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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Phonon modal analysis of thermal transport in ThO 2 with point defects using equilibrium molecular dynamics

Defects can significantly degrade the thermal conductivity of ThO 2 , an advanced nuclear fuel material as well as a surrogate for other fluorite-structured materials. Here, we investigate how point defects in ThO 2 impact phonon mode-resolved thermal transport. By incorporating phonon modes from lattice dynamics, we decompose the trajectory and heat flux to phonon normal mode space and extract key phonon properties, including phonon relaxation times and their contributions to thermal conductivity. We implement two methods. The first method is based on the Green Kubo formalism to resolve the contribution of each phonon mode to thermal conductivity. The second resolves the lifetime of individual phonon modes and the thermal conductivity is calculated using the Boltzmann transport equation within relaxation time approximation. Notably, a lower contribution of acoustic modes is revealed compared to perturbative approaches considering only three-phonon scattering processes. The effects of four types of point defects are evaluated. The strongest impact on a reduction in thermal conductivity is from Th interstitials, followed by Th vacancies. O interstitials/vacancies have a similar impact, albeit smaller than defects on the thorium sublattice. These observations are consistent with previous studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

The importance of localized modes spectral contribution to thermal conductivity in amorphous polymers

Abstract Polymers are a unique class of materials from the perspective of normal mode analysis. Polymers consist of individual chains with repeating units and strong intra-chain covalent bonds, and amorphous arrangements among chains with weak inter-chain van der Waals and for some polymers also electrostatic interactions. Intuitively, this strong heterogeneity in bond strength can give rise to special features in the constituent phonons, but such effects have not been studied deeply before. Here, we use lattice dynamics and molecular dynamics to perform modal analysis of the thermal conductivity in amorphous polymers. We find an abnormally large population of localized modes in amorphous polymers, which is fundamentally different from amorphous inorganic materials. Contrary to the common picture of thermal transport, localized modes in amorphous polymers are found to be the dominant contributors to thermal conductivity. We find that a significant portion of the localization happens within individual chains, but heat is dominantly conducted when localized modes involve two chains. These results suggest localized modes generally play a key role in thermal transport for different polymers. The results provide an alternative perspective on why polymer thermal conductivity is generally quite low and gives insight into how to potentially change it.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Simulation of Plasma Emission in Magnetized Plasmas

The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

First-principles electronic structure in second-moment calculation of mode frequencies: Failure of quasiharmonic approximation in silicon

Using first-principles electronic structure calculations (local density approximation), we present second-moment calculations of the temperature dependence of the vibrational normal mode frequencies in Si up to 1500 K . The method is based on simple ensemble averages of displacements and forces and is easy to implement. These efficient calculations incorporate all interactions nonperturbatively, implicitly including all high order force constants, in contrast to typical perturbative approaches. Also in this work, we propose and apply to our classical calculations an estimated quantum correction that could be used for classical approaches other than the moments method. We compare our results to available experiments, including recent inelastic neutron scattering data and conclude that the second-moment gives the frequency shift to within a factor of 2 in contrast to quasiharmonic approaches that fail by an order of magnitude to predict the anharmonic shift. Noting the relative simplicity and speed of the calculations, we conclude that the second-moment approximation reasonably accounts for anharmonicity in a system that has been very closely studied experimentally and may reliably be applied in an exploratory way to more complex systems. Finally, we suggest that further improvement on the results could be obtained by incorporating the fourth moment, which can be implemented with little additional cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Low-frequency Raman active modes of twisted bilayer MoS 2

Abstract We study the low-frequency Raman active modes of twisted bilayer MoS 2 for several twist angles using a force-field approach and a parametrized bond polarizability model. We show that twist angles near high-symmetry stacking configurations exhibit stacking frustration that leads to significant buckling of the moiré superlattice. We find that atomic relaxation due to the twist is of prime importance. The periodic displacement of the Mo atoms shows the realization of a soliton network, and in turn, leads to the emergence of a number of frequency modes not seen in the high-symmetry stacking systems. Some of the modes are only seen in the XZ Raman polarization setup while others are seen in the XY setup. The symmetry of the normal modes, and how this affects the Raman tensors is examined in detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Quantum-to-classical crossover in generalized spin systems: Temperature-dependent spin dynamics of FeI 2

Simulating quantum spin systems at finite temperatures is an open challenge in many-body physics. This work studies the temperature-dependent spin dynamics of a pivotal compound, FeI 2 , to determine if universal quantum effects can be accounted for by a phenomenological renormalization of the dynamical spin structure factor $S$(q, $ω$) measured by inelastic neutron scattering. Renormalization schemes based on the quantum-to-classical correspondence principle are commonly applied at low temperatures to the harmonic oscillators describing normal modes. However, it is not clear how to extend this renormalization to arbitrarily high temperatures. Here we introduce a temperature-dependent normalization of the classical moments, whose magnitude is determined by imposing the quantum sum rule, e.g., $∫$ $dωd$q$S$ ($q, ω$) = $N$ $S$ $S$ ($S$ + 1)for $N$ $S$ dipolar magnetic moments. We show that this simple renormalization scheme significantly improves the agreement between the calculated and measured $S$(q, $ω$) for FeI 2 at all temperatures. In conclusion, due to the coupled dynamics of dipolar and quadrupolar moments in that material, this renormalization procedure is extended to classical theories based on SU(3) coherent states, and by extension, to any SU($N$) coherent state representation of local multipolar moments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Radiative properties of an artificial atom coupled to a Josephson-junction array

We study the radiative properties—the Lamb shift, Purcell decay rate, and spontaneous emission dynamics—of an artificial atom coupled to a long, multimode cavity formed by an array of Josephson junctions. Introducing a tunable coupling element between the atom and the array, we demonstrate that such a system can exhibit a crossover from a perturbative to a nonperturbative regime of light-matter interaction as one strengthens the coupling between the atom and the Josephson-junction array. As a consequence, the concept of spontaneous emission as the occupation of the local atomic site being governed by a single complex-valued exponent breaks down. This breakdown, we show, can be interpreted in terms of formation of hybrid atom-resonator modes with radiative losses that are nontrivially related to the effective coupling between individual modes. We develop a singular function expansion approach for the description of the open quantum system dynamics in such a multimode nonperturbative regime. This modal framework generalizes the normal-mode description of quantum fields in a finite volume, incorporating exact radiative losses and incident quantum noise at the delimiting surface. Our results are pertinent to recent experiments with Josephson atoms coupled to high-impedance Josephson-junction arrays.

42 ENGINEERING↗
DOE OSTI2023

Molecular Cage Reports on Its Contents: Spectroscopic Signatures of Cryo-Cooled K + - and Ba 2+ -Benzocryptand Complexes

UV photofragment spectroscopy and IR–UV double resonance methods are used to determine the structure and spectroscopic responses of a three-dimensional [2.2.2]-benzocryptand cage to the incorporation of a single K + or Ba 2+ imbedded inside it (labeled as K + -BzCrypt, Ba 2+ -BzCrypt). We studied the isolated ion-cryptand complex under cryo-cooled conditions, brought into the gas phase by nano-electrospray ionization. Incorporation of a phenyl ring in place of the central ethyl group in one of the three N-CH 2 -CH 2 -O-CH 2 -CH 2 -O-CH 2 -CH 2 -N chains provides a UV chromophore whose S 0 –S 1 transition we probe. K + -BzCrypt and Ba 2+ -BzCrypt have their S 0 –S 1 origin transitions at 35,925 and 36,446 cm –1 , respectively, blue-shifted by 174 and 695 cm –1 from that of 1,2-dimethoxybenzene. These origins are used to excite a single conformation of each complex selectively and record their IR spectra using IR–UV dip spectroscopy. The alkyl CH stretch region (2800–3000 cm –1 ) is surprisingly sensitive to the presence and nature of the encapsulated ion. We carried out an exhaustive conformational search of cage conformations for K + -BzCrypt and Ba 2+ -BzCrypt, identifying two conformations (A and B) that lie below all others in energy. Here, we extend our local mode anharmonic model of the CH stretch region to these strongly bound ion-cage complexes to predict conformation-specific alkyl CH stretch spectra, obtaining quantitative agreement with experiment for conformer A, the gas-phase global minimum. The large electrostatic effect of the charge on the O- and N-lone pairs affects the local mode frequencies of the CH 2 groups adjacent to these atoms. The localized CH 2 scissors modes are pushed up in frequency by the adjacent O/N-atoms so that their overtones have little effect on the alkyl CH stretch region. However, the localized CH 2 wags are nearly degenerate and strongly coupled to one another, producing an array of delocalized wag normal modes, whose highest frequency members reach up above 1400 cm –1 . As such, their overtones mix significantly with the CH stretch modes, most notably involving the CH 2 symmetric stretch fundamentals of the central ethyl groups in the all-alkyl chains and the CH stretches adjacent to the N-atoms and antiperiplanar to the nitrogen lone pair.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Computational Spectroscopy of the Cr–Cr Bond in Coordination Complexes

In this work, we report the accurate computational vibrational analysis of the Cr–Cr bond in dichromium complexes using second-order multireference complete active space methods (CASPT2), allowing direct comparison with experimental spectroscopic data both to facilitate interpreting the low-energy region of the spectra and to provide insights into the nature of the bonds themselves. Recent technological development by the authors has realized such computation for the first time. Accurate simulation of the vibrational structure of these compounds has been hampered by their notorious multiconfigurational electronic structure that yields bond distances that do not correlate with bond order. Some measured Cr–Cr vibrational stretching modes, ν(Cr 2 ), have suggested weaker bonding, even for so-called ultrashort Cr–Cr bonds, while others are in line with the bond distance. Here, we optimize geometries and compute ν(Cr 2 ) with CASPT2 for three well-characterized complexes, Cr 2 (O 2 CCH 3 ) 4 (H 2 O) 2 , Cr 2 (mhp) 4 , and Cr 2 (dmp) 4 . We obtain CASPT2 harmonic ν(Cr 2 ) modes in good agreement with experiment at 282 cm –1 for Cr 2 (mhp) 4 and 353 cm –1 for Cr 2 (dmp) 4 , compute 50 Cr and 54 Cr isotope shifts, and demonstrate that the use of the so-called IPEA shift leads to improved Cr–Cr distances. Additionally, normal mode sampling was used to estimate anharmonicity along ν(Cr 2 ), leading to an anharmonic mode of 272 cm –1 for Cr 2 (mhp) 4 and 333 cm –1 for Cr 2 (dmp) 4 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

An Experimental and Theoretical Study of the Valence Shell Electronic Structure of Nitromethane

Vibrationally resolved CH 3 NO 2 and CD 3 NO 2 photoelectron spectra and angular distribution parameters, β, have been measured in the photon energy range 20–80 eV. This allows a comprehensive investigation of conflicting literature interpretations of the two outermost photoelectron bands, complemented by high-level calculations characterizing the three O lone-pair-based orbital ionizations expected in this region. Franck–Condon simulations allow the regular vibrational progressions observed at the beginning of the first and second bands to be assigned as predominantly modes v 5 and v 6 of the D 0 and D 2 cation states, respectively. Irregular structuring observed midband in both bands is attributed to avoided crossings between the adiabatic D 0 /D 1 and D 1 /D 2 states as identified in potential surface cuts taken along the v 5 and v 6 normal mode coordinates. The associated D 0 /D 1 and D 1 /D 2 conical intersections were located and characterized, allowing possible vibronic coupling and its impact on the photoelectron spectra of the D 0 , D 1 , and D 2 states to be discussed. This helps rationalize the apparently missing D 1 ionization in this region, although some contribution by this state may be identifiable in the β-parameter spectra. Theoretical analysis of the complete valence region spectrum identifies the early breakdown of the independent electron model beyond these first two bands.

Powis, Ivan [University of Nottingham (United King↗
DOE OSTI2020

Mode-specific pressure effects on the relaxation of an excited nitromethane molecule in an argon bath

The vibrational and rotational mode-specific relaxations of CH 3 NO 2 with 50 kcal/mol of initial internal energy in an argon bath is computed at 300 K at pressures of 10-400 atm. This work uses archived information from our previously published [J. Chem. Phys. 142, 014303 (2015)] molecular dynamics simulations and employs our previous published [J. Chem. Phys. 151, 034303 (2019)] method for projecting time-dependent Cartesian velocities onto normal mode eigenvectors. The computed relaxations cover three types of energies: vibrational, rotational, and Coriolis. In general, rotational and Coriolis relaxations in all modes are initially fast followed by an orders of magnitude slower relaxation. For all modes, that slower relaxation rate is approximately comparable to the vibrational relaxation rate. For all three types of energies, there are small-scale mode-to-mode variations. Of particular prominence is the exceptionally fast relaxation shared in common by the external rotation about the C-N axis, the internal hindered rotation of the CH 3 group relative to the NO 2 group, and the symmetric stretch of the CH 3 group.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Global System Reduction Order Modeling for Localized Feature Inclusion

The development of reduced-order models remains an active research area, despite advances in computational resources. Here we develop a novel order-reduction approach that is designed to incorporate isolated regions that contain, for example, nonlinearitites or accumulating damage. The approach is designed to use global modes of the overall system response, which are then naturally coupled to the response in the isolated region of interest. Two examples are provided to demonstrate both the accuracy and the computational efficiency of the proposed approach. The performance of this approach is compared to the exact response corresponding to a finite element simulation for the chosen problems. In addition, the accuracy and computational efficiency are shown relative to a standard Galerkin reduction based on the linear normal modes. It is found that the proposed reduction offer computational efficiency comparable to a Galerkin reduction, but more accurately represents the response of the system when both are compared to the finite element simulation.

42 ENGINEERING↗
DOE OSTI2020

Photoexcited energy relaxation and vibronic couplings in π-conjugated carbon nanorings

Conjugated carbon nanorings exhibit unique photophysical properties that, combined with their tunable sizes and conformations, make them suitable for a variety of practical applications. These properties are intimately associated to their strained, bent and sterically hindered cyclic structures. Herein we perform a comparative analysis of the photoinduced dynamics in carbon nanorings composed of nine phenyl units([9]CPP) and nine naphthyl units ([9]CN) respectively. The sterically demanding naphthyl units lead to large dihedral angles between neighboring units. Nevertheless, the ultrafast electronic and vibrational energy relaxation and redistribution is found to be similar for both systems. We observe that vibronic couplings, introduced by nonadiabatic energy transfer between electronic excited states, ensure the intramolecular vibrational energy redistribution through specific vibrational modes. The comparative impact of the internal conversion process on the exciton spatial localization and intra-ring migration indicates that naphthyl units in [9]CN achieve more efficient but less dynamical self-trapping compared to that of phenyl units in [9]CPP. That is, during the photoinduced process, the exciton in [9]CN is more static and localized than the exciton in [9]CPP. Furthermore, the internal conversion processes take place through a specific set of middle- to high-frequency normal modes, which directly influence the spatial exciton redistribution during the internal conversion, self-trapping and intra-ring migration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Membrane-mediated dimerization of spherocylindrical nanoparticles

Here we present a numerical investigation of the modes of adhesion and endocytosis of two spherocylindrical nanoparticles (SCNPs) on planar and tensionless lipid membranes, using systematic molecular dynamics simulations of an implicit-solvent model, with varying values of the SCNPs' adhesion strength and dimensions. We found that at weak values of the adhesion energy per unit of area, ξ, the SCNPs are monomeric and adhere to the membrane in the parallel mode. As ξ is slightly increased, the SCNPs dimerize into wedged dimers, with an obtuse angle between their major axes that decreases with increasing ξ. However, as ξ is further increased, we found that the final adhesion state of the two SCNPs is strongly affected by the initial distance, d 0 , between their centers of mass, upon their adhesion. Namely, the SCNPs dimerize into wedged dimers, with an acute angle between their major axes, if d 0 is relatively small. However, for relatively high d 0 , they adhere individually to the membrane in the monomeric normal mode. For even higher values of ξ and small values of d 0 , the SCNPs cluster into tubular dimers. However, they remain monomeric if d 0 is high. Finally, the SCNPs endocytose either as a tubular dimer, if d 0 is low or as monomers for large d 0 , with the onset value of ξ of dimeric endocytosis being lower than that of monomeric endocytosis. Dimeric endocytosis requires that the SCNPs adhere simultaneously at nearby locations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Convergent Concordant Mode Approach for Molecular Vibrations: CMA-2

The concordant mode approach (CMA) is a promising new scheme for dramatically increasing the system size and level of theory achievable in quantum chemical computations of molecular vibrational frequencies. Here, we achieve advances in the CMA hierarchy by computations targeting CCSD(T)/cc-pVTZ (coupled cluster singles and doubles with perturbative triples using a correlation-consistent polarized-valence triple-ζ basis set) benchmarks within the G2 molecular test set, executing a statistical analysis for 1501 frequencies from 111 compounds and then separately solving the refractory case of pyridine. First, MP2/cc-pVTZ (second-order Møller–Plesset perturbation theory with the same basis set) proves to be an excellent and preferred choice for generating the underlying (Level B) normal modes of the CMA scheme. Utilizing this Level B within the CMA-0A method reproduces the 1501 benchmark frequencies with a mean absolute error (MAE) of only 0.11 cm –1 and an attendant standard deviation of 0.49 cm –1 . Second, a convergent CMA-2 method is constituted that allows efficient computation of higher level (Level A) frequencies to any reasonable accuracy threshold by using only Hartree–Fock (HF) and MP2 or density functional theory (DFT) data to generate ξ parameters, which select the sparse off-diagonal force field elements for explicit evaluation at Level A. When Level B = MP2/cc-pVTZ, a cutoff of ξ = 0.02 provides an average maximum absolute error per molecule of only 0.17 cm –1 by incurring merely a 33% increase in average cost over CMA-0A. This CMA-2 method also eradicates the 4 problematic CMA-0A outliers of pyridine with even less effort (ξ = 0.04, 22% increase). Finally, the newly developed CMA procedures are shown to be highly successful when applied to 1-(1H-pyrrol-3-yl)ethanol, a new test molecule with diverse types of vibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Reducing the L-H transition power threshold in ITER-similar-shape DIII-D hydrogen plasmas

Recent dedicated DIII-D experiments in low-torque, ITER-similar-shape (ISS) hydrogen plasmas (at a plasma current I p ~ 1.5 MA and ITER-similar edge safety factor q 95 ~ 3.6) show that the L-H transition power threshold P LH can be reduced substantially (~30%) with L-mode helium admixtures n He /n e $\leqslant$ 25%. In the ensuing H-mode, helium ion fractions n He /n H remain below 25%. H-mode normalized pressure and confinement quality are only slightly affected by helium seeding, and Z eff $\leqslant$ 2.15 (including helium and carbon content). The plasmas investigated here are electron-heat dominated, with temperatures T e (0)/T i (0) $\geqslant$ 1 and edge heat flux ratio Q e /Q i (ρ = 0.95) ~ 1.2–1.5. Without mitigation, P LH is higher by a factor of 2–3 in comparison to similar ISS deuterium plasmas. ISS hydrogen plasmas with lower plasma current I p ~ 1 MA (increased edge safety factor q 95 ~ 5.1) exhibit a substantially lower power threshold. This plasma current dependence, also observed previously on ASDEX-U and in JET, is not accounted for by the commonly used 2008 ITPA multi-machine threshold scaling, but could potentially allow H-mode access at marginal heating power during the initial plasma current ramp-up. Attempts to reduce P LH with low-field- and high-field-side hydrogen pellet injection, using 1.7 mm diameter pellets, have not demonstrated a robust threshold reduction, in contrast to successful earlier experiments with larger 2.7 mm pellets. Finally, techniques for reducing P LH are very important for ITER, in particular for accessing H-mode in hydrogen plasmas during the Pre-Fusion Power Operation-1 (PFPO-1) campaign with marginal auxiliary heating power (20–30 MW of ECH).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Concordant Mode Approach (CMA): Vibrational Analysis of New and Upgraded Intermolecular Benchmarks for Noncovalent Bonding

The Concordant Mode Approach (CMA) is a novel method that offers tremendous potential for increasing the system size and the level of theory attainable in quantum chemical computations of molecular vibrational frequencies. To investigate the extension of CMA to intermolecular vibrations, computations with coupled cluster singles and doubles with perturbative triples theory [CCSD(T)] using two augmented correlation-consistent polarized-valence triple-ζ basis sets (aug-cc-pVTZ or h-aug-ccpVTZ) were performed on 17 prototypical loosely bound complexes of hydrogen-bonded, dispersion, and mixed character. These Level A results provide new and upgraded benchmarks for noncovalent bonding and a severe test for CMA vibrational analyses. The Level A target frequencies were recovered remarkably well using second-order Møller−Plesset perturbation theory (MP2) with h-aug-cc-pVTZ for generating the underlying (Level B) normal modes of the CMA scheme. Employing this Level B within the lowest-rung CMA-0A method reproduces the 435 benchmark frequencies with a mean absolute error (MAE) of 0.23 cm −1 and a corresponding standard deviation (σ) of 0.84 cm −1 ; strikingly, the corresponding subset of 106 interfragment frequencies exhibits MAE = 0.34 cm −1 and σ = 0.90 cm −1 . Subsequent application of the higher-rung CMA-2A scheme eliminates all outliers and reduces the overall MAE to a minuscule 0.08 cm −1 with the inclusion of only 3.0% of the off-diagonal couplings not accounted for by CMA-0A. Accordingly, the highly efficient CMA methodology proves to be robust even for vibrations on flat potential energy surfaces.

Aromatic compounds↗
DOE OSTI2023

Measurement of the branching fractions for Cabibbo-suppressed decays D + → K + K - π + π 0 and D ( s ) + → K + π - π + π 0 at Belle

We present measurements of the branching fractions for the singly Cabibbo-suppressed decays and , and the doubly Cabibbo-suppressed decay , based on of data recorded by the Belle experiment at the KEKB e + ⁢e - collider. We measure these modes relative to the Cabibbo-favored modes D + → K - ⁢π + ⁢π + ⁢π 0 and D$^{+}_{s}$ → K + ⁢K -⁢ π + ⁢π 0 . Our results for the ratios of branching fractions are $\mathscr{B}$⁡(D + →K + ⁢K -⁢ π + ⁢π 0 )/$\mathscr{B}$⁡(D + → K - ⁢π + ⁢π + ⁢π 0 ) =(11.32±0.13±0.26)%, $\mathscr{B}$⁡(D + →K + π - ⁢π + ⁢π 0 )/$\mathscr{B}$(D + →K -⁢ π + ⁢π + ⁢π 0 ) =(1.68±0.11±0.03)%, and $\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢π - π + ⁢π 0 )/$\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢K - π + π 0 ) =(17.13±0.62±0.51)%, where the uncertainties are statistical and systematic, respectively. The second value corresponds to (5.83 ±0.42) ×tan 4 ⁡θ C , where θ C is the Cabibbo angle; this value is larger than other measured ratios of branching fractions for a doubly Cabibbo-suppressed charm decay to a Cabibbo-favored decay. Multiplying these results by world average values for $\mathscr{B}$⁡(D + → K - ⁢π + ⁢π + ⁢π 0 ) and $\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢K - π + π 0 ) yields $\mathscr{B}$( + →K + ⁢K -⁢ π + ⁢π 0 ) = (7.08±0.08±0.16±0.20)×10 -3 , $\mathscr{B}$⁡(D + → K +⁢ π - π + ⁢π 0 ) =(1.05±0.07±0.02±0.03)×10 -3 , and $\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢π - π + ⁢π 0 ) =(9.44±0.34±0.28±0.32)×10 -3 , where the third uncertainty is due to the branching fraction of the normalization mode. The first two results are consistent with, but more precise than, the current world averages. The last result is the first measurement of this branching fraction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗