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At least 361 records · Page 20

Reconfigurable Microwave Phase Delay Element for Frequency Reference and Phase-Shifter Applications

A technique was developed to provide a reconfigurable high-precision micro - wave electrical phase delay for resonators and phase shifters. The invention employs multiple branches of transmission lines with open-ended or ground-ended terminations as configurable bits or digits. This technique minimizes the errors due to limited precision of switching devices. In addition, the proposed linear analytical approach significantly produces a much simpler design than that of other prior inventions at the time of this reporting. Microwave components such as filters, phase delay elements, or resonators require a method that can accurately adjust their frequency responses. Most tuning techniques offer very wide frequency tuning range; however, it is often difficult and expensive to tune their response in a very narrow operating frequency, especially when the tuning element reaches its minimum discrete step due to fabrication tolerances. The problem becomes worse as the operating frequency is in mm-wave frequency range (>26 GHz). The electrical tuning sensitivity of a microwave line is dependent on the position of the tuning element with respect to the reference termination. By placing this tuning element away from this reference with the main transmission line connecting the two elements together the sensitivity of the tuning element can change significantly. This concept can be used in the system that requires multiple tuning sensitivities. In this case, multiple tuning branches are superimposed in the main transmission line. The proposed invention allows the transmission-line electrical length to be accurately programmed using switching elements that have limited accuracy. The invention consists of multiple branches of transmission lines connected to discrete switching devices with open-ended terminations. They are used as discrete tuning elements. These elements are connected to the main microwave transmission line and are separated by a well-defined electrical degree spacing. Each branch is programmed to have different electrical degree sensitivity, such as a combination of discrete steps in each branch, which results in a reflective line with a unique effective phase response. To reduce the number of switching devices, it is desirable to program the devices in binary configuration where each branch represents one bit in the base-2 number system. This invention allows the transmission line electrical length to be tuned precisely with customizable sensitivity based on the known sensitivity of the base tuning circuit. The tuning resolution is dependent on the distance among tuning branches.

Hsieh, Wen-Ting↗

Pressure-Dependent Yields and Product Branching Ratios in the Broadband Photolysis of Chlorine Nitrate

The photolysis of chlorine nitrate was studied using broadband flash photolysis coupled with long-path ultraviolet-visible absorption spectroscopy. Branching ratios for the Cl + NO3 and ClO + NO2 product channels were determined from time-dependent measurements of ClO and NO3 concentrations. Yields of the ClO and NO3 products displayed a dependence on the bath gas density and the spectral distribution of the photolysis pulse. Product yields decreased with increasing bath gas density regardless of the spectral distribution of the photolysis pulse; however, the decrease in product yield was much more pronounced when photolysis was limited to longer wavelengths. For photolysis in a quartz cell (lambda > 200 nm) the yield decreased by a factor of 2 over the pressure 10-100 Torr. In a Pyrex cell (lambda > 300 nm), the yield decreased by a factor of 50 over the same pressure range. When photolysis was limited to lambda > 350 nm, the yield decreased by a factor of 250. Branching ratios for the photolysis channels [ClONO2 + h.nu yields ClO + NO2 (1a) and ClONO2 + h.nu yields Cl + NO3 (lb)] were determined from the relative ClO and NO3 product yields at various pressures. Although the absolute product yield displayed a pressure dependence, the branching between the two channels was independent of pressure. The relative branching ratios (assuming negligible contributions from other channels) are 0.61 +/- 0.20 for channel 1a and 0.39 +/- 0.20 for channel lb for photolysis with lambda > 200 nm and 0.44 +/- 0.08 for channel 1a and 0.56 +/- 0.08 for channel 1b for photolysis with lambda > 300 nm. The implications of these results for the chemistry of the lower stratosphere are discussed.

Nickolaisen, Scott L.↗

Search for charged Higgs bosons produced in top-quark decays or in association with top quarks and decaying via H±→τ±ντ in 13 TeV pp collisions with the ATLAS detector

Charged Higgs bosons produced either in top-quark decays or in association with a top quark, subsequently decaying via , are searched for in of proton-proton collision data at recorded with the ATLAS detector. Depending on whether the top quark is produced together with the decays hadronically or semileptonically, the search targets or final states, in both cases with a -lepton decaying into a neutrino and hadrons. No significant excess over the Standard Model background expectation is observed. For the mass range of , upper limits at 95% confidence level are set on the production cross section of the charged Higgs boson times the branching fraction in the range 4.5 pb–0.4 fb. In the mass range 80–160 GeV, assuming the Standard Model cross section for production, this corresponds to upper limits between 0.27% and 0.02% on .

Aad, G↗

Searches for additional Higgs bosons and for vector leptoquarks in $ττ$ final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Three searches are presented for signatures of physics beyond the standard model (SM) in $ττ$ final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb -1 . Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay into $τ$ leptons and the cross sections for the production of a new boson $\phi$, in addition to the H(125) boson, via gluon fusion (gg$\phi$) or in association with b quarks, ranging from $\mathcal{O}$(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5 TeV each. The data reveal two excesses for gg$\phi$ production with local $p$-values equivalent to about three standard deviations at m $\phi$ = 0.1 and 1.2 TeV. In a search for $t$-channel exchange of a vector leptoquark U 1 , 95% CL upper limits are set on the dimensionless U 1 leptoquark coupling to quarks and $τ$ leptons ranging from 1 for a mass of 1 TeV to 6 for a mass of 5 TeV, depending on the scenario. In the interpretations of the $M^{125}_{h}$ and $M^{125}_{h,EFT}$ minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for single production of a vector-like T quark decaying to a top quark and a neutral scalar boson in the lepton+jets final state in proton-proton collisions at $\sqrt{s}=13$ TeV

A search for single production of a vector-like T quark with charge 2e/3, decaying to a top quark and a neutral scalar boson is presented. The boson can be a standard model Higgs boson (H) or a new scalar boson (ϕ). In the first case, a branching fraction of 25% is assumed for the decay T → tH, while in the second case the T quark is assumed to decay exclusively to tϕ. The top quark is identified via its lepton+jets decay, and the neutral boson via its decay into a bottom quark-antiquark pair. Final states with Lorentz-boosted topologies are considered and machine-learning techniques are exploited for optimal event classification. The analysis uses data collected by the CMS experiment in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb −1 recorded at the CERN LHC in 2016–2018. Upper limits at 95% confidence level are set on the product of cross section and branching fraction for a T quark in a narrow-width approximation. They vary between 14.7 and 0.1 fb, for T quark masses in the range 1.3–3.0 TeV and ϕ boson masses in the range 25–250 GeV. These are the first exclusion limits set on the production of a single T quark decaying into a top quark and a new neutral scalar boson. For the decay channel into a top quark and a standard model Higgs boson, the results provide the best limits on production cross sections to date, for T quark masses above 2 TeV.

hadron-hadron scattering↗

Impact of the continuum on the γ decay of the lowest 2 + states in 14 C

The half-life, T 1/2 =14.6(33) fs, of the 7012-keV 2$^{+}_{1}$ state in 14 C was measured in an experiment employing the 9 Be( 6 Li,pγ) fusion-evaporation reaction and the GODDESS setup. The γ decay from the 2$^{+}_{2}$ near-threshold resonance, located 142 keV above the 8176-keV neutron-emission threshold, was also investigated. An upper limit of 4.0 × 10 –5 was established for the γ-decay branching ratio with respect to the neutron-decay channel. The B(E2) transition probabilities for these 2$^{+}_{1}$ and 2$^{+}_{2}$ states were compared to predictions from the Shell Model Embedded in the Continuum (SMEC). Significant modifications of these B(E2) probabilities, with respect to the standard shell model, are expected due to the coupling to the continuum. For calculations using the YSOX interaction, agreement was found for large negative values of V 0 , the coupling constant to the continuum. The central value V 0 = −645 MeV fm 3 results in a retardation by a factor ∼ 3.5 for the 2$^{+}_{1}$ → 0$^{+}_{1}$ transition, and an enhanced probability by a factor ∼ 2.5 for the γ-decay out of the 2$^{+}_{2}$ state. The latter factor reflects the effect of collectivization of the 2$^{+}_{2}$ excitation when the coupling to the continuum is taken into account.

14C↗

Search for a τ + τ - Resonance in e + e - → μ + μ - τ + τ - Events with the Belle II Experiment

We report the first search for a nonstandard-model resonance decaying into $τ$ pairs in $e^+e^-$ → $μ^+μ^-τ^+τ^-$ events in the 3.6–10 GeV/c 2 mass range. We use a 62.8 fb -1 sample of $e^+e^-$ collisions collected at a center-of-mass energy of 10.58 GeV by the Belle II experiment at the SuperKEKB collider. The analysis probes three different models predicting a spin-1 particle coupling only to the heavier lepton families, a Higgs-like spin-0 particle that couples preferentially to charged leptons (leptophilic scalar), and an axionlike particle, respectively. We observe no evidence for a signal and set exclusion limits at 90% confidence level on the product of cross section and branching fraction into $τ$ pairs, ranging from 0.7 to 24 fb, and on the couplings of these processes. We obtain world-leading constraints on the couplings for the leptophilic scalar model for masses above 6.5 GeV/c 2 and for the axionlike particle model over the entire mass range.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for Baryon-Number-Violating Processes in B − Decays to the Ξ ¯ c 0 Λ ¯ c − Final State

We report the results of the first search for B − decays to the Ξ ¯ c 0 Λ ¯ c − final state using 711 fb − 1 of data collected at the ϒ ( 4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. The results are interpreted in terms of both direct baryon-number-violating B − decay and Ξ c 0 − Ξ ¯ c 0 oscillations which follow the standard model decay B − → Ξ c 0 Λ ¯ c − . We observe no evidence for baryon number violation and set the 95% confidence-level upper limits on the ratio of baryon-number-violating and standard model branching fractions B ( B − → Ξ ¯ c 0 Λ ¯ c − ) / B ( B − → Ξ c 0 Λ ¯ c − ) to be < 2.7 % and on the effective angular frequency of mixing ω in Ξ c 0 − Ξ ¯ c 0 oscillations to be < 0.76 ps − 1 (equivalent to τ mix > 1.3 ps ). Published by the American Physical Society 2024

Physics↗

Search for supersymmetry in final states with missing transverse momentum and three or more b-jets in 139 fb$^{-1}$ of proton–proton collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

A search for supersymmetry involving the pair production of gluinos decaying via off-shell third-generation squarks into the lightest neutralino ($\tilde {χ}_{1}^{0}$) is reported. It exploits LHC proton–proton collision data at a centre-of mass energy $\sqrt{s} = 13$ TeV with an integrated luminosity of 139 fb -1 collected with the ATLAS detector from 2015 to 2018. The search uses events containing large missing transverse momentum, up to one electron or muon, and several energetic jets, at least three of which must be identified as containing b-hadrons. Both a simple kinematic event selection and an event selection based upon a deep neural network are used. No significant excess above the predicted background is found. In simplified models involving the pair production of gluinos that decay via off-shell top (bottom) squarks, gluino masses less than 2.44 TeV (2.35 TeV) are excluded at 95% CL for a massless $\tilde {χ}_{1}^{0}$. Limits are also set on the gluino mass in models with variable branching ratios for gluino decays to $b$$\overline{b}$$\tilde {χ}_{1}^{0}$, $t$$\overline{t}$$\tilde {χ}_{1}^{0}$ and $t$$\overline{b}$$\tilde {χ}_{1}^{-}$ / $t$$\overline{b}$$\tilde {χ}_{1}^{+}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

How Long Does the Hydrogen Atom Live?

It is possible that the proton is stable while atomic hydrogen is not. This is the case in models with new particles carrying baryon number which are light enough to be stable themselves, but heavy enough so that proton decay is kinematically blocked. Models of new physics that explain the neutron lifetime anomaly generically have this feature, allowing for atomic hydrogen to decay through electron capture on a proton. We calculate the radiative hydrogen decay rate involving the emission of a few hundred keV photon, which makes this process experimentally detectable. In particular, we show that the low energy part of the Borexino spectrum is sensitive to radiative hydrogen decay, and turn this into a limit on the hydrogen lifetime of order 10 30 s or stronger. For models where the neutron mixes with a dark baryon, X, this limits the mixing angle to roughly 10 –11 , restricting the n → XY branching to 10 –4 , over a wide range of parameter space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Almost medium-free measurement of the Hoyle state direct-decay component with a TPC

The structure of the Hoyle state, a highly α -clustered state at 7.65 MeV in 12 C, has long been the subject of debate. Understanding if the system comprises of three weakly interacting α particles in the 0s orbital, known as an α-condensate state, is possible by studying the decay branches of the Hoyle state. The direct decay of the Hoyle state into three α particles, rather than through the 8 Be ground state, can be identified by studying the energy partition of the three α particles arising from the decay. This paper provides details on the breakup mechanism of the Hoyle stating using a new experimental technique. Method: By using β-delayed charged-particle spectroscopy of 12 N using the Texas active target time-projection chamber, a high-sensitivity measurement of the direct 3α decay ratio can be performed without contributions from pileup events. A Bayesian approach to understanding the contribution of the direct components via a likelihood function shows that the direct component is <0.043% at the 95% confidence level. This value is in agreement with several other studies, and, here, we can demonstrate that a small nonsequential component with a decay fraction of about 10 –4 is most likely. Here, the measurement of the non-sequential component of the Hoyle state decay is performed in an almost medium-free reaction for the first time. The derived upper limit is in agreement with previous studies and demonstrates sensitivity to the absolute branching ratio. Further experimental studies would need to be combined with robust microscopic theoretical understanding of the decay dynamics to provide additional insight into the idea of the Hoyle state as an α condensate.

6 ≤ A ≤ 19↗

Compressing branch-and-bound trees

A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same (or stronger) bound by either (1) applying a different disjunction at some node in T or (2) removing leaves from T? Here we believe such post-hoc analysis of BB trees may assist in identifying helpful general disjunctions in BB algorithms. We initiate our study by considering computational complexity and limitations of TCP. We then conduct experiments to evaluate the compressibility of realistic branch-and-bound trees generated by commonly-used branching strategies, using both an exact and a heuristic compression algorithm.

97 MATHEMATICS AND COMPUTING↗

Search for heavy neutral resonances decaying to tau lepton pairs in proton-proton collisions at $\sqrt{s}$=13 TeV

A search for heavy neutral gauge bosons (𝑍′) decaying into a pair of tau leptons is performed in proton-proton collisions at $\sqrt{s}$ =13 TeV at the CERN LHC. The data were collected with the CMS detector and correspond to an integrated luminosity of 138 fb −1 . The observations are found to be in agreement with the expectation from standard model processes. Limits at 95% confidence level are set on the product of the 𝑍′ production cross section and its branching fraction to tau lepton pairs for a range of 𝑍′ boson masses. For a narrow resonance in the sequential standard model scenario, a 𝑍′ boson with a mass below 3.5 TeV is excluded. This is the most stringent limit to date from this type of search.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Niobium in the clean limit: An intrinsic type-I superconductor

Niobium is one of the most researched superconductors, both theoretically and experimentally. It is enormously significant in all branches of superconducting applications, from powerful magnets to quantum computing. It is therefore imperative to understand its fundamental properties in great detail. In this work, we use the results of recent microscopic calculations of anisotropic electronic, phonon, and superconducting properties, and apply a thermodynamic criterion for the type of superconductivity, more accurate and straightforward than a conventional Ginzburg-Landau parameter κ-based delineation, to show that pure niobium is a type-I superconductor in the clean limit. However, disorder (impurities, defects, strain, stress) pushes it to become a type-II superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Search in diphoton and dielectron final states for displaced production of Higgs or Z bosons with the ATLAS detector in s = 13 TeV p p collisions

A search is presented for displaced production of Higgs bosons or Z bosons, originating from the decay of a neutral long-lived particle (LLP) and reconstructed in the decay modes H → γ γ and Z → ee . The analysis uses the full Run 2 dataset of proton-proton collisions delivered by the LHC at an energy of $\sqrt{s}$ = 13 TeV between 2015 and 2018 and recorded by the ATLAS detector, corresponding to an integrated luminosity of 139 fb -1 . Exploiting the capabilities of the ATLAS liquid argon calorimeter to precisely measure the arrival times and trajectories of electromagnetic objects, the analysis searches for the signature of pairs of photons or electrons which arise from a common displaced vertex and which arrive after some delay at the calorimeter. The results are interpreted in a gauge-mediated supersymmetry breaking model with pair-produced Higgsinos that decay to LLPs, and each LLP subsequently decays into either a Higgs boson or a Z boson. The final state includes at least two particles that escape direct detection, giving rise to missing transverse momentum. No significant excess is observed above the background expectation. The results are used to set upper limits on the cross section for Higgsino pair production, up to a $\bar{χ}^0_1$ mass of 369 (704) GeV for decays with 100% branching ratio of $\bar{χ}^0_1$ to Higgs (Z) bosons for a $\bar{χ}^0_1$ lifetime of 2 ns. A model-independent limit is also set on the production of pairs of photons or electrons with a significant delay in arrival at the calorimeter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for the doubly heavy baryons $ {{{{\varOmega}_{bc}^{0}}}} $ and $ {{{{\varXi}_{bc}^{0}}}} $ decaying to $ {{{{\varLambda}^+_c}}} {{{{\pi}^-}}} $ and $ {{{{\varXi}^+_c}}} {{{{\pi}^-}}} $ *

The first search for the doubly heavy $ {{{{\varOmega}_{bc}^{0}}}} $ baryon and a search for the $ {{{{\varXi}_{bc}^{0}}}} $ baryon are performed using $ pp $ collision data collected via the $ {\rm{LHCb}} $ experiment from 2016 to 2018 at a centre-of-mass energy of $ 13 \;{\rm{TeV}} $, corresponding to an integrated luminosity of 5.2 $ \;{\rm{f}}{{\rm{b}}^{ - 1}} $. The baryons are reconstructed via their decays to $ {{{{\varLambda}^+_c}}} {{{{\pi}^-}}} $ and $ {{{{\varXi}^+_c}}} {{{{\pi}^-}}} $. No significant excess is found for invariant masses between 6700 and 7300 $ \;{\rm{MeV}}/{c^2} $, in a rapidity range from 2.0 to 4.5 and a transverse momentum range from 2 to 20 $ \;{\rm{MeV}}/{c} $. Upper limits are set on the ratio of the $ {{{{\varOmega}_{bc}^{0}}}} $ and $ {{{{\varXi}_{bc}^{0}}}} $ production cross-section times the branching fraction to $ {{{{\varLambda}^+_c}}}{{{{\pi}^-}}} $ ( $ {{{{\varXi}^+_c}}}{{{{\pi}^-}}} $) relative to that of the $ {{{{\varLambda}^0_b}}} $ ( $ {{{{\varXi}_{b}^{0}}}} $) baryon, for different lifetime hypotheses, at 95% confidence level. The upper limits range from $ 0.5\times10^{-4} $ to $ 2.5\times10^{-4} $ for the $ {{{{{{{{\varOmega}_{bc}^{0}}}}{{\rightarrow }}{{{{\varLambda}^+_c}}}{{{{\pi}^-}}}}}}} $ ( $ {{{{{{{{\varXi}_{bc}^{0}}}}{{\rightarrow }}{{{{\varLambda}^+_c}}}{{{{\pi}^-}}}}}}} $) decay, and from $ 1.4\times10^{-3} $ to $ 6.9\times10^{-3} $ for the $ {{{{{{{{\varOmega}_{bc}^{0}}}}{{\rightarrow }}{{{{\varXi}^+_c}}}{{{{\pi}^-}}}}}}} $ ( $ {{{{{{{{\varXi}_{bc}^{0}}}}{{\rightarrow }}{{{{\varXi}^+_c}}}{{{{\pi}^-}}}}}}} $) decay, depending on the considered mass and lifetime of the $ {{{{\varOmega}_{bc}^{0}}}} $ ( $ {{{{\varXi}_{bc}^{0}}}} $) baryon.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for light pseudoscalar boson pairs produced from Higgs boson decays using the 4τ and 2μ2τ final states in proton-proton collisions at $\sqrt{s}=13$ TeV

A search for a pair of light pseudoscalar bosons (a 1 ) produced in the decay of the 125 GeV Higgs boson is presented. The analysis examines decay modes where one a 1 decays into a pair of tau leptons and the other decays into either another pair of tau leptons or a pair of muons. The a1 boson mass probed in this study ranges from 4 to 15 GeV. The data sample was recorded by the CMS experiment in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponds to an integrated luminosity of 138 fb −1 . No excess above standard model (SM) expectations is observed. The study combines the 4τ and 2μ2τ channels to set upper limits at 95% confidence level (CL) on the product of the Higgs boson production cross section and the branching fraction to the 4τ final state, relative to the Higgs boson production cross section predicted by the SM. In this interpretation, the a 1 boson is assumed to have Yukawa-like couplings to fermions, with coupling strengths proportional to the respective fermion masses. The observed (expected) upper limits range between 0.007 (0.011) and 0.079 (0.066) across the mass range considered. The results are also interpreted in the context of models with two Higgs doublets and an additional complex singlet field (2HD+S). The tightest constraints are obtained for the Type III 2HD+S model. In this case, assuming the Higgs boson production cross section equals the SM prediction, values of the branching ratio for the Higgs boson decay into a pair of a1 bosons exceeding 16% are excluded at 95% CL for a1 boson masses between 5 and 15 GeV and tan β > 2, with the exception of scenarios in which the a1 boson mixes with charm or bottom quark-antiquark bound states.

Higgs physics↗

Uranium Immobility in Tims Branch Wetland

The objective of this study was to address an item identified by the Low-Level Waste Disposal Facility Federal Review Group (LFRG) panel during their review of the Savannah River Site’s Composite Analysis. Their concern was that the Tims Branch wetland, which has elevated levels of uranium (U) originating from site operations between 1952 to 1985, may be a secondary source term, posing a human health risk. This report briefly describes three studies dealing with: 1) quantifying the mass of U remaining in the wetland, 2) quantifying the tendency of U to release from Tims Branch sediment, and 3) describing the distribution of U in aqueous and suspended solids in Tims Branch water during episodic storm events. The Tims Branch wetland has been extremely effective for the last 50 years at immobilizing U released to the system. A detailed map including 270,000 gamma spectra of the U distribution in the wetland indicated that 84% of the initial 43,500 kg U introduced in the system remain there after 50 years (Kaplan et al., 2020). The effectiveness of immobilizing U is supported by stream water measurements collected over the last several decades indicating that U concentrations have been consistently below drinking water regulatory limits (i.e., the EPA Maximum Contaminant Level, 30 pg/L (SRNS, 2019)). Furthermore, using contaminated Tims Branch sediments, in situ desorption Kd values (ratio of U sediment/U Water) were extremely high, ranging from 104to 106 L/kg, suggesting the U is strongly bound to these wetland sediments. Finally, a detailed study of Tims Branch stream water properties during episodic rain events indicated that essentially all the U transported in this stream was associated with suspended solids (Batson et al., 1996). Together these findings indicate that the Tims Branch wetland is extremely effective in its present state at immobilizing U and that the small masses of U released downstream will be predominantly in association with suspended solids.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗