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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Elective Lymph Node Irradiation With Intensity-Modulated Radiotherapy: Is Conventional Dose Fractionation Necessary?

Purpose: Intensity-modulated radiation therapy (IMRT) is the standard of care for head-and-neck cancer (HNC). We treated patients with HNC by delivering either a moderate hypofractionation (MHF) schedule (66 Gy at 2.2 Gy per fraction to the gross tumor [primary and nodal]) with standard dose fractionation (54-60 Gy at 1.8-2.0 Gy per fraction) to the elective neck lymphatics or a conventional dose and fractionation (CDF) schedule (70 Gy at 2.0 Gy per fraction) to the gross tumor (primary and nodal) with reduced dose to the elective neck lymphatics. We analyzed these two cohorts for treatment outcomes. Methods and Materials: Between November 2001 and February 2009, 89 patients with primary carcinomas of the oral cavity, larynx, oropharynx, hypopharynx, and nasopharynx received definitive IMRT with or without concurrent chemotherapy. Twenty patients were treated using the MHF schedule, while 69 patients were treated with the CDF schedule. Patient characteristics and dosimetry plans were reviewed. Patterns of failure including local recurrence (LR), regional recurrence (RR), distant metastasis (DM), disease-free survival (DFS), overall survival (OS), and toxicities, including rate of feeding tube placement and percentage of weight loss, were reviewed and analyzed. Results: Median follow-up was 31.2 months. Thirty-five percent of patients in the MHF cohort and 77% of patients in the CDF cohort received chemotherapy. No RR was observed in either cohort. OS, DFS, LR, and DM rates for the entire group at 2 years were 89.3%, 81.4%, 7.1%, and 9.4%, respectively. Subgroup analysis showed no significant differences in OS (p = 0.595), DFS (p = 0.863), LR (p = 0.833), or DM (p = 0.917) between these two cohorts. Similarly, no significant differences were observed in rates of feeding tube placement and percentages of weight loss. Conclusions: Similar treatment outcomes were observed for MHF and CDF cohorts. A dose of 50 Gy at 1.43 Gy per fraction may be sufficient to electively treat low-risk neck lymphatics.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2019

Probabilistic Forecast of Single–Phase Flow in Porous Media With Uncertain Properties

Uncertainty about geologic makeup and properties of the subsurface renders inadequate a unique quantitative prediction of flow and transport. Instead, multiple alternative scenarios have to be explored within the probabilistic framework, typically by means of Monte Carlo simulations (MCS). These can be computationally expensive, and often prohibitively so, especially when the goal is to compute the tails of a distribution, i.e., probabilities of rare events, which are necessary for risk assessment and decision making under uncertainty. We deploy the method of distributions to derive a deterministic equation for the cumulative distribution function (CDF) of hydraulic head in an aquifer with uncertain (random) hydraulic conductivity. The CDF equation relies on a self-consistent closure approximation, which ensures that the resulting CDF of hydraulic head has the same mean and variance as those computed with either statistical moment equation (the approach used herein) or MCS. We conduct a series of numerical experiments dealing with steady-state two-dimensional flow driven by either a natural hydraulic head gradient or a pumping well. Furthermore, these experiments reveal that the CDF method remains accurate and robust for highly heterogeneous formations with the variance of log conductivity as large as five. For the same accuracy, it is also up to four orders of magnitude faster than MCS in computing hydraulic head with a required degree of confidence (probability).

42 ENGINEERING↗
DOE OSTI2023

Hadronic uncertainties versus new physics for the W boson mass and Muon g – 2 anomalies

There are now two single measurements of precision observables that have major anomalies in the Standard Model: the recent CDF measurement of the W mass shows a 7σ deviation and the Muon g – 2 experiment at FNAL confirmed a long-standing anomaly, implying a 4.2σ deviation. Doubts regarding new physics interpretations of these anomalies could stem from uncertainties in the common hadronic contributions. We demonstrate that these two anomalies pull the hadronic contributions in opposite directions by performing electroweak fits in which the hadronic contribution was allowed to float. The fits show that including the g – 2 measurement worsens the tension with the CDF measurement and conversely that adjustments that alleviate the CDF tension worsen the g – 2 tension beyond 5σ. This means that if we adopt the CDF W mass measurement, the case for new physics in either the W mass or muon g – 2 is inescapable regardless of the size of the SM hadronic contributions. Lastly, we demonstrate that a mixed scalar leptoquark extension of the Standard Model could explain both anomalies simultaneously.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

THE 4 Ms CHANDRA DEEP FIELD-SOUTH NUMBER COUNTS APPORTIONED BY SOURCE CLASS: PERVASIVE ACTIVE GALACTIC NUCLEI AND THE ASCENT OF NORMAL GALAXIES

We present 0.5-2 keV, 2-8 keV, 4-8 keV, and 0.5-8 keV (hereafter soft, hard, ultra-hard, and full bands, respectively) cumulative and differential number-count (log N-log S) measurements for the recently completed Almost-Equal-To 4 Ms Chandra Deep Field-South (CDF-S) survey, the deepest X-ray survey to date. We implement a new Bayesian approach, which allows reliable calculation of number counts down to flux limits that are factors of Almost-Equal-To 1.9-4.3 times fainter than the previously deepest number-count investigations. In the soft band (SB), the most sensitive bandpass in our analysis, the Almost-Equal-To 4 Ms CDF-S reaches a maximum source density of Almost-Equal-To 27,800 deg{sup -2}. By virtue of the exquisite X-ray and multiwavelength data available in the CDF-S, we are able to measure the number counts from a variety of source populations (active galactic nuclei (AGNs), normal galaxies, and Galactic stars) and subpopulations (as a function of redshift, AGN absorption, luminosity, and galaxy morphology) and test models that describe their evolution. We find that AGNs still dominate the X-ray number counts down to the faintest flux levels for all bands and reach a limiting SB source density of Almost-Equal-To 14,900 deg{sup -2}, the highest reliable AGN source density measured at any wavelength. We find that the normal-galaxy counts rise rapidly near the flux limits and, at the limiting SB flux, reach source densities of Almost-Equal-To 12,700 deg{sup -2} and make up 46% {+-} 5% of the total number counts. The rapid rise of the galaxy counts toward faint fluxes, as well as significant normal-galaxy contributions to the overall number counts, indicates that normal galaxies will overtake AGNs just below the Almost-Equal-To 4 Ms SB flux limit and will provide a numerically significant new X-ray source population in future surveys that reach below the Almost-Equal-To 4 Ms sensitivity limit. We show that a future Almost-Equal-To 10 Ms CDF-S would allow for a significant increase in X-ray-detected sources, with many of the new sources being cosmologically distant (z {approx}> 0.6) normal galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

RESOLVING THE COSMIC FAR-INFRARED BACKGROUND AT 450 AND 850 μm WITH SCUBA-2

We use the SCUBA-2 submillimeter camera mounted on the James Clerk Maxwell Telescope to obtain extremely deep number counts at 450 and 850 μm. We combine data on two cluster lensing fields, A1689 and A370, and three blank fields, CDF-N, CDF-S, and COSMOS, to measure the counts over a wide flux range at each wavelength. We use statistical fits to broken power law representations to determine the number counts. This allows us to probe to the deepest possible level in the data. At both wavelengths our results agree well with the literature in the flux range over which they have been measured, with the exception of the 850 μm counts in CDF-S, where we do not observe the counts deficit found by previous single-dish observations. At 450 μm, we detect significant counts down to ∼1 mJy, an unprecedented depth at this wavelength. By integrating the number counts above this flux limit, we measure 113.9{sup +49.7}{sub -28.4} Jy deg{sup –2} of the 450 μm extragalactic background light (EBL). The majority of this contribution is from sources with S{sub 450{sub μm}} between 1-10 mJy, and these sources are likely to be the ones that are analogous to the local luminous infrared galaxies. At 850 μm, we measure 37.3{sup +21.1}{sub -12.9} Jy deg{sup –2} of the EBL. Because of the large systematic uncertainties on the COBE measurements, the percentage of the EBL we resolve could range from 48%-153% (44%-178%) at 450 (850) μm. Based on high-resolution Submillimeter Array observations of around half of the 4 σ 850 μm sample in CDF-N, we find that 12.5{sup +12.1}{sub -6.8}% of the sources are blends of multiple fainter sources. This is a low multiple fraction, and we find no significant difference between our original SCUBA-2 850 μm counts and the multiplicity-corrected counts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Nearest neighbour distributions: New statistical measures for cosmological clustering

ABSTRACT The use of summary statistics beyond the two-point correlation function to analyse the non-Gaussian clustering on small scales, and thereby, increasing the sensitivity to the underlying cosmological parameters, is an active field of research in cosmology. In this paper, we explore a set of new summary statistics – the k-Nearest Neighbour Cumulative Distribution Functions (kNN-CDF). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the k-nearest data points, and is sensitive to all connected N-point correlations in the data. The kNN-CDF can be used to measure counts in cell, void probability distributions, and higher N-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets – both discrete points, and the generalization for continuous fields. We use data from a large suite of N-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of kNN-CDF improves the constraints on the cosmological parameters by more than a factor of 2 when applied to the clustering of dark matter in the range of scales between 10 and $40\, h^{-1}\, {\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of haloes in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the kNN-CDF are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data, provided the higher order correlation functions are sensitive to cosmology on the scales of interest.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Experimental Studies of Elementary Particle Interactions at High Energies

This is the final report of a program of research on "Experimental Studies of Elementary Particle Interactions at High Energies'' of the High Energy Physics (HEP) group of The Rockefeller University. The research was carried out using the Collider Detector at Fermilab (CDF) and the Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) at CERN. Three faculty members, two research associates, and two postdoctoral associates participated in this project. At CDF, we studied proton-antiproton collisions at an energy of 1.96 TeV. We focused on diffractive interactions, in which the colliding antiproton loses a small fraction of its momentum, typically less than 1%, while the proton is excited into a high mass state retaining its quantum numbers. The study of such collisions provides insight into the nature of the diffractive exchange, conventionally referred to as Pomeron exchange. In studies of W and Z production, we found results that point to a QCD-based interpretation of the diffractive exchange, as predicted in a data-driven phenomenology developed within the Rockefeller HEP group. At CMS, we worked on diffraction, supersymmetry (SUSY), dark matter, large extra dimensions, and statistical applications to data analysis projects. In diffraction, we extended our CDF studies to higher energies working on two fronts: measurement of the single/double diffraction and of the rapidity gap cross sections at 7 TeV, and development of a simulation of diffractive processes along the lines of our successful model used at CDF. Working with the PYTHIA8 Monte Carlo simulation authors, we implemented our model as a PYTHIA8-MBR option in PYTHIA8 and used it in our data analysis. Preliminary results indicate good agreement. We searched for SUSY by measuring parameters in the Constrained Minimal Supersymmetric extension of the Standard Model (CMSSM) and found results which, combined with other experimental constraints and theoretical considerations, indicate that the CMSSM is not a viable model. Expressing our results in terms of simple topologies, we exclude squark masses below 0.75 TeV and gluino masses below 1.1 TeV. Astrophysical measurements suggest that about 80% of the matter density of the Universe is non-luminous. One of the theories on dark matter attributes it to Weakly Interacting Massive Particles (WIMPs). We searched for WIMPs in 7 TeV and 8 TeV collisions at CMS and set limits on WIMP production rates, which are competitive and complementary to those of direct detection experiments. Searching for monojets (events with only one jet), which in a popular model could be produced by a jet paired by a gravitino that escapes into extra dimensions, we significantly improved the previously set limit. Our results have been used to set limits on Higgs decay to invisible particles and on production of top squarks in compressed SUSY scenarios. Statistics. We computed Bayesian reference priors for several types of measurement and used them in the analysis of CMS data; investigated the applicability of bootstrap methods to HEP measurements; studied several issues associated with simple-versus-simple hypothesis testing and applied the resulting methods to the measurement of some properties of the top quark and Higgs boson.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2011

Mars as a Destination in a Capability-Driven Framework

This paper describes NASA s current plans for the exploration of Mars by human crews within NASA s Capability-Driven Framework (CDF). The CDF describes an approach for progressively extending human explorers farther into the Solar System for longer periods of time as allowed by developments in technology and spacecraft systems. Within this framework, Mars defines the most challenging objective currently envisioned for human spaceflight. The paper first describes the CDF and potential destinations being considered within this framework. For destinations relevant to the exploration of Mars, this includes both the Martian surface and the two moons of Mars. This is followed by a brief review of our evolving understanding of Mars to provide the context for the specific objectives set for human exploration crews. This includes results from robotic missions and goals set for future Martian exploration by NASA's community-based forum, the Mars Exploration Program Analysis Group (MEPAG) and the MEPAG-sponsored Human Exploration of Mars - Science Analysis Group (HEM-SAG). The paper then reviews options available for human crews to reach Mars and return to Earth. This includes a discussion of the rationale used to select from among these options for envisioned Mars exploration missions. The paper then concludes with a description of technological and operational challenges that still face NASA in order to be able to achieve the exploration goals for Mars within the CDF.

Hoffman, S. J.↗
NASA NTRS2012

The 4 Ms CHANDRA Deep Field-South Number Counts Apportioned by Source Class: Pervasive Active Galactic Nuclei and the Ascent of Normal Galaxies

We present 0.5-2 keV, 2-8 keV, 4-8 keV, and 0.5-8 keV (hereafter soft, hard, ultra-hard, and full bands, respectively) cumulative and differential number-count (log N-log S ) measurements for the recently completed approx. equal to 4 Ms Chandra Deep Field-South (CDF-S) survey, the deepest X-ray survey to date. We implement a new Bayesian approach, which allows reliable calculation of number counts down to flux limits that are factors of approx. equal to 1.9-4.3 times fainter than the previously deepest number-count investigations. In the soft band (SB), the most sensitive bandpass in our analysis, the approx. equal to 4 Ms CDF-S reaches a maximum source density of approx. equal to 27,800 deg(sup -2). By virtue of the exquisite X-ray and multiwavelength data available in the CDF-S, we are able to measure the number counts from a variety of source populations (active galactic nuclei (AGNs), normal galaxies, and Galactic stars) and subpopulations (as a function of redshift, AGN absorption, luminosity, and galaxy morphology) and test models that describe their evolution. We find that AGNs still dominate the X-ray number counts down to the faintest flux levels for all bands and reach a limiting SB source density of approx. equal to 14,900 deg(sup -2), the highest reliable AGN source density measured at any wavelength. We find that the normal-galaxy counts rise rapidly near the flux limits and, at the limiting SB flux, reach source densities of approx. equal to 12,700 deg(sup -2) and make up 46% plus or minus 5% of the total number counts. The rapid rise of the galaxy counts toward faint fluxes, as well as significant normal-galaxy contributions to the overall number counts, indicates that normal galaxies will overtake AGNs just below the approx. equal to 4 Ms SB flux limit and will provide a numerically significant new X-ray source population in future surveys that reach below the approx. equal to 4 Ms sensitivity limit. We show that a future approx. equal to 10 Ms CDF-S would allow for a significant increase in X-ray-detected sources, with many of the new sources being cosmologically distant (z greater than or approx. equal to 0.6) normal galaxies.

Field-South↗
DOE OSTI2011

Review of Heavy Flavor Physics at the Tevatron

The D0 and CDF detectors at the Fermilab Tevatron have each accumulated more that 9 fb{sup -1} of integrated luminosity. The corresponding large datasets enable the two experiments to perform unprecedented studies of heavy flavor hadron properties. We present recent D0 and CDF measurements, focusing on rare decays and CP violation in B-meson decays. Flavor Physics probes new phenomena by either searching for small deviations from the Standard Model (SM) based theoretical predictions or by measuring quantities which are highly suppressed within the SM. Searching for small deviations from the SM are performed using large strange, charm or bottom hadron samples, mostly by kaon experiments of B factories. Measurements of highly suppressed quantities, such as CP violation phases and asymmetries in the neutral B{sub s}-meson system or searches for rare B decays, are performed with the hope that new physics effects would be large enough to significantly affect the measured quantities and so, lead to observations of deviations from the SM expectations. The D0 and CDF detectors at the Fermilab Tevatron have each accumulated more that 9 fb{sup -1} of integrated luminosity. The corresponding large datasets enable the two experiments to perform unprecedented studies of heavy flavor hadron properties. We present recent D0 and CDF measurements, focusing on rare decays and CP violation in B-meson decays.

43 PARTICLE ACCELERATORS↗
DOE OSTI2012

Uncertainty quantification in kinematic wave models

We developed a probabilistic approach to quantify parametric uncertainty in first-order hyperbolic conservation laws (kinematic wave equations). The approach relies on the derivation of a deterministic equation for the cumulative density function (CDF) of the system state, in which probabilistic descriptions (probability density functions or PDFs) of the system parameters and/or initial and boundary conditions serve as inputs. In contrast to PDF equations, which are often used in other contexts, CDF equations allow for straightforward and unambiguous determination of boundary conditions with respect to sample variables.The accuracy and robustness of solutions of the CDF equation for one such system, the Saint-Venant equations of river flows, were investigated via comparison with Monte Carlo simulations.

UQ, CDF methods, surface flow, kinematic wave, hyp↗
DOE OSTI2014

Summary of Single top quark production at the Tevatron

The production of single-top quarks occurs via the weak interaction at the Fermilab Tevatron proton-antiproton collider. Single top quark events are selected in the lepton+jets final state by CDF and D0 and in the missing transverse energy plus jets final state by CDF. Multivariate classifiers separate the s-channel and t-channel single-top signals from the large backgrounds. The combination of CDF and D0 results leads to the first observation of the s-channel mode of single top quark production. The t-channel and single top combined cross sections have also been measured.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

What the Tevatron Found?

The CDF collaboration has reported a 4.1{sigma} excess in their lepton, missing energy, and dijets channel. This excess, which takes the form of an approximately Gaussian peak centered at a dijet invariant mass of 147 GeV, has provoked a great deal of experimental and theoretical interest. Although the D0 collaboration has reported that they do not observe a signal consistent with CDF, there is currently no widely accepted explanation for the discrepancy between these two experiments. A resolution of this issue is of great importance - not least because it may teach us lessons relevant for future searches at the LHC - and it will clearly require additional information. In this paper, we consider the ability of the Tevatron and LHC detectors to observe evidence associated with the CDF excess in a variety of channels. We also discuss the ability of selected kinematic distributions to distinguish between Standard Model explanations of the observed excess and various new physics scenarios.

43 PARTICLE ACCELERATORS↗
DOE OSTI2014

Drift Chamber Alignment using Cosmic Rays

The Collider Detector at Fermilab (CDF) is a general-purpose experimental apparatus with an inner tracking detector for measuring charged particles, surrounded by a calorimeter for measurements of electromagnetic and hadronic showers, and a muon detector system. We present a technique for, and results of, a precise relative alignment of the drift chamber wires of the CDF tracker. This alignment has been an important component of the track momentum calibration, which is the basis for the charged-lepton calibration for the measurement of the W boson mass at CDF.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Initial demonstration of automated fuel performance modeling with 1977 EBR-II metallic fuel pins using BISON code with FIPD and IMIS databases

Using the BISON fuel performance code, simulations were conducted using an automated process to read initial and operating conditions from the Fuels Irradiation and Physics Database (FIPD) and Integral Fast Reactor materials information system (IMIS) database, which contains metallic fuel data from the Experimental Breeder Reactor-II (EBR-II). This work demonstrates use of an integrated framework to access the vast majority of EBR-II experimental fuel pin data to support rapid development of fuel performance models for next-generation metallic fuel systems. With this capability, validation for fuel qualification can be performed rapidly. Between IMIS and FIPD, there is enough information to conduct 1977 unique EBR-II metallic fuel pin histories from 24 different experiments, at varying levels of detail between the two databases. Each of these histories includes a high-resolution power history, flux history, coolant channel flow rates, and coolant channel temperatures. Fission gas release (FGR), cumulative damage fraction (CDF), fuel axial swelling, cladding profilometry, and burnup were all simulated in BISON. The results were compared to post-irradiation examination (PIE) results for the initial demonstration of automated BISON modeling. BISON simulations conducted with IMIS and FIPD were in rough agreement with PIE measurements and calculations. Cladding profilometry, FGR, and fuel axial swelling were found to be in rough agreement with PIE measurements, depending on the physics used within the BISON input files. Here, the mechanical contact solver chosen was found to significantly impact axial fuel swelling and cladding strain predictions. CDF values were assessed to see whether pin failure may have been predicted (CDF ≥ 1). This work suggests that continued development of an automated tool for BISON should focus on inclusion of the Fast Flux Test Facility (FFTF) experimental data for a larger database for metallic fuel, improved physical models to better capture fuel performance, such as fuel-cladding interactions, and a more detailed comparison with available PIE data to further the BISON model development.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2011

Dark Forces At The Tevatron

A simple explanation of the W + dijet excess recently reported by the CDF collaboration involves the introduction of a new gauge boson with sizable couplings to quarks, but with no or highly suppressed couplings to leptons. Anomaly-free theories which include such a leptophobic gauge boson must also include additional particle content, which may include a stable and otherwise viable candidate for dark matter. Based on the couplings and mass of the Z` required to generate the CDF excess, we predict such a dark matter candidate to possess an elastic scattering cross section with nucleons on the order of σ ~ 10 -40 cm 2 , providing a natural explanation for the signals reported by the CoGeNT and DAMA/LIBRA collaborations. In this light, CDF may be observing the gauge boson responsible for the force which mediates the interactions between the dark and visible matter of our universe.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A model study of assisted adiabatic transfer of population in the presence of collisional dephasing

Previous studies have demonstrated that when experimental conditions generate non-adiabatic dynamics that prevents highly efficient population transfer between states of an isolated system by stimulated Raman adiabatic passage (STIRAP), the addition of an auxiliary counter-diabatic field (CDF) can restore most or all of that efficiency. This paper examines whether that strategy is also successful in a non-isolated system in which the energies of the states fluctuate, e.g., when a solute is subject to collisions with solvent. We study population transfer in two model systems: (i) the three-state system used by Demirplak and Rice [J. Chem. Phys. 116, 8028 (2002)] and (ii) a four-state system, derived from the simulation studies of Demirplak and Rice [J. Chem. Phys. 125, 194517 (2006)], that mimics HCl in liquid Ar. Simulation studies of the vibrational manifold of HCl in dense fluid Ar show that the collision induced vibrational energy level fluctuations have asymmetric distributions. Representations of these asymmetric energy level fluctuation distributions are used in both models (i) and (ii). We identify three sources of degradation of the efficiency of STIRAP generated selective population transfer in model (ii): too small pulse areas of the laser fields, unwanted interference arising from use of strong fields, and the vibrational detuning. For both models (i) and (ii), our examination of the efficiency of STIRAP + CDF population transfer under the influence of the asymmetric distribution of the vibrational energy fluctuations shows that there is a range of field strengths and pulse durations under which STIRAP + CDF control of population transfer has greater efficiency than does STIRAP generated population transfer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗