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Full-Text Articles in Physics

Non-Hermitian Physics Achieved Via Non-Local Gilbert Damping, Trevor Joshua Macintosh Jan 2024

Non-Hermitian Physics Achieved Via Non-Local Gilbert Damping, Trevor Joshua Macintosh

Electronic Theses and Dissertations

In this thesis, we study a simple model for a ferromagnet starting with Heisenberg exchange interaction including the effects of dissipation. Gilbert damping is consid- ered and generalized from an on-site term to include non-local damping interactions between neighbouring spins. The strength of the damping interaction between neigh- bours can be tuned individually to provide the freedom to change the parameters of the system and explore the range of possible non-Hermitian behaviours. We consider the example of a honeycomb lattice ferromagnet featuring Dirac cones and two sub- lattices and analyse the resulting spectra and eigenstates. Under periodic boundary conditions, we …


Stimulated Raman Spectroscopy With Widely Tunable Probe Pulse For Measuring Dissolved Inorganic Phosphorus In The Great Lakes, Nathan Gregory Drouillard Jan 2024

Stimulated Raman Spectroscopy With Widely Tunable Probe Pulse For Measuring Dissolved Inorganic Phosphorus In The Great Lakes, Nathan Gregory Drouillard

Electronic Theses and Dissertations

The eutrophication of freshwater ecosystems remains a persistent global problem threatening biodiversity, drinking water, and economic interests. Among the Laurentian Great Lakes, Lake Erie is most severely impacted by eutrophication, experiencing annual harmful algal blooms that are thought to result from excess phosphate deposition into the ecosystem. Efforts to study and mitigate the effects of eutrophication require accurate monitoring of phosphate concentrations. The current method for measuring phosphate, the molybdenum blue method, suffers from signal interference. In this thesis, I recommend Raman spectroscopy as a label-free, reagent-free spectroscopic technique for accurately measuring phosphate in freshwater. I verify the Raman spectrum …


Single-Stage Few-Cycle Pulse Amplification, Sagnik Ghosh, Nathan G. Drouillard, Tj Hammond Jan 2024

Single-Stage Few-Cycle Pulse Amplification, Sagnik Ghosh, Nathan G. Drouillard, Tj Hammond

Physics Publications

Kerr instability can be exploited to amplify visible, near-infrared, and midinfrared ultrashort pulses. We use the results of Kerr instability amplification theory to inform our simulations amplifying few-cycle pulses. We show that the amplification angle dependence is simplified to the phase-matching condition of four-wave mixing when the intense pump is considered. Seeding with few-cycle pulses near the pump leads to broadband amplification without spatial chirp, while longer pulses undergo compression through amplification. Pumping in the midinfrared leads to multioctave spanning amplified pulses with single-cycle duration not previously predicted. We discuss limitations of the amplification process and optimizing pump and seed …


Electromagnetically Induced Transparency In An Ensemble Of Three-Level Lambda Systems, Sara Moezzi Sep 2023

Electromagnetically Induced Transparency In An Ensemble Of Three-Level Lambda Systems, Sara Moezzi

Electronic Theses and Dissertations

Electromagnetically induced transparency (EIT) is a technique whereby a medium otherwise opaque to radiation of a particular frequency can be made transparent at that frequency by applying radiation of an appropriate second frequency. EIT demonstrates numerous current applications, with a notable focus on its utilization within the field of quantum information. Given the absence of an established theory of EIT in atomic ensembles, my primary focus is to develop theoretical models that describe both the quantum mechanical origin of EIT as well as the effect of interatomic interactions. In this thesis, I present two theoretical models of EIT in an …


Detection And Diagnosis Of Bacterial Pathogens In Blood And Urine Using Laser-Induced Breakdown Spectroscopy, Emma J.M. Blanchette Jan 2023

Detection And Diagnosis Of Bacterial Pathogens In Blood And Urine Using Laser-Induced Breakdown Spectroscopy, Emma J.M. Blanchette

Electronic Theses and Dissertations

The aim of this thesis is to expand on and improve the existing techniques used for detecting and identifying bacterial pathogens in clinical specimens with laser-induced breakdown spectroscopy (LIBS). Specifically, the existing experimental procedures, including bacterial sample preparation and data acquisition, as well as the data analysis with chemometric algorithms were investigated. Substantial reductions in LIBS background signal were achieved by implementing rigorous cleaning steps and the introduction of the use of ultrapure water. Following this, a database of LIBS spectra was acquired from specimens of E. coli, S. aureus, E. cloacae, M. smegmatis, and P. …


Calculated Charge State Distributions And Anisotropies Following The Β-Decay Of 6he, Eva E. Sculhoff Feb 2022

Calculated Charge State Distributions And Anisotropies Following The Β-Decay Of 6he, Eva E. Sculhoff

Electronic Theses and Dissertations

According to the standard model the beta-decay of 6He is a pure Gamow-Teller transition. The aim of this thesis is to provide theoretical support in the search for new physics beyond the standard model by examining the angular distribution of beta particles following decay. The simple structure of 6He, along with its ability to under go beta-decay into 6Li+ makes it an ideal candidate for studying the weak force. Due to the sudden increase in nuclear charge from Z = 2 to Z = 3, and the recoil momentum of the daughter nucleus resulting from the emitted leptons, this decay …


Quantitative Magnetic Resonance Imaging Methodology Development, Layale Bazzi Feb 2022

Quantitative Magnetic Resonance Imaging Methodology Development, Layale Bazzi

Electronic Theses and Dissertations

Magnetic Resonance Imaging (MRI) is a non-invasive medical imaging modality that provides excellent soft tissue contrast and resolution. Objects with high magnetic susceptibility distort the magnetic field, leading to severe artifacts in conventional MRI. It is very challenging to image around metal implants. Novel strategies may exploit the field distortion for spatial encoding. The magnetic field map is required in the development of these methods. A robust field map can also be employed to quantify high susceptibility particles that play a major role in cell tracking studies and hyperthermic treatment of cancers.

Pure phase encoding (PPE) techniques with short encoding …


Simple Measurement For Ultrafast Field Reconstruction, Chathurangani Jayalath Arachchige Jan 2022

Simple Measurement For Ultrafast Field Reconstruction, Chathurangani Jayalath Arachchige

Electronic Theses and Dissertations

Ultrashort pulses are important for resolving electron motion in semiconductors to measure electronic transport properties. Electron wave packet motion is on the order of attoseconds, requiring temporal resolution on this time scale. However, a major constraint on femtosecond (1 fs = 10−15 s) and attosecond (1 as = 10−18 s) science is how well we can control and compress the excitation and measurement pulses in pump-probe experiments. Such ultrashort pulses require a broad spectrum with careful phase control across its bandwidth to minimize the duration. We discuss a new optical measurement technique that can directly measure the electric field that …


Spectral Broadening For Pulse Compression Using Liquid Alcohols, Jacob A. Stephen, Chathurangani J. Arachchige, Tj Hammond Jan 2022

Spectral Broadening For Pulse Compression Using Liquid Alcohols, Jacob A. Stephen, Chathurangani J. Arachchige, Tj Hammond

Physics Publications

Although gases, and more recently solids, have been used to create few-cycle pulses, we explore using liquid alcohols for spectral broadening and femtosecond pulse compression. By using a series of 1 cm cuvettes filled with 1-decanol, we have compressed a pulse from 83.6 fs down to 31.3 fs with a spectrum capable of supporting 25 fs pulses without filamentation.We measure the nonlinear index of refraction for various liquids, measuring n2 = (6.8 ± 0.5) × 10−20 m2 W−1 for 1-decanol.We demonstrate liquids to be a compact, simple, versatile, and cost-effective material to obtain broad spectra.


Measurement Of Dispersion And Index Of Refraction Of 1-Decanol With Spectrally Resolved White Light Interferometry, Nathan G. Drouillard, Tj Hammond Jan 2022

Measurement Of Dispersion And Index Of Refraction Of 1-Decanol With Spectrally Resolved White Light Interferometry, Nathan G. Drouillard, Tj Hammond

Physics Publications

The high density, high nonlinearity, and stability of liquids make them an attractive medium for spectral broadening and supercontinuum generation in ultrafast experiments. To understand ultrashort pulse propagation in these media, their indices of refraction and dispersions must be characterized. We employ a Mach-Zehnder interferometer to generate a series of interferograms, which we refer to as a spectrogram, to develop a new method of using spectrally resolved white light interferometry to determine the refractive indices of materials. We determine the indices of refraction of BK7, sapphire, ethanol, and 1-decanol at 24°C across the visible and near infrared. To our knowledge, …


Optimization Of An Ultrasonic Non-Destructive Evaluation Technique For Laser Brazing, Dimitri Shinas Jan 2022

Optimization Of An Ultrasonic Non-Destructive Evaluation Technique For Laser Brazing, Dimitri Shinas

Electronic Theses and Dissertations

Brazing joins two sheets along a seam using a filler metal. In the brazing process, the filler metal is heated, along with the parts to be joined, to a temperature above the melting temperature of the filler material. This allows the filler metal to wet the surfaces of the parts to be joined through capillary action, resulting in the formation of metallic bonds, ultimately forming the joint.

Brazing, like all joining methods, is also susceptible to process variations. These process variations can include wear of the laser, plate misalignment, and external temperature changes. If left unchecked, such variations can eventually …


Femtosecond Pulse Compression Via Self-Phase Modulation In 1-Decanol, Jacob A. Stephen Jan 2022

Femtosecond Pulse Compression Via Self-Phase Modulation In 1-Decanol, Jacob A. Stephen

Electronic Theses and Dissertations

Ultrafast science is a branch of photonics with far reaching applications in and outside the realm of physics. Ultrashort laser pulses on the order of femtoseconds (1 fs = 1 × 10−15 s) are widely used for ultrafast science. Many lasers can produce pulses on the order of 100 fs, with state of the art, high end lasers being capable of producing pulses around 30 fs. However, many experiments require pulses around 10 fs or shorter. Femtosecond pulses are typically generated using spectral broadening via self-phase modulation, followed by dispersion compensation. The most common spectral broadening technique exploits the nonlinear …


Variational Energies For The Rydberg P States Of Helium, Cody Mcleod Oct 2021

Variational Energies For The Rydberg P States Of Helium, Cody Mcleod

Electronic Theses and Dissertations

The aim of this work is to solve the quantum mechanical three-body problem for helium, and to obtain high precision eigenvalues for the higher-lying Rydberg states where previous methods have been of limited accuracy. A variational method in correlated Hylleraas coordinates is used involving three distinct distance scales, called a triple basis set. The eigenvalues and matrix elements of other operators are computed for P states of helium up to n = 15 using the varational method with a triple basis set in Hylleraas coordinates. The construction of the wave functions, as well as the behaviour of the asymptotic, intermediate …


A Simple And Efficient Centrifugation Filtration Method For Bacterial Concentration And Isolation Prior To Testing Liquid Specimens With Laser-Induced Breakdown Spectroscopy, Dylan J. Malenfanta, Alexandra E. Paulick, Steven J. Rehse Aug 2019

A Simple And Efficient Centrifugation Filtration Method For Bacterial Concentration And Isolation Prior To Testing Liquid Specimens With Laser-Induced Breakdown Spectroscopy, Dylan J. Malenfanta, Alexandra E. Paulick, Steven J. Rehse

Physics Publications

An inexpensive filtration device was designed and constructed to rapidly concentrate bacteria in a liquid suspension on the surface of a disposable filter medium while at the same time separating the bacterial cells from larger contaminants in the suspension on the basis of their size. The device consists of a two-stage insert that is held rigidly in a standard tube during bacterial suspension centrifugation. The filters can be easily removed from the insert for subsequent testing with laser-induced breakdown spectroscopy in a process that takes only three minutes. Filter media of 0.45 micron pore size was found to capture approximately …


Concentration Of Bacterial Specimens During Centrifugation Prior To Laser-Induced Breakdown Spectroscopy Analysis, Alexandra E. Paulicka, Dylan J. Malenfanta, Steven J. Rehse Jul 2019

Concentration Of Bacterial Specimens During Centrifugation Prior To Laser-Induced Breakdown Spectroscopy Analysis, Alexandra E. Paulicka, Dylan J. Malenfanta, Steven J. Rehse

Physics Publications

A metal cone device has been designed and fabricated for use with a custom centrifuge tube insert to allow the simple and rapid concentration of bacterial cells in a circular area with a diameter of 1 mm. The device concentrates cells suspended in up to 1 mL of liquid at the center of a highly flat disposable filter medium which can be easily removed from the centrifuge tube insert for subsequent testing with laser-induced breakdown spectroscopy. Two-dimensional elemental mapping of the filter evidenced a high concentration of bacteria on the filter under the location of the cone hole, as well …


A Review Of The Use Of Laser-Induced Breakdown Spectroscopy For Bacterial Classification, Quantification, And Identification, Steven J. Rehse Apr 2019

A Review Of The Use Of Laser-Induced Breakdown Spectroscopy For Bacterial Classification, Quantification, And Identification, Steven J. Rehse

Physics Publications

The use of laser-induced breakdown spectroscopy to determine the elemental composition of bacterial cells has been described in the peer-reviewed literature since 2003. Fifteen years on, significant accomplishments have been reported that have served to clarify and underscore the areas of bacteriological investigation that LIBS is well-suited for as well as the challenges that yet remain to be faced. This review will attempt to summarize the state of the field by surveying the available body of knowledge. The early days of these experiments, roughly from 2003 to 2007, in which many of the most fundamental experiments were initially conducted will …


Helium Tune-Out Wavelength: Gauge Invariance And Retardation Corrections, Gordon W. F. Drake, Jacob Gabriel Manalo, Pei-Pei Zhang, Kenneth George Herbert Baldwin Mar 2019

Helium Tune-Out Wavelength: Gauge Invariance And Retardation Corrections, Gordon W. F. Drake, Jacob Gabriel Manalo, Pei-Pei Zhang, Kenneth George Herbert Baldwin

Physics Publications

The problem of calculating the tune-out wavelength for an atom interacting with a plane electromagnetic wave is formulated as a zero in the Rayleigh scattering cross section, rather than a zero in the dynamic polarizability. Retardation (finite wavelength) corrections are discussed in the velocity gauge, and possible gauge transformations to a length form are investigated. For the special case of S-states, it is shown that a pure length form exists for the leading pxz retardation correction, even though one does not exist in general. The results of high-precision calculations in Hylleraas coordinates are presented for the tune-out wavelength of …


N (2p) Production In Electron-N2 Collisions, Wladyslaw Kedzierski, Jeff Dech, J. W. Mcconkey Oct 2017

N (2p) Production In Electron-N2 Collisions, Wladyslaw Kedzierski, Jeff Dech, J. W. Mcconkey

Physics Publications

A unique detector which is selectively sensitive to low energy metastable atoms, has been used to study the production of ground state N (2P) atoms following collisions of low energy (0-200 eV) electrons with molecular nitrogen. TOF techniques have revealed the existence of at least two distinct mechanisms yielding this dissociation product. Released kinetic energies in the dissociation have allowed positioning of the parent molecular states in the Franck-Condon region. This has allowed probable parent states, such as B' 3Σu¯, b' 1Σu+ and C' 3Πu, to be identified making use of recent theoretical calculations. Both direct and predissociation processes are …


Determination Of The Zinc Concentration In Human Fingernails By Laser-Induced Breakdown Spectroscopy, Steven J. Rehse, Vlora A. Riberdy, Christopher J. Frederickson Apr 2017

Determination Of The Zinc Concentration In Human Fingernails By Laser-Induced Breakdown Spectroscopy, Steven J. Rehse, Vlora A. Riberdy, Christopher J. Frederickson

Physics Publications

The absolute concentration of zinc in human fingernail clippings tested ex vivo was determined by 1064 nm laser-induced breakdown spectroscopy and confirmed by speciated isotope dilution mass spectrometry. A nail testing protocol that sampled across the nail (perpendicular to the direction of growth) was developed and validated by scanning electron microscopy energy dispersive x-ray spectroscopy. Using this protocol, a partial least squares regression model predicted the zinc concentration in five subjects’ fingernails to within 7 ppm on average. The variation of the zinc concentration with depth into the nail as determined by laser-induced breakdown spectroscopy was studied and found to …


Use Of Solid N2 Surfaces In Metastable Particle Detection, Wladyslaw Kedzierski, J. W. Mcconkey Dec 2016

Use Of Solid N2 Surfaces In Metastable Particle Detection, Wladyslaw Kedzierski, J. W. Mcconkey

Physics Publications

A novel detector is described in which solid nitrogen at 17 K is used as the most significant element. Metastable particles impinge on this element and immediately transfer their internal energy to the solid nitrogen producing photons, via excimer formation or otherwise, whose wavelength depends on the metastable being detected and the energy transfer process. The performance of the instrument for the detection of atomic oxygen and molecular nitrogen metastables is discussed.


Selective Detection Of Singlet Gerade Metastable States Of N-2, Wladyslaw Kedzierski, J. W. Mcconkey Jul 2016

Selective Detection Of Singlet Gerade Metastable States Of N-2, Wladyslaw Kedzierski, J. W. Mcconkey

Physics Publications

Metastable N-2 molecules produced by electron impact on N2 are detected using a unique solid nitrogen matrix detector. The time-of-flight system is shown to be selectively sensitive to a(1)Pi(g) and (1)Sigma(+)(g) or (1)Gamma(g) metastable species. The latter species had been identified theoretically previously but was detected experimentally for the first time in the present investigation. Their identification and excitation as a function of electron energy from threshold to 300 eV are presented. Comparison is made with the data obtained by other techniques. Published by AIP Publishing.


Vuv Study Of Electron Impact Dissociative Excitation Of Thymine, C. J. Tiessen, J. A. Trocchi, J. D. Hein, J. Dech, Wladyslaw Kedzierski, J. W. Mcconkey May 2016

Vuv Study Of Electron Impact Dissociative Excitation Of Thymine, C. J. Tiessen, J. A. Trocchi, J. D. Hein, J. Dech, Wladyslaw Kedzierski, J. W. Mcconkey

Physics Publications

Dissociative excitation of thymine following electron impact was studied in the energy range up to 430 eV. Emissions in the vacuum ultra-violet spectral region below 150 nm were studied and found to be dominated by the hydrogen Lyman series. Emission cross section data reveal that Lyman-α excitation displays a broad maximum at an electron impact energy of 160 eV. The probability of extracting other excited atoms from the parent molecule is found to be insignificant. Possible excitation and dissociation mechanisms in the parent molecule are discussed.


Modern Study Of Environmental Pollution From The Emission Of Alpha Particles In Human Blood Samples In The City Of Najaf, Iraq, Basim A. Almayahi Aug 2015

Modern Study Of Environmental Pollution From The Emission Of Alpha Particles In Human Blood Samples In The City Of Najaf, Iraq, Basim A. Almayahi

21st International Conference on Environmental Indicators (ICEI 2015)

No abstract provided.


Advances In Atomic, Molecular, And Optical Physics, J. W. Mcconkey, Wladyslaw Kedzierski Jan 2014

Advances In Atomic, Molecular, And Optical Physics, J. W. Mcconkey, Wladyslaw Kedzierski

Physics Publications

The use of rare gas matrices for the detection of a variety of low-energy metastable species, particularly those from atoms with an np4 outer electron configuration, is discussed in detail. The historical development of the detector is outlined and its performance as a function of rare gas, matrix temperature, and metastable species is discussed. Examples of its use are given for electron impact dissociation of a wide variety of oxygen and sulfur containing targets.


Production Of O(1d) Following Electron Impact On Co2, Wladyslaw Kedzierski, J. D. Hein, C. J. Tiessen, D. Lukic, J. A. Trocchi, T. Z. Mlinaric, J. W. Mcconkey Jul 2013

Production Of O(1d) Following Electron Impact On Co2, Wladyslaw Kedzierski, J. D. Hein, C. J. Tiessen, D. Lukic, J. A. Trocchi, T. Z. Mlinaric, J. W. Mcconkey

Physics Publications

We have studied the excitation of metastable O(1D) following dissociative excitation of CO2 in the electron impact energy range from threshold to 400 eV. A solid Ne matrix at ∼20 K forms the heart of the detector. This is sensitive to the metastable species through the formation of excited excimers (NeO*), The resultant excimer radiation is readily detected, providing a means of measuring the production of the metastables. Using a pulsed electron beam and time-of-flight techniques, we have measured the O(1D) kinetic energy spectrum and its relative production cross sections as a function of electron …


Sensitive And Specific Discrimination Of Pathogenic And Nonpathogenic Escherichia Coli Using Raman Spectroscopy - A Comparison Of Two Multivariate Analysis Techniques, Steven Rehse, Khozima Hamasha, Qassem I. Mohaidat, Russell A. Putnam, Ryan C. Woodman, Sunil Palchaudhuri Jan 2013

Sensitive And Specific Discrimination Of Pathogenic And Nonpathogenic Escherichia Coli Using Raman Spectroscopy - A Comparison Of Two Multivariate Analysis Techniques, Steven Rehse, Khozima Hamasha, Qassem I. Mohaidat, Russell A. Putnam, Ryan C. Woodman, Sunil Palchaudhuri

Physics Publications

The determination of bacterial identity at the strain level is still a complex and time-consuming endeavor. In this study, visible wavelength spontaneous Raman spectroscopy has been used for the discrimination of four closely related Escherichia coli strains: pathogenic enterohemorrhagic E. coli O157:H7 and non-pathogenic E. coli C, E. coli Hfr K-12, and E. coli HF4714. Raman spectra from 600 to 2000 cm-1 were analyzed with two multivariate chemometric techniques, principal component-discriminant function analysis and partial least squares-discriminant analysis, to determine optimal parameters for the discrimination of pathogenic E. coli from the non-pathogenic strains. Spectral preprocessing techniques such as smoothing with …


A Comparison Of Multivariate Analysis Techniques And Variable Selection Strategies In A Laser-Induced Breakdown Spectroscopy Bacterial Classification, Russell Putnam, Q.I. Mohaidat, Andrew Daabous, Steven Rehse Jan 2013

A Comparison Of Multivariate Analysis Techniques And Variable Selection Strategies In A Laser-Induced Breakdown Spectroscopy Bacterial Classification, Russell Putnam, Q.I. Mohaidat, Andrew Daabous, Steven Rehse

Physics Publications

Laser-induced breakdown spectroscopy has been used to obtain spectral fingerprints from live bacterial specimens from thirteen distinct taxonomic bacterial classes representative of five bacterial genera. By taking sums, ratios, and complex ratios of measured atomic emission line intensities three unique sets of independent variables (models) were constructed to determine which choice of independent variables provided optimal genuslevel classification of unknown specimens utilizing a discriminant function analysis. A model composed of 80 independent variables constructed from simple and complex ratios of the measured emission line intensities was found to provide the greatest sensitivity and specificity. This model was then used in …


Pathogen Identification With Laser-Induced Breakdown Spectroscopy: The Effect Of Bacterial And Biofluid Specimen Contamination, Q.I. Mohaidat, K. Sheikh, S. Palchaudhuri, Steven J. Rehse Jan 2012

Pathogen Identification With Laser-Induced Breakdown Spectroscopy: The Effect Of Bacterial And Biofluid Specimen Contamination, Q.I. Mohaidat, K. Sheikh, S. Palchaudhuri, Steven J. Rehse

Physics Publications

In this paper, the potential use of laser-induced breakdown spectroscopy (LIBS) for the rapid discrimination and identification of bacterial pathogens in realistic clinical specimens is investigated. Specifically, the common problem of sample contamination was studied by creating mixed samples to investigate the effect that the presence of a second contaminant bacterium in the specimen had on the LIBS-based identification of the primary pathogen. Two closely related bacterial specimens, Escherichia coli strain ATCC 25922 and Enterobacter cloacae strain ATCC 13047, were mixed together in mixing fractions of 10:1, 100:1, and 1000:1. LIBS spectra from the three mixtures were reliably classified as …


Spin-Forbidden Helium I Transition Rates, D. C. Morton, Gordon W. F. Drake Jan 2012

Spin-Forbidden Helium I Transition Rates, D. C. Morton, Gordon W. F. Drake

Physics Publications

We have calculated spin-forbidden transition rates in neutral helium using the spin-orbit and spin-other-orbit Breit-Pauli operators.


Variational Energies And The Fermi Contact Term For The Low-Lying States Of Lithium: Basis-Set Completeness, L. M. Lang, Z. C. Yan, H. X. Qiao, Gordon W. F. Drake Jan 2012

Variational Energies And The Fermi Contact Term For The Low-Lying States Of Lithium: Basis-Set Completeness, L. M. Lang, Z. C. Yan, H. X. Qiao, Gordon W. F. Drake

Physics Publications

Nonrelativistic energies for the low-lying states of lithium are calculated using the variational method in Hylleraas coordinates. Variational eigenvalues for the infinite nuclear mass case with up to 34020 terms are -7.478060323910147(1) a.u. for 1s22s2S, -7.35409842144437(1) a.u. for 1s23s2S, -7.31853084599891(1) a.u. for 1s24s2S, -7.41015653265241(4) a.u. for 1s22p2P, and -7.335523543524688(3) a.u. for 1s23d2D. The selection of the minimum set of angular momentum configurations is discussed, with the 2P and 3D states as examples to demonstrate the impact of various configurations on the variational energies. It is shown by numerical example that the second spin function (i.e., coupled to form a triplet …