Total Nucleon-nucleon Cross Section Research Articles

A study of the nucleus-nucleus total reaction cross section of stable systems at intermediate energies: An application to 12C

A semi-microscopic analytical expression of the nucleus-nucleus total reaction cross section (σR) was proposed based on the strong absorption model. It is suitable for stable nuclei at intermediate energies. The matter density distributions of nuclei and the nucleon-nucleon total cross section were both considered. Particularly, the Fermi motion effect of the nucleons in a nucleus was also taken into account. The parametrization of σR was applied to the colliding systems including 12C. The experimental data at energies from 30 to 1000 MeV/nucleon were well reproduced, according to which an approach of deriving σR without adjustable parameters was developed. The necessity of considering the Fermi motion effect in the parametrization was discussed.

Holographic description of total hadronic cross sections at high energies

We investigate the hadron-hadron total cross sections at high energies in the framework of holographic QCD. In our model setup, the involved strong interaction is described by the Brower-Polchinski-Strassler-Tan Pomeron exchange kernel, and the two form factors are obtained from the bottom-up AdS/QCD models. We show that the resulting nucleon-nucleon total cross section is consistent with the experimental data recently measured by the TOTEM collaboration at the LHC. As examples to see the general versatility of the model, we also present our analysis on the pion-nucleon and pion-pion cases, which can be predicted because all the adjustable parameters are fixed by the nucleon-nucleon data.

Supernovae and Weinberg\u2019s Higgs portal dark radiation and dark matter

The observed burst duration and energies of the neutrinos from Supernova 1987A strongly limit the possibility of any weakly-interacting light particle species being produced in the proto-neutron star (PNS) core and leading to efficient energy loss. We reexamine this constraint on Weinberg’s Higgs portal model, in which the dark radiation particles (the Goldstone bosons) and the dark matter candidate (a Majorana fermion) interact with Standard Model (SM) fields solely through the mixing of the SM Higgs boson and a light Higgs boson. In order for the Goldstone bosons to freely stream out of the PNS core region, the Higgs portal coupling has to be about a factor of 4-9 smaller than the current collider bound inferred from the SM Higgs invisible decay width. We find that in the energy loss rate calculations, results obtained by using the one-pion exchange (OPE) approximation and the SP07 global fits for the nucleon-nucleon total elastic cross section differ only by a factor ≲ 3. The SN 1987A constraints surpass those set by laboratory experiments or by the energy loss arguments in other astrophysical objects such as the gamma-ray bursts, even with other nuclear uncertainties taken into account. Furthermore, the SN 1987A constraints are comparable to bounds from the latest dark matter direct search for low-mass WIMPs (≲10 GeV.)

Inelastic versus total nucleon-nucleon cross section at largeNc

In this paper, the implication of the extreme large $N_c$ limit for nucleon-nucleon cross section is examined. Starting from the $N_c$ scaling of the S-matrix elements, a relation between the total inelastic and total cross sections is derived for the regime in which the momenta are much larger than the QCD scale. A conceptual complication arise from the fact that there is a tower of baryons, such as the $\Delta$, with mass splittings from the nucleon which go to zero at large $N_c$. Since these baryons are stable at large $N_c$, the meaning of elasticity must be modified. Processes which only transform nucleons to these baryons are considered elastic; processes in which at least one additional meson is produced are considered inelastic. It is shown that in the extreme large $N_c$ limit, the total inelastic cross section is exactly one eighth of the total cross section. In contrast, in the physical world of $N_c=3$ the total cross section for high-energy nucleon-nucleon scattering is dominated by inelastic processes.

PACIAE 2.1: An updated issue of the parton and hadron cascade model PACIAE 2.0

We have updated the parton and hadron cascade model PACIAE 2.0 for relativistic nuclear collisions (cf. Comput. Phys. Comm. 183(2012)333) to the new issue of PACIAE 2.1. The PACIAE model is based on PYTHIA. In the PYTHIA model, once the generated particle/parton transverse momentum $p_T$ is randomly selected, its component of $[p_x,p_y]$ was originally put on the circle with radius $p_T$ randomly. It is now replaced by put on the circumference of ellipse with half major and minor axes of $p_T(1+\delta_p)$ and $p_T(1-\delta_p)$, respectively, in order to investigate better the transverse momentum anisotropy in final hadronic state.

Total Nucleon-Nucleon Cross Section at LargeNc

It is shown that at sufficiently large $N_c$ for incident momenta which are much larger than the QCD, the total nucleon-nucleon cross section is independent of incident momentum and given by $\sigma^{\rm total}=2 \pi \log^2(N_c) / (m^2_{\pi})$. This result is valid in the extreme large $N_c$ regime of $\log(N_c) \gg 1$ and has corrections of relative order $\log (\log(N_c))/\log(N_c)$. A possible connection of this result to the Froissart-Martin bound is discussed.

EXCLUSIVE PRODUCTION OF π+π- PAIRS IN PROTON-PROTON AND PROTON-ANTIPROTON COLLISIONS

We report on a detailed investigation of four-body pp → ppπ+π- and [Formula: see text] reactions which constitute an irreducible background to three-body processes pp → ppM, where M is a broad resonance in the π+π- channel, e.g. M = σ, ρ0, f0(980), f2(1275), f0(1500). We include double-diffractive contribution (both pomeron and reggeon exchanges) as well as the pion-pion rescattering contributions. The first process dominates at higher energies and small pion-pion invariant masses while the second becomes important at lower energies and higher pion-pion invariant masses. We compare our results with the experimental data. We make predictions for future experiments at PANDA, RHIC, Tevatron and LHC energies. The two-dimensional distribution in rapidity space of pions (yπ+, yπ-) is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of pions. The processes considered constitute a sizeable contribution to the total nucleon-nucleon cross section as well as to pion inclusive cross section.

Distinction between Proton-Neutron Density Distribution of Halo Nuclei at the Nuclear Surface via Reaction Cross Sections

Reaction cross sections ( σ R ) for 11Be and 8B on proton targets at 50 A ∼ 120 A MeV have been measured to distinguish between the proton- and neutron- density distributions at the nuclear surface. The σ R is connected with the nucleon density distributions by the Glauber theory. Since the nucleon-nucleon total cross sections in that energy region have a large isospin dependence, the σ R on proton targets should have a large difference between the proton and neutron in the halo structure. The experimental σ R on proton targets are in good agreement with the calculated ones assuming that the tail dominantly consists of a neutron for 11Be and a proton for 8B.

Exclusivepp→ppπ+π−reaction: From the threshold to LHC

We evaluate differential distributions for the four-body $pp\ensuremath{\rightarrow}pp{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ (and $p\overline{p}\ensuremath{\rightarrow}p\overline{p}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$) reaction which constitutes an irreducible background to three-body processes $pp\ensuremath{\rightarrow}ppM$, where $M$ are a broad resonances in the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ channel, e.g., $M=\ensuremath{\sigma}$, ${\ensuremath{\rho}}^{0}$, ${f}_{0}(980)$, ${f}_{2}(1275)$, ${f}_{0}(1500)$. We include both double-diffractive contribution (both Pomeron and Reggeon exchanges) as well as pion-pion rescattering contribution. The first process dominates at higher energies and small pion-pion invariant masses while the second becomes important at lower energies and higher pion-pion invariant masses. The amplitude(s) is(are) calculated in the Regge approach. We compare our results with measured cross sections for the Intersecting Storage Ring and Fermi National Accelerator Laboratory experiments. We make predictions for future experiments at the anti-Proton ANnihilation at DArmstadt (PANDA), Relativistic Heavy Ion Collider, Tevatron, and LHC energies. Differential distributions in invariant two-pion mass, pion rapidities and transverse momenta of pions are presented. The two-dimensional distribution in $({y}_{{\ensuremath{\pi}}^{+}},{y}_{{\ensuremath{\pi}}^{\ensuremath{-}}})$ is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of pions. The processes considered constitute a sizeable contribution to the total nucleon-nucleon cross section as well as to pion inclusive cross section.

Nucleon-nucleon, γp and γγ scattering using factorization: the Aspen model and analytic amplitude analysis

Using the Aspen, model, a QCD-inspired eikonal model, we fit high energy nucleon-nucleon total cross sections, nuclear slopes and ϱ-values, including cosmic ray p-air data. This model which is crossing symmetric, insures unitarity and analyticity, as well as satisfying the Froissrt bound. Assuming that the ratio of σelastic/σtotal is independent of process, the Aspen model predicts factorization. Utilizing the model parameters found for nucleon-nucleon scattering, we predict the total cross sections and nuclear slope parameters for γp reactions, as well as total cross sections for γγ scattering, by invoking the naive quark model and vector dominance. In particular, by making a χ2 fit to the nuclear slope parameters for the ‘elastic’ reactions γ + p → ϱ+p, γ+p → φ+p, γ+p → ω+p, we find the proportionality constant κ = 0.661±0.008, in excellent agreement with the value of κ = 23 predicted by the naive vector quark model (2 quarks in the vector meson-like photon and 3 quarks in the nucleon). We next test the (lack of) sensitivity of the factorization theorems to the assumed distributions of the impact parameter b, for nucleon-nucleon, γp and γγ scattering, that are used in the eikonal. Finally, making an independent analysis utilizing real analytical amplitudes and assuming factorization, we make a simultaneous fit to the total cross sections for pp, pp, γp and γγ cross sections, as well as the ϱ-values for pp and pp. In this global fit we separately fit to the results of L3 and OPAL obtained using either the PHOJET or PYTHIA Monte Carlo program—the published values use the average of the two. It should be noted that these two Monte Carlos give different normalizations as well as different energy behaviors. The overall fit is good using PHOJET and poor using PYTHIA, lending strong support for the factorization hypothesis, as well as the naive quark model and vector dominance.

Pions in the light-cone nucleon and electromagnetic form factors

The light-cone Fock-state decomposition of the nucleon involves pion-quark core (π′N′ andπ′Δ′) components. The size of the quark core is at present of special importance for the analysis of the onset of colour transparency in the A(e,e′p) reactions. With the light-coneNπ′N′ andNπ′Δ′ vertex functions deduced from experimental data on high-energy proton fragmentation into nucleons and isobars, we evaluate the effect of the pionic cloud on the electromagnetic form factors of nucleons. We find the quark core radius to be about 10% smaller than the nucleon's radius. Analysis of the renormalization of the total nucleon-nucleon cross section for the presence of the pionic cloud suggests a similar core radius.

Description of inelastic scattering between heavy ions in the Glauber model.

The optical limit of the Glauber model is used for the description of inelastic processes in heavy-ion reactions at intermediate energies. Different prescriptions are investigated to obtain the inelastic scattering amplitude from the corresponding microscopic nucleon-nucleon amplitude. Besides the standard one in which the target excitation is ascribed to a projectile-nucleon collision and contributions from multiple-scattering processes are preliminarily summed to produce the elastic projectile-nucleon amplitude, we suggest the alternative approach in which a single nucleon-nucleon collision causes the inelastic transition. In all cases the formalism is modified to take into account the deflection of the classical orbits due to the strong repulsive Coulomb field. Parameter-free predictions for the inelastic excitation, based on experimental nucleon-nucleon total cross sections and standard densities, show a remarkable agreement with both experiment and distorted-wave Born approximation calculations.

Modified Glauber model for the description of elastic scattering between heavy ions.

The standard form of the optical limit of the Glauber model used for the description of elastic scattering is modified to account for the Coulomb distortion of the trajectory occurring in the case of heavy ion scattering at relatively low bombarding energies. We retain the description of the process in terms of nucleon-nucleon collisions, but we relate the nuclear density overlaps for each partial wave to the distance of closest approach of the associated Rutherford trajectory, rather than to the asymptotic value of the impact parameter. Parameter-free predictions for the elastic scattering of $^{13}\mathrm{C}$ at 390 MeV and of $^{40}\mathrm{Ar}$ at 1760 MeV from $^{208}\mathrm{Pb}$, based on experimental nucleon-nucleon total cross sections and standard densities, show a remarkable improvement for both differential and reaction cross sections. The consistency of the approach is strengthened by a correlated method for the inversion of the phase shifts, which, for the examined cases, yields optical potentials very similar to those obtained by optical-model fit analysis.

Pauli blocking and Fermi motion effects in ion-ion collisions

A geometrical model for Pauli blocking and Fermi motion effects in ion-ion collisions is presented. The results, given as effective nucleon-nucleon total cross sections, incicate that the Pauli blocking reduces the nucleon-nucleon cross section in the ion-ion environment by a larger amount than previously estimated.

Microscopic Description of Nucleon-Nucleus Total Reaction Cross Sections

Microscopic calculations of the total reaction cross sections for protons on $^{12}\mathrm{C}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$, and neutrons on $^{27}\mathrm{Al}$ and $^{208}\mathrm{Pb}$ have been made, which provide for the first time an excellent description of the data for projectile energies from 15 MeV through 1 GeV. The calculations are based on the experimental nucleon-nucleon total cross sections and explicitly include the effects of the real nuclear potential, the Coulomb potential, Pauli blocking, and Fermi motion.

Geometrical aspects of high-energy peripheral nucleus-nucleus collisions

The abrasion-ablation model of relativistic nucleus-nucleus (heavy ion) fragmentation reactions is extended to mass number dependence and factorization properties of the cross sections. Weak (fragment-target) factorization is approximately valid while strong (projectile-target) factorization is violated. Calculated projectile-target factors γ PT for the fragmentation of 12C or 16O agree with the Berkeley and Orsay experiments. We propose using the fitted exponent y of the expression σ exp ∼(A P 1 3 + A T 1 3 ) y as a geometrical signature for discriminating peripheral and non-peripheral collisions for medium and heavy nuclei. The weak, logarithmic dependence of n-nucleon processes on the total nucleon-nucleon cross section σ NN implies weak beam energy dependence of fragmentation cross sections. A number of definite experimental predictions are made.

Collisions between composite particles at medium and high energies

Collisions between nuclei are studied by means of a simple extension of the Glauber high energy approximation. An expression for the optical phase shift function, exact within the framework of the Glauber approximation, is expanded in an infinite series and includes the effects of nuclear correlations. The first term corresponds to the standard optical limit result of the Glauber theory, and the higher order corrections arise from the processes in which one or more nucleons of either nucleus can undergo multiple collisions. The center-of-mass correlation is treated consistently so that our results do not exhibit the large-q divergence which characterizes the usual optical limit. It is shown that with realistic constraints on nucleon-nucleon total cross sections, the optical phase shift function does not approach the usual optical limit result when the mass numbers of the colliding nuclei become very large. With a proper treatment of center-of-mass correlations, the optical phase shift series converges rapidly for light nuclei and allows one to perform realistic calculations. The effects of higher order corrections on total and inelastic cross sections and on elastic scattering intensities are examined. The effects of the Coulomb field are included in an average phase approximation and results are comparedmore » with measurements.« less

Is (Ins)2 rise in nucleon-nucleon total cross section excluded by cosmic ray data?

Problem of extraction of nucleon-nucleon total cross section from data on zenith angle dependence of frequencies of extensive air showers is discussed. It is shown that one cannot in this way distinguish even between asymptotically constant cross section and that increasing like (Ins)2.

Elastic scattering of heavy ions — The simplest interpretation?

Elastic scattering of heavy ions with incident energies well above the Coulomb barrier is predicted from a simple extension of the Glauber theory for high energy particle-nucleus scattering. The only parameters needed are the “measured” nuclear density distribution function and the measured forward amplitude for free nucleon-nucleon scattering. An extensive comparison between theory and experiment is presented. It is demonstrated that the nuclear absorption needed to reproduce the measured differential cross section for elastic scattering can be well reproduced by means of the measured free nucleon-nucleon total cross section and the nuclear density distribution as “measured” for instance by electron scattering. Remarkable agreement between theory and experiment is demonstrated.

Do extensive air shower data provide reliable information on the proton-proton total cross section?

The zenith angle dependence of frequencies of extensive air showers is discussed from the point of view of nucleon-nucleon total cross sections. It is shown that this kind of data cannot (without additional assumptions) distinguish between asymptotically constant cross sections and those increasing as In s or even as (In s)2.