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Interference Between Diffraction And Transmission In The Mie Extinction Efficiency, James A. Lock, Leiming Yang Jul 1991

Interference Between Diffraction And Transmission In The Mie Extinction Efficiency, James A. Lock, Leiming Yang

Physics Faculty Publications

We give simple analytic and numerical demonstrations showing that the interference structure in the Mie extinction efficiency of a sphere is caused by the interference of the light waves that are diffracted and transmitted in the near-forward direction.


Crystal Field Splitting And Charge Flow In The Buckled-Dimer Reconstruction Of Si(100)—2× 1, G. K. Wertheim, D. Mark Riffe, J. E. Rowe, P. H. Citrin Jul 1991

Crystal Field Splitting And Charge Flow In The Buckled-Dimer Reconstruction Of Si(100)—2× 1, G. K. Wertheim, D. Mark Riffe, J. E. Rowe, P. H. Citrin

All Physics Faculty Publications

The effect of the 2×1 reconstruction on the core-electron binding energies of the outermost Si(100) layers has been determined using high-resolution photoemission data. A previously unobserved 190-meV crystal-field splitting is resolved for the up-atoms of the asymmetric surface dimers, whose average core-level shift is -400 meV. The signal from the down-atoms is clearly identified and has a shift of +220 meV. These new findings indicate a charge flow of ∼0.05e from the subsurface to the surface layers, with a substantially larger difference of ∼0.34e between the up-atoms and down-atoms in the dimer.


Near-Infrared Imaging Of Hydroxyl Wave Structure Over An Ocean Site At Low Latitudes, Michael J. Taylor, M. J. Hill Jul 1991

Near-Infrared Imaging Of Hydroxyl Wave Structure Over An Ocean Site At Low Latitudes, Michael J. Taylor, M. J. Hill

All Physics Faculty Publications

Coordinated observations of wave structure in the near infrared hydroxyl (OH) nightglow emission have been made from Maui, Hawaii using a suite of narrow angle and all‐sky TV cameras. Two sets of data were obtained, the first in conjunction with the ALOHA‐90 campaign and the second during the subsequent new moon period. Well formed, short period (<20 min) wave patterns of comparable morphology, dynamics and abundance to those regularly imaged from mid‐latitude mountain sites were detected on several occasions. Although the Hawaiian islands comprise several high volcanic peaks, the patterns were not consistent with gravity waves generated by the interaction of strong winds with the local island topography. This suggests that other mid‐latitude wave patterns may also not be of mountain origin. The wave patterns imaged during ALOHA‐90 were of significantly lower contrast than those detected later. This effect may be related to changes in the characteristics of the middle atmosphere that occur shortly after the spring equinox.


Infrared Quenching And Thermal Recovery Of Thermally Stimulated Current Spectra In Gaas, Z-Q. Fang, David C. Look Jul 1991

Infrared Quenching And Thermal Recovery Of Thermally Stimulated Current Spectra In Gaas, Z-Q. Fang, David C. Look

Physics Faculty Publications

Thermally stimulated current (TSC) spectra stimulated by infrared (hν≤1.12 eV) light at 90 K have been used to study the photoquenching and thermal recovery of several dominant TSC peaks in Ga‐rich, semi‐insulating GaAs. The filling‐pulse‐length dependence of the quenching for these traps, and the temperature dependence of their recovery are clearly identified with the ground‐to‐metastable state transition of EL2. The data are consistent with the traps having a direct association with EL2 or EL2∗ rather than an indirect association which could result from a change in the dominant‐free carriers as EL2 transforms to EL2∗. If so, they likely …


Dielectronic Recombination On And Electron-Impact Excitation Of Heliumlike Argon, Rami M. Ali, Chander P. Bhalla, C. Lewis Cocke, Michael Schulz, Martin P. Stockli Jul 1991

Dielectronic Recombination On And Electron-Impact Excitation Of Heliumlike Argon, Rami M. Ali, Chander P. Bhalla, C. Lewis Cocke, Michael Schulz, Martin P. Stockli

Physics Faculty Research & Creative Works

We have measured cross sections for Δn=1 dielectronic recombination (DR) on He-like argon and found good agreement with theoretical calculations based on the Hartree-Fock atomic model. Experimental absolute cross sections were obtained by using the electron-energy dependence of yields of He-like and Li-like argon ions from the Kansas State University electron-beam ion source to measure the ratio of the DR cross section on He-like argon to the electron-impact-ionization cross section of Li-like argon and normalizing to the latter. The K x-ray emission spectra due to Δn=1,2 DR and n=1→2 electron-impact excitation of He-like argon were also observed with a Si(Li) …


Study Of The Effect Of Relativistic Time Dilation On Cosmic Ray Muon Flux - Undergraduate Modern Physics Experiment, Nalini Easwar, Douglas A. Macintire Jul 1991

Study Of The Effect Of Relativistic Time Dilation On Cosmic Ray Muon Flux - Undergraduate Modern Physics Experiment, Nalini Easwar, Douglas A. Macintire

Physics: Faculty Publications

An experiment to study the effect of relativistic time dilation on secondary muon fluxes observed at different altitudes is described in this article. Muons, produced as secondary particles from the interaction of primary cosmic rays with the upper atmosphere, form a natural and abundant source of subatomic ``clocks'' moving at very high speeds. The measured muon flux on a mountain relative to that measured at sea level can be compared to predictions from calculations that take into account the relativistic time dilation in the muon frame. Situations under which such an experiment can be successfully performed are explored with a …


Angular Distribution Of Electrons Following Two-Photon Ionization Of The Ar Atom And Two-Photon Detachment Of The F- Ion, Cheng Pan, Anthony F. Starace Jul 1991

Angular Distribution Of Electrons Following Two-Photon Ionization Of The Ar Atom And Two-Photon Detachment Of The F- Ion, Cheng Pan, Anthony F. Starace

Anthony F. Starace Publications

Angular-distribution asymmetry parameters for photoelectrons produced by two-photon ionization of the Ar atom and two-photon detachment of the F- ion are calculated for photon energies below the thresholds for single-photon ionization and single-photon detachment, respectively. Effects of electron correlations are included by perturbative methods. Good agreement is obtained between our results and those of a recent experimental angular-distribution measurement of two-photon detachment of the F- ion at λ=532 nm [C. Blondel, M. Crance, C. Delsart, and A. Giraud (unpublished)].


On Shock Capturing For Liquid And Gas Media, Tze Jang Chen Jul 1991

On Shock Capturing For Liquid And Gas Media, Tze Jang Chen

Mathematics & Statistics Theses & Dissertations

The numerical investigation of shock phenomena in gas or liquid media where a specifying relation for internal energy is absent poses special problems. Classically, for gas dynamics the usual procedure is to employ a splitting scheme to remove the source terms from the Euler equations, then up-wind biased shock capturing algorithms are built around the Riemann problem for the system which remains. However, in the case where the Euler equations are formulated in the term of total enthalpy, a technical difficulty associated with equation splitting forces a pressure time derivative to be treated as a source term. This makes it …


Application Of Sensitivity Analysis To The Euler Equations, Vamshi Mohan Korivi Jul 1991

Application Of Sensitivity Analysis To The Euler Equations, Vamshi Mohan Korivi

Mechanical & Aerospace Engineering Theses & Dissertations

An approximation method is presented for efficiently predicting the changes which occur in a steady-state numerical solution of the Euler equations as a consequence of a small change in the geometric shape of the domain. The method is extended to develop a general procedure for calculating aerodynamic sensitivity derivatives with respect to variations of geometric shape. The techniques are implemented using an upwind cell centered finite volume formulation, and are applied to two test cases, (1) a subsonic nozzle (M∞ = 0.85), and (2) a supersonic inlet (M∞ = 2.0). Conventional numerical solutions are first obtained for flow …


Computer Simulations Of Quasilattice Models For Novel Ferroelectric Liquid Crystals, Rolfe G. Petschek Jun 1991

Computer Simulations Of Quasilattice Models For Novel Ferroelectric Liquid Crystals, Rolfe G. Petschek

Faculty Scholarship

It has been suggested that ferroelectric smectic phases may be formed by fraternal-twin liquid-crystal molecules, consisting of two very different mesogens bonded together by an appropriate spacer [R. G. Petschek and K. M. Wiefling, Phys. Rev. Lett. 59, 343 (1987)]. We discuss the range in which these ferroelectric phases appear in a Monte Carlo simulation of a simple computer model for such mesogens. The mesogens consist of two identical flexible segments that are bonded to two rigid segments with very different lengths which, in turn, are bonded together by a flexible segment. In the computer model these monomers can move …


Dynamics Of The Nematic-Electroclinic Effect, Rajesh Ambigapathy, Rolfe G. Petschek, Charles Rosenblatt Jun 1991

Dynamics Of The Nematic-Electroclinic Effect, Rajesh Ambigapathy, Rolfe G. Petschek, Charles Rosenblatt

Faculty Scholarship

The effective response time eff of the nematic-electroclinic effect was determined as a function of driving frequency and temperature. Near the nematicsmectic-A transition temperature TNSm-A, eff was found to be a function of driving frequency, indicating the existence of more than one physical process. Several degrees above TNSm-A, eff was found to be frequency independent up to 100 kHz. At these temperatures, moreover, the effective response times are quite small, of order 100 ns.


Investigation Of Real-Time Optical Scanning Holography, Bradley D. Duncan Jun 1991

Investigation Of Real-Time Optical Scanning Holography, Bradley D. Duncan

Electro-Optics and Photonics Faculty Publications

Real-time holographic recording using an optical heterodyne scanning technique was proposed by Poon in 1985. The first part of this dissertation provides a detailed theoretical treatment of the technique, based on a Gaussian beam analysis. Topics to be addressed include the derivations of the optical transfer function (OTF) and impulse response of the scanning holographic recording system, reconstructed image resolution and magnification, methods of carrier frequency hologram generation and experimental verification of the recording technique based on careful measurements of a hologram corresponding to a simple transmissive slit. Furthermore, computer simulations are presented pertaining to the incoherent nature of the …


Ulf Waves In The Low‐Latitude Boundary Layer And Their Relationship To Magnetospheric Pulsations: A Multisatellite Observation, K. Takahashi, D. G. Sibeck, P. T. Newell, Harlan E. Spence Jun 1991

Ulf Waves In The Low‐Latitude Boundary Layer And Their Relationship To Magnetospheric Pulsations: A Multisatellite Observation, K. Takahashi, D. G. Sibeck, P. T. Newell, Harlan E. Spence

Physics & Astronomy

On April 30 (day 120), 1985, the magnetosphere was compressed at 0923 UT and the subsolar magnetopause remained near 7 REgeocentric for ∼2 hours, during which the four spacecraft Spacecraft Charging At High Altitude (SCATHA), GOES 5, GOES 6, and Active Magnetospheric Particle Tracer Explorers (AMPTE) CCE were all in the magnetosphere on the morning side. SCATHA was in the low-latitude boundary layer (LLBL) in the second half of this period. The interplanetary magnetic field was inferred to be northward from the characteristics of precipitating particle fluxes as observed by the low-altitude satellite Defense Meteorological Satellite Program (DMSP) F7 and …


One- And Two-Photon Detachment Of H- With Excitation Of H(N=2), Chih-Ray Liu, Ning-Yu Du, Anthony F. Starace Jun 1991

One- And Two-Photon Detachment Of H- With Excitation Of H(N=2), Chih-Ray Liu, Ning-Yu Du, Anthony F. Starace

Anthony F. Starace Publications

The cross sections for one- and two-photon detachment of H- with excitation of the degenerate H(2s) and H(2p) levels are calculated within an adiabatic hyperspherical representation. Both the partial cross sections, σ(2s) and σ(2s), and the photoelectron angular distribution asymmetry parameters are obtained. Our one-photon detachment results are dominated by the 1P0 shape resonance feature above threshold, which is well known from prior theoretical and experimental work, with which our results are compared in detail. Our two-photon detachment cross sections and angular distribution asymmetry parameters exhibit a half-cycle of dipole-field-induced …


Onset Of Convection For Autocatalytic Reaction Fronts: Laterally Bounded Systems, D. A. Vasquez, Boyd F. Edwards, J. W. Wilder Jun 1991

Onset Of Convection For Autocatalytic Reaction Fronts: Laterally Bounded Systems, D. A. Vasquez, Boyd F. Edwards, J. W. Wilder

All Physics Faculty Publications

Linear hydrodynamics yields the onset of convection for ascending autocatalytic reaction fronts in laterally bounded geometries. The system is studied in the limit of infinite and zero thermal diffusivity. For convection in a vertical slab of thickness a or a long vertical cylinder of radius a, the appropriate dimensionless driving parameter scrS=δga3/νDc involves the fractional density difference δ between the unreacted and reacted fluids, the acceleration of gravity g, the kinematic viscosity ν, and the catalyst molecular diffusivity Dc. Calculated critical values scrSc for onset of convection agree with recent experiments on iodate–arsenous acid …


On-Wafer Hall-Effect Measurement System, P. D. Mumford, David C. Look Jun 1991

On-Wafer Hall-Effect Measurement System, P. D. Mumford, David C. Look

Physics Faculty Publications

A novel system capable of making on‐wafer Hall‐effect measurements of a patterned wafer during the fabrication sequence has been developed. A flat, powerful rare‐earth magnet provides the magnetic field required. The wafer need only have van der Pauw patterns available for on‐wafer measurement capability. Measurement of room temperature Hall mobility can quickly and easily be obtained, making possible detailed study of carrier concentration and mobility variations during wafer fabrication.


Comparison Of Deep Centers In Semiinsulating Liquid-Encapsulated Czochralski And Vertical-Gradient Freeze Gaas, Z-Q. Fang, David C. Look Jun 1991

Comparison Of Deep Centers In Semiinsulating Liquid-Encapsulated Czochralski And Vertical-Gradient Freeze Gaas, Z-Q. Fang, David C. Look

Physics Faculty Publications

Three‐inch, semi‐insulating (SI) GaAs, grown by the vertical gradient freeze (VGF) technique, has been studied by IR absorption, temperature‐dependent dark current and Hall‐effect, thermally stimulated current (TSC), and photoinduced current transient spectroscopy and has been compared with undoped, SI GaAs, both As‐rich and Ga‐rich, grown by the high‐pressure liquid‐encapsulated Czochralski method. The results clearly indicate that (1) the VGF GaAs contains less EL2, which suggests a less As‐rich crystal stoichiometry; (2) in some VGF samples activation energies of 0.43 or 0.46 eV are deduced from temperature‐dependent carrier concentration or resistivity measurements, respectively, and (3) VGF samples often show a thermal …


Double Ionization Of Helium By Intermediate To High Velocity He+ Projectiles, Jun Forest Jun 1991

Double Ionization Of Helium By Intermediate To High Velocity He+ Projectiles, Jun Forest

Masters Theses

Ionization of helium target atoms by He+ projectiles colliding with helium at energies of 0.125 to 3.0 MeV/u is investigated. Cross sections for single and double ionization, and ratios o f double-to-single ionization are determined for each outgoing projectile charge state, and are compared to previous studies. For the lowest energies investigated, the ratios are consistent with the two-step mechanism in which the projectile interacts separately with each target electron. At the highest energies, the ratios reach nearly constant values indicating approach to the high velocity limit. At these high energies, however, the ratios are all higher than the …


A Valence Quark Model, Tony A. Forest Jun 1991

A Valence Quark Model, Tony A. Forest

Masters Theses

A quark model of the baryons has been developed for calculating properties of nucleons which can be useful in nuclear interactions. A Hamiltonian, motivated by QCD, was diagonalized in a harmonic oscillator basis. In addition to predicting the proton charge radius and Delta-Nucleon mass difference, this work also yields a value of the axial vector coupling constant which compares well with experiment. Electric and magnetic form factors represent the major success of this model. The electromagnetic transitions predicted by this model compete well with other models but are not able to reproduce experimental results completely. The advantage of this model …


Resonant Electron Transfer And K-Shell Excitation Of FQ+ (Q=6,8) In Collisions With Neutral He And H2 Targets, Konstantinos E. Zaharakis Jun 1991

Resonant Electron Transfer And K-Shell Excitation Of FQ+ (Q=6,8) In Collisions With Neutral He And H2 Targets, Konstantinos E. Zaharakis

Masters Theses

Measurements of resonant transfer and excitation (RTE) were conducted for 16.5-38 MeV F6+ (Li-like) ions colliding with H2. In the RTE process electron capture and projectile excitation take place simultaneously due to the electronelectron interaction. In previous work, for the same collision system, at the Oak Ridge National Laboratory (Oak Ridge, TN) , the magnitude of the measured RTE cross sections was found to be nearly a factor of two smaller than theory. In order to investigate RTE in F6+ H2 collisions more completely, we undertook measurements at Western Michigan University using the EN tandem …


Fock-Tani Hamiltonian For Reactions Involving Two-Electron Atoms, Jack C. Straton Jun 1991

Fock-Tani Hamiltonian For Reactions Involving Two-Electron Atoms, Jack C. Straton

Physics Faculty Publications and Presentations

The Fock-Tani Hamiltonian is found for scattering processes involving up to two ions and two electrons. Possible bound-state species include one or two electrons bound on an ion fixed at the origin, and a one-electron projectile atom. A diagrammatic technique is illustrated that simplifies the algebra of the transformation. Coulomb- or plane-wave states are automatically generated by the same asymptotic Hamiltonian for all arrangement channels.


Behavior Of An Ion In A Bubble In The Ground State, Joung Hoon Oh May 1991

Behavior Of An Ion In A Bubble In The Ground State, Joung Hoon Oh

Dissertations and Theses

Deuterons might be trapped in a bubble embryo which occur s due to statistical fluctuation in heavy water. The size of the bubble embryo is expected to be an order of a small molecule. The ground state energy level which the deuteron may occupy in the bubble is calculated by solving the Schroedinger equation, and by considering the interaction between the trapped deuteron by a spherical bubble and the surrounding polarized liquid medium (heavy water). From the dependence of the energy eigenvalue of the ground state on the bubble radius, the pressure exerted on the bubble wall is obtained. It …


The Dimension Of A Chaotic Attractor, Roslyn Gay Lindquist May 1991

The Dimension Of A Chaotic Attractor, Roslyn Gay Lindquist

Dissertations and Theses

Tools to explore chaos are as far away as a personal computer or a pocket calculator. A few lines of simple equations in BASIC produce fantastic graphic displays. In the following computer experiment, the dimension of a strange attractor is found by three algorithms; Shaw's, Grassberger-Procaccia's and Guckenheimer's. The programs were tested on the Henon attractor which has a known fractal dimension. Shaw's and Guckenheimer's algorithms were tested with 1000 data points, and Grassberger's with 100 points, a data set easily handled by a PC in one hour or less using BASIC or any other language restricted to 640K RAM. …


Abnormal Behaviour Of Zero Degree Δ-Electron Emission On The Projectile Ionic Charge, O. Jagutzkit, S. Hagtnanni, H. Schmidt-Bockingt, Ronald E. Olson, D. R. Schultz, R. Dornert, R. Kocht, A. Skutlartz, A. González, T. B. Quinterosi, C. Kelbcht, P. Richardt May 1991

Abnormal Behaviour Of Zero Degree Δ-Electron Emission On The Projectile Ionic Charge, O. Jagutzkit, S. Hagtnanni, H. Schmidt-Bockingt, Ronald E. Olson, D. R. Schultz, R. Dornert, R. Kocht, A. Skutlartz, A. González, T. B. Quinterosi, C. Kelbcht, P. Richardt

Physics Faculty Research & Creative Works

The 0° δ-electron emission was investigated by an electron-projectile coincidence technique as a function of incoming and outgoing projectile charge state for 0.53 MeV u-1Cuq+ on He. The electron emission spectra vary strongly with initial and final projectile charge state. For pure ionization channels the cross sections follow for low electron energy the q2-scaling law whereas in the binary encounter regime the scaling is reversed. Ctmc calculations are in fair agreement with the experimental data. © 1991 IOP Publishing Ltd.


Selective Decay And Coherent Vortices In Two-Dimensional Incompressible Turbulence, William H. Matthaeus, W. Troy Stribling, Daniel Martinez, Sean Oughton, David Montgomery May 1991

Selective Decay And Coherent Vortices In Two-Dimensional Incompressible Turbulence, William H. Matthaeus, W. Troy Stribling, Daniel Martinez, Sean Oughton, David Montgomery

Dartmouth Scholarship

Numerical solution of two-dimensional incompressible hydrodynamics shows that states of a near-minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the late-time similarity of the streamlines to Ewald potential contours.


Anisotropic, Time-Dependent Solutions In Maximally Gauss-Bonnet Extended Gravity, T. Kitaura, James Thomas Wheeler May 1991

Anisotropic, Time-Dependent Solutions In Maximally Gauss-Bonnet Extended Gravity, T. Kitaura, James Thomas Wheeler

All Physics Faculty Publications

In an arbitrary number of dimensions, we find the full exact anisotropic, time-dependent, diagonal-metric solutions to maximally Gauss-Bonnet extended gravity theory. This class of theories, for which the lagrangian is an arbitrary linear combination of dimensionally extended Euler forms, is the most general gravitational theory in which the field equations contain no more than second derivatives of the metric.

We show that the space-time exponentially approaches an asymptotic state of constant, anisotropic curvature and prove three theorems concerning two generic types of singularities. The first theorem gives conditions for the existence of Kasner-like curvature singularities. For these the metric diverges …


Comment On “Microdosimetry And Katz’S Track Structure Theory” By Marco Zaider, Robert Katz May 1991

Comment On “Microdosimetry And Katz’S Track Structure Theory” By Marco Zaider, Robert Katz

Robert Katz Publications

To test radiobiological models one needs data from X- or γ-ray and HZE track segment irradiations of the widest possible dynamic range in dose, LET, end points, and test objects (enzymes, viruses, bacteria, cells, tissues, organs, and organisms). Some data are currently available. There are excellent data on the inactivation of dry enzymes and viruses which should serve as a test of every biophysical model. On many occasions Zaider has asserted the superiority of microdosimetric over track structure models, asserting that “radial dose distributions (on which track structure theory is based) are generally poor substitutes for exact microdosimetric distributions.” I …


Novel Methods For Deposition Of Boron Carbide Films, J. Mazurowski, S. Baral-Tosh, G. Ramseyer, J.T. Spencer, Yoon-Gi Kim, Peter A. Dowben May 1991

Novel Methods For Deposition Of Boron Carbide Films, J. Mazurowski, S. Baral-Tosh, G. Ramseyer, J.T. Spencer, Yoon-Gi Kim, Peter A. Dowben

Peter Dowben Publications

By combining pentaborane (B5H9) and decarborane (B10H14) with methane in a plasma reactor, a variety of boron-carbides can be made over a wide range of compositions. The resulting thin films have uniform composition and appear to be polycrystalline.


Thermal Desorption Of Hg Monolayers From Cu(100), Y.J. Kime, Jiandi Zhang, Peter A. Dowben May 1991

Thermal Desorption Of Hg Monolayers From Cu(100), Y.J. Kime, Jiandi Zhang, Peter A. Dowben

Peter Dowben Publications

A two dimensional phase transition from one adlayer structure to another is an inherent part of the thermal desorption of one monolayer of Hg on Cu(100). The energetics of this phase transition have been studied using thermal desorption spectroscopy (TDS). The TDS spectra reflect the coexistence of the two structural phases for a range of Hg exposures. The TDS spectra have been analyzed within a Polanyi-Wigner framework modified to account for the phase transition.


Population Of Highly Excited Intermediate Resonance States By Electron Transfer And Excitation, Reinhold S. Schuch, Edson L B Justiniano, Michael Schulz, Sheldon Datz, Peter F. Dittner, J. P. Giese, Herbert F. Krause, Harald Schone, Charles Randy Vane, Stephen M. Shafroth May 1991

Population Of Highly Excited Intermediate Resonance States By Electron Transfer And Excitation, Reinhold S. Schuch, Edson L B Justiniano, Michael Schulz, Sheldon Datz, Peter F. Dittner, J. P. Giese, Herbert F. Krause, Harald Schone, Charles Randy Vane, Stephen M. Shafroth

Physics Faculty Research & Creative Works

Coincidences between two sulfur K x rays were detected from collisions of hydrogenlike S ions with H2 gas in the projectile energy range between 150 and 225 MeV. These K x rays are emitted in the decay of doubly excited states formed in the collisions via transfer and excitation. The excitation function for two coincident Kβ transitions peaks at about 175 MeV, slightly above the expected KMM resonance energy for resonant transfer and excitation (RTE). This demonstrates the occurrence of ΔN≥2 transitions (i.e., KMM and higher resonances) in the RTE process. The cross sections for the population of the …