Proton Distribution Research Articles

Explaining the formation of the 36 smallest known atomic isotopes: from hydrogen to krypton

This work presents a novel approach to understanding the formation and structure of the 36 smallest known atomic isotopes, ranging from hydrogen to krypton, through the lens of the KUPT model. Focusing on the Small Known Isotope (SKI) of each atom, this study meticulously examines the distribution of protons across five nuclear layers (1E, 2T, 3T, 4E, and 4C), constructing a proton tree that spans from hydrogen to krypton atoms. With the aid of Artificial Intelligence, specifically Chat GPT-4, an in-depth analysis was conducted for each atom within the KUPT model framework. This process involved defining minimum stability rules for the nuclear structure, particularly regarding neutron inclusion, across the model’s first five layers. Remarkably, in 35 out of 36 cases, the KUPT model’s predictions aligned perfectly with the SKI data, underscoring the model’s accuracy and reliability. However, an intriguing discrepancy emerged in the case of the Gallium atom (62Ga), suggesting the possible existence of an unknown, lighter isotope with two or three fewer protons (59Ga or 60Ga). This discrepancy not only highlights the KUPT model’s predictive capability but also points to a fertile ground for further experimental investigation, aiming to uncover potentially undiscovered isotope forms of Gallium.

Dip-Bump Structure in Proton’s Single Diffractive Dissociation at the Large Hadron Collider

By extending the dipole Pomeron (DP) model, successful in describing elastic nucleon–nucleon scattering, to proton single diffractive dissociation (SD), we predict a dip-bump structure in the squared four-momentum transfer (t) distribution of proton’s SD. Structures in the t distribution of single diffractive dissociation are predicted around t=−4GeV2 at LHC energies in the range of 3 GeV2≲|t|≲ 7 GeV2. Apart from the dependence on s (total energy squared) and t (squared momentum transfer), we predict also a dependence on missing masses. We include the minimum set of Regge trajectories, namely the Pomeron and the Odderon, indispensable at the LHC. Further generalization, e.g., by the inclusion of non-leading Regge trajectories, is straightforward. The present model contains two types of Regge trajectories: those connected with t-channel exchanges (the Pomeron, the Odderon, and non-leading (secondary) reggeons) appearing at small and moderate −t, where they are real and nearly linear, as well as direct-channel trajectories α(M2) related to missing masses. In this paper, we concentrate on structures in t neglecting (for the time being) resonances in M2.

Direct Evidence of Drift‐Compressional Wave Generation in the Earth's Magnetosphere Detected by Arase

AbstractWe present the first direct evidence of an in situ excitation of drift‐compressional waves driven by drift resonance with ring current protons in the magnetosphere. Compressional Pc4–5 waves with frequencies of 4–12 mHz were observed by the Arase satellite near the magnetic equator at L ∼ 6 in the evening sector on 19 November 2018. Estimated azimuthal wave numbers (m) ranged from −100 to −130. The observed frequency was consistent with that calculated using the drift‐compressional mode theory, whereas the plasma anisotropy was too small to excite the drift‐mirror mode. We discovered that the energy source of the wave was a drift resonance instability, which was generated by the negative radial gradient in a proton phase space density at 20–25 keV. This proton distribution is attributed to a temporal variation of the electric field, which formed the observed multiple‐nose structures of ring current protons.

The LHC as a Neutrino-Ion Collider

Proton-proton collisions at the LHC generate a high-intensity collimated beam of neutrinos in the forward (beam) direction, characterised by energies of up to several TeV. The recent observation of LHC neutrinos by FASERν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and SND@LHC signifies that this previously overlooked particle beam is now available for scientific investigation. Here we quantify the impact that neutrino deep-inelastic scattering (DIS) measurements at the LHC would have on the parton distributions (PDFs) of protons and heavy nuclei. We generate projections for DIS structure functions for FASERν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and SND@LHC at Run III, as well as for the FASERν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}2, AdvSND, and FLArE experiments to be hosted at the proposed Forward Physics Facility (FPF) operating concurrently with the High-Luminosity LHC (HL-LHC). We determine that up to one million electron-neutrino and muon-neutrino DIS interactions within detector acceptance can be expected by the end of the HL-LHC, covering a kinematic region in x and Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2$$\\end{document} overlapping with that of the Electron-Ion Collider. Including these DIS projections in global (n)PDF analyses, specifically PDF4LHC21, NNPDF4.0, and EPPS21, reveals a significant reduction in PDF uncertainties, in particular for strangeness and the up and down valence PDFs. We show that LHC neutrino data enable improved theoretical predictions for core processes at the HL-LHC, such as Higgs and weak gauge boson production. Our analysis demonstrates that exploiting the LHC neutrino beam effectively provides CERN with a “Neutrino-Ion Collider” without requiring modifications in its accelerator infrastructure.

Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions. II. Central Pb + Pb collisions

This paper represents a continuation of our investigation into the limitations on total, proton, and neutron particle number densities, as well as the asymmetry of proton and neutron density distributions achievable in central heavy-ion collisions. We explore these aspects at low and medium energies within the framework of the Boltzmann-Uhlenbeck-Uehling (pBUU) transport and time-dependent Hartree-Fock (TDHF) models. Previous studies, focusing on symmetric and asymmetric collisions of Ca and Sn nuclei [1], and initial results on Pb-nuclei collisions [2], emphasized the role of the Coulomb interaction in these events. Our findings indicated that: (i) the highest total densities predicted at Ebeam=800 MeV/nucleon were on the order of ≈2.5ρ0 (ρ0=0.16fm−3), (ii) the proton-neutron asymmetry for maximal densities, δ=(ρnmax−ρpmax)/(ρnmax+ρpmax), did not generally exceed the asymmetry in the initial state of the collision at all beam energies and tended to decrease during the reaction, and (iii) a significant portion of this asymmetry had its microscopic origin in Coulomb forces, masking the pure nuclear contribution. These new findings, particularly relevant in the astrophysical context, are further examined in this work, focusing on the heaviest target-projectile combination Pb212,208 accessible in an experiment. We introduce the SkT3 Skyrme force model, not previously used for the Pb system, and compare it to the SV-bas and SV-sym34 models to explore the symmetry-energy dependence of the results. Contour plots of nucleonic densities are presented, contrasting the time evolution of the density distributions in low (TDHF) and high (pBUU) models. We also present the evolution of normalized maximal proton, neutron, and total nucleon number density with increasing beam energy in the full pBUU model and the Vlasov approximation, aiming to explore the impact of correlations in the reaction. The time evolution of the proton and neutron density distributions in the plane transverse to the beam direction is illustrated at both low and high beam energy. In conclusion, our detailed examination of the Pb system in this work provides further essential evidence that the aforementioned findings (i)–(iii) are only weakly dependent on system size and a symmetry-energy model, and thus, they are of more general importance. Published by the American Physical Society 2024

Presented to Kepler Ulianov Proton Tree, A Way to Distribute Protons and Neutrons Within the Atomic Nucleus. First part: From Hydrogen to Krypton

This work presents a novel approach to understanding the formation and structure of the 36 smallest known atomic isotopes, ranging from hydrogen to krypton, through the lens of the KUPT model. Focusing on the Small Known Isotope (SKI) of each atom, this study meticulously examines the distribution of protons across five nuclear layers (1E, 2T, 3T, 4E, and 4C), constructing a proton tree that spans from hydrogen to krypton atoms. With the aid of Artificial Intelligence, specifically Chat GPT-4, an in-depth analysis was conducted for each atom within the KUPT model framework. This process involved defining minimum stability rules for the nuclear structure, particularly regarding neutron inclusion, across the model’s first five layers. Remarkably, in 35 out of 36 cases, the KUPT model’s predictions aligned perfectly with the SKI data, underscoring the model’s accuracy and reliability. However, an intriguing discrepancy emerged in the case of the Gallium atom (62Ga), suggesting the possible existence of an unknown, lighter isotope with two or three fewer protons (59Ga or 60Ga). This discrepancy not only highlights the KUPT model’s predictive capability but also points to a fertile ground for further experimental investigation, aiming to uncover potentially undiscovered isotope forms of Gallium.

Ion Dynamics Across a Low Mach Number Bow Shock

AbstractA thorough understanding of collisionless shocks requires knowledge of how different ion species are accelerated across the shock. We investigate a bow shock crossing using the Magnetospheric Multiscale spacecraft after a coronal mass ejection crossed Earth, which led to solar wind consisting of protons, alpha particles, and singly charged helium ions. The three species are resolved upstream of the shock. The low Mach number of the bow shock enabled the ions to be partly distinguished downstream of the shock due to the relatively low ion heating. Some of the protons are specularly reflected and produce quasi‐periodic fine structures in the velocity distribution functions downstream of the shock. Heavier ions are shown to transit the shock without reflection. However, the gyromotion of the heavier ions partially obscures the fine structure of proton distributions. Additionally, the calculated proton moments are unreliable when the different ion species are not distinguished by the particle detector. The need for high time‐resolution mass‐resolving ion detectors when investigating collisionless shocks is discussed.

Radioisotope production using lasers: From basic science to applications

The discovery of chirped pulse amplification has led to great improvements in laser technology, enabling energetic laser beams to be compressed to pulse durations of tens of femtoseconds and focused to a few micrometers. Protons with energies of tens of MeV can be accelerated using, for instance, target normal sheath acceleration and focused on secondary targets. Under such conditions, nuclear reactions can occur, with the production of radioisotopes suitable for medical application. The use of high-repetition lasers to produce such isotopes is competitive with conventional methods mostly based on accelerators. In this paper, we study the production of 67Cu, 63Zn, 18F, and 11C, which are currently used in positron emission tomography and other applications. At the same time, we study the reactions 10B(p,α)7Be and 70Zn(p,4n)67Ga to put further constraints on the proton distributions at different angles, as well as the reaction 11B(p,α)8Be relevant for energy production. The experiment was performed at the 1 PW laser facility at Vega III in Salamanca, Spain. Angular distributions of radioisotopes in the forward (with respect to the laser direction) and backward directions were measured using a high purity germanium detector. Our results are in reasonable agreement with numerical estimates obtained following the approach of Kimura and Bonasera [Nucl. Instrum. Methods Phys. Res., Sect. A 637, 164–170 (2011)].

Impact of inclusive electron ion collider data on collinear parton distributions

A study is presented of the impact of updated simulated inclusive electron ion collider deep inelastic scattering data on the determination of the proton and nuclear parton distribution functions (PDFs) at next-to-next-to-leading and next-to-leading order in QCD, respectively. The influence on the proton PDFs is evaluated relative to the HERAPDF2.0 set, which uses inclusive HERA data only, and also relative to the global fitting approach of the MSHT20 PDFs. The impact on nuclear PDFs is assessed relative to the EPPS21 global fit and is presented in terms of nuclear modification ratios. For all cases studied, significant improvements in the PDF uncertainties are observed for several parton species. The most striking impact occurs for the nuclear PDFs in general and for the region of high Bjorken x in the proton PDFs, particularly for the valence quark distributions. Published by the American Physical Society 2024

Resonant Plasma Acceleration at Jupiter Driven by Satellite‐Magnetosphere Interactions

AbstractThe Juno spacecraft had previously observed intense high frequency wave emission, broadband electron and energetic proton energy distributions within magnetic flux tubes connected to Io, Europa, Ganymede, and their wakes. In this work, we report consistent enhancements in <46 keV energy proton fluxes during these satellite flux tube transit intervals. We find enhanced fluxes at discrete energies linearly separated in velocity for proton distributions within Io wake flux tubes, and both proton and electron distributions within Europa and Ganymede wake flux tubes. We propose these discrete enhancements to be a result of resonances between particles' bounce motion with standing Alfvén waves generated by the satellite‐magnetosphere interaction. We corroborate this hypothesis by comparing the bounce and field‐line resonance periods expected at the satellites' orbits. Hence, we find bounce‐resonant acceleration is a fundamental process that can accelerate particles in Jupiter's inner magnetosphere and other astrophysical plasmas.

Fine Structure of Magnetospheric Magnetosonic Waves: 1. Elementary Rising‐Tone Emissions Within Individual Harmonic

AbstractThe present study uncovers the fine structures of magnetosonic waves by investigating the EFW waveforms measured by Van Allen Probes. We show that each harmonic of the magnetosonic wave may consist of a series of elementary rising‐tone emissions, implying a nonlinear mechanism for the wave generation. By investigating an elementary rising‐tone magnetosonic wave that spans a wide frequency range, we show that the frequency sweep rate is likely proportional to the wave frequency. We studied compound rising‐tone magnetosonic waves, and found that they typically consist of multiple harmonics in the source region, and may gradually become continuous in frequency as they propagate away from source. Both elementary and compound rising‐tone magnetosonic waves last for ∼1 min which is close to the bounce period of the ring proton distribution, but their relation is not fully understood.

Study of Nuclear Structure and Elastic Electron Scattering Form Factors for Neutron Halo Nuclei (22N ,23O and 24F) Using Full Correlation Functions with Two Size Parameters

The study of neutron-rich nuclei's form factors, root-mean-square radius (rms), and nuclear density distributions is the focus of this work for the nuclei (22N,23 O and 24F). With the use of a strong short-range effect and a strong tensor force, the nucleons distribution function of the two oscillating harmonic particles in a two-frequency shell model operates with two different parameters: the first (bcore), for the inner (core) orbits, and the second (bvalence) for the outer (halo) orbits. This work demonstrated the existence of neutron halo nuclei for the nuclei (22N, 23O and 24F) in the (2s1/2) shell. The computed density distribution of neutron, proton and matter for these nuclei displayed the long tail performance. Using the Borne approximation of the plane wave, the elastic form factor of the electron scattering from the alien nucleus was calculated, this form factor is independent of the neutrons that make up the halo, but rather it results from a difference in the proton density distribution of the last proton in the nuclei. Fortran 95 power station program was used to the neutron, proton and matter density, elastic electron scattering form factor, and rms radii. The calculated outcomes for these exotic nuclei were in good agreement with the experimental data.

Light-yield response of liquid scintillators using 2–6 MeV tagged neutrons

Knowledge of the neutron light-yield response is crucial to the understanding of scintillator-based neutron detectors. In this work, neutrons from 2–6MeV have been used to study the scintillation light-yield response of the liquid scintillators NE 213A, EJ 305, EJ 331 and EJ 321P using event-by-event waveform digitization. Energy calibration was performed using a GEANT4 model to locate the edge positions of the Compton distributions produced by gamma-ray sources. The simulated light yield for neutrons from a PuBe source was compared to measured recoil proton distributions, where neutron energy was selected by time-of-flight. This resulted in an energy-dependent Birks parameterization to characterize the non-linear response to the lower energy neutrons. The NE 213A and EJ 305 results agree very well with existing data and are reproduced nicely by the simulation. New results for EJ 331 and EJ 321P, where the simulation also reproduces the data well, are presented.

Archimedean Spiral Distribution of Energetic Particles in Earth's Inner Radiation Belt

AbstractArchimedean spirals are common in various fields such as biology, engineering, astronomy, and space physics. Here we report the discovery of patterns resembling the general Archimedean spirals in particle distributions in the Earth radiation belt. Our analytic theory and numerical simulations demonstrate that electrons with initially asymmetric spatial distributions form such spirals in the inner magnetosphere, where particles at smaller radial distances move more slowly in angular velocity. These spirals result in time‐varying peaks and valleys in particle fluxes, referred to as “zebra stripes,” which are well consistent with Van Allen Probes measurements. Although the initial asymmetric distribution may be seeded by the electric field in the magnetosphere, the spiral formation does not require them. Furthermore, we show that, due to the same fundamental motion of charged particles in regions dominated by dipole fields, this spiral phenomenon may also appear in the proton distributions, as well as in planetary magnetospheres.

Skewness and kurtosis of solar wind proton distribution functions: The normal inverse-Gaussian model and its implications

Context. In the solar wind (SW), the particle distribution functions are generally not Gaussian. They present nonthermal features that are related to underlying acceleration and heating processes. These processes are critical in the overall dynamics of this expanding astrophysical fluid. Aims. The Proton Alpha Sensor (PAS) on board Solar Orbiter commonly observes skewed proton distributions, with a more populated high-energy side in the magnetic field direction than the Gaussian distribution. Our objectives are: (1) to identify a theoretical statistical function that adequately models the observed distributions and (2) to use its statistical interpretation to constrain the acceleration and heating processes. Methods. We analyzed the 3D velocity distribution functions (VDFs) measured by PAS and compared them to model statistical functions. Results. We show that the normal inverse Gaussian (NIG), a type of hyperbolic statistical distribution, provides excellent fits of skewed and leptokurtic proton distributions. NIG can model both the core distribution and the beam, if present. We propose an interpretation that is inspired by the mathematical formulation of the NIG. It assumes that the acceleration or heating mechanism can be modeled as a drifting diffusion process in velocity space, controlled (or subordinated) by the time of interaction of the particles with “accelerating structures”. The probability function of the interaction time is an inverse Gaussian (IG), obtained by considering a random drift across structures of a given size. The control of the diffusion by interaction times that follow an IG probability function formally defines the NIG distribution. Following this model, we show that skewness and kurtosis can be used to estimate the kinetic and thermal energy gains provided by the interaction with structures. For example, in the case studies presented here, the analyzed populations would have gained kinetic energy representing approximately two to four times their thermal energy, with an increase in velocity – due to acceleration – of from one-tenth to one-third of the observed flow velocity. We also show that the model constrains the initial temperature of the populations. Conclusions. Overall, the NIG model offers excellent fits of the observed proton distributions. Combining the skewness and the kurtosis, it also leads to constraints in the part of acceleration and heating due to the interactions with structures in the formation of the proton populations. We suggest that these effects add to the classical thermal evolution of the bulk velocity and temperature resulting from SW expansion.

Energetic particles in the central starburst, disc, and halo of NGC253

ABSTRACT Detailed modelling of the spectro-spatial distributions of energetic electrons and protons in galactic discs and haloes of starburst galaxies (SBGs) is needed in order to follow their interactions with the magnetized interstellar medium and radiation fields, determine their radiative yields, and for estimating their residual spectral densities in intergalactic environments. We have developed a semi-analytical approach for calculating the particle spectro-spatial distributions in the disc and halo based on a diffusion model for particle propagation from acceleration sites in the central SB and disc regions, including all their relevant interaction modes. Important overall normalization of our models is based on previous modelling of the Galactic disc (with the galprop code), scaled to the higher star-formations rate in NGC253, and on spatially resolved radio measurements of the central SB and disc. These provide the essential input for determining the particle distributions and their predicted radiative yields in the outer disc and inner halo for a range of values of the key parameters that affect diffusion rate and energy losses. Results of our work clearly indicate that quantitative description of non-thermal emission in SBGs has to be based on modelling of the particle distributions in the entire disc, not just the central SB region.

Exploration of the ground state properties of neutron-rich sodium isotopes using the deformed relativistic mean field theory in complex momentumrepresentations with BCS pairings* *Partly supported by the National Natural Science Foundation of China (11935001, 11575001), the Natural Science Foundation of Anhui Province (2008085MA26), Anhui project (Z010118169), the Heavy Ion Research Facility in Lanzhou (HIRFL) (HIR2021PY007), and the project of Key

This study explores the ground-state characteristics of neutron-rich sodium isotopes, encompassing two-neutron separation energies, root-mean-square radii, quadrupole moments of proton and neutron distributions, single-particle levels of bound and resonant states, and neutron density distributions and shapes. Simultaneously, special attention is paid to the distinctive physical phenomena associated with these isotopes. The deformed relativistic mean field theory in complex momentum representations with BCS pairings (DRMF-CMR-BCS) employed in our research provides resonant states with real physics, offering insights into deformed halo nuclei. Four effective interactions (NL3, NL3*, PK1, and NLSH) were considered to assess the influence of continuum and deformation effects on halo structures. Calculations for odd-even nuclei 35–43Na revealed the dependence on the chosen effective interaction and number of considered resonant states. Neutron occupation patterns near the Fermi surface, particularly in orbitals and , were determined to be crucial in halo formation. The study provided detailed insights into the density distributions, shape evolution, and structure of neutron-rich sodium isotopes, contributing valuably to the field of nuclear physics.

Exploring the mass radius of He4 and implications for nuclear structure

In this study, we determine the mass radius of He4, a very light nucleus, by examining the near-threshold ϕ-meson photoproduction data of the LEPS Collaboration. To assess the gravitational form factor of He4, we employ multiple models for the mass distribution, including Yukawa-type, exponential, Gaussian, and uniform functions. The mass radius of He4 is measured to be 1.70±0.14 fm, which is approximately equal to the charge radius of He4. Surprisingly, in contrast to the findings of the proton, no noticeable discrepancy between the charge radius and the mass radius is noted for the He4 nucleus. The proton and neutron distributions within He4 are likely to be identical, confirming its regular tetrahedral structure in a new way. We propose exploring the difference between charge and mass radii as a new approach to examine the nuclear structure. Published by the American Physical Society 2024

Coulomb and symmetry-energy effects on proton and neutron density-distributions in central heavy-ion collisions, across beam energies and system masses

In this contribution, we review our current and previous investigations of total, proton, and neutron particle number densities and the asymmetry of proton and neutron density distributions achievable in central heavy-ion collisions at beam energy below 800 MeV/nucleon. Furthermore, the effects of the Coulomb interaction and the dependence on a system size in three representative symmetric and asymmetric Ca, Sn and Pb systems are studied. The Boltzmann-Uhlenbeck-Uehling (pBUU) transport and Time-Dependent Hartree-Fock (TDHF) models, employing the SVbas, SkT3 and SVsym Skyrme interactions, are used in these simulations. We find that (i) the highest total densities predicted at Ebeam = 800 MeV/nucleon are on the order of ∼ 2.5ρ0 (ρ0 = 0.16 fm−3), (ii) the proton-neutron asymmetry for maximal densities, δ = (ρnmax−ρpmax)/(ρnmax+ρpmax) do not generally exceed the asymmetry in the initial state of the collision at all beam energies and tend to decrease during the reaction, and (iii) a significant portion of this asymmetry has its microscopic origin in Coulomb forces, masking the pure nuclear contribution. In addition, the evolution of normalized maximal proton, neutron, and total nucleon number density with increasing beam energy, the impact of correlations in the reaction, and the time evolution of the proton and neutron density distributions in the plane transverse to the beam direction are illustrated and discussed.

Inelastic scattering reaction as a probe for monopole, dipole and quadrupole excitations

The study of collective motions within atomic nuclei, such as monopole, dipole, and quadrupole excitations, is crucial for understanding nuclear structure and properties, which provide insights into the spatial distribution and dynamic nature of protons and neutrons in nuclei. By analyzing the angular distributions of these modes excited via inelastic scattering reactions, we can determine the transition characteristics and deformation lengths of nuclei. Specific case studies, including quadrupole excitations and dipole excitations indicating exotic cluster structures in light nuclei, highlight the utility of modern experimental setups like the solenoidal spectrometer and the active target detector.