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Abstract Coulomb fields of charged particle beams in circular machines determine, together with wake fields, modes of the collective beam oscillations, for both transverse and longitudinal degrees of freedom. Recent progress in these two areas of beam dynamics is discussed.
The Mu2e experiment at Fermilab will search for evidence of charged lepton flavor violation by observing the conversion of a negative muon into an electron in the Coulomb field of a nucleus without emission of neutrinos and will probe effective new-physics mass scales in the 103-104 TeV range. One of the main parts of the Mu2e experimental setup is its target station in which negative pions are generated in interactions of the 8 GeV primary proton beam with a tungsten target, which will be capable of producing $2\times10^{17}$ negative muons per year. Mu2e can be extended by a next generation experiment, Mu2e-II, with a sensitivity improved by another factor of 10 or more as enabled by the PIP-II accelerator upgrade project. PIP-II is a 250-meter-long linac capable of accelerating a 2 mA proton beam to a kinetic energy of 800 MeV corresponding to 1.6 MW of power. To achieve another factor of ten improvement in sensitivity, Mu2e-II will require about 100 kW of proton beam on target, and the added power requires a new target design. We will present our progress in RD of a target station conceptual design for Mu2e-II, using the MARS15 and G4beamline Monte-Carlo codes toward a selection between granular, conveyor, and rotating cylindrical target options.
The Mu2e experiment at Fermilab will search for the charged-lepton flavour violating conversion of negative muons into electrons in the coulomb field of an Al nucleus, planning to reach a single event sensitivity of about $3\cdot10^{−17}$, four orders of magnitude beyond the current best limit.The conversion electron has a clear monoenergetic signature at 104.967 MeV, slightly below the muon rest mass, and will be identified by a complementary measurement carried out by a high-resolution tracker and an electromagnetic calorimeter (EMC). The calorimeter is composed of 1348 pure CsI crystals, each read by two custom UV-extended SiPMs, that are arranged in two annular disks. The EMC should achieve better than 10% energy resolution and 500 ps timing resolution for 100 MeV electrons and maintain extremely high levels of reliability and stability and in a harsh operating environment with high vacuum, 1 T B-field and radiation exposures up to 100 krad and $10^{12} \rm{n}_\rm{1MeVeq}/\rm{cm}^{2}$.The calorimeter technological choice, along with the design of the custom front-end electronics, cooling and mechanical systems were validated through an electron beam test on a large-scale 51-crystals prototype (Module-0) and extensive test campaigns that characterised and verified the performance of crystals, photodetectors, analogue and digital electronics. This included hardware stress tests and irradiation campaigns with neutrons, protons, and photons.The production and QC phases of all calorimeter components is completed apart for the digital electronics that has been revised for improving its resilience to SEU and SEL. A series of vertical slice tests with the final electronics is being carried out on the Module-0 at LNF along with the implementation and validation of the calibration procedures. The first disk has been assembled in 2022 while the second disk is under assembly at the moment of writing. Status of construction will be summarised, along with plans for commissioning and first calibration of the fully assembled disks.
In most calculations on inelastic collision of electrons with atoms there has been a general lack of agreement with observation mainly due to the treatment of the interelectronic interaction as a perturbation. In a recent calculation by Vainshtein et al., full account is given to this interaction by treating the problem as a binary collision between the incident and atomic electrons with the motion of their center of mass in the Coulomb field of the nucleus, and marked improvement in comparison of theory and observation has resulted. Three approximations are applied in this calculation which will be described briefly.
The stopping power of a plasma for a relativistic heavy ion is calculated in a simplified derivation. The total contribution results from (1) individual electron scattering in the Coulomb field of the ion wherein large momentum transfers are involved and (2) small momentum transfers in which quantized plasma oscillations are excited. The resulting general formula for the stopping power is in agreement with a specialization of the results of a more elaborate treatment by Tsytovich. The nonrelativistic limit of the general formula agrees with an expression given earlier by Larkin from field-theory techniques and by the author in a Born-approximation approach. However, the general formula differs slightly in its details from that given by Hayakawa and Kitao.
Observations of cosmic and gamma radiation by SAS-2 satellite are summarized and analyzed to determine processes responsible for producing observed galactic radiation. In addition to the production of gamma rays in discrete galactic objects such as pulsars, there are three main mechanisms by which high-energy (greater than 100 MeV) radiation is produced by high-energy interactions involving cosmic rays in interstellar space. These processes, which produce what may be called diffuse galactic gamma-rays, are: (1) the decay of pi mesons produced by interactions of cosmic ray nucleons with interstellar gas nuclei; (2) the bremsstrahlung radiation produced by cosmic ray electrons interacting in the Coulomb fields of nuclei of interstellar gas atoms; and (3) Compton interactions between cosmic ray electrons and low-energy photons in interstellar space.
Plasmon and exciton superconductivity mechanisms are discussed. Superconductivity in a three layer metal semiconductor metal and insulator semimetal insulator sandwich structure was described in terms of the temperature dependent Green function of the longitudinal (Coulomb) field. The dependences of the superconducting transition temperature on structure parameters were obtained. In a semiconducting film, as a result of interactions of degenerate free carriers with excitons, superconductivity exists only in a certain range of parameter values, and the corresponding critical temperature is much lower than in the plasmon mechanism of superconductivity.
Deuteron-carbon elastic scattering is studied within the framework of the Glauber approximation. The full Glauber multiple scattering series is evaluated with simplified nuclear wave functions. An approximation in which deuteron-nucleus scattering is expressed in terms of nucleon-nucleus scattering amplitudes is shown to be accurate for small momentum transfers. The effects of the Coulomb field and the deuteron D state are investigated. The impressive fit to the 650 MeV d-(C-12) elastic scattering data, obtained in a recent calculation, is shown to be due to additional approximations made in that analysis.
Methods for calculating cross sections for the breakup of galactic heavy ions by the Coulomb fields of the interacting nuclei are presented. By using the Weizsacker-Williams method of virtual quanta, estimates of electromagnetic dissociation cross sections for a variety of reactions applicable to galactic cosmic ray shielding studies are presented and compared with other predictions and with available experimental data.
The Coulomb dissociation contributions to fragmentation cross sections in relativistic heavy ion collisions, where more than one nucleon is removed, are estimated using the Weizsacker-Williams method of virtual quanta. Photonuclear cross sections taken from experimental results were used to fold into target photon number spectra calculated with the Weizsacker-Williams method. Calculations for several projectile target combinations over a wide range of charge numbers, and a wide range of incident projectile energies, are reported. These results suggest that multiple nucleon knockout by the Coulomb field may be of negligible importance in galactic heavy ion studies for projectiles lighter than Fe-56.
The performance of Ti:Al2O3 lasers is impaired generally by an infrared absorption that occurs in the laser output wavelength region. On the basis of data for as-grown and annealed samples cut from Ti:Al2O3 crystals grown by the vertical-gradient-freeze (VGF) technique, we previously proposed that the residual absorption is due to Ti(3+) to Ti(4+) pairs. In this report, we present additional data that confirm this ion-pair model for the residual absorption, which can be attributed to excitation of the 3d electron of the Ti(3+) ion perturbed by the Coulomb field of the neighboring Ti(4+) ion and/or an associated Al vacancy.
The need to include dynamical collision momentum transfer contributions, arising from interacting nuclear and Coulomb fields, to estimates of fragment momentum distributions is discussed. Methods based upon an optical potential model are presented. Comparisons with recent experimental data of the Siegen group for variances of transverse momentum distributions for gold nuclei at 980 A MeV fragmenting on silver foil and plastic nuclear track detector targets are made. The agreement between theory and experiment is good.
High Charge and Energy Semiempirical Nuclear Fragmentation Model (HZEFRG1) computer program developed to be computationally efficient, user-friendly, physics-based program for generating data bases on fragmentation of atomic nuclei. Data bases generated used in calculations pertaining to such radiation-transport applications as shielding against radiation in outer space, radiation dosimetry in outer space, cancer therapy in laboratories with beams of heavy ions, and simulation studies for designing detectors for experiments in nuclear physics. Provides cross sections for production of individual elements and isotopes in breakups of high-energy heavy ions by combined nuclear and Coulomb fields of interacting nuclei. Written in ANSI FORTRAN 77.
The threshold law for photoejection of two electrons from atoms (PDI) is derived from a modification of the Coulomb-dipole (C-D) theory. The C-D theory applies to two-electron ejection from negative ions (photo-double detachment:PDD). The modification consists of correctly accounting for the fact that in PDI that the two escaping electrons see a Coulomb field, asymptotically no matter what their relative distances from the residual ion are. We find in the contralinear spherically symmetric model that the analytic threshold law Q(E),i. e. the yield of residual ions, to be Qf(E)approaches E + CwE(sup gamma(w)) + CE(sup 5/4)sin[1/2 ln(E + theta)]/ln(E). The first and third terms are beyond the Wannier law. Our threshold law can only be rigorously justified for residual energies less than or equal to 10(exp -3) eV. Nevertheless in the present experimental range (0.1 - 4 eV), the form, even without the second term, can be fitted to experimental results of PDI for He, Li, and Be, in contrast to the Wannier law which has a larger deviation from the data for Li and Be, for both of which the data show signs of modulation.
The threshold law for photoejection of two electrons from atoms (PDI) is derived from a modification of the Coulomb-dipole (C-D) theory. The C-D theory applies to two-electron ejection from negative ions (photo-double detachment:PDD). The modification consists of correctly accounting for the fact that in PDI that the two escaping electrons see a Coulomb field, asymptotically no matter what their relative distances from the residual ion are. We find in the contralinear spherically symmetric model that the analytic threshold law Q(E), i.e. the yield of residual ions, to be Q Integral of (E) varies as E + (C(sub w) E(sup gamma W)) +CE(sup 5/4) sin [1/2 ln E + phi]/ln(E). The first and third terms are beyond the Wannier law. Our threshold law can only be rigorously justified for residual energies <= 10(exp -3) eV. Nevertheless in the present experimental range (0.1 - 4 eV), the form, even without the second term, can be fitted to experimental results of PDI for He, Li, and Be, in contrast to the Wannier law which has a larger deviation from the data for Li and Be.
Quantum electrodynamics in very strong Coulomb fields is one scope which has not yet been tested experimentally with sufficient accuracy to really determine whether the perturbative approach is valid. One sensitive test is the determination of the 1s Lamb shift in highly-charged very heavy ions. The 1s Lamb shift of hydrogen-like lead (Pb81+) and gold (Au78+) has been determined using the novel detector concept of silicon microcalorimeters for the detection of hard x-rays. The results of (260 +/- 53) eV for lead and (211 +/- 42) eV for gold are within the error bars in good agreement with theoretical predictions. To our knowledge, for hydrogen-like lead, this represents the most accurate determination of the 1s Lamb shift.
Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges–local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. Furthermore, the simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent–solvent and solute–solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.
We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice.