Smooth Energy Dependence Research Articles

Inclusive rates from smeared spectral densities in the two-dimensional O(3) non-linear σ-model

This work employs the spectral reconstruction approach of ref. [1] to determine an inclusive rate in the 1 + 1 dimensional O(3) non-linear σ-model, analogous to the QCD part of e+e− → hadrons. The Euclidean two-point correlation function of the conserved current j is computed using Monte Carlo lattice field theory simulations for a variety of spacetime volumes and lattice spacings. The spectral density of this correlator is related to the inclusive rate for j → X in which all final states produced by the external current are summed. The ill-posed inverse problem of determining the spectral density from the correlation function is made tractable through the determination of smeared spectral densities in which the desired density is convolved with a set of known smearing kernels of finite width ϵ. The smooth energy dependence of the underlying spectral density enables a controlled ϵ → 0 extrapolation in the inelastic region, yielding the real-time inclusive rate without reference to individual finite-volume energies or matrix elements. Systematic uncertainties due to cutoff effects and residual finite-volume effects are estimated and taken into account in the final error budget. After taking the continuum limit, the results are consistent with the known analytic rate to within the combined statistical and systematic errors. Above energies where 20-particle states contribute, the overall precision is sufficient to discern the four-particle contribution to the spectral density.

Can a protophobic vector boson explain the ATOMKI anomaly?

In 2016, the ATOMKI collaboration announced [Phys. Rev. Lett. 116, 042501 (2016)] observing an unexpected enhancement of the e+-e−pair production signal in one of the Be8 nuclear transitions induced by an incident proton beam on a 7Li target. Many beyond-standard-model physics explanations have subsequently been proposed. One popular theory is that the anomaly is caused by the creation of a protophobic vector boson (X) with a mass around 17 MeV [e.g. Phys. Rev. Lett. 117, 071803 (2016)] in the nuclear transition. We study this hypothesis by deriving an isospin relation between photon and X couplings to nucleons. This allows us to find simple relations between protophobic X-production cross sections and those for measured photon production. The net result is that X production is dominated by direct transitions induced by E1X and L1X (transverse and longitudinal electric dipoles) and C1X (charge dipole) without going through any nuclear resonance (i.e. Bremsstrahlung radiation) with a smooth energy dependence that occurs for all proton beam energies above threshold. This contradicts the experimental observations and invalidates the protophobic vector boson explanation.

Measurement of neutron spectra in a silicon filtered neutron beam using stilbene detectors at the LVR-15 research reactor

A well-defined neutron spectrum is an essential tool for calibration and tests of spectrometry and dosimetry detectors, and evaluation methods for spectra processing. Many of the nowadays used neutron standards are calibrated against a fission spectrum which has a rather smooth energy dependence. In recent time, at the LVR-15 research reactor in Rez, an alternative approach was tested for the needs of fast neutron spectrometry detector calibration. This process comprises detector tests in a neutron beam, filtered by one meter of single-crystalline silicon, which contains several significant peaks in the fast neutron energy range. Tests in such neutron field can possibly reveal specific problems in the deconvolution matrix of the detection system, which may stay hidden in fields with a smooth structure and can provide a tool for a proper energy calibration. Test with several stilbene scintillator crystals in two different beam configurations supplemented by Monte-Carlo transport calculations have been carried out. The results have shown a high level of agreement between the experimental data and simulation, proving thus the accuracy of used deconvolution matrix. The chosen approach can, thus, provide a well-defined neutron reference field with a peaked structure for further tests of spectra evaluation methods and scintillation detector energy calibration.

A Lane consistent optical model potential for nucleon scattering on actinide nuclei with extended coupling

An extension for odd-A actinides of a previously derived dispersive coupledchannel optical model potential (OMP) for 238 U and 232 Th nuclei is presented. It is used to fit simultaneously all the available experimental databases including neutron strength functions for nucleon scattering on 232 Th, 233,235,238 U and 239 Pu nuclei. Quasi-elastic (p,n) scattering data on 232 Th and 238 U to the isobaric analogue states of the target nucleus are also used to constrain the isovector part of the optical potential. For even-even (odd) actinides almost all low-lying collective levels below 1 MeV (0.5 MeV) of excitation energy are coupled. OMP parameters show a smooth energy dependence and energy independent geometry.

Pp interactions in extended air showers

Applying the recently constructed analytic representation for the pp scattering amplitudes, we present a study of p-air cross sections, with comparison to the data from Extensive Air Shower (EAS) measurements. The amplitudes describe with precision all available accelerator data at ISR, SPS and LHC energies, and its theoretical basis, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permit reliable extrapolation to higher energies and to asymptotic ranges. The comparison with cosmic ray data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behaviour of cross sections is investigated in view of the geometric scaling property of the amplitudes. The amplitudes predict that the proton does not behave as a black disk even at asymptotically high enegies, and we discuss possible non-trivial consequences of this fact for pA collision cross sections at higher energies.

Pp interaction at very high energies in cosmic ray experiments

An analysis of p-air cross section data from extensive air shower measurements is presented, based on an analytical representation of the pp scattering amplitudes that describes with high precision all available accelerator data at ISR, SPS and LHC energies. The theoretical basis of the representation, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permits reliable extrapolation to high energy cosmic ray (CR) and asymptotic energy ranges. Calculations of based on Glauber formalism are made using the input values of the quantities , , BI and BR at high energies, with attention given to the independence of the slope parameters, with . The influence of contributions of diffractive intermediate states, according to Good–Walker formalism, is examined. The comparison with CR data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behaviour of cross sections is investigated in view of the geometric scaling property of the amplitudes. The observed energy dependence of the ratio between p-air and pp cross sections in the data is shown to be related to the nature of the pp cross section at high energies, that does not agree with the black disk image.

Strange and multistrange particle production in Au + Au collisions atsNN=62.4 GeV

We present results on strange and multi-strange particle production in Au+Au collisions at $\sqrt{s_{NN}}=62.4$ GeV as measured with the STAR detector at RHIC. Mid-rapidity transverse momentum spectra and integrated yields of $K^{0}_{S}$, $\Lambda$, $\Xi$, $\Omega$ and their anti-particles are presented for different centrality classes. The particle yields and ratios follow a smooth energy dependence. Chemical freeze-out parameters, temperature, baryon chemical potential and strangeness saturation factor obtained from the particle yields are presented. Intermediate transverse momentum ($p_T$) phenomena are discussed based on the ratio of the measured baryon-to-meson spectra and nuclear modification factor. The centrality dependence of various measurements presented show a similar behavior as seen in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.

Instantaneous shape sampling: A model for theγ-absorption cross section of transitional nuclei

The influence of the quadrupole shape fluctuations on the dipole vibrations in transitional nuclei is investigated in the framework of the instantaneous shape sampling model, which combines the interacting boson model for the slow collective quadrupole motion with the random phase approximation for the rapid dipole vibrations. Coupling to the complex background configurations is taken into account by folding the results with a Lorentzian with an energy-dependent width. The low-energy portion of the $\ensuremath{\gamma}$-absorption cross section, which is important for photonuclear processes, is studied for the isotopic series of Kr, Xe, Ba, and Sm. The experimental cross sections are well reproduced. The low-energy cross section is determined by the Landau fragmentation of the dipole strength and its redistribution caused by the shape fluctuations. Collisional damping only wipes out fluctuations of the absorption cross section, generating the smooth energy dependence observed in experiment. In the case of semimagic nuclei, shallow pygmy resonances are found, in agreement with experiment.

Is a global coupled-channel dispersive optical model potential for actinides feasible?

An isospin-dependent coupled-channel optical model potential containing a dispersive term with a nonlocal contribution is used to simultaneously fit the available experimental database (including strength functions and scattering radius) for neutron and proton scattering on strongly deformed $^{238}\mathrm{U}$ and $^{232}\mathrm{Th}$ nuclei. The energy range 0.001--200 MeV is covered. A dispersive coupled-channel optical model (DCCOM) potential with parameters that show a smooth energy dependence and energy-independent geometry are determined from fits to the entire data set. Calculations using the obtained DCCOM potential reproduce measured total cross-section differences between $^{232}\mathrm{Th}$ and $^{238}\mathrm{U}$ within experimental uncertainty. The isovector terms and the observed very weak dependence of the geometrical parameters on mass number A allow us to extend the derived potential parameters to neighboring actinide nuclei with great confidence.

Dispersive coupled-channel analysis of nucleon scattering fromTh232up to 200 MeV

An isospin-dependent coupled-channels optical model potential containing a dispersive term (including nonlocal contribution) is used to simultaneously fit the available experimental database (including strength functions and scattering radius) for neutron and proton scattering on strongly deformed $^{232}\mathrm{Th}$ nucleus. The energy range 0.001--200 MeV is covered. A dispersive coupled-channel optical model potential with parameters that show a smooth energy dependence and energy independent geometry are determined from fits to the entire data set. Dispersive contribution is shown to be the dominant Coulomb correction to the proton real potential below the Coulomb barrier. Inclusion of nonlocality effects in the absorptive volume potential and its corresponding dispersive contribution to the real potential is needed to achieve an excellent agreement above 100 MeV.

Analysis of deuteron elastic scattering on 6,7Li up to 50 MeV

An analysis of the elastic scattering of deuterons on 6,7Li, for energies up to 50 MeV, has been carried out by using a phenomenological optical potential. Energy-dependent average parameters of the optical model potential have been obtained in the analysis of the corresponding real and imaginary volume integrals, pointing out an “anomalous” behavior of the real potential when the imaginary part approaches zero. This could be a consequence of the dispersion relations, but may be also related to the non-locality of the basic real potential term which introduces a slow and smooth energy dependence. On the other hand, the coupled reaction channels method has been used in order to describe the Li 6 ( d , d 0 ) Li 6 experimental angular distributions including the backward hemisphere at 14.7 and 19.6 MeV but not at 50 MeV. The comparison between the experimental and calculated elastic scattering angular distributions proves the reliability of the present average optical potentials, at variance with the extrapolation of the deuteron global potentials to other mass and energy domains.

E1−E2interference in the vuv photoionization of He

We have measured the forward-backward asymmetry of photoelectron angular distributions produced in the vacuum ultraviolet photoionization of helium. This asymmetry, a consequence of the breakdown of the dipole approximation, measures the real part of the ratio of the quadrupole and dipole matrix elements. In the autoionization region, the strong energy dependence of the asymmetry permits an experimental separation of the ratio of those magnitudes from their phase difference. We experimentally determined the Fano parameters of the ${2p}^{2}{}^{1}{D}_{2}$ quadrupole resonance, and report improved values of the width $\ensuremath{\Gamma}$ and line profile parameter q from those previously available from electron scattering. Off resonance, the smooth energy dependence of the asymmetry is found to agree well with the theoretical treatment presented here which incorporates higher-multipole effects.

Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?

We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the problem of scattering on a finite-range potential, which is based on the separation of the configuration space into two segments, internal and external. The scattering amplitude is expressed in terms of the resolvent of a non-Hermitian operator H. The explicit form of this operator depends on both the radius of separation and the boundary conditions at this place, which can be chosen in many different ways. We discuss this freedom and show explicitly that the physical scattering amplitude is, nevertheless, unique, although not all choices are equally adequate from the physical point of view. The energy-dependent operator H should not be confused with the non-Hermitian effective Hamiltonian H(eff) which is usually exploited to describe interference of overlapping resonances. We note that the simple Breit-Wigner approximation is as a rule valid for any individual resonance in the case of few-channel scattering on a flat billiardlike cavity, leaving no room for nontrivial H(eff) to appear. The physics is appreciably richer in the case of an open chain of L connected similar cavities whose spectrum has a band structure. For a fixed band of L overlapping resonances, the smooth energy dependence of H can be ignored so that the constant LxL submatrix H(eff) approximately describes the time evolution of the chain in the energy domain of the band and the complex eigenvalues of H(eff) define the energies and widths of the resonances. We apply the developed formalism to the problem of a chain of L delta barriers, whose solution is also found independently in a closed form. We construct H(eff) for the two commonly considered types of boundary conditions (Neumann and Dirichlet) for the internal motion. Although the final results are in perfect coincidence, somewhat different physical patterns arise of the trend of the system with growing openness. Formation in the outer well of a short-lived doorway state shifted in energy is explicitly demonstrated together with the appearance of L-1 long-lived states trapped in the inner part of the chain.

Transport properties of the three-dimensional Penrose lattice

Transport properties of the three-dimensional (3-D) quasiperiodic systems have been studied for the 3-D Penrose lattice at zero temperature. The linear scaling with respect to the sample width (cross-section) is observed. With increasing sample width, the conductance fluctuation as a function of the Fermi energy is suppressed and a smooth energy dependence is obtained for larger samples. This suggests that the transport properties of the 3-D quasiperiodic systems are less anomalous than those of the low-dimensional quasiperiodic systems. The sample-length dependence of the conductance is, on the other hand, not that expected for extended Bloch waves and the conductance decreases with increasing sample length.

Dispersive spherical optical model of neutron scattering from27Alup to 250 MeV

A spherical optical model potential (OMP) containing a dispersive term is used to fit the available experimental database of angular distribution and total cross section data for n + Al27 covering the energy range 0.1- 250 MeV using relativistic kinematics and a relativistic extension of the Schroedinger equation. A dispersive OMP with parameters that show a smooth energy dependence and energy independent geometry are determined from fits to the entire data set. A very good overall agreement between experimental data and predictions is achieved up to 150 MeV. Inclusion of nonlocality effects in the absorptive volume potential allows to achieve an excellent agreement up to 250 MeV.

Measurements of the spin rotation parameter A in the elastic pion-proton scattering in the D13(1700) resonance region

The spin rotation parameters A and R were measured for the elastic pion-proton scattering by the PNPI-ITEP collaboration in the D13(1700) resonance region. The main goal of the experimental program is to resolve the current partial-wave analyses (PWA) uncertainties. Simultaneously with A and R the polarization parameter P was measured with the purpose to improve the experimental database and estimate systematic errors. The constraint which demands a smooth energy dependence of all π-p transverse amplitude zeros in the complex plane together with the new experimental data on A parameter can lead to the conclusion that the Barrelet branch of “zero trajectories" is chosen improperly in PWA of the Carnegie-Mellon-Lawrence-Berkely-Laboratory groups at the range of the pion beam momentum near 1.0 GeV/c. The setup included a longitudinally polarized proton target with superconductive magnet, multiwire spark chambers and carbon polarimeter with thick filter. The experiment was performed at the ITEP proton synchrotron, Moscow.

Poincaré section decomposition for quantum scatterers

We consider here scatterers that may be modeled as a cavity with an entrance lead. The decomposition is achieved by sectioning the cavity and adding new leads, thus generating two new scatterers. So a resonant scatterer, whose S -matrix has sharp energy peaks, can be resolved into a pair of scatterers with smooth energy dependence. The resonant behaviour is concentrated in a spectral determinant obtained from a dissipative section map. The semiclassical limit of this theory coincides with the orbit resummation previously proposed by Georgeot and Prange. A numerical example for a semiseparable scatterer is investigated, revealing the accurate portrayal of the Wigner time delay by the spectral determinant.

Shadowing corrections and diffractive production in DIS on nuclei

We calculate, in the Glauber–Mueller approach, the ratio of the diffractive dissociation cross section to the total cross section for nuclei. We observe that shadowing corrections (SC) in the calculated σ diff/ σ tot ratio are significant, but they do not lead to a smooth energy dependence of the ratio for a proton target as was observed at HERA.

Decomposition of Resonant Scatterers by Surfaces of Section

Scattering on the energy shell is viewed here as the relation between the bound states of the Hamiltonian, restricted to sections on leads that are asymptotically independent, far away from the interaction region. The decomposition is achieved by sectioning this region and adding new leads, thus generating two new scatterers, so a resonant scatterer, whose S matrix has sharp energy peaks, can be resolved into a pair of scatterers with smooth energy dependence. The resonant behaviour is concentrated in a spectral determinant obtained from a dissipative section map. The semiclassical limit of this theory coincides with the orbit resummation previously proposed by Georgeot and Pranges (Phys. Rev. Lett.74, 4110 (1995)). A numerical example for a semiseparable scatterer is investigated, revealing the accurate portrayal of the Wigner time delay by the spectral determinant.

Unitarity constraints in modified effective-range theory

The effect of a long-range polarization force on the low-energy scattering of an electron by a neutral atom may be accounted for by adopting a form of distorted-wave theory in which the phase shift is represented as the sum of a polarization phase and a relative phase. From this latter phase an effective-range function is formed having a smooth energy dependence in the neighborhood of threshold. Multichannel extensions of this approach have been described. For highly polarizable targets, and for scattering energies sufficiently removed from threshold, the polarization phase takes on complex values. The relative phase, and hence the effective-range parameters, must then be complex as well since unitarity requires that the physical phase shift be real. For scattering by short-range potentials unitarity is preserved by formulating approximation procedures in terms of a Hermitian reaction matrix. This standard approach is generalized here in the context of effective-range theory involving strong polarization forces. The hermiticity condition on the reaction matrix is replaced by a more general requirement relating its Hermitian and anti-Hermitian components. Methods for imposing unitarity constraints in approximation procedures are described and illustrated, for resonant and nonresonant systems, in numerical examples.