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At least 937 records · Page 52

Renormalons and power corrections in pseudo- and quasi-GPDs

High-order behavior of the perturbative expansion for short-distance observables in QCD is intimately related to the contributions of small momenta in the corresponding Feynman diagrams and this correspondence provides one with a useful tool to investigate power-suppressed nonperturbative corrections. We use this technique to study the structure of power corrections to parton quasi- and pseudo-GPDs which are used in lattice calculations of generalized parton distributions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-GPDs on x variable for nonzero skewedness parameter ξ . The kinematic point x = ± ξ turns out to be special. We find that the nonperturbative corrections to quasi-GPDs at this point are suppressed by the first power of the hard scale only. These contributions come from soft momenta and have nothing to do with the known UV renormalon in the Wilson line. We also show that power corrections can be strongly suppressed by the normalization procedure. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Nonperturbative aspects of the electromagnetic pion form factor at high energies

The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor.

Form factors↗

Specifications of FIPD Fission Gas Release Data

All fission gas release data stored in the Fuels Irradiation & Physics Database (FIPD) was originally measured using the Gas Assay, Sample and Recharge (GASR) System in the Hot Fuel Examination Facility (HFEF). It is therefore called GASR data in FIPD. During the measurement of a sample, such as an irradiated EBR-II fuel element/capsule, a pinhole-sized region near the top of the element plenum was melted by a laser. Plenum gas then expanded into a calibrated volume (note: in this document, “sample” and “capsule/element” are used interchangeably consistent with GASR documents in FIPD). The pressure rise in the volume was recorded. Helium backfilling and expansion was then performed to determine the sample (e.g., fuel element plenum) volume using Boyle’s Law and assuming ideal gas behavior at constant temperature. With the plenum volume and the recorded pressure rise, the sample (e.g., fuel element plenum) pressure was derived with assumption of ideal gas law behavior. The plenum volume and pressure as well as the cladding temperature during the measurement were collected (GASR data in FIPD). Other records associated with the fission gas release data include: raw GASR data records including volumes and post-puncture pressures of seal head/sealing head and manifold, calibration data, backfilling gas pressure data, and the data analysis records. A sample(s) of the fission gas released from the plenum was collected by the GASR system into sample bottles. The chemical and isotopic composition of the gas sample was analyzed separately from GASR data, and will be discussed in a separate specification. The plenum volume, pressure, and cladding temperature during the measurement are typically utilized to determine the number of moles of gas in the plenum. This quantity is often compared to the number of moles of gas generated by fission events. However, calculating these values and their associated uncertainty is beyond the scope of this document, as it necessitates additional assumptions. The most important document to understand the FIPD fission gas data is the GASR operational manual (title: Gas Assay, Sample and Recharge System (GASR) operation and maintenance manual, HFEF/N OMM 4381, DOC. NO. W0018-0032-ES-00). This manual provides: (1) description of the GASR and the functions of each component (laser drilling, welding, seal head/sealing head, manifold, vacuum system, sample system, purge and gas tag system, etc.); (2) step-by-step guidance on calibrations, operations, and measurements; and (3) maintenance procedures and other details relating to the structure and operation of the GASR. Note that the original GASR operated until 2020. A new GASR with the same design and measurement methodology was installed in 2021. The specifications of the GASR presented on the HFEF website at this time are consistent with the ones given in the operational manual. The methods to calculate the plenum volume and pressures were not included in the operational manual, but were recorded in the legacy data analysis files. Details of the methods are given in Chapter 3.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Observation of the Charged-Particle Multiplicity Dependence of 𝜎 𝜓⁡(2⁢𝑆 )/𝜎 𝐽/𝜓 in 𝑝-Pb Collisions at 8.16 TeV

Bound states of charm and anticharm quarks, known as charmonia, have a rich spectroscopic structure that can be used to probe the dynamics of hadron production in high-energy hadron collisions. Here, the cross section ratio of excited (𝜓⁡(2⁢𝑆)) and ground state (𝐽/𝜓) vector mesons is measured as a function of the charged-particle multiplicity in proton-lead (𝑝⁢Pb) collisions at a center-of-mass (CM) energy per nucleon pair of 8.16 TeV. The data corresponding to an integrated luminosity of 175 nb −1 were collected using the CMS detector. The ratio is measured separately for prompt and nonprompt charmonia in the transverse momentum range 6.5 < 𝑝 T < 30 GeV and in four rapidity ranges spanning −2.865 < 𝑦 CM < 1.935. For the first time, a statistically significant multiplicity dependence of the prompt cross section ratio is observed in proton-nucleus collisions. There is no clear rapidity dependence in the ratio. The prompt measurements are compared with a theoretical model which includes interactions with nearby particles during the evolution of the system. These results provide additional constraints on hadronization models of heavy quarks in nuclear collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bespoke Liquid/Liquid Interfaces (Final Technical Report)

The goal of DE-SC0001815 was to advance the basic science of liquid:liquid interface formation, to develop a deeper understanding of the mechanisms of phase separation and the essential relationships between solution composition, organization and dynamics that underlie the kinetic regime of solvent extraction. This included learning how interfacial organization and dynamics alters the properties of the primary coordination sphere of ions and the free energy of transport of ions complexes across a phase boundary. We relied primarily upon classical molecular dynamics studies to determine the equilibrium ensembles of these complex systems, but also utilized ab-initio MD and cluster-based density functional theory (DFT) calculations when more detailed investigation of the electronic structure was needed. We continued development of graph-theory based analyses to elucidate hierarchical correlations and expanded into geometric topology methods to quantify the collectively organized structures that can organize at a liquid/liquid interface during solute transport. One of the main conclusions was from the observation of two distinct mechanisms for solute transport - those that derive from amplifications of interfacial heterogeneity and surface roughness, and those wherein surface roughness has been dampened and instead collectively organized macrostructures work to bring solutes into the organic phase. It was our aim to create a concrete chemical model of the underlying driving forces behind interfacial primary and secondary structure formation and to map out the energetic features of solute transport so that tailored liquid/liquid can be developed that have characteristic kinetic features associated with mass transport.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Theoretical study of the electronic, thermodynamic, and thermo-conductive properties of y-LiAlO2 with 6Li isotope substitutions for tritium production

Lithium aluminate has attracted researchers’ interests due to its wide applications. The structural, electronic, optical, lattice phonon thermodynamic, and thermo-conductive properties of ?-LiAlO2 with 6Li-isotope substitution are investigated by density functional theory and lattice phonon dynamics. The calculated results show that ?-LiAlO2 possesses a wide band-gap of 4.63 eV. The valence band is mainly formed by p orbitals of Li, O, and Al. The calculated lattice thermal conductivity of ?-LiAlO2 is found to be in good agreement over a wide range of temperatures with the available experimental data. The calculated dielectric matrix shows anisotropic behavior along z and x (or y) axes. Due to the wide band-gap, the optical conductivity of ?-LiAlO2 is mainly contributed from the electron hopping between valence-conduction bands. Substitution of 7Li with 6Li isotope in ?-LiAlO2 leads to observable differences in the lattice phonon frequencies at higher frequencies (>8THz) and to slight changes in corresponding thermal conductivity and the infrared and Raman spectra which are in good agreement with the measured data. The relevance of these properties for tritium production through 6Li absorbing neutron in nuclear reactors is discussed.

ab initio thermodynamics, ?-LiAlO2 and 6Li-isotope↗

Elucidating the Solvation Structures and Dynamics in Iron-Based TFSI – Aqueous Systems

This study investigates the solvation structures and dynamics of bis(trifluoromethanesulfonyl)imide (TFSI – )-based aqueous electrolytes, focusing on Fe(TFSI) 2 and Fe(TFSI) 3 . Using advanced characterization techniques, including small-angle X-ray scattering, molecular dynamics simulations, Raman spectroscopy, Fourier-transform infrared spectroscopy, and nuclear magnetic resonance, we elucidate how the electrolyte concentration influences ion association, solvation structures, and transport properties. Furthermore, our findings show that higher electrolyte concentrations promote the formation of contact ion pairs and anion networks, leading to reduced ion mobility and altered hydrogen-bonding dynamics. These insights provide a deeper understanding of solvation phenomena in TFSI-based electrolytes and contribute to the development of efficient and environmentally friendly iron electrodeposition processes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The Large Hadron–Electron Collider at the HL-LHC

The Large Hadron–Electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy-recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High-Luminosity Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron–proton and proton–proton operations. This report represents an update to the LHeC’s conceptual design report (CDR), published in 2012. It comprises new results on the parton structure of the proton and heavier nuclei, QCD dynamics, and electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics by extending the accessible kinematic range of lepton–nucleus scattering by several orders of magnitude. Due to its enhanced luminosity and large energy and the cleanliness of the final hadronic states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, this report contains a detailed updated design for the energy-recovery electron linac (ERL), including a new lattice, magnet and superconducting radio-frequency technology, and further components. Challenges of energy recovery are described, and the lower-energy, high-current, three-turn ERL facility, PERLE at Orsay, is presented, which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution, and calibration goals that arise from the Higgs and parton-density-function physics programmes. This paper also presents novel results for the Future Circular Collider in electron–hadron (FCC-eh) mode, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Correlation of Injury Simulation with Clinical Assessment of Traumatic Brain Injury

This report contains a summary of our efforts to correlate head injury simulations predicting intracranial fluid cavitation with clinical assessments of brain injury from blunt impact to the head. Magnetic resonance imaging (MRI) data, collected on traumatic brain injury (TBI) subjects by researchers at the MIND Institute of New Mexico, was acquired for the current work. Specific blunt impact TBI case histories were selected from the TBI data for further study and possible correlation with simulation. Both group and single-subject case histories were examined. We found one single-subject case that was particularly suited for correlation with simulation. Diffusion tensor image (DTI) analysis of the TBI subject identified white matter regions within the brain displaying reductions in fractional anisotropy (FA), an indicator of local damage to the white matter axonal structures. Analysis of functional magnetic resonance image (fMRI) data collected on this individual identified localized regions of the brain displaying hypoactivity, another indicator of brain injury. We conducted high fidelity simulations of head impact experienced by the TBI subject using the Sandia head-neck-torso model and the shock physics computer code CTH. Intracranial fluid cavitation predictions were compared with maps of DTI fractional anisotropy and fMRI hypoactivity to assess whether a possible correlation exists. The ultimate goal of this work is to assess whether one can correlate simulation predictions of intracranial fluid cavitation with the brain injured sites identified by the fMRI and DTI analyses. The outcome of this effort is described in this report.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Predicting magnetic properties of single-molecule magnets from self-interaction-free density-functional theory (Final Report)

In this project we investigated electronic structure of an intermediate-sized copper-based molecule and magnetic and hyperfine properties of several small non-magnetic and magnetic molecules including transition-metal elements by applying self-interaction corrections to density functional theory (DFT). In a sufficient number of cases, DFT-calculated electronic structure and magnetic properties of single-molecule magnets qualitatively differ from corresponding experimental data. This is partly due to self-interacting electrons within the DFT formalism. Recently, an efficient method to correct the self-interactions was proposed, i.e., Fermi-Lowdin prbital (FLO) based self-interaction corrected (SIC) methodology, within DFT. Henceforth, this method is referred to as FLO-SIC method which exists in FLOSIC code. We used this FLO-SIC method for our studies of electronic structure and magnetic and hyperfine properties of small magnetic molecules and non-magnetic molecules. Our study will provide insight into predictions of magnetic properties of single-molecule magnets where self-interaction corrections play a critical role. There are two components of this project. In the first work, we studied the electronic structure of a planar mononuclear Cu-based molecule in two oxidation states, using DFT with the FLO-SIC method. We chose this system because it is small enough and it includes a transition metal element. We found that the standard FLO-SIC method takes too much compute time even for the small transition-metal molecule and so we slightly modified the method in order to expedite the process. In the dianionic state, we found that the FLO-SIC spin density agrees quantitatively with accurate quantum chemistry methods, while DFT spin density without self-interaction corrections are severely deviated from the quantum chemistry methods. We also showed that the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the dianionic state is larger than that of the monoanionic state. This result is consistent with experimental data. In the second work, we investigated how the interaction between the electron spin and nuclear spin is affected by electron self-interactions within small non-magnetic and magnetic molecules. Such an interaction is called hyperfine interaction. For molecules without significant orbital angular momentum, the hyperfine interaction consists of Fermi contact and dipolar interaction terms. Since the Fermi contact term depends on electron spin density at the nuclear site, it would be highly affected by self-interaction corrections. Therefore, we calculated the hyperfine interaction for the small molecules using DFT with the slightly modified expedited FLO-SIC method which was obtained in the first work, and compared the results to experimental data and DFT calculations without self-interaction corrections. We found significant improvement of the Fermi contact term computed using the FLO-SIC method for small magnetic molecules. Overall, the first and second work provided positive outlook of application of the FLO-SIC method to magnetic molecules and systems including transition-metal elements.

36 MATERIALS SCIENCE↗

Electromagnetic properties of indium isotopes illuminate the doubly magic character of 100 Sn

Understanding the nuclear properties in the vicinity of 100 Sn, which has been suggested to be the heaviest doubly magic nucleus with proton number Z equal to neutron number N, has been a long-standing challenge for experimental and theoretical nuclear physics. In particular, contradictory experimental evidence exists regarding the role of nuclear collectivity in this region of the nuclear chart. Here, we provide further evidence for the doubly magic character of 100 Sn by measuring the ground-state electromagnetic moments and nuclear charge radii of indium (Z = 49) isotopes as N approaches 50 from above using precision laser spectroscopy. Our results span almost the complete range between the two major closed neutron shells at N = 50 and N = 82 and reveal parabolic trends as a function of the neutron number, with a clear reduction towards these two closed neutron shells. Furthermore, a detailed comparison between our experimental results and numerical results from two complementary nuclear many-body frameworks (density functional theory and ab initio methods) exposes deficiencies in nuclear models and establishes a benchmark for future theoretical developments.

100Sn↗

Quantum simulations of nuclear resonances with variational methods

Background: The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices. Purpose: This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator. Methods: We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform 𝜃-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray code (GC) encoding to reduce qubit requirements. Results: We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic 𝛼−𝛼 nuclear potential and compute the 𝐷- and 𝐺-wave resonance energies with a basis size of 𝑁=16, using only four qubits. The quantum simulation results closely match the classical values, demonstrating the feasibility of our approach. Conclusions: This study demonstrates, for the first time, that the complete 𝜃-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems and lays the foundation for future investigations into resonance structures in nuclear, atomic, and molecular physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High-Temperature Latent Heat Storage System using Transportable Heat Pipes for Versatile Integration with Emerging Microreactors

With the growing interest in the development of micro nuclear reactors and their application to microgrid, high-temperature thermal energy storage (TES) has also been receiving great attention as a technology to reinforce the energy utilization and profitability of this class of reactors. Given the importance and research needs of the TES technology, a research project is underway at Idaho National Laboratory (INL) to develop high-temperature TES that can be easily interfaced with emerging micro nuclear reactors. Currently under development is the Heat pipe-Integrated Thermal Battery (HITB), a novel latent heat storage design that enables flexible and robust integration with any design of currently considered micro nuclear reactors. The development of detailed design based on the proposed TES concept, HITB, requires not only development and validation of modeling and simulation capabilities, but also research that spans thermal performance analysis, component- and system-scale design optimization, and experimental demonstrations including high-temperature feasibility testing. The current research efforts (and plans) are divided into the following four areas: (i) Thermal and structural modeling and analysis at both system- and component-scales for evaluating performance and conducting design optimization, (ii) Small-scale experimental demonstrations for the key components of the proposed HITB design, (iii) Modelica-based dynamic model development for developing a control strategy under dynamic operation within integrated energy systems configuration, (iv) Integrated experimental testing and demonstration. This paper introduces the overall research efforts that have been and are being conducted to develop and demonstrate the novel design of the high-temperature latent heat storage device, HITB. The key design features, ongoing research efforts including the development of modeling and simulation capabilities, small-scale demonstrations of the HITB’s key functionalities prior to scaled-up experimental demonstration, are discussed. Then, this paper concludes with a remark on the future research plans for this project.

25 ENERGY STORAGE↗

Role of the isovector spin-orbit potential in mitigating the CREX-PREX dilemma

Pioneering electroweak measurements of the neutron skin thickness in lead-208 and calcium-48 are challenging our understanding of nuclear dynamics. Many theoretical models suggest that the slope of the symmetry energy controls the development of a neutron skin in neutron-rich nuclei. This led to the expectation that if lead-208 exhibits a large neutron skin, calcium-48 should as well. Given that the PREX Collaboration reported a relatively thick neutron skin in lead, we anticipated that calcium would also have a significant neutron skin. Instead, the CREX Collaboration reported a thin neutron skin in calcium. Although many suggestions have been proposed, the “CREX-PREX dilemma” remains unsolved. Recently, an intriguing scenario has emerged, suggesting that an enhanced isovector spin-orbit interaction could simultaneously account for both results. Following this approach, we performed relativistic mean-field calculations with an increased isovector spin-orbit potential. Our findings indicate that, while this modification significantly affects the structure of calcium-48, it has only a marginal impact on lead-208, thereby bringing the results into better agreement with experiment. Furthermore, the strong enhancement required to mitigate the CREX-PREX dilemma destroys the agreement with a successful spin-orbit phenomenology, primarily by modifying the well-known ordering of spin-orbit partners.

Neutron skin thickness↗

Robust ab initio prediction of nuclear electric quadrupole observables by scaling to the charge radius

Meaningful predictions for electric quadrupole (E2) observables from ab initio nuclear theory are necessary, if the ab initio description of collective correlations is to be confronted with experiment, as well as to provide predictive power for unknown E2 observables. However, converged results for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI) approaches. Matrix elements of the E2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion. Similar convergence challenges beset ab initio prediction of the nuclear charge radius. We demonstrate that the convergence patterns of the E2 and radius observables are strongly correlated, and that meaningful predictions for the absolute scale of E2 observables may be made by calibrating to the experimentally-known ground-state charge radius. Here, we illustrate by providing robust ab initio predictions for several E2 transition strengths and quadrupole moments in p-shell nuclei, in cases where experimental results are available for comparison.

6 ≤ A ≤ 19↗

Crystal growth, density functional theory, and scintillation properties of Tl 3 LnCl 6 :Ce 3+ and TlLn 2 Cl 7 :Ce 3+ (Ln = Y, Gd)

In this paper we report on the crystal growth, density functional theory (DFT) calculations and scintillation properties of Tl 3 LnCl 6 :Ce and TlLn 2 Cl 7 :Ce(Ln = Y, Gd). Crystals were grown by the Vertical Bridgman technique up to 16 mm in diameter and 25 mm long. Crystals of Tl 3 YCl 6 :Ce and Tl 3 GdCl 6 :Ce belong to the family of the Nesohalides which have the monoclinic crystal structure. Crystals of TlY 2 Cl 7 :Ce and TlGd 2 Cl 7 :Ce belong to the family of the Phyllohalides which have either the monoclinic or the orthorhombic crystal structure. We report the light yields of these Nesohalides and Phyllohalides are typically on the order of 35,000–40,000 ph/MeV.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Extraction of the worm-gear TMD g1t from COMPASS , HERMES and JLab data on semi-inclusive DIS

Transverse momentum dependent parton distributions (TMDs) are an important class of functions required to understand the 3D structure of hadrons in terms of their underlying partons. One of the least known TMDs in terms of a global QCD analysis is the worm-gear TMD g1t . It carries the probabilistic interpretation of finding longitudinally polarized quarks inside transversely polarized hadrons. In this proceedings, we present the first-ever global QCD analysis of the semi-inclusive DIS $A^ {cos(φ_h-φ_S)}_{LT}$ data using Monte Carlo techniques to extract the worm-gear TMD g1T . The relevant data are available from COMPASS, HERMES and JLab. We compare our results for g1T with different theoretical approaches, including the large-N c approximation, the Wandzura Wilczek-type approximation, and lattice QCD.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. Here, we recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗