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At least 397 records · Page 22

Combined visualisation of cavitation and vortical structures in a real-size optical diesel injector

A high-speed flow visualisation set-up comprising of combined diffuse backlight illumination (DBI) and schlieren imaging has been developed to illustrate the highly transient, two-phase flow arising in a real-size optical fuel injector. The different illumination nature of the two techniques, diffuse and parallel light respectively, allows for the capturing of refractive-index gradients due to the presence of both interfaces and density gradients within the orifice. Hence, the onset of cavitation and secondary-flow motion within the sac and injector hole can be concurrently visualised. Experiments were conducted utilising a diesel injector fitted with a single-hole transparent tip (ECN spray D) at injection pressures of 700–900 bar and ambient pressures in the range of 1–20 bar. High-speed DBI images obtained at 100,000 fps revealed that the orifice, due to its tapered layout, is mildly cavitating with relatively constant cavity sheets arising mainly in regions of manufacturing imperfections. Nevertheless, schlieren images obtained at the same frame rate demonstrated that a multitude of vortices with short lifetimes arise at different scales in the sac and nozzle regions during the entire duration of the injection cycle but the vortices do not necessarily result in phase change. The magnitude and exact location of coherent vortical structures have a measurable influence on the dynamics of the spray emerging downstream the injector outlet, leading to distinct differences in the variation of its cone angle depending on the injection and ambient pressures examined.

42 ENGINEERING↗

Galaxy Clusters Selected via the Sunyaev–Zel’dovich Effect in the SPTpol 100-square-degree Survey

In this work, we present a catalog of galaxy cluster candidates detected in 100 square degrees surveyed with the SPTpol receiver on the South Pole Telescope. The catalog contains 89 candidates detected with a signal-to-noise ratio greater than 4.6. The candidates are selected using the Sunyaev–Zel'dovich effect at 95 and 150 GHz. Using both space- and ground-based optical and infrared telescopes, we have confirmed 81 candidates as galaxy clusters. We use these follow-up images and archival images to estimate photometric redshifts for 66 galaxy clusters and spectroscopic observations to obtain redshifts for 13 systems. An additional two galaxy clusters are confirmed using the overdensity of near-infrared galaxies only and are presented without redshifts. We find that 15 candidates (18% of the total sample) are at redshift z ≥ 1.0, with a maximum confirmed redshift of ${z}_{\max }=1.38\pm 0.10$. We expect this catalog to contain every galaxy cluster with ${M}_{500c}\gt 2.6\times {10}^{14}{M}_{\odot }{{h}}_{70}^{-1}$ and z > 0.25 in the survey area. The mass threshold is approximately constant above z = 0.25, and the complete catalog has a median mass of approximately ${M}_{500c}=2.7\times {10}^{14}{M}_{\odot }{{h}}_{70}^{-1}$. Compared to previous SPT works, the increased depth of the millimeter-wave data (11.2 and 6.5 μK-arcmin at 95 and 150 GHz, respectively) makes it possible to find more galaxy clusters at high redshift and lower mass.

79 ASTRONOMY AND ASTROPHYSICS↗

Confirming X-ray Parametric Down Conversion by Time-Energy Correlation

We present measurements of X-ray Parametric Down Conversion at the Advanced Photon Source synchrotron facility. Using an incoming pump beam at 22 keV, we observe the simultaneous, elastic emission of down-converted photon pairs generated in a diamond crystal. The pairs are detected using high count rate silicon drift detectors with low noise. Production by down-conversion is confirmed by measuring time-energy correlations in the detector signal, where photon pairs within an energy window ranging from 10 to 12 keV are only observed at short time differences. By systematically varying the crystal misalignment and detector positions, we obtain results that are consistent with the constant total of the down-converted signal. Our maximum rate of observed pairs was 130 /hour, corresponding to a conversion efficiency for the down-conversion process of 5.3±0.5×10 -13 .

47 OTHER INSTRUMENTATION↗

High-sensitivity electronic Stark spectrometer featuring a laser-driven light source

We report developmental details of a high-sensitivity Stark absorption spectrometer featuring a laser-driven light source. The light source exhibits intensity fluctuations of ~0.3% over timescales ranging from 1 min to 12 h, minimal drift (≤0.1%/h), and very little 1/f noise at frequencies greater than 200 Hz, which are comparable to or better than an arc-driven light source. Additional features of the spectrometer include balanced detection with multiplex sampling, which yielded lower noise in A, and constant wavelength or wavenumber (energy) spectral bandpass modes. We achieve noise amplitudes of ~7 × 10 –4 and ~6 × 10 –6 in measurements of single A and ΔA spectra (with 92 data points) taking ~7 and ~19 min, respectively.

47 OTHER INSTRUMENTATION↗

Using Strain in the Vadose Zone During Sinusoidal-Rate Well Tests to Characterize an Aquifer

Well tests with sinusoidal variation in pumping rate are appealing because of the ability to filter competing signals and they also can be set up with no net removal of water, which is an advantage at contaminated sites. Current methods of interpreting sinusoidal-rate well tests analyze the phase lag and amplitude of pressure signals in the aquifer. This approach is restricted by the availability of monitoring wells. An alternative approach could be to measure the stain in the vadose zone instead of pressure in the aquifer. The goal of this research is to evaluate the feasibility of using signals from in-situ sensors in the vadose zone to characterize sinusoidal-rate well tests. Well tests with a variety of periods and amplitudes were performed using a well completed in an unconfined saprolite aquifer with a water table at 9m depth at our test site near Clemson, South Carolina. Vertical strain was measured every meter between 1 to 7 m using a distributed optical fiber sensing technique called coherence length gated microwave photonics interferometry (CMPI). A novel packaging system was designed to couple the optical fiber to the saprolite. The results show that strain measured in the vadose zone during sinusoidal-rate pumping varies periodically with amplitudes from 0.1 to 3 microstrain, depending on the amplitude of the sinusoidal pumping rate. Hydraulic heads at similar radial distances were also periodic with changing amplitudes ranging up to ±0.2 meters. The strain in the vadose zone responds to pressure in the underlying aquifer—the strain is tensile when the pressure is falling, and compressive when the pressure is rising. The phase lag between the pumping rate and the strain was 3 min with a pumping period of 15 minutes, and this gives a hydraulic diffusivity of 0.06 m2/s. This is the same diffusivity obtained by analyzing a constant rate pumping test, and it is slightly larger than the diffusivity (0.044 m2/s) obtained by analyzing the phase lag of the pressure in a nearby monitoring well. Strain measurements in the vadose zone could be made with much less cost and effort than installing a deep monitoring well. These results suggest that strain measurements in the vadose zone could be used to supplement monitoring wells, thereby increasing the resolution, and reducing costs of analyzing well tests.

well test, sinusoidal, periodic pumping, strain↗

Symmetric Bloch oscillations of matter waves

Cold atoms in an optical lattice provide an ideal platform for studying Bloch oscillations. Here we extend Bloch oscillations to two superposed optical lattices that are accelerated away from one another, and show that these symmetric Bloch oscillations can split, reflect, and recombine matter waves coherently. Using the momentum parity symmetry of the Hamiltonian, we map out the energy band structure of the process and show that superpositions of momentum states are created by adiabatically following the ground state of the Hamiltonian. The relative phase and velocity of the two lattices completely determines the trajectories of different branches of the matter wave. Experimentally we demonstrate symmetric Bloch oscillations using cold cesium atoms where we form interferometers with up to 240ℏk momentum splitting, one of the largest coherent momentum splittings achieved to date. This work has applications in macroscopic tests of quantum mechanics, measurements of fundamental constants, and searches for new physics.

36 MATERIALS SCIENCE↗

Design of experiments to spectroscopically characterize radiation flow in stochastic media

Precise characterization of experimental radiation flow is required to validate the high energy density physics models, numerical methods, and codes that are used to simulate radiation-hydrodynamics phenomena such as thermal radiation transport in stochastic media. The Cassio code is used to simulate thermal radiation flow through inhomogeneous, stochastic-media-foam configurations containing optically thick clumps dispersed within an optically thin background aerogel. Cassio can model small inhomogeneous problems directly, but most problems require approximations to meet computer limitations on run-times and memory usage. Various examples of these approximations are methods that produce, in one calculation, an ensemble-averaged solution and associated standard deviation; reduced spatial dimensionality with approximate geometries; and full material homogenization with no geometric detail. Cassio simulations are used to design experiments at the OMEGA-60 Laser Facility that can measure the radiation flow using the spatially resolved COAX absorption spectroscopy diagnostic. The experimental platforms flow radiation through foam targets ranging from a background-only aerogel, to a single configuration of a specified stochastic medium, to a fully homogenized foam of the background and clump materials. Under constant total clump mass, larger clumps (here, larger than 10 μm diameter) will mix more slowly with the background such that the bulk radiation flow is faster than it would be in a fully homogenized material. The COAX platform can be used to infer temperature and density profiles in both the background material and clumps, simultaneously, and therefore to differentiate radiation flow in a range of stochastic and homogeneous media.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Synthesis of a series of rare-earth-based multi-anion chalcogenide iodides RE 3 Si 2 Se x S 8− x I (RE = La, Ce, Pr, and Nd) using the flux-assisted boron–chalcogen mixture method

Single crystals and polycrystalline powders of rare earth mixed chalcogenide iodides La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, Pr 3 Si 2 Se 1.22 S 6.78 I, and Nd 3 Si 2 Se 1.18 S 6.82 I were prepared using the reactive flux-assisted boron–chalcogen mixture (BCM) method at 850 °C. All compounds crystallized in the monoclinic crystal system, space group C2/c (space group number 15). The series adopts the La 3 Si 2 O 8 Cl structure type, containing isolated SiQ 4 tetrahedra connected by REQ 8 (RE = La, Ce, Pr and Nd) polyhedra; this arrangement creates tunnels that are filled by I atoms. The partial substitution of S by Se was carried out to modulate the optical properties. Phase pure samples and uniform solid solutions were obtained for all compositions as determined using powder X-ray diffraction patterns. Polycrystalline powders were used for physical property measurements, including magnetic susceptibility and UV-Vis diffuse reflectance. The solid-state UV-Vis data for the polycrystalline La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, and Pr 3 Si 2 Se 1.22 S 6.78 I samples revealed band gaps of E g = 2.5(1), 2.2(1), and 2.3(1) eV, typical of semiconductors. Magnetic measurements indicated that Ce 3 Si 2 Se 1.39 S 6.61 I and Nd 3 Si 2 Se 1.18 S 6.82 I exhibit paramagnetic behavior with slightly negative Weiss constants θ = −25 and −38. The photoluminescence spectrum of Ce 3 Si 2 Se 1.39 S 6.61 I exhibits a broad emission band around ∼493 nm.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lattice dynamics of high-pressure hydrides studied by inelastic neutron scattering

Due to the small mass and anomalously large neutron scattering cross-section of proton (about 80 barns compared to a few barns for other nuclei), inelastic neutron scattering is considered as one of the most effective tools in studying optical vibrations of hydrogen atoms in metal hydrides. The current review is focused on the binary hydrides of 3d- and 4d-metals of groups VI–VIII, which were produced at high hydrogen pressures of several gigapascals in relatively large quantities of hundreds of mg, quenched to low temperature and studied by INS ex situ at ambient pressure with high statistical accuracy. One of the unusual effects revealed by INS is a strong increase in the strength of the metal-hydrogen interactions with decreasing atomic number of the d-metal accompanied by an increase in the Me-H distance. Based on the available experimental results, the spectra g(E) of the phonon density of states and temperature dependencies CV(T) of the heat capacity at constant volume at T up to 1000 K have been derived in this paper and presented both in the figures and in digital form. This provides the reference data for the theoretical investigations of the crystal structures and compositions of new practically important hydrides giving the opportunity to validate calculation methods by comparing the calculated g(E) and CV(T) with the accurate experimental dependencies for the binary hydrides. Recent INS studies showed [R.A. Klein et al., J. Alloy. Compd. 894 (2022) 162381] that the fingerprints of anomalously short H-H separations of 1.6 Å violating the “2 Å rule” can be easily and unambiguously identified in the complex INS spectra of quaternary hydrides (La,Ce)NiInH 1+x . This makes neutron spectroscopy an attractive means for obtaining valuable data in the search for novel hydrides with a record high hydrogen capacity.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Electrochemical Switching of a Fluorescent Molecular Rotor Embedded within a Bistable Rotaxane

We report how the nanoconfined environment, introduced by the mechanical bonds within an electrochemically switchable bistable [2]rotaxane, controls the rotation of a fluorescent molecular rotor, namely, an 8-phenyl-substituted boron dipyrromethene (BODIPY). The electrochemical switching of the bistable [2]rotaxane induces changes in the ground-state coconformation and in the corresponding excited-state properties of the BODIPY rotor. In the starting redox state, when no external potential is applied, the cyclobis(paraquat-p-phenylene) (CBPQT4+) ring component encircles the tetrathiafulvalene (TTF) unit on the dumbbell component, leaving the BODIPY rotor unhindered and exhibiting low fluorescence. Upon oxidation of the TTF unit to a TTF2+ dication, the CBPQT4+ ring is forced toward the molecular rotor, leading to an increased energy barrier for the excited state to rotate the rotor into the state with a high nonradiative rate constant, resulting in an overall 3.4-fold fluorescence enhancement. On the other hand, when the solvent polarity is high enough to stabilize the excited charge-transfer state between the BODIPY rotor and the CBPQT4+ ring, movement of the ring toward the BODIPY rotor produces an unexpectedly strong fluorescence signal decrease as the result of photoinduced electron transfer from the BODIPY rotor to the CBPQT4+ ring. The nanoconfinement effect introduced by mechanical bonding can effectively lead to modulation of the physicochemical properties as observed in this bistable [2]rotaxane. On account of the straightforward synthetic strategy and the facile modulation of switchable electrochromic behavior, our approach could pave the way for the development of new stimuli-responsive materials based on mechanically interlocked molecules for future electro-optical applications, such as sensors, molecular memories, and molecular logic gates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Giant topological longitudinal circular photo-galvanic effect in the chiral multifold semimetal CoSi

The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light’s polarization, known as the circular photo-galvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material parameters and the incident frequency. In this work, we perform terahertz emission spectroscopy with tunable photon energy from 0.2 –1.1 eV in the chiral topological semimetal CoSi. We identify a large longitudinal photocurrent peaked at 0.4 eV reaching ~550 μ A/V 2 , which is much larger than the photocurrent in any chiral crystal reported in the literature. Using first-principles calculations we establish that the peak originates only from topological band crossings, reaching 3.3 ± 0.3 in units of the quantization constant. Our calculations indicate that the quantized circular photo-galvanic effect is within reach in CoSi upon doping and increase of the hot-carrier lifetime. The large photo-conductivity suggests that topological semimetals could potentially be used as novel mid-infrared detectors.

79 ASTRONOMY AND ASTROPHYSICS↗

Possibilistic simulation of quantum circuits by classical circuits

In a breakthrough work, Bravyi, Gosset, and König (BGK) [Science 362, 308 (2018)] unconditionally proved that constant-depth quantum circuits are more powerful than their classical counterparts. Here, their result is equivalent to saying that a particular family of constant-depth quantum circuits takes classical circuits at least Ω⁡(log⁡n) depth to “simulate,” in a certain sense. In our paper, we formalize their sense of simulation, which we call “possibilistic simulation” or “p-simulation,” and construct explicit classical circuits that can p-simulate any depth-d quantum circuit with Clifford and t T-gates in depth O(d+t). Our classical circuits use {NOT,AND,OR} gates of fan-in ≤ 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Many-Body Signatures of Collective Decay in Atomic Chains

Fully inverted atoms placed at exactly the same location synchronize as they deexcite, and light is emitted in a burst (known as “Dicke’s superradiance”). We investigate the role of finite interatomic separation on correlated decay in mesoscopic chains and provide an understanding in terms of collective jump operators. We show that the superradiant burst survives at small distances, despite Hamiltonian dipole-dipole interactions. However, for larger separations, competition between different jump operators leads to dephasing, suppressing superradiance. Collective effects are still significant for arrays with lattice constants of the order of a wavelength, and lead to a photon emission rate that decays nonexponentially in time. We calculate the two-photon correlation function and demonstrate that emission is correlated and directional, as well as sensitive to small changes in the interatomic distance. Furthermore, these features can be measured in current experimental setups, and are robust to realistic imperfections.

74 ATOMIC AND MOLECULAR PHYSICS↗

Influence of pilot-fuel mixing on the spatio-temporal progression of two-stage autoignition of diesel-sprays in low-reactivity ambient fuel-air mixture

The spatial and temporal locations of autoignition for direct-injection compression-ignition engines depend on fuel chemistry, temperature, pressure, and mixing trajectories in the fuel jets. Dual-fuel systems can provide insight into both fuel-chemistry and physical effects by varying fuel reactivities and engine operating conditions. In this context, the spatial and temporal progression of two-stage autoignition of a diesel-fuel surrogate, n-heptane, in a lean-premixed charge of synthetic natural-gas (NG) and air is imaged in an optically accessible heavy-duty diesel engine. The lean-premixed charge of NG is prepared by fumigation upstream of the engine intake manifold. Optical diagnostics include high-speed (15kfps) cool-flame chemiluminescence-imaging as an indicator of low-temperature heat-release (LTHR) and OH* chemiluminescence-imaging as an indicator high-temperature heat-release (HTHR). NG prolongs the ignition delay of the pilot fuel and increases the combustion duration. Zero-dimensional chemical-kinetics simulations provide further understanding by replicating a Lagrangian perspective for mixtures evolving along streamlines originating either at the fuel nozzle or in the ambient gas, for which the pilot-fuel concentration is either decreasing or increasing, respectively. The zero-dimensional simulations predict that LTHR initiates most likely on the air streamlines before transitioning to HTHR, either on fuel-streamlines or on air-streamlines in regions of near-constant φ. Due to the relatively short pilot-fuel injection-durations, the transient increase in entrainment near the end of injection (entrainment wave) is important for quickly creating auto-ignitable mixtures. To achieve desired combustion characteristics, e.g., multiple ignition-kernels and favorable combustion phasing and location (e.g., for reducing wall heat-transfer or optimizing charge stratification), adjusting injection parameters could tailor mixing trajectories to offset changes in fuel ignition chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transition metal dichalcogenide monolayers in an ultrashort optical pulse: Femtosecond currents and anisotropic electron dynamics

We theoretically study the interaction of an ultrafast intense linearly polarized optical pulse with monolayers of transition metal dichalcogenides (TMDCs). Such a strong pulse redistributes electrons between the bands and generates femtosecond currents during the pulse. Due to the large bandwidth of the incident pulse, this process is completely an off-resonant. While in TMDCs, the time-reversal symmetry is conserved, the inversion symmetry is broken, and these monolayers have axial symmetry along the armchair direction but not along with the zigzag one. The pulse, polarized along with asymmetric directions of TMDC monolayer, generates both longitudinal, i.e., along the direction of polarization, and transverse, i.e., in the perpendicular direction, currents. Such currents result in charge transfer through the system. Finally, we study different TMDC materials and show how the femtosecond transport in TMDC monolayers depend on their parameters, such as lattice constant and bandgap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Investigating the large-scale environment of wide-angle tailed radio galaxies in the local Universe

We present a statistical analysis of the large-scale (up to two Mpc) environment of a homogeneous and complete sample, both in radio and optical selection, of wide-angle tailed radio galaxies (WATs) in the local Universe (i.e., with redshifts z ≲ 0.15). The analysis is carried out using the parameters obtained from cosmological neighbors within two Mpc of the target source. Results regarding the large-scale environments of the WATs are then compared with those of Fanaroff–Riley type I (FR Is) and type II (FR IIs) radio galaxies listed in two other homogeneous and complete catalogs and selected with the same criterion adopted for the WATs catalog. We obtain indication that at low redshift, WATs inhabit environments with a larger number of galaxies than those of FR Is and FR IIs. In the explored redshift range, the physical size of the galaxy group or cluster in which the WATs reside appears to be almost constant with respect to FR Is and FR IIs, being around one Mpc. From the distribution of the concentration parameter, defined as the ratio between the number of cosmological neighbors lying within 500 kpc and within one Mpc, we conclude that WATs tend to inhabit the central region of the group or cluster in which they reside, in agreement with the general paradigm that WATs are the brightest cluster or group galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗

Distributed Real-time Plume Monitoring for Deep Sea Mineral Extraction​

In the emerging industry of deep-sea mining for minerals and deposits (e.g. polymetallic nodules for nickel, cobalt, copper, and manganese), more data is required to understand the effects of sediment plume generation and predict the distribution of disturbed sediment. There are two main sources of plume generation, the first being at the active mining site where the “collector” directly removes the top layer of the sea floor. The other is the “midwater plume” consisting of unwanted sediment that was collected during extraction that is pumped back into the aphotic zone. The vast majority of plume generation is caused by the collector, causing detrimental and long-lasting impacts on seafloor ecosystems due to the lack of wave activity or strong currents at the sea floor. Therefore, it is crucial to invest in the infrastructure to support the study and constant monitoring over a large area of the sea floor where plume generation is present. Due to the limited number of usable channels and power requirements, current subsea wireless communications technologies are not well suited to instrumenting the large areas of the sea floor needed to monitor plume migration. The scope of this effort is to transition experimental demonstrations of high-bandwidth, full-duplex scalable underwater laser communications to the seafloor in an open ocean environment. Specifically tackling challenges associated with the dynamic nature of the subsea world, including but not limited to, deployment logistics, sustainability, and range. The goal is to enable the internet of underwater things for deep sea industries by broadening the capabilities of subsea communications. By using high-precision laser transmitters, many of the challenges current subsea optical systems face can be circumvented, such as power consumption, interference, and bandwidth limitations. This approach lends itself to wireless interlinking multi-node networks, in series or parallel, facilitating the implementation of a wide array of sensor types. This interlinking allows all the data gathered from the network to be processed through a single hardline uplink to the surface, lowering the complexity required for near real-time data processing. Additionally, the laser control systems produce metadata that can be used to help characterize the water column between the nodes. Combining data from various sensors such as turbidity, temperature, current velocity with metadata such as beam attenuation and deflection can produce a high-resolution model of sea floor conditions around an active mining zone. The resulting near real-time model can be used to optimize location and flow rate of the mining operation to minimize and quantify the environmental impact.

Mons, Ishan↗

Exciton–Polaritons in CsPbBr 3 Crystals Revealed by Optical Reflectivity in High Magnetic Fields and Two-Photon Spectroscopy

Cesium lead bromide (CsPbBr3) is a representative material of the emerging class of lead halide perovskite semiconductors that possess remarkable optoelectronic properties. Its optical properties in the vicinity of the bandgap energy are greatly contributed by excitons, which form exciton polaritons due to strong light–matter interactions. Exciton–polaritons in solution-grown CsPbBr 3 crystals are examined by means of circularly polarized reflection spectroscopy measured in high magnetic fields up to 60 T. The excited 2P exciton state is measured by two-photon absorption. Comprehensive modeling and analysis provides detailed quantitative information about the exciton–polariton parameters: exciton binding energy of 32.5 meV, oscillator strength characterized by longitudinal–transverse splitting of 5.3 meV, damping of 6.7 meV, reduced exciton mass of 0.18$m$ 0 , exciton diamagnetic shift of 1.6 μeV T -2 , and exciton Landé factor $g$ x = + 2.35. It is shown that the exciton states can be described within a hydrogen-like model with an effective dielectric constant of 8.7. From the measured exciton longitudinal–transverse splitting, Kane energy of E p = 15 eV is evaluated, which is in reasonable agreement with values of 11.8–12.5 eV derived from the carrier effective masses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗