Engineering topics

Smith, M.

Publications and source records attributed to Smith, M..

At least 91 records · Page 5

DOE OSTI2022

From the Fire: A Deeper Look at the Phoenix Stream

We use 6 yr of data from the Dark Energy Survey to perform a detailed photometric characterization of the Phoenix stellar stream, a 15° long, thin, dynamically cold, low-metallicity stellar system in the Southern Hemisphere. We use natural splines, a nonparametric modeling technique, to simultaneously fit the stream track, width, and linear density. This updated stream model allows us to improve measurements of the heliocentric distance (17.4 ± 0.1 (stat.) ±0.8 (sys.) kpc) and distance gradient (−0.009 ± 0.006 kpc deg$^{−1}$) of Phoenix, which corresponds to a small change of 0.13 ± 0.09 kpc in heliocentric distance along the length of the stream. We measure linear intensity variations on degree scales, as well as deviations in the stream track on ∼2° scales, suggesting that the stream may have been disturbed during its formation and/or evolution. We recover three peaks and one gap in linear intensity along with fluctuations in the stream track. Compared to other thin streams, the Phoenix stream shows more fluctuations and, consequently, the study of Phoenix offers a unique perspective on gravitational perturbations of stellar streams. We discuss possible sources of perturbations to Phoenix, including baryonic structures in the Galaxy and dark matter subhalos.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Dark Energy Survey Year 3 results: galaxy clustering and systematics treatment for lens galaxy samples

ABSTRACT In this work, we present the galaxy clustering measurements of the two DES lens galaxy samples: a magnitude-limited sample optimized for the measurement of cosmological parameters, maglim, and a sample of luminous red galaxies selected with the redmagic algorithm. maglim/redmagic sample contains over 10 million/2.5 million galaxies and is divided into six/five photometric redshift bins spanning the range z ∈ [0.20, 1.05]/z ∈ [0.15, 0.90]. Both samples cover 4143 $\deg ^2$ over which we perform our analysis blind, measuring the angular correlation function with an S/N ∼ 63 for both samples. In a companion paper, these measurements of galaxy clustering are combined with the correlation functions of cosmic shear and galaxy–galaxy lensing of each sample to place cosmological constraints with a 3 × 2pt analysis. We conduct a thorough study of the mitigation of systematic effects caused by the spatially varying survey properties and we correct the measurements to remove artificial clustering signals. We employ several decontamination methods with different configurations to ensure the robustness of our corrections and to determine the systematic uncertainty that needs to be considered for the final cosmology analyses. We validate our fiducial methodology using lognormal mocks, showing that our decontamination procedure induces biases no greater than 0.5σ in the (Ωm, b) plane, where b is the galaxy bias.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Dark Energy Survey Year 3 Results: Measuring the Survey Transfer Function with Balrog

Abstract We describe an updated calibration and diagnostic framework, Balrog , used to directly sample the selection and photometric biases of the Dark Energy Survey (DES) Year 3 (Y3) data set. We systematically inject onto the single-epoch images of a random 20% subset of the DES footprint an ensemble of nearly 30 million realistic galaxy models derived from DES Deep Field observations. These augmented images are analyzed in parallel with the original data to automatically inherit measurement systematics that are often too difficult to capture with generative models. The resulting object catalog is a Monte Carlo sampling of the DES transfer function and is used as a powerful diagnostic and calibration tool for a variety of DES Y3 science, particularly for the calibration of the photometric redshifts of distant “source” galaxies and magnification biases of nearer “lens” galaxies. The recovered Balrog injections are shown to closely match the photometric property distributions of the Y3 GOLD catalog, particularly in color, and capture the number density fluctuations from observing conditions of the real data within 1% for a typical galaxy sample. We find that Y3 colors are extremely well calibrated, typically within ∼1–8 mmag, but for a small subset of objects, we detect significant magnitude biases correlated with large overestimates of the injected object size due to proximity effects and blending. We discuss approaches to extend the current methodology to capture more aspects of the transfer function and reach full coverage of the survey footprint for future analyses.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Accuracy of environmental tracers and consequences for determining the Type Ia supernova magnitude step

Type Ia Supernovae (SNe Ia) are standardizable candles that allow us to measure the recent expansion rate of the Universe. Due to uncertainties in progenitor physics, potential astrophysical dependencies may bias cosmological measurements if not properly accounted for. The dependency of the intrinsic luminosity of SNe Ia with their host-galaxy environment is often used to standardize SNe Ia luminosity and is commonly parameterized as a step function. This functional form implicitly assumes two-populations of SNe Ia. In the literature, multiple environmental indicators have been considered, finding different, sometimes incompatible, step function amplitudes. We compare these indicators in the context of a two-populations model, based on their ability to distinguish the two populations. We show that local Hα-based specific star formation rate (lsSFR) and global stellar mass are better tracers than, for instance, host galaxy morphology. We show that tracer accuracy can explain the discrepancy between the observed SNe Ia step amplitudes found in the literature. Using lsSFR or global mass to identify the two populations can explain all other observations, though lsSFR is favoured. As lsSFR is strongly connected to age, our results favour a prompt and delayed population model. In any case, there exists two populations that differ in standardized magnitude by at least 0.121 ± 0.010 mag.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Dark Energy Survey Year 3 Results: Galaxy mock catalogs for BAO analysis

The calibration and validation of scientific analysis in simulations is a fundamental tool to ensure unbiased and robust results in observational cosmology. In particular, mock galaxy catalogs are a crucial resource to achieve these goals in the measurement of baryon acoustic oscillation (BAO) in the clustering of galaxies. Here we present a set of 1952 galaxy mock catalogs designed to mimic the Dark Energy Survey Year 3 BAO sample over its full photometric redshift range 0.6 < zphoto < 1.1. The mocks are based upon 488 ICE-COLA fast N-body simulations of full-sky light cones and were created by populating halos with galaxies, using a hybrid halo occupation distribution – halo abundance matching model. This model has ten free parameters, which were determined, for the first time, using an automatic likelihood minimization procedure. We also introduced a novel technique to assign photometric redshift for simulated galaxies, following a two-dimensional probability distribution with VIMOS Public Extragalactic Redshift Survey data. The calibration was designed to match the observed abundance of galaxies as a function of photometric redshift, the distribution of photometric redshift errors, and the clustering amplitude on scales smaller than those used for BAO measurements. An exhaustive analysis was done to ensure that the mocks reproduce the input properties. Finally, mocks were tested by comparing the angular correlation function w(θ), angular power spectrum Cℓ, and projected clustering ξp(r⊥) to theoretical predictions and data. The impact of volume replication in the estimate of the covariance is also investigated. The success in accurately reproducing the photometric redshift uncertainties and the galaxy clustering as a function of redshift render this mock creation pipeline as a benchmark for future analyses of photometric galaxy surveys.Key words: catalogs / large-scale structure of Universe / galaxies: distances and redshifts / Galaxy: halo / methods: numerical

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Characterisation of signal-induced noise in Hamamatsu R11265 Multianode Photomultiplier Tubes

Signal-induced noise is observed in Hamamatsu R11265 Multianode Photomultiplier Tubes, manifesting up to several microseconds after the single photoelectron response signal and localised in specific anodes. The mean number of noise pulses varies between devices, and shows significant dependence on the applied high-voltage. The characterisation of this noise and the mitigation strategies to perform optimal single-photon counting at 40 MHz, as required by the LHCb Ring-Imaging Cherenkov detectors, are reported.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Dark Energy Survey Year 3 Results: clustering redshifts – calibration of the weak lensing source redshift distributions with redMaGiC and BOSS/eBOSS

ABSTRACT We present the calibration of the Dark Energy Survey Year 3 (DES Y3) weak lensing (WL) source galaxy redshift distributions n(z) from clustering measurements. In particular, we cross-correlate the WL source galaxies sample with redMaGiC galaxies (luminous red galaxies with secure photometric redshifts) and a spectroscopic sample from BOSS/eBOSS to estimate the redshift distribution of the DES sources sample. Two distinct methods for using the clustering statistics are described. The first uses the clustering information independently to estimate the mean redshift of the source galaxies within a redshift window, as done in the DES Y1 analysis. The second method establishes a likelihood of the clustering data as a function of n(z), which can be incorporated into schemes for generating samples of n(z) subject to combined clustering and photometric constraints. Both methods incorporate marginalization over various astrophysical systematics, including magnification and redshift-dependent galaxy-matter bias. We characterize the uncertainties of the methods in simulations; the first method recovers the mean z of tomographic bins to RMS (precision) of ∼0.014. Use of the second method is shown to vastly improve the accuracy of the shape of n(z) derived from photometric data. The two methods are then applied to the DES Y3 data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

C/2014 UN 271 (Bernardinelli-Bernstein): The Nearly Spherical Cow of Comets

Abstract Comet C/2014 UN 271 (Bernardinelli-Bernstein), incoming from the Oort cloud, is remarkable in having the brightest (and presumably largest) nucleus of any well-measured comet and having been discovered at the heliocentric distance r h ≈ 29 au, farther than any Oort cloud comet. In this work, we describe the discovery process and observations and the properties that can be inferred from images recorded until the first reports of activity in 2021 June. The orbit has i = 95°, with a perihelion of 10.97 au to be reached in 2031 and a previous aphelion at 40,400 ± 260 au. Backward integration of the orbit under a standard Galactic tidal model and known stellar encounters suggests a perihelion of q ≈ 18 au on its previous perihelion passage 3.5 Myr ago; hence, the current data could be the first ever obtained of a comet that has not been inside Uranus’s orbit in 4 Gyr. The photometric data show an unresolved nucleus with absolute magnitude H r = 8.0, colors that are typical of comet nuclei or Damocloids, and no secular trend as it traversed the range 34–23 au. For the r -band geometric albedo p r , this implies a diameter of 150 ( p r / 0.04 ) − 0.5 km. There is strong evidence of brightness fluctuations at the ±0.2 mag level, but no rotation period can be discerned. A coma, nominally consistent with a “stationary” 1/ ρ surface brightness distribution, grew in scattering cross section at an exponential rate from A f ρ ≈ 1 to ≈150 m as the comet approached from 28 to 20 au. The activity rate is consistent with a very simple model of sublimation of a surface species in radiative equilibrium with the Sun. The inferred enthalpy of sublimation matches those of CO 2 and NH 3 . More volatile species, such as N 2 , CH 4 , and CO, must be far less abundant on the sublimating surfaces.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Dark Energy Survey Year 3 results: galaxy sample for BAO measurement

Here, we present and validate the galaxy sample used for the analysis of the baryon acoustic oscillation (BAO) signal in the Dark Energy Survey (DES) Y3 data. The definition is based on a colour and redshift-dependent magnitude cut optimized to select galaxies at redshifts higher than 0.5, while ensuring a high-quality determination. The sample covers ~ 4100 square degrees to a depth of i = 22.3 (AB) at 10σ. It contains 7,031,993 galaxies in the redshift range from z = 0.6 to 1.1, with a mean effective redshift of 0.835. Redshifts are estimated with the machine learning algorithm DNF, and are validated using the VIPERS PDR2 sample. We find a mean redshift bias of z bias ~ 0.01 and a mean uncertainty, in units of 1 + z, of σ 68 ~ 0.03$. We evaluate the galaxy population of the sample, showing it is mostly built upon Elliptical to Sbc types. Furthermore, we find a low level of stellar contamination of ≲ 4 %. We present the method used to mitigate the effect of spurious clustering coming from observing conditions and other large-scale systematics. We apply it to the BAO sample and calculate weights that are used to get a robust estimate of the galaxy clustering signal. This paper is one of a series dedicated to the analysis of the BAO signal in DES Y3. In the companion papers, we present the galaxy mock catalogues used to calibrate the analysis and the angular diameter distance constraints obtained through the fitting to the BAO scale.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Dark Energy Survey Y3 results: blending shear and redshift biases in image simulations

ABSTRACT As the statistical power of galaxy weak lensing reaches per cent level precision, large, realistic, and robust simulations are required to calibrate observational systematics, especially given the increased importance of object blending as survey depths increase. To capture the coupled effects of blending in both shear and photometric redshift calibration, we define the effective redshift distribution for lensing, nγ(z), and describe how to estimate it using image simulations. We use an extensive suite of tailored image simulations to characterize the performance of the shear estimation pipeline applied to the Dark Energy Survey (DES) Year 3 data set. We describe the multiband, multi-epoch simulations, and demonstrate their high level of realism through comparisons to the real DES data. We isolate the effects that generate shear calibration biases by running variations on our fiducial simulation, and find that blending-related effects are the dominant contribution to the mean multiplicative bias of approximately $-2{{\ \rm per\ cent}}$. By generating simulations with input shear signals that vary with redshift, we calibrate biases in our estimation of the effective redshift distribution, and demonstrate the importance of this approach when blending is present. We provide corrected effective redshift distributions that incorporate statistical and systematic uncertainties, ready for use in DES Year 3 weak lensing analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Reducing Ground-based Astrometric Errors with Gaia and Gaussian Processes

Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2D distortion field is curl-free. Applied to several hundred 90 s exposures from the Dark Energy Survey as a test bed, we find that the GPR correction reduces the variance of the turbulent astrometric distortions ≈12× , on average, with better performance in denser regions of the Gaia catalog. The rms per-coordinate distortion in the riz bands is typically ≈7 mas before any correction and ≈2 mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas rms, the residuals to an orbit fit to riz-band observations over 5 yr of the r = 18.5 trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5D stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Deep Learning Systems for Increased Safeguards Surveillance Review Productivity

Nuclear safeguards inspectors expend significant time and maintain intense focus in reviewing video surveillance for safeguards relevant events. To increase efficiency and reduce the time burden of safeguards inspectors performing surveillance data review, this paper presents a novel deep learning (DL) systems concept to integrate generalized DL models into the safeguards surveillance review workflow. The Agency is investigating several DL algorithms for object recognition, localization, tracking, and flagging relevant activities. The project team is working closely with nuclear safeguards inspectors to identify review use cases (based on specific safeguards objectives) and collect their associated requirements. We focused on CANDU and LWR Nuclear Power Plants (NPPs) and their associated dry storage areas as these present a particularly heavy burden on the inspector surveillance review process due to the number of these facilities under safeguards worldwide. Initial DL algorithm results on safeguards data are promising. Using a convolutional neural network, the team attained a mean average precision (mAP) of 92.9% identifying and localizing spent fuel (SF) casks from a 475 surveillance image dataset. Further, the team had initial success in training a recurrent neural network to identify reactor area activities in video clips, successfully indicating when SF casks enter or exit a pool. We discuss how such DL algorithms would be integrated into the Next Generation Surveillance Review (NGSR) software application. Another issue impacting review productivity is the long time inspectors may have to wait when running these algorithms in NGSR. We present a concept to pre-process remotely collected surveillance data with DL models as the data arrives to IAEA headquarters so that results are already available when starting a new review in NGSR. The proposed DL system concept shows a pathway and workflow for increasing an inspector’s surveillance review productivity by quickly and accurately identifying declared and undeclared safeguards relevant objects and activities in large quantities of surveillance imagery data.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2021

Design and Analyses of the NSTX-U PF1A Poloidal Field Coil Support

New poloidal field (PF) coils and supports have been designed for the National Spherical Torus Experiment Upgrade (NSTX-U) Recovery project. The PF1A coil structural requirements demand a large preload to pre-compress the coil insulation. Coil support design accounts for all operational conditions and loads of NSTX-U including bakeout, seismic events, and electromagnetic loads. Background magnetic fields produce coil Lorentz forces that react on the structural supports. These Lorentz forces include interactions from the coil current and all plasma events: normal operations, disruptions, and vertical displacement events. This paper will detail the design and design loads and highlight some of the analyses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A Deeper Look at DES Dwarf Galaxy Candidates: Grus i and Indus ii

We present deep g- and r-band Magellan/Megacam photometry of two dwarf galaxy candidates discovered in the Dark Energy Survey (DES), Grus i and Indus ii (DES J2038–4609). For the case of Grus i, we resolved the main sequence turn-off (MSTO) and ~2 mags below it. The MSTO can be seen at g 0 ~24 with a photometric uncertainty of 0.03 mag. We show Grus i to be consistent with an old, metal-poor (~13.3 Gyr, [Fe/H] ~ -1.9) dwarf galaxy. We derive updated distance and structural parameters for Grus i using this deep, uniform, wide-field data set. We find an azimuthally-averaged halflight radius more than two times larger (~151 +21 -31 pc; ~$4\buildrel{\,\prime}\over{.} {16}_{-0.74}^{+0.54}$) and an absolute V-band magnitude ~-4.1 that is ~1 magnitude brighter than previous studies. We obtain updated distance, ellipticity, and centroid parameters that are in agreement with other studies within uncertainties. Although our photometry of Indus ii is ~2–3 magnitudes deeper than the DES Y1 public release, we find no coherent stellar population at its reported location. The original detection was located in an incomplete region of sky in the DES Y2Q1 data set and was flagged due to potential blue horizontal branch member stars. The best-fit isochrone parameters are physically inconsistent with both dwarf galaxies and globular clusters. We conclude that Indus ii is likely a false positive, flagged due to a chance alignment of stars along the line of sight.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Galaxy morphological classification catalogue of the Dark Energy Survey Year 3 data with convolutional neural networks

ABSTRACT We present in this paper one of the largest galaxy morphological classification catalogues to date, including over 20 million galaxies, using the Dark Energy Survey (DES) Year 3 data based on convolutional neural networks (CNNs). Monochromatic i-band DES images with linear, logarithmic, and gradient scales, matched with debiased visual classifications from the Galaxy Zoo 1 (GZ1) catalogue, are used to train our CNN models. With a training set including bright galaxies (16 ≤ i < 18) at low redshift (z < 0.25), we furthermore investigate the limit of the accuracy of our predictions applied to galaxies at fainter magnitude and at higher redshifts. Our final catalogue covers magnitudes 16 ≤ i < 21, and redshifts z < 1.0, and provides predicted probabilities to two galaxy types – ellipticals and spirals (disc galaxies). Our CNN classifications reveal an accuracy of over 99 per cent for bright galaxies when comparing with the GZ1 classifications (i < 18). For fainter galaxies, the visual classification carried out by three of the co-authors shows that the CNN classifier correctly categorizes discy galaxies with rounder and blurred features, which humans often incorrectly visually classify as ellipticals. As a part of the validation, we carry out one of the largest examinations of non-parametric methods, including ∼100 ,000 galaxies with the same coverage of magnitude and redshift as the training set from our catalogue. We find that the Gini coefficient is the best single parameter discriminator between ellipticals and spirals for this data set.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Rates and delay times of type Ia supernovae in the Dark Energy Survey

We use a sample of 809 photometrically classified Type Ia supernovae (SNe Ia) discovered by the Dark Energy Survey (DES) along with 40 415 field galaxies to calculate the rate of SNe Ia per galaxy in the redshift range 0.2 < z < 0.6. We recover the known correlation between SN Ia rate and galaxy stellar mass across a broad range of scales 8.5 ≤ log (M*/M ⊙ ) ≤ 11.25. We find that the SN Ia rate increases with stellar mass as a power law with index 0.63 ± 0.02, which is consistent with the previous work. We use an empirical model of stellar mass assembly to estimate the average star formation histories (SFHs) of galaxies across the stellar mass range of our measurement. Combining the modelled SFHs with the SN Ia rates to estimate constraints on the SN Ia delay time distribution (DTD), we find that the data are fit well by a power-law DTD with slope index β = –1.13 ± 0.05 and normalization A = 2.11 ± 0.05 × 10 –13 SNe M ⊙ –1 yr –1 , which corresponds to an overall SN Ia production efficiency N Ia /M * = 0.9 $^{+4.0}_{–0.7}$ × 10 –3 SNe M$^{–1}_{⊙}$. Upon splitting the SN sample by properties of the light curves, we find a strong dependence on DTD slope with the SN decline rate, with slower-declining SNe exhibiting a steeper DTD slope. We interpret this as a result of a relationship between intrinsic luminosity and progenitor age, and explore the implications of the result in the context of SN Ia progenitors.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Assessing tension metrics with dark energy survey and Planck data

ABSTRACT Quantifying tensions – inconsistencies amongst measurements of cosmological parameters by different experiments – has emerged as a crucial part of modern cosmological data analysis. Statistically significant tensions between two experiments or cosmological probes may indicate new physics extending beyond the standard cosmological model and need to be promptly identified. We apply several tension estimators proposed in the literature to the dark energy survey (DES) large-scale structure measurement and Planck cosmic microwave background data. We first evaluate the responsiveness of these metrics to an input tension artificially introduced between the two, using synthetic DES data. We then apply the metrics to the comparison of Planck and actual DES Year 1 data. We find that the parameter differences, Eigentension, and Suspiciousness metrics all yield similar results on both simulated and real data, while the Bayes ratio is inconsistent with the rest due to its dependence on the prior volume. Using these metrics, we calculate the tension between DES Year 1 3 × 2pt and Planck, finding the surveys to be in ∼2.3σ tension under the ΛCDM paradigm. This suite of metrics provides a toolset for robustly testing tensions in the DES Year 3 data and beyond.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Constraints on dark matter to dark radiation conversion in the late universe with DES-Y1 and external data

We study a phenomenological class of models where dark matter converts to dark radiation in the low redshift epoch. This class of models, dubbed DMDR, characterizes the evolution of comoving dark-matter density with two extra parameters, and may be able to help alleviate the observed discrepancies between early and late-time probes of the Universe. We investigate how the conversion affects key cosmological observables such as the cosmic microwave background (CMB) temperature and matter power spectra. Combining 3x2pt data from Year 1 of the Dark Energy Survey, Planck-2018 CMB temperature and polarization data, supernovae (SN) Type Ia data from Pantheon, and baryon acoustic oscillation (BAO) data from BOSS DR12, MGS and 6dFGS, we place new constraints on the amount of dark matter that has converted to dark radiation and the rate of this conversion. The fraction of the dark matter that has converted since the beginning of the Universe in units of the current amount of dark matter, ζ, is constrained at 68% confidence level to be <0.32 for DES-Y1 3x2pt data, <0.030 for CMB+SN+BAO data, and <0.037 for the combined dataset. The probability that the DES and CMB+SN+BAO datasets are concordant increases from 4% for the ΛCDM model to 8% (less tension) for DMDR. The tension in S8=σ8Ωm/0.3 between DES-Y1 3x2pt and CMB+SN+BAO is slightly reduced from 2.3σ to 1.9σ. We find no reduction in the Hubble tension when the combined data is compared to distance-ladder measurements in the DMDR model. The maximum-posterior goodness-of-fit statistics of DMDR and ΛCDM model are comparable, indicating no preference for the DMDR cosmology over ΛCDM.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗