field approximation, such as the coherent density fluctuation model (CDFM) and the one based on the light-front dynamics method. The results are compared with those obtained using the relativistic Fermi gas (RFG) model and the extended RFG model (ERFG). Our method utilizes in an equivalent way both basic nuclear quantities, density and momentum distributions, showing their role for the scaling and superscaling phenomena. The approach is extended to consider scaling function for medium and heavy nuclei with $Z\ensuremath{\ne}N$ for which the proton and neutron densities are not similar. The asymmetry of the CDFM quasielastic scaling function is introduced, simulating in a phenomenological way the effects that violate the symmetry for ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\geqslant}0$, including the role of the final-state interaction. The superscaling properties of the electron scattering are used to predict charge-changing neutrino-nucleus cross sections at energies from 1 to 2 GeV. A comparison with the results of the ERFG model is made. The analyses make it possible to gain information about the nucleon correlation effects on both local density and nucleon momentum distributions.

Measurement of the Analyzing Power inp→d→(pp)nwith a Fast ForwardS01Proton Pair

A measurement of the analyzing power A(y) of the p-->d--> (p p) + n reaction was carried out at the ANKE spectrometer at COSY at beam energies of 0.5 and 0.8 GeV by detection of a fast forward proton pair of small excitation energy E(pp) < 3 MeV. The S-wave dominance in the fast diproton is experimentally demonstrated in this reaction. While at T(p) = 0.8 GeV the measured analyzing power almost vanishes, it rises to nearly unity at T(p) = 0.5 GeV for neutrons emitted at theta(c.m.)(n) = 167 degrees. The results are compared with a model taking into account one-nucleon exchange, single scattering, and Delta(1232) excitation in the intermediate state. The model describes fairly well the unpolarized cross section obtained earlier and the analyzing power at 0.8 GeV; it fails to reproduce A(y) at 0.5 GeV.

WroNG – Wrocław Neutrino Generator of events for single pion production

We constructed a new Monte Carlo generator of events for neutrino CC single pion production on free nucleon targets. The code uses dynamical models of the DIS with the PDFs modified according to the recent JLab data and of the Delta excitation. A comparison with experimental data was done in three channels for the total cross sections and for the distributions of events in invariant hadronic mass.

Role of baryonic resonances in the dilepton emission in nucleon-nucleon collisions

Within an effective Lagrangian model, we present calculations for cross sections of the dilepton production in proton-proton and proton-neutron collisions at laboratory kinetic energies in 1-5 GeV range. Production amplitudes include contributions from the nucleon-nucleon bremsstrahlung as well as from the mechanism of excitation, propagation, and radiative decay of Delta(1232) and N*(1520) intermediate baryonic resonances. It is found that the delta isobar terms dominate the cross sections in the entire considered beam energy range. Our calculations are able to explain the data of the DLS collaboration on the dilepton production in proton-proton collisions for beam energies below 1.3 GeV. However, for incident energies higher than this the inclusion of contributions from other dilepton sources like Dalitz decay of pi0 and eta mesons, and direct decay of rho and omega mesons is necessary to describe the data.

Nuclear pion photoproduction in theΔresonance region

A measurement of the /sup 12/C( gamma , pi /sup +/n)/sup 11/B reaction in quasifree pi -production kinematic regimes has been performed using tagged photons in conjunction with large solid angle pi and n detectors. The aim of the experiment was to investigate predicted modifications to the Delta excitation of nucleons and their subsequent propagation and decay, brought about by the nuclear medium. Differential cross sections are presented for photon energies spanning the Delta (1232) excitation region. The measurements are consistent with distorted wave impulse approximation calculations in which the amplitude for proton Delta excitation, followed by Delta propagation and decay to pi /sup +/+n, is reduced compared to that for a free p. However, because of uncertainties in the magnitudes of the final state interactions, it is concluded that improved calculations are required to obtain a quantitative estimate of Delta - medium effects.

Effective spin dependent interactions for reactions: The case ofNN→NΔ

A general formalism to discuss the role of noncentral forces in reactions with arbitrary spins is outlined. The formalism is applied to the particular case of Delta excitation in inelastic nucleon-nucleon scattering. [S0556-2813(98)03510-9].

Projectile delta excitation in alpha-proton scattering

The (α, α′) reaction in the Δ-region is a clear example of projectile delta excitation. We study the reaction theoretically and compare the results to a recent experiment. The agreement is rather good. On the other hand the reaction offers a test for models of coherent pion production. Finally, the use of the present model should provide the appropriate background to extract the excitation strength of the Roper resonance observed in the same reaction.

INCLUSIVE (3He, t) REACTION IN DELTA EXCITATION REGION

Using the one step reaction mechanism, calculations are presented for the overall features of the inclusive (3 He , t) reaction on various target nuclei in the delta excitation region. The interaction for the elementary pp→nΔ++ process is given by one-pion-exchange, and is written in the covariant relativistic form. The values of the parameters in the interaction are chosen such that the interaction successfully describes the spin averaged experimental elementary cross-sections. The distortion in the entrance and exit channels is described in the eikonal approximation, and the nuclear response is described in the “distorted wave Fermi gas model”. The cross-sections for the triton energy spectrum, angular distribution, and the total events at 0° on several nuclei, are calculated and compared with the corresponding experimental data. The main features of the measured cross-sections are reproduced.

Differential cross sections for the electron impact excitation of the a1 Delta g and b1 Sigma g+ electronic states of O2

Experimental and theoretical differential cross sections for the electron impact excitation of the a1 Delta g and b1 Sigma g+ electronic states of O2 have been determined at ten incident energies ranging from 5 eV to 20 eV. The current experimental differential cross sections were obtained for the scattering range 10 degrees to 90 degrees by analysing energy loss spectra in O2 at a number of fixed scattering angles within that range. This data represents an extension to and comprehensive remeasurement of the pioneering work of Trajmar and co-workers for this scattering system. The present theoretical results were obtained using the R-matrix method with a model including nine electronic states of the target molecule and configuration interaction (CI) representations of the target wavefunctions. It represents one of the first ab initio calculations of electron scattering from an open-shell molecule.

Delta excitation in nuclei and coherent meson production

We report on inclusive cross sections for reactions of the type ( 3He,t), (p,n), (p,p′) on nuclei around the Δ excitation region. Particular emphasis is made on the coherent process which leaves the nucleus in the ground state and produce pions. Coherent pion production leads to an excitation function with a Δ peak shifted towards lower excitation energies and is an important ingredient in the explanation of the shift of the total inclusive cross section. Coherent eta production is also studied and it is shown to be an excellent tool to determine the coupling g ηNN , so far unknown experimentally.

Delta excitations in compressed finite nuclei.

We treat $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, and $^{56}\mathrm{Ni}$ as systems of baryons which can exist in either the ground (nucleon) state or first excited (delta) state and follow their behavior under static comrpession using constrained spherical Hartree-Fock approximation (SHF). We use realistic effective nucleon-nucleon interactions with meson-exchange-based nucleon-delta transition potentials and delta-delta interactions and we make phenomenological adjustments to obtain SHF equilibrium properties in agreement with experiment. We then show how physical properties are affected by delta excitation under compression. We find that a significant fraction of the increase in energy of these nuclei under compression is stored in the form of \ensuremath{\Delta}-mass creation. This, in turn, may have implications for an enhanced role for nuclear compression in subthreshold pion production in nucleus-nucleus collisions. In addition, including the deltas leads to a lower compressibility of each of these nuclei.

Proton and light ion induced charge exchange reactions in nuclei

We study the different channels which contribute to the charge exchange reactions of the type (3He, t) (p, n) etc., in the region of excitation of the delta resonance. We show that the shift of the delta peak in nuclei is due to a collaboration of many processes: delta excitation in the projectile, quasi-elastic collisions, virtual pion absorption and coherent pion production. The first three processes are responsible for a considerable shift of strength but do not move the peak position, while the addition of the coherent channel produces finally the shift of the peak.

Quasi-elastic delta excitation in the charge response of the nucleus

We have studied the general relation between nuclear and free-nucleon longitudinal and transverse responses and shown that nuclear Fermi motion implies admixtures from transverse nucleon currents in the longitudinal (or Coulomb) nuclear response and vice versa. We give the general expression for the relation between the nucleon and nuclear responses in the Fermi-gas model including the case of isobar excitation. In the particular case of the Δ-resonance we have shown that at large transferred momenta (i.e.⩾1GeV/ c) an important tail is produced beyond the nucleon quasi-elastic peak which has nothing to do with Coulomb strength.

Inclusive (p, Delta ++) and (p,p' pi + reactions.

Formulas are derived for cross sections for inclusive (p,${\mathrm{\ensuremath{\Delta}}}^{++}$) and (p,p\ensuremath{'} ${\mathrm{\ensuremath{\pi}}}^{+}$) reactions; these are shown to depend on the pion self-energy in the nucleus, and the production and decay vertices of the ${\mathrm{\ensuremath{\Delta}}}^{++}$. The pion self-energy includes both nucleon excitation (${\mathrm{NN}}^{\ensuremath{-}1}$) as well as delta excitation (\ensuremath{\Delta}${\mathrm{N}}^{\ensuremath{-}1}$) in the nucleus. The pion-nucleon couplings in the transition vertex as well as in the self-energy are written using relativistic pseudovector coupling; results are compared with a nonrelativistic reduction. The distortions of the continuum particles are included in a ``distorted-wave Fermi gas'' approximation. Calculations are made for the excitation spectrum of the nucleus, d\ensuremath{\sigma}/d\ensuremath{\omega}, and the angular distribution in the (p,${\mathrm{\ensuremath{\Delta}}}^{++}$) reaction, for proton beam energies from threshold to 3 GeV. For the (p,p\ensuremath{'} ${\mathrm{\ensuremath{\pi}}}^{+}$) reaction cross sections are calculated for the proton spectrum and the distribution d\ensuremath{\sigma}/d${\mathrm{\ensuremath{\Omega}}}_{\mathrm{\ensuremath{\pi}}}$\ensuremath{\Omega}p\ensuremath{'}${\mathrm{dE}}_{\mathrm{p}\ensuremath{'}}$${\mathrm{dE}}_{\mathrm{\ensuremath{\pi}}}$ at fixed values of the proton and proton angles and a fixed value of ${\mathrm{E}}_{\mathrm{p}\ensuremath{'}}$. The latter essentially gives the excitation energy spectrum of the nucleus. Many interesting features are seen in these spectra. The differences in results using relativistic pion-nucleon coupling and its nonrelativistic reduction are shown to increase with the beam energy. Around 400 MeV, there is little difference in the cross sections but at 1 GeV and beyond the difference becomes large, changing both the magnitude and shape of the distributions. The inclusion of distortions reduces the magnitude of the cross section but leaves the shape unchanged.

Rho exchange in charge-exchange reactions.

We have studied the role of rho meson exchange in the transition potential for the charge-exchange reactions p(n,p)n and p(p,n)${\mathrm{\ensuremath{\Delta}}}^{++}$ at intermediate energies. The cross sections are calculated in the distorted-wave Born approximation. The calculated results are compared with the available experimental data. It is found that, for reproducing these data, while in the p(n,p)n reaction, in addition to one-pion exchange, we need the rho exchange in the transition potential; in the delta excitation the rho exchange is not needed.

Projectile and target delta excitation in the ( 3He, t) and ( 3He, 3He) reactions

We study simultaneously the ( 3He , t) and ( 3He, 3He) reactions on proton and neutron targets in the region of the delta excitation resonance. We observe that the mechanism of delta excitation in the target dominates the ( 3He, t) reaction on the proton, but the mechanism of delta excitation in the projectile is important in the ( 3He, t) reaction on the neutron, and largely dominates the ( 3He, 3He) reaction on proton and neutron targets. The two mechanisms give rise to different shapes in the energy distributions of the t or 3He outgoing particles and the weights and shapes of the mechanism change appreciably with the energy of the projectile. The combined experimental study of both reactions as a function of energy is thus a much richer source of information on the dynamics of these problems than the study of the ( 3He, t) reaction alone, where the experimental efforts have so far concentrated.

The l-forbidden m1 decay of the 2522 keV level in 39K

The mean lifetime of the first excited 1 2 + level in 39K has been measured to be τ = 93 ± 13 fs by high recoil velocity DSAM. The level was excited by bombarding a 4He-implanted Ta target with a 100 MeV 39K beam. The lifetime was determined by fitting the Doppler-broadened lineshape of the 2522 keV gamma-ray transition to the 3 2 + ground state. Together with the measured B(E2), the B (M1; d 3 2 → S 1 2 ) for this l-forbidden M1 transition was determined to be 0.0100 ±0.0027 μ 2 N . A theoretical calculation, taking into account core polarization, delta excitation and mesonexchange current contributions, underestimates the B( M)1) by more than a factor of six. The experiment also measured the lifetimes of the 3019 keV and 3883 keV levels to be 20 ±4 fs and 11 ± 6 fs, respectively.