Nucleon Spectrum Research Articles

Fluxes of atmospheric neutrinos and related cosmic rays

The atmospheric neutrino beam simultaneously spans a range of pathlengths from ten to ten thousand kilometers, which correspond respectively to downward- and upward-going neutrinos. As with any neutrino oscillation experiment, also in this case the interpretation of the data depends on a detailed knowledge of the neutrino beam. The ingredients are the primary spectrum of cosmic-ray nucleons, the geomagnetic fields in which the charged particles propagate and the properties of interactions of hadrons in the atmosphere. In this talk I review the status of calculations in light of the recent evidence for neutrino oscillations from Super-Kamiokande.

Coalescence and flow in ultrarelativistic heavy ion collisions

Using a density matrix approach to describe the process of coalescence, we calculate the coalescence probabilities and invariant momentum spectra for deuterons and antideuterons. We evaluate our expressions with a hydrodynamically motivated parametrization for the source at freeze-out which implements rapid collective expansion of the collision zone formed in heavy ion collisions. We find that the coalescence process is governed by the same lengths of homogeneity which can be extracted from HBT interferometry. They appear in the absolute cluster yield via an effective volume factor as well as in a quantum mechanical correction factor which accounts for the internal structure of the deuteron cluster. Our analysis provides a new interpretation for the parameters in the popular phenomenological coalescence model and for the effective overlap volume in Hagedorn's model for cluster production in pp collisions. Using source parameters extracted from a recent HBT analysis of two-pion correlations, we successfully describe deuteron and antideuteron production data from Pb+Pb collisions at the CERN SPS as measured by the NA44 and NA52 collaborations. We also confirm the recent finding by Polleri et al. that the different measured slopes of nucleon and deuteron transverse mass spectra require a transverse density profile of the source which is closer to a box than to a Gaussian shape.

Leading nucleons from peripheral processes in lepton deep inelastic scattering and the nucleon structure

The experimental information on nucleon production in lepton deep inelastic scattering (DIS) is rather scarce. Recently there is a growing interest in understanding the mechanism of the production of baryons in DIS, stimulated by recent results on leading protons and neutrons from electron-proton scattering at HERA. I review on different peripheral mechanisms of nucleon (proton or neutron) production in lepton DIS and discuss their role in understanding the spectra of nucleons for both fixed target and collider experiments. In DIS ep → e′Xh, the QCD hardness scale gradually diminishes from the hard scale, Q 2, in the virtual photon (current) fragmentation region to the soft, hadronic, scale in the proton (target) fragmentation region. This suggests a similarity of the inclusive spectra of leading protons and neutrons, h = p, n, in high energy hadron-proton collisions and in lepton DIS at small Bjorken-χ. The semi-inclusive cross section for production of slow protons in charged-current deep inelastic (anti)neutrino scattering on protons and neutrons is discussed. The standard hadronization models based upon the color neutralization mechanism appear to underestimate the rate of slow proton production on hydrogen. The presence of the virtual mesons (pions) in the nucleon leads to an additional mechanism for proton production, referred to as spectator process. The results of the calculations are compared with the CERN bubble chamber (BEBC) data. I discuss the structure of deep-inelastic events induced by the pione-xchange at HERA kinematics. Most of the event characteristics do not provide a possibility to distinguish the ordinary DIS fragmentation events from those induced by the pion-exchange mechanism. The only exception is the energy distribution of outgoing neutrons. The pion cloud model predicts energy distribution of neutrons which differs significantly from the standard hadronization models which can in principle be verified experimentally. A detailed analysis of semi-exclusive diffractive processes in ep DIS at HERA, with the diffractive final states in the forward direction is presented. The contributions of the subleading f 0; ω,a 2, ρ reggeons and the pion exchanges to the diffractive structure function with the forward proton or neutron are estimated. It is found that the ( a 2, ρ) reggeons are entirely responsible for the forward neutron production at χ IP < 10 −3. The π N production in the forward region is estimated using the Deck mechanism. The significance of this reaction for the processes measured at HERA is discussed. In the DIS production of leading protons DIS off neutral pions must be supplemented by a contribution from isoscalar reggeon ( f0) exchange extrapolated down to moderate values of χ L . I comment on the χ and Q 2 dependence of leading proton production as a probe of a universal pattern of the χ, Q 2 evolution of the nucleon and meson (reggeon) structure functions at small χ.

Production and Propagation of Cosmic‐Ray Positrons and Electrons

We have made a new calculation of the cosmic-ray secondary positron spectrum using a diffusive halo model for Galactic cosmic-ray propagation. The code computes self-consistently the spectra of primary and secondary nucleons, primary electrons, and secondary positrons and electrons. The models are first adjusted to agree with the observed cosmic-ray Boron/Carbon ratio, and the interstellar proton and Helium spectra are then computed; these spectra are used to obtain the source function for the secondary positrons/electrons which are finally propagated with the same model parameters. The primary electron spectrum is evaluated, again using the same model. Fragmentation and energy losses are computed using realistic distributions for the interstellar gas and radiation fields, and diffusive reacceleration is also incorporated. Our study includes a critical re-evaluation of the secondary decay calculation for positrons. The predicted positron fraction is in good agreement with the measurements up to 10 GeV, beyond which the observed flux is higher than that calculated. Since the positron fraction is now accurately measured in the 1-10 GeV range our primary electron spectrum should be a good estimate of the true interstellar spectrum in this range, of interest for gamma ray and solar modulation studies. We further show that a harder interstellar nucleon spectrum, similar to that suggested to explain EGRET diffuse Galactic gamma ray observations above 1 GeV, can reproduce the positron observations above 10 GeV without requiring a primary positron component.

New precompound decay model: Angular distributions

A new Monte Carlo precompound decay model is used to calculate double-differential spectra using an approach based on conservation of linear momentum between an incident nucleon and the three quasiparticles activated in the collisions of the equilibration process. The angular distribution theory is presented as it is applied to the individual three-exciton cascades of the precompound model. The importance of multiple precompound decay beyond two nucleons per nucleus is illustrated for ${}^{90}$Zr$(p,xn)$ reactions for incident protons up to 256 MeV. These components are shown to be important for extending the useful range of the precompound approach to energies beyond 80 MeV. The contribution to nucleon spectra due to hole conversion processes is illustrated. We compare results of the formulation described with experimental angular distributions for ${}^{90}$Zr$(p,xn)$ reactions at incident energies of 45, 80, and 160 MeV, and for the ${}^{90}$Zr$(p,xp)$ reactions at incident energies of 80, 160, and 200 MeV. Additionally, ${}^{208}$Pb$(p,xn)$ spectra at 7.5\ifmmode^\circ\else\textdegree\fi{}, 30\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}, 120\ifmmode^\circ\else\textdegree\fi{}, and 150\ifmmode^\circ\else\textdegree\fi{} are compared with two experimental data sets for 256 MeV incident proton energy, and ${}^{90}$Zr$(p,xn)$ spectra at the same five angles are compared with predicted results for 256 MeV incident protons. At 256 MeV incident proton energy, the higher energy emission spectra are seriously overpredicted at 60\ifmmode^\circ\else\textdegree\fi{}. All other results are reproduced quite well, including back-angle yields. The quasielastic peak measured at 7.5\ifmmode^\circ\else\textdegree\fi{} at 256 MeV incident proton energy is shown to be in quite reasonable agreement with experimental results.

Soft-hard interplay and factorization for baryon production in the target fragmentation region in ep collisions

We discuss baryon production in the nucleon fragmentation region in deep inelastic scattering. The dependence of the nucleon spectra on Bjorken-$x$ is evaluated within the parton model and in QCD, and ways to look for the break-down of the DGLAP approximation via baryon production are suggested. We argue also that the leading neutron production in these small $x$ processes is rather insensitive to the pion parton densities of the nucleon.

Inclusive nucleon production from alpha air nucleus collisions

It is shown that nucleon spectra produced in αα collisions can be given by 5 different distributions in the Feynman x variable. The same 5 distributions are used to describe inclusive nucleon spectra produced in proton air nucleus collisions. The forward region of these inclusive nucleon spectra are decreasing with increasing energy and the number of spectator nucleons from alpha particles is practically energy independent.

MUON FLUXES DERIVED FROM THE DIRECTLY MEASURED PRIMARY COSMIC RAY ELEMENTAL SPECTRA

The muon energy spectra at 0° and 89° have been estimated from the decay of nonprompt and prompt mesons created by the individual elemental primary cosmic ray groups during nucleus-air collisions in the upper atmosphere and the results are found to be fairly comparable with the measured muon fluxes obtained from the direct magnetic spectrograph results in Refs. 2–4, and also from the underground indirect measurements in Refs. 5–10. The muon spectrum derived from the single slope primary nucleon spectrum with a constant spectral index of value −2.73 is only slightly different from the present result for energies below 20 TeV. The present muon spectra at large zenith angle exhibit steeper spectral indices when compared to the expected results obtained from primary elemental groups by Parente et al.

Super-high-energy neutrino spectra in the atmosphere derived from the latest JACEE, MSU, SOKOL and CRN primary spectrum usingZ-factors for p-air collisions estimated from Fermi national accelerator data

The absolute spectra of atmospheric neutrinos in the vertical direction and at large zenith angle have been estimated directly from the primary cosmic-ray nucleon spectrum based on the latest JACEE, MSU, SOKOL and CRN data surveyed by Swordy. The Fermi National Accelerator Laboratory results for pp→K±X, pp→K±X and pp→pX inclusive reactions have been used for theZ-factor calculations for meson production and these were modified for p-air and A-A collisions. The derived muon and electron neutrino spectra at 0° and 89° from non-prompt meson decay are found comparable with the results of Volkova and Zatsepin, and Butkevichet al. An estimate of the prompt muon neutrino spectra at 0° and 89° fromtthe charmed-meson decay has been given along with the earlier results of different authors. The present result for muon neutrino spectra at zenith angles 0° and 89° is found in approximate agreement with the EAS-TOP results of the Gran Sasso group.

Pi N scattering in a large-Nc sigma model.

We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi mesons to the nucleon are echoed by couplings to the entire tower of I=J baryons (including the Delta) as dictated by large-N_c group theory. We sum the complete set of multi-loop meson-exchange \pi N --> \pi N and \pi N --> \sigma N Feynman diagrams, to leading order in 1/N_c. The key idea, reviewed in detail, is that large-N_c allows the approximation of LOOP graphs by TREE graphs, so long as the loops contain at least one baryon leg; trees, in turn, can be summed by solving classical equations of motion. We exhibit the resulting partial-wave S-matrix and the rich nucleon and Delta resonance spectrum of this simple model, comparing not only to experiment but also to pion-nucleon scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-baryon S-matrix which hitherto has been uncovered only with skyrmion methods, can also be described by models with explicit baryon fields, thanks to the 1/N_c expansion.

Quark model predictions for the process [formula omitted] and the status of the [formula omitted] rule

Single and double coincidence nucleon spectra in the Λ-hypernuclei weak decay are evaluated and discussed using a microscopic formalism. Nuclear matter is employed together with the local density approximation which allows us to analyze the 12ΛC hypernucleus non-mesonic weak decay. Final state interactions (FSI) are included via the first order (in the nuclear residual interaction) terms to the RPA, where the strong residual interaction is modelled by a Bonn potential. At this level of approximation, these FSI are pure quantum interference terms between the primary decay (ΛN→NN) and (ΛN→NN→NN), where the strong interaction is responsible for the last piece in the second reaction. Also the Pauli exchange contributions are explicitly evaluated. We show that the inclusion of Pauli exchange terms is important. A comparison with data is made. We conclude that the limitations in phase space in the RPA make this approximation inadequate to reproduce the nucleon spectra. This fact does not allow us to draw a definite conclusion about the importance of the interference terms.

Effect of Σ components in nonmesonic weak decay of Λ particle in nuclear medium

In this review we discuss the present status of strange nuclear physics, with special attention to the weak decay of Λ-hypernuclei. The models proposed for the evaluation of the Λ decay widths are summarized and their results are compared with the data. The rates ΓNM=Γn+Γp(+Γ2), Γπ0 and Γπ− are well explained by several calculations. Despite the intensive investigations of the last years, the main open problem remains a sound theoretical interpretation of the large experimental values of the ratio Γn/Γp. However, the large uncertainties involved in the experimental determination of the ratio do not allow to reach any definitive conclusion. The Γn/Γp puzzle is strongly related to the so-called ΔI=1/2 rule on the isospin change in the non-mesonic decay, whose possible violation cannot be established at present, again due to the insufficient precision of the data. Although recent works offer a step forward in the solution of the puzzle, further efforts (especially on the experimental side) must be invested in order to understand the detailed dynamics of the non-mesonic decay. Even if, by means of single nucleon spectra measurements, the error bars on Γn/Γp have been considerably reduced very recently at KEK (however, with central data compatible with older experiments), a clean extraction of Γn/Γp is needed. What is missing at present, but planned for the next future, are measurements of (1) nucleon energy spectra in double coincidence and (2) nucleon angular correlations: such observations allow to disentangle the nucleons produced in one- and two-body induced decays and lead to a direct determination of Γn/Γp. Notably, the two-body component of the non-mesonic decay rates has not been measured yet, due to the too low counting rates expected for a coincidence experiment. For the asymmetric non-mesonic decay of polarized hypernuclei the situation is even more puzzling. Indeed, strong inconsistencies appear already among data. A recent experiment obtained a positive intrinsic Λ asymmetry parameter, aΛ, for Λ5H→e. This is in complete disagreement with a previous measurement, which obtained a large and negative aΛ for p-shell hypernuclei, and with theory, which predicts a negative value moderately dependent on nuclear structure effects. Also in this case, improved experiment establishing with certainty the sign and magnitude of aΛ for s- and p-shell hypernuclei will provide a guidance for a deeper understanding of hypernuclear dynamics and decay mechanisms.

SUPERSYMMETRIC QUANTUM MECHANICS APPLIED TO NONRELATIVISTIC QUARK MODELS

We examine the effect of changing the energy levels and normalization constants of bound states corresponding to baryons and mesons in nonrelativistic quark models. We do this by applying the transformations of supersymmetric quantum mechanics (SUSYQM) to the potentials used in these models. In particular, we fit the spectra and leptonic decay widths of [Formula: see text] and [Formula: see text] mesons by modifying several existing [Formula: see text] potentials by means of supersymmetric transformations. It is found that the potentials are unchanged beyond 2 fm, and that fitting the widths induces greater oscillations in the potentials than those generated by adjusting the energy levels only. Transformations of SUSYQM are applied to the hypercentral potential in order to accommodate the Roper resonance in the s-wave nucleon spectrum. The quark-quark potential found by inverting the transformed hypercentral potential via a new exact Abel transform differs significantly from the original potential up to 5 fm from the origin and violates the concavity requirement. The [Formula: see text] potential related to this potential by Lipkin’s rule does not reproduce the meson spectrum. As the Hall-Post lower bound is also accurate for baryons, the results of the application of supersymmetric transformations in this approximation scheme are also considered and compared to the upper bound of the hypercentral approximation.

Description of heavy ion collisions with medium dependent forces

One of the proclaimed goals of heavy ion collisions with 100 MeV up to 2000 MeV per nucleon is the determination of the equation of state of nuclear matter, which one needs for example for neutron stars, supernova explosions and the early universe. But the situation in heavy ion collisions is quite different from thermal equilibrium with a spherical momentum distribution and a fixed temperature. The effective nucleon-nucleon interaction as determined for example by the solution of the Bethe-Goldstone equation depends through the Pauli operator and through the single particle energies on the surrounding nuclear matter. This dependence is especially pronounced since the nucleon-nucleon interacting is highly momentum dependent: It is attractive at small relative momenta and repulsive at higher values. Thus the effective nucleon-nucleon interaction in heavy ion collisions depends on the distribution of the surrounding nuclear matter in orbital and momentum space. Here results are presented using for the description of heavy ion reactions at intermediate energies Quantum Molecular Dynamics (QMD) in a non-relativistic and in a completely covariant (RQMD) form. We show that the production of gamma-rays, pions and the inclusive spectra of nucleons and light nuclei are not sensitive to the equation of states. An observable sensitive to the equation of state is the perpendicular momentum distribution in heavy ion collisions. Also sensitive is the production of heavier particles like K + and K − mesons and antiprotons below the NN threshold. These collisions can have enough energy to compress and heat up nuclear matter and since they are below the NN threshold several nucleons must cooperate.

Sea level muon spectra at large zenith angles derived from the latest JACEE primary nucleon spectrum

Sea level muon energy spectra at large zenith angles have been derived from the latest JACEE primary spectrum using the Fermilab Single-Arm Spectrometer data on charged-meson production. The role of increasing total cross-section on the final result for the energy spectra has been investigated here with special emphasis. The inclusion of the rising total cross-section at cosmic range of energies, it is seen, has come into much use in explaining the observed data at very high energies.

Periodic structure in nuclear matter.

The properties of nuclear matter are studied in the framework of quantum hadrodynamics. Assuming an {omega}-meson field, periodic in space, a self-consistent set of equations is derived in the mean-field approximation for the description of nucleons interacting via {sigma}-meson and {omega}-meson fields. Solutions of these self-consistent equations have been found: The baryon density is constant in space, however, the baryon current density is periodic. This high density phase of nuclear matter can be produced by anisotropic external pressure, occurring, e.g., in relativistic heavy ion reactions. The self-consistent fields developing beyond the instability limit have a special screw symmetry. In the presence of such an {omega} field, the energy spectrum of the relativistic nucleons exhibits allowed and forbidden bands, similar to the energy spectrum of the electrons in solids.

Angular distribution of fast protons from the pre-equilibrium process of the 165Ho( alpha,p) reaction.

The concept of the exciton model for nucleon-induced nuclear reactions has been extended to \ensuremath{\alpha}-induced pre-equilibrium reactions in order to calculate angular distributions and energy spectra of fast ejectile nucleons. The effect of the nucleon motion on the cascade nucleon-nucleon scattering inside the nucleus and the geometrical optical effects at the exit channel are taken into account for the first time in the \ensuremath{\alpha}-induced pre-equilibrium reaction. Angular distributions of protons from the $^{165}\mathrm{Ho}$(\ensuremath{\alpha},p) reaction at ${\mathit{E}}_{\mathrm{\ensuremath{\alpha}}}$=109 MeV were calculated. The observed distributions of the fast protons in the pre-equilibrium region were found to be reproduced well by the calculation.

The Nonperturbative QCD Correction to the Quark-Quark Potential11The project partially supported by National Natural Science Foundation of China

A potential describing the interaction between quarks is obtained by considering not only perturbative effects of QCD, but also the nonperturbative contributions via and condensates. In this potential, a linear confinement type term and a new term can be automatically obtained. A tendency to flatten the potential at large distance is observed and it is consistent with the phenomenologically introduced potential which gives a better fit for nucleon spectrum.

The energy dependence of the leading nucleon distribution and the evolution of the nucleonic cosmic ray component in the atmosphere

We show that in order to obtain a fairly accurate description of the nucleonic component of cosmic ray at sea level the energy dependence of the leading nucleon distribution has to be taken into account. By relating the collision inelasticity to the impact parameter overlap function we are able to estimate the energy dependence of the leading nucleon spectrum and to obtain good agreement with cosmic ray data at sea level in the energy range 1≦E (GeV)≦104.

Cross sections for production of eta nuclei by photons

The cross sections for production of eta nuclei (eta A) by photons are calculated in the framework of the potential nonrelativistic model. The total cross sections of the gamma +12C to p+eta 11B and delta +16O to p+eta 15N reactions characterized by predominant forward emission of protons are shown to take on the maximum values of 0.4 mu b and 1.5 mu b, respectively, at a 0.75 GeV photon energy. The photoproduction of eta nuclei must give rise to characteristic peaks in the nucleon spectra of the gamma A to pX reactions.