Energy-dependent Function Research Articles

Quantitative validation of Monte Carlo SPECT simulation: application to a Mediso AnyScan GATE simulation

BackgroundMonte Carlo (MC) simulations are used in nuclear medicine imaging as they provide unparalleled insight into processes that are not directly experimentally measurable, such as scatter and attenuation in an acquisition. Whilst MC is often used to provide a ‘ground-truth’, this is only the case if the simulation is fully validated against experimental data. This work presents a quantitative validation for a MC simulation of a single-photon emission computed tomography (SPECT) system.MethodsAn MC simulation model of the Mediso AnyScan SCP SPECT system installed at the UK National Physical Laboratory was developed in the GATE (Geant4 Application for Tomographic Emission) toolkit. Components of the detector head and two collimator configurations were modelled according to technical specifications and physical measurements. Experimental detection efficiency measurements were collected for a range of energies, permitting an energy-dependent intrinsic camera efficiency correction function to be determined and applied to the simulation on an event-by-event basis. Experimental data were collected in a range of geometries with ^{99text {m}}Tc for comparison to simulation. The procedure was then repeated with ^{177}Lu to determine how the validation extended to another isotope and set of collimators.ResultsThe simulation’s spatial resolution, sensitivity, energy spectra and the projection images were compared with experimental measurements. The simulation and experimental uncertainties were determined and propagated to all calculations, permitting the quantitative agreement between simulated and experimental SPECT acquisitions to be determined. Statistical agreement was seen in sinograms and projection images of both ^{99text {m}}Tc and ^{177}Lu data. Average simulated and experimental sensitivity ratios of (0.991 pm 0.011) were seen for emission and scatter windows of ^{99text {m}}Tc, and (0.897 pm 0.014) and (0.839 pm 0.014) for the 113 and 208 keV emissions of ^{177}Lu, respectively.ConclusionsMC simulations will always be an approximation of a physical system and the level of agreement should be assessed. A validation method is presented to quantify the level of agreement between a simulation model and a physical SPECT system.

Double folding analysis of the α+28Si elastic scattering system

Using the double folding model (DFM), we reanalyzed 20 sets of experimental angular distributions for the elastic scattering [Formula: see text]+[Formula: see text]Si system in a wide energy range of [Formula: see text]-particles from 12.7[Formula: see text]MeV to 240[Formula: see text]MeV. We used three effective nucleon–nucleon (NN) interactions that are CDM3Y6, São Paulo Potential (SPP2), and Brazilian Nuclear Potential (BNP) to generate the DF potentials. The data analysis was performed using semi-microscopic (SM) and fully microscopic (FM) methods. In the SM approach, the real part of the optical potential (OP) is created with the DFM, and the Woods–Saxon (WS) potential is considered for the imaginary part of the OP. In the FM approach, the DF potential renormalization factors [Formula: see text] and [Formula: see text] for the real and imaginary parts of the OP were extracted. We investigated the energy dependencies of the [Formula: see text] and [Formula: see text] factors, as well as of nuclear potential volume integrals and reaction cross-sections. We reasonably reproduced the data using [Formula: see text] and [Formula: see text] factors obtained from their energy-dependent functions.

Exact Green's functions for localized irreversible potentials

We study the quantum-mechanical problem of scattering caused by a localized obstacle that breaks spatial and temporal reversibility. Accordingly, we follow Maxwell's prescription to achieve a violation of the second law of thermodynamics by means of a momentum-dependent interaction in the Hamiltonian, resulting in what is known as Maxwell's demon. We obtain the energy-dependent Green's function analytically, as well as its meromorphic structure. The poles lead directly to the solution of the evolution problem, in the spirit of M. Moshinsky's work published in the 1950s. Symmetric initial conditions are evolved in this way, showing important differences between classical and wave-like irreversibility in terms of collapses and revivals of wave packets. Our setting can be generalized to other wave operators, e.g. electromagnetic cavities in a classical regime.

A new 103Rh Unresolved Resonance Region evaluation

A new evaluation in the Unresolved Resonance Region has been performed for 103Rh, an important fission product. The evaluation was done in coordination with and is consistent with a new Resolved Resonance Region evaluation. It was determined using measured total cross section data that there is significant structure in the underlying dilute-average cross section within the unresolved resonance energy range of the evaluation (8–40.146 keV). Energy-dependent strength functions are provided to more accurately represent this structure. A covariance matrix for the average parameters that represent the entire Unresolved Resonance Region is provided to comply with the current ENDF-6 format. This new evaluation more closely matches the experimental data available when compared to the current evaluations.

Study of e+e−→Ω−Ω¯+ at center-of-mass energies from 3.49 to 3.67 GeV

Using data samples of e+e− collisions collected with the BESIII detector at eight center-of-mass energy points between 3.49 and 3.67 GeV, corresponding to an integrated luminosity of 670 pb−1, we present the upper limits of Born cross sections and the effective form factor for the process e+e−→Ω−Ω¯+. A fit to the cross sections using a perturbative QCD-derived energy-dependent function shows no significant threshold effect. The upper limit on the measured effective form factor is consistent with a theoretical prediction within the uncertainty of 1σ. These results provide new experimental information on the production mechanism of Ω.Received 7 December 2022Accepted 5 January 2023DOI:https://doi.org/10.1103/PhysRevD.107.052003Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasForm factorsParticle interactionsParticles & Fields

Solution of the coupled β functions of the Standard Model and its minimal supersymmetric extension

The Standard Model contains three coupling constants α1, α2 and α3 associated to the intern symmetry groups. However, even such constants are named like that, in fact they are not, they are energy dependent functions. The functional form of the evolution satisfies a set of coupled differential equations the coupled β functions. In general these β functions are highly coupled, from this arises the necessity of using numerical methods for the solution of the problem, because it is not possible to obtain it analytically. In this work it is used the adaptive Runge-Kutta method for a set of ordinary differential equations. The physical motivation of this work arise from the fact that the coupling constants α1, α2 and α3 are associated to the electromagnetic interaction, the weak interaction and the strong interaction, respectively. In the Standard Model, the solutions for α1 and α2 intersect in a point, which can be interpreted as a unification of two fundamental interactions exists. Nevertheless, using the minimal supersymmetric extension of the Standard Model, the three coupling constants intersect in a region, reaching what is known as the Grand Unification.

Feasibility of irrigation monitoring with cosmic-ray neutron sensors

Abstract. Accurate soil moisture (SM) monitoring is key in irrigation as it can greatly improve water use efficiency. Recently, cosmic-ray neutron sensors (CRNSs) have been recognized as a promising tool in SM monitoring due to their large footprint of several hectares. CRNSs also have great potential for irrigation applications, but few studies have investigated whether irrigation monitoring with CRNSs is feasible, especially for irrigated fields with a size smaller than the CRNS footprint. Therefore, the aim of this study is to use Monte Carlo simulations to investigate the feasibility of monitoring irrigation with CRNSs. This was achieved by simulating irrigation scenarios with different field dimensions (from 0.5 to 8 ha) and SM variations between 0.05 and 0.50 cm3 cm−3. Moreover, the energy-dependent response functions of eight moderators with different high-density polyethylene (HDPE) thickness or additional gadolinium thermal shielding were investigated. It was found that a considerable part of the neutrons that contribute to the CRNS footprint can originate outside an irrigated field, which is a challenge for irrigation monitoring with CRNSs. The use of thin HDPE moderators (e.g. 5 mm) generally resulted in a smaller footprint and thus stronger contributions from the irrigated area. However, a thicker 25 mm HDPE moderator with gadolinium shielding improved SM monitoring in irrigated fields due to a higher sensitivity of neutron counts with changing SM. This moderator and shielding set-up provided the highest chance of detecting irrigation events, especially when the initial SM was relatively low. However, variations in SM outside a 0.5 or 1 ha irrigated field (e.g. due to irrigation of neighbouring fields) can affect the count rate more than SM variations due to irrigation. This suggests the importance of retrieving SM data from the surrounding of a target field to obtain more meaningful information for supporting irrigation management, especially for small irrigated fields.

Investigation of polycapillary half lenses for quantitative confocal micro-X-ray fluorescence analysis.

The use of polycapillary optics in confocal micro-X-ray fluorescence analysis (CMXRF) enables the destruction-free 3D investigation of the elemental composition of samples. The energy-dependent transmission properties, concerning intensity and spatial beam propagation of three polycapillary half lenses, which are vital for the quantitative interpretation of such CMXRF measurements, are investigated in a monochromatic confocal laboratory setup at the Atominstitut of TU Wien, and a synchrotron setup on the BAMline beamline at the BESSY II Synchrotron, Helmholtz-Zentrum-Berlin. The empirically established results, concerning the intensity of the transmitted beam, are compared with theoretical values calculated with the polycap software package and a newly presented analytical model for the transmission function. The resulting form of the newly modelled energy-dependent transmission function is shown to be in good agreement with Monte Carlo simulated results for the complete energy regime, as well as the empirically established results for the energy regime between 6 keV and 20 keV. An analysis of possible fabrication errors was conducted via pinhole scans showing only minor fabrication errors in two of the investigated polycapillary optics. The energy-dependent focal spot size of the primary polycapillary was investigated in the laboratory via the channel-wise evaluation of knife-edge scans. Experimental results are compared with data given by the manufacturer as well as geometric estimations for the minimal focal spot size. Again, the resulting measurement points show a trend in agreement with geometrically estimated results and manufacturer data.

Aubry-André Anderson model: Magnetic impurities coupled to a fractal spectrum

The Anderson model for a magnetic impurity in a one-dimensional quasicrystal is studied using the numerical renormalization group (NRG). The main focus is elucidating the physics at the critical point of the Aubry-Andre (AA) Hamiltonian, which exhibits a fractal spectrum with multifractal wave functions, leading to an AA Anderson (AAA) impurity model with an energy-dependent hybridization function defined through the multifractal local density of states at the impurity site. We first study a class of Anderson impurity models with uniform fractal hybridization functions that the NRG can solve to arbitrarily low temperatures. Below a Kondo scale $T_K$, these models approach a fractal strong-coupling fixed point where impurity thermodynamic properties oscillate with $\log_b T$ about negative average values determined by the fractal dimension of the spectrum. The fractal dimension also enters into a power-law dependence of $T_K$ on the Kondo exchange coupling $J_K$. To treat the AAA model, we combine the NRG with the kernel polynomial method (KPM) to form an efficient approach that can treat hosts without translational symmetry down to a temperature scale set by the KPM expansion order. The aforementioned fractal strong-coupling fixed point is reached by the critical AAA model in a simplified treatment that neglects the wave-function contribution to the hybridization. The temperature-averaged properties are those expected for the numerically determined fractal dimension of $0.5$. At the AA critical point, impurity thermodynamic properties become negative and oscillatory. Under sample-averaging, the mean and median Kondo temperatures exhibit power-law dependences on $J_K$ with exponents characteristic of different fractal dimensions. We attribute these signatures to the impurity probing a distribution of fractal strong-coupling fixed points with decreasing temperature.

Systematic study of probable target-projectile combinations for the synthesis of Z = 120 isotopes using the Skyrme energy density formalism

The synthesis of superheavy elements is an interesting field of research for both theoretical as well as experimental physicists. Till now superheavy element from Z=104 to 118 has been synthesized in various laboratories using cold and hot fusion reactions. Recent predictions of various theoretical models state that Z=120 and N=184 seems most probable doubly magic pair in the island of stability. Hence, we aim to the predict most probable target-projectile combinations of 300,302,304120 superheavy nuclei, so that relevant inputs may be imparted for future synthesis of superheavy nuclei. The target-projectile combinations are taken in reference to the minima's of the fragmentation potential calculated using the Quantum Mechanical Fragmentation Theory (QMFT). In addition, the target-projectile combinations from literature are also considered for which attempts were made for the synthesis of Z=120. The barrier height (VB) of the considered target-projectile combinations are calculated using the spherical and deformed choices of decay fragments. The percentage change in the barrier height ΔVB is explored for the hot and cold fusion approaches. The nuclear interaction potential is obtained within the Skyrme energy density formalism (SEDF) using the GSkI force parameters. For the feasible target-projectile (t-p) combinations, the capture cross-sections of these three isotopes 300,302,304120 are calculated using ℓ-summed Wong model and their comparative analysis is worked out. The probability of formation of compound nucleus (PCN) is determined using the energy dependent function. Among the thirty-six considered target-projectile combinations, the Ti-based reactions with Cf targets and also Cr-based reactions with Cm targets are identified as most suitable combinations for the synthesis of the superheavy element with Z=120. For 300120 isotope are 48Ti+252Cf, 50Ti+250Cf, 50Cr+250Cm, 52Cr+248Cm; whereas 50Ti+252Cf, 54Cr+248Cm, and 54Cr+250Cm form most probable target-projectile pair respectively, for 302120 and 304120 superheavy nuclei.

Approximate time–energy uncertainty relationship from the fixed-energy sum over paths approach

In this article, we show how an approximate time–energy uncertainty relationship of the form Δ EΔ t ≃ ℏ can be derived in the context of the fixed-energy sum over paths approach to quantum bound systems. The relationship connects the indeterminacy Δ t on the travel time of the quantum object to the width Δ E of the resonance in the approximate Green function corresponding to an allowed value of energy. The mathematical origin of the relationship is to be tracked to the Fourier transform relationship between the time propagator and energy-dependent Green function; however, the core of the derivation does not use advanced mathematics, may be carried out using mostly graphical and geometrical methods, and may provide insight to students on the meaning and origin of the time–energy uncertainty relationship. Our work may contribute to close a gap by which the time–energy relationship is most often taught with insufficient explanation at elementary level.

Calculation of thermomagnetic properties using first-principles density functional theory

The BoltzWann code uses the first-principles density-functional theory to calculate the material’s response to an electric field and temperature gradient within the constant relaxation time approximation. We extend this code to include the response of the system to a magnetic field. The carrier dynamic is described by the semi-classical Boltzmann transport equation. This equation is solved in the presence of an external magnetic field within the constant relaxation time approximation and using the Jones–Zener expansion. This is done through a Wannier interpolation of the density functional theory bands using the Boltzwann code, followed by the computation of group velocities and effective masses leading to the energy-dependent transport function. This work leads to a generalized method for the calculation of thermomagnetic properties of materials. The results are validated by comparison to the analytical solutions of the thermomagnetic properties for several simple energy dispersion types and close agreements at moderate computational costs are achieved. This method can pave the path for the discovery of materials with potentially high thermomagnetic power factor.

Analysis of Polarimetry Data with Angular Uncertainties

Abstract For a track based polarimeter, such as the Imaging X-ray Polarimetry Explorer (IXPE), the sensitivity to polarization depends on the modulation factor, which is a strong function of energy. In previous work, a likelihood method was developed that would account for this variation in order to estimate the minimum detectable polarization (MDP). That method essentially required that the position angles of individual events should be known precisely. In a separate work, however, it was shown that using a machine-learning method for measuring event tracks can generate track angle uncertainties, which can be used in the analysis. Here, the maximum likelihood method is used as a basis for revising the estimate of the MDP in a general way that can include uncertainties in event track position angles. The resultant MDP depends solely upon the distribution of track angle uncertainties present in the input data. Due to the physics of the IXPE detectors, it is possible to derive a simple relationship between these angular uncertainties and the energy-dependent modulation function as a step in the process.

Dalitz plot studies of D0→KS0K+K− decays in a factorization approach

The $\textit{BABAR}$ Collaboration data of the $D^0 \to K^0_S K^+ K^-$ process are analyzed within a quasi two-body factorization framework. In earlier studies, assuming $D^0$ transitions to two kaons and the transitions between one kaon and two kaons to proceed through the dominant intermediate resonances, we approximated them as being proportional to the kaon form factors. To obtain good fits, one has to multiply the scalar-kaon form factors, derived from unitary relativistic coupled-channel models or in a dispersion relation approach, by phenomenological energy-dependent functions. The final state kaon-kaon interactions in the $S$-, $P$- and $D$- waves are taken into account. All $S$-wave channels are treated in a unitary way. The $K^+K^-$ and $\bar K^0 K^+$ $S$-wave effective mass squared distributions, corrected for phase space, are shown, in a model-independent manner, to be significantly different. Then the $f_0(980)$ resonance must be included at variance with the BABAR analysis. The best fit has 19 free parameters and indicates i) the dominance of annihilation amplitudes, ii) a large dominance of the $f_0(980)$ meson in the near threshold $K^+K^-$ invariant mass distribution and iii) a sizable branching fraction to the $K_S^0 \ [\rho(770)^+ + \rho(1450)^+ + \rho(1700)^+] $ final states. An appendix provides an update of the determination of the isoscalar-scalar meson-meson amplitudes based on an enlarged set of data. A second appendix proposes two alternative fits based on scalar-kaon form factors calculated from the Muskhelishvili-Omn\`es dispersion relation approach. These fits have $\chi^2$ quite close to that of the best fit but they show important contributions from both the $f_0$ and $a_0^0$ mesons and a weaker role of the $\rho^+$ mesons.

Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law

The thermal scattering law (TSL), i.e., S(α,β), represents the momentum and energy exchange phase space for a material. The incoherent and coherent components of the TSL correlate an atom’s trajectory with itself and/or with other atoms in the lattice structure. This structural information is especially important for low energies where the wavelength of neutrons is on the order of the lattice interatomic spacing. Both thermal neutron scattering as well as low energy resonance broadening involve processes where incoming neutron responses are lattice dependent. Traditionally, Doppler broadening for absorption resonances approximates these interactions by assuming a Maxwell–Boltzmann distribution for the neutron velocity. For high energies and high temperatures, this approximation is reasonable. However, for low temperatures or low energies, the lattice structure binding effects will influence the velocity distribution. Using the TSL to determine the Doppler broadening directly introduces the material structure into the calculation to most accurately capture the momentum and energy space. Typically, the TSL is derived assuming cubic lattice symmetry. This approximation collapses the directional lattice information, including the polarization vectors and associated energies, into an energy-dependent function called the density of states. The cubic approximation, while valid for highly symmetric and uniformly bonded materials, is insufficient to capture the true structure. In this work, generalized formulation for the exact, lattice-dependent TSL is implemented within the Full Law Analysis Scattering System Hub (FLASSH) using polarization vectors and associated energies as fundamental input. These capabilities are utilized to perform the generalized structure Doppler broadening analysis for UO2.

Application of an energy-dependent instrument response function to analysis of nTOF data from cryogenic DT experiments

Neutron time-of-flight (nTOF) detectors are used to diagnose the conditions present in inertial confinement fusion (ICF) experiments and basic laboratory physics experiments performed on an ICF platform. The instrument response function (IRF) of these detectors is constructed by convolution of two components: an x-ray IRF and a neutron interaction response. The shape of the neutron interaction response varies with incident neutron energy, changing the shape of the total IRF. Analyses of nTOF data that span a broad range of energies must account for this energy-dependence in order to accurately infer plasma parameters and nuclear properties in ICF experiments. This work briefly reviews a matrix multiplication approach to convolution, which allows for an energy-dependent change in the shape of the IRF. This method is applied to synthetic data resembling symmetric cryogenic DT implosions to examine the effect of the energy-dependent IRF on the inferred areal density. The results of forward fits that infer ion temperatures and areal densities from nTOF data collected during cryogenic DT experiments on OMEGA are also discussed.

A generalized forward fit for neutron detectors with energy-dependent response functions

To date, most of the analysis of neutron time-of-flight data from inertial confinement fusion experiments has focused on the relatively small range of energies corresponding to the primary neutrons from deuterium–deuterium and deuterium–tritium fusion and has, therefore, employed instrument response functions (IRFs) corresponding to monoenergetic 2.45-MeV or 14.03-MeV neutrons. For the analysis of time-of-flight signals corresponding to broader ranges of neutron energies, accurate treatment of the data requires the use of an energy-dependent IRF. This work describes interpolation of the IRF for neutrons of arbitrary energy, construction of an energy-dependent IRF, and application of this IRF in a forward fit via matrix multiplication. As an example of the application of this method, an analysis of synthetic data relevant to tritium–tritium fusion experiments at the Omega Laser Facility is discussed. This example is used to illustrate the differences between a forward fit that uses an energy-dependent IRF and a forward fit that uses a monoenergetic IRF. Use of the energy-dependent IRF is shown to result in accurate inference of the fit parameters of interest.

Fast neutron measurements with solid state detectors at pulsed spallation sources

Fast neutron measurements have been performed with silicon and diamond detectors at nTOF, ChipIr, and CHARM facilities. The detectors have been used in pulse mode; the deposited energy and time stamp is measured event by event for each signal above threshold. The pulsed nature of the spallation sources gives high instantaneous counting rates that dictate the use of a fast electronic chain including a current preamplifier and digital acquisition. The energy-dependent response functions of these detectors to fast neutrons can be extracted from nTOF data using time-of-flight to provide energy tagging. These measured response functions can then be used both to benchmark Monte Carlo simulations of the response functions and to interpret the measurements at ChipIR and CHARM, facilities used for the irradiation of microelectronics, where time-of-flight energy measurement at these neutron energies is not possible.

Coupled analysis to probe the effect of angular assignments on the secondary electron yield (SEY) from copper electrodes

Secondary electron emission from copper is probed utilizing Monte Carlo simulations that take account of elastic scattering based on the Mott theory and inelastic collisions based on energy-dependent energy loss functions. The loss function and stopping power were obtained through first-principles density functional theory. Angular assignment of electrons following elastic scattering or the creation of secondaries is shown to affect the energy-dependent secondary electron yield (SEY). A good match of the simulation results (with a peak SEY of ∼180% at around 300 eV and less than 10% deviation over the 0 to 1000 eV energy range) to available experimental data is shown based on an energy and momentum conservation scheme. Also, the distribution of delay times for the generation of secondaries, the SEY behavior at different incident angles, the energy distribution of emergent secondaries, and their creation profiles as a function of depth are computed to provide a more complete picture of the governing mechanisms and predicted responses.

Hypothesis: A Novel Neuroprotective Role for Glucose-6-phosphatase (G6PC3) in Brain—To Maintain Energy-Dependent Functions Including Cognitive Processes

The isoform of glucose-6-phosphatase in liver, G6PC1, has a major role in whole-body glucose homeostasis, whereas G6PC3 is widely distributed among organs but has poorly-understood functions. A recent, elegant analysis of neutrophil dysfunction in G6PC3-deficient patients revealed G6PC3 is a neutrophil metabolite repair enzyme that hydrolyzes 1,5-anhydroglucitol-6-phosphate, a toxic metabolite derived from a glucose analog present in food. These patients exhibit a spectrum of phenotypic characteristics and some have learning disabilities, revealing a potential linkage between cognitive processes and G6PC3 activity. Previously-debated and discounted functions for brain G6PC3 include causing an ATP-consuming futile cycle that interferes with metabolic brain imaging assays and a nutritional role involving astrocyte-neuron glucose-lactate trafficking. Detailed analysis of the anhydroglucitol literature reveals that it competes with glucose for transport into brain, is present in human cerebrospinal fluid, and is phosphorylated by hexokinase. Anhydroglucitol-6-phosphate is present in rodent brain and other organs where its accumulation can inhibit hexokinase by competition with ATP. Calculated hexokinase inhibition indicates that energetics of brain and erythrocytes would be more adversely affected by anhydroglucitol-6-phosphate accumulation than heart. These findings strongly support the paradigm-shifting hypothesis that brain G6PC3 removes a toxic metabolite, thereby maintaining brain glucose metabolism- and ATP-dependent functions, including cognitive processes.