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Radiative Width of K*(892) from Lattice Quantum Chromodynamics

In this dissertation, we use lattice quantum chromodynamics to explore the radiative transitions of ?K to K, to calculate the radiative-width of the resonant K?(892) which appears in the P-wave ?K ? ?K transition amplitude. The matrix elements are extracted from three-point functions calculated in a finite-volume discretized lattice with a pion mass of 284 MeV. The finite-volume amplitudes, which are constrained over a large number of ?K energy-points and four-momentum transfers, are mapped to the infinite volume transition amplitude by using the Lellouch-Lüscher formalism. The radiative width is determined to be ? = 35 ± 8 keV by analytically continuing the amplitude into the complex energy plane and calculating the residue at the K? pole.

Radhakrishnan, Archana↗

Measured drift of irradiated and unirradiated W3%Re/W25%Re thermocouples at a nominal 2000 K.

Seven tantalum sheathed, BeO insulated, 0.157-cm-diam, grounded-junction W-3%Re/W-25%Re thermocouples were irradiated in a helium-argon environment at a temperature of 1900 to 2100 K. Six other thermocouples from the same lot were operated out-of-pile with the same temperature history as the in-pile thermocouples. Drift-in-pile was determined by periodically replacing a 'reference' thermocouple in the irradiation capsule. Drift out-of-pile was determined with an optical pyrometer. After 8000 hours irradiation, the estimated neutron fluence was 4 x 10 to the 21st power thermal neutrons/sq cm and 0.9 x 10 to the 21st power fast neutrons/sq cm (E greater than 0.18 MeV). At this time the in-pile group had decreased in output the equivalent of 340 K at 2073 K, while the out-of-pile group had decreased in output the equivalent of 54 K at 2073 K. The maximum deviation in drift between thermocouples of the in-pile group and between thermocouples of the out-of-pile group was less than plus or minus 15 K and less than plus or minus 10 K, respectively.

Heckelman, J. D.↗

K and U systematics and average concentrations on the moon

The K-U, Th-U, and Th-Al systematics for lunar samples from the Apollo 11-17 missions and the Luna 16 and 20 missions are summarized. With few exceptions (granitic portion of 12013 and the Apollo 17 mare basalts) the Th/U ratio is 3.8 plus or minus 0.2. The K/U ratio for lunar samples is about 2600 and is distinctly different from the K/U ratio found in terrestrial samples and in the majority of meteorites. The K-U systematics are similar to the K-La, K-Sm, K-Ba, and K-Zr systematics, suggesting that the moon accreted approximately homogeneously. Based on a model the moon contains an average abundance of about 80 ppb U, about 200 ppm K, and about 7 times chondritic abundances for all the refractory elements such as Al, Ca, Ti, Zr, Ba, Sr, and REE. The Th-Al systematics of many lunar highland rocks are dominated by the presence of the rock-type KREEP.

Schonfeld, E.↗

On the colors of Jupiter's satellite Io - Irradiation of solid sulfur at 77 K

The colors of seven sulfur allotropes at 77 K have been investigated both before and after irradiation by a high-pressure mercury lamp. S8 is white at 77 K but turns intense yellow within a few minutes on irradiation through quartz or DURAN. On warming, the yellow species (presumably chain-like sulfur diradicals characterized by an absorption at 430 nm) decomposes near 260 K and polymeric sulfur (S-infinity) is formed; the sample color changes gradually to the very similar color of an S8-S-infinity mixture, resulting in no visually detectable color change with temperatures from 77 K to 260 K. This is consistent with the lack of posteclipse brightening on Io. Other sulfur forms also turn intense yellow (S7, S10), grayish yellow (S12, S20, S-infinity), or brownish yellow (S6) on irradiation at 77 K, and these colors also change to the normal colors of the starting materials on warming to 298 K. It is suggested that the yellowish features on Io are caused by the effect of solar radiation on elemental sulfur. The yellow color thus produced may subsequently be modified by deposits of SO2 frosts and volcanic ash.

Steudel, R.↗

Mineralogical and geochemical anomalous data of the K-T boundary samples

Cretaceous-Tertiary boundary problem has been discussed previously from the geological research, mainly by fossil changes. Although geochemical bulk data of Ir anomaly suggest the extraterrestrial origin of the K-T boundary, the exact formation process discussed mainly by mineralogical and geochemical study has been started recently, together with noble gas contents. The K-T boundary sample at Kawaruppu River, Hokkaido was collected, in order to compare with the typical K-T boundary samples of Bubbio, Italy, Stevns Klint, Denmark, and El Kef, Tunisia. The experimental data of the silicas and calcites in these K-T boundary samples were obtained from the X-ray unit-cell dimension (i.e., density), ESR signal and total linear absorption coefficient, as well as He and Ne contents. The K-T boundary samples are usually complex mixture of the terrestrial activities after the K-T boundary event. The mineralogical and geochemical anomalous data indicate special terrestrial atmosphere at the K-T boundary formation probably induced by asteroid impact, followed the many various terrestrial activities (especially the strong role of sea-water mixture, compared with terrestrial highland impact and impact craters in the other earth-type planetary bodies).

Miura, Y.↗

Relations between the photospheric magnetic field and the emission from the outer atmospheres of cool stars. I - The solar Ca II K line core emission

Observations of a solar active region complex and its surroundings are used to establish a quantitative relation between the Ca II K line core intensity and magnetic flux density. The Ca II K line core intensity is transformed to a Ca II H + K line core flux density to facilitate a comparison of solar and stellar data. A new absolute calibration for the Mount Wilson Ca II H + K fluxes for G-type dwarfs is derived. The minimum Ca II K flux, found in the centers of supergranulation cells in quiet regions on the sun, is identical to the minimum flux that is observed for solar-type stars. An expression is presented for the nonlinear trend between the Ca II H + K line core excess flux density and the absolute value of the magnetic flux density. Models that explain the nonlinearity of the mean trend and the large intrinsic scatter about it are discussed. The solar data define a relation that is similar to the relation between stellar hemisphere-average magnetic flux densities and Ca II H + K excess flux densities.

Schrijver, C. J.↗

Correction analysis for a supersonic water cooled total temperature probe tested to 1370 K

The authors address the thermal analysis of a water cooled supersonic total temperature probe tested in a Mach 2 flow, up to 1366 K total temperature. The goal of this experiment was the determination of high-temperature supersonic jet mean flow temperatures. An 8.99 cm exit diameter water cooled nozzle was used in the tests. It was designed for exit Mach 2 at 1366 K exit total temperature. Data along the jet centerline were obtained for total temperatures of 755 K, 1089 K, and 1366 K. The data from the total temperature probe were affected by the water coolant. The probe was tested through a range of temperatures between 755 K and 1366 K with and without the cooling system turned on. The results were used to develop a relationship between the indicated thermocouple bead temperature and the freestream total temperature. The analysis and calculated temperatures are presented.

Lagen, Nicholas T.↗

RE 0044+09: A new K dwarf rapid rotator with a white dwarf companion

We report the discovery of a new K dwarf rapid rotator with a potential white dwarf companion. The white dwarf accounts for over 90% of the observed extreme ultraviolet flux detected from this system. Analysis of ROSAT Wide Field Camera (WFC) and IUE data both suggest a white dwarf temperature of approximately 28,700 K. Optical photometry and the IUE long wavelength prime (LWP) spectrum (with the white dwarf contribution removed) imply that the late-type star has a spectral type of K1-3 V, and a distance of 55 +/- 5 pc. Using this distance, the observed IUE SWP flux, and the best-fit temperature results in a white dwarf radius of 0.0088 solar radius. The estimated white dwarf mass is then approximately 0.91 solar mass; somewhat over-massive compared to field white dwarfs. Optical photometry of the K star reveals a 'spot' modulation period of approximately 10 hr (now observed over 3 yr). However, radial velocity observations have revealed no significant variations. Spectroscopic observations place a low limit on the lithium abundance, but do show rapid rotation with a v sin i of 90 +/- 10 km/s. The K star was detected as a radio source at 3.6 cm (on two occasions) and 6 cm by the Very Large Array (VLA). The most likely evolutionary scenario is that the K star and hot white dwarf from either a wide binary or common proper motion pair with an age of 0.1-0.1 Gyr-consistent with the evolutionary timescale of the white dwarf and the rapid rotation of the K star. However, from the proper motion of the K star, this system does not seem to be associated with any of the known young stellar groups.

Kellett, Barry J.↗

Calibration of the advanced microwave sounding unit-A for NOAA-K

The thermal-vacuum chamber calibration data from the Advanced Microwave Sounding Unit-A (AMSU-A) for NOAA-K, which will be launched in 1996, were analyzed to evaluate the instrument performance, including calibration accuracy, nonlinearity, and temperature sensitivity. The AMSU-A on NOAA-K consists of AMSU-A2 Protoflight Model and AMSU-A1 Flight Model 1. The results show that both models meet the instrument specifications, except the AMSU-A1 antenna beamwidths, which exceed the requirement of 3.3 +/- 10%. We also studied the instrument's radiometric characterizations which will be incorporated into the operational calibration algorithm for processing the in-orbit AMSU-A data from space. Particularly, the nonlinearity parameters which will be used for correcting the nonlinear contributions from an imperfect square-law detector were determined from this data analysis. It was found that the calibration accuracies (differences between the measured scene radiances and those calculated from a linear two-point calibration formula) are polarization-dependent. Channels with vertical polarizations show little cold biases at the lowest scene target temperature 84K, while those with horizontal polarizations all have appreciable cold biases, which can be up to 0.6K. It is unknown where these polarization-dependent cold biases originate, but it is suspected that some chamber contamination of hot radiances leaked into the cold scene target area. Further investigation in this matter is required. The existence and magnitude of nonlinearity in each channel were established and a quadratic formula for modeling these nonlinear contributions was developed. The model was characterized by a single parameter u, values of which were obtained for each channel via least-squares fit to the data. Using the best-fit u values, we performed a series of simulations of the quadratic corrections which would be expected from the space data after the launch of AMSU-A on NOAA-K. In these simulations, the cosmic background radiance corresponding to a cold space temperature 2.73K was adopted as one of the two reference points of calibration. The largest simulated nonlinear correction is about 0.3K, which occurs at channel 15 when the instrument temperature is at 38.09 deg C. Others are less than 0.2K in the remaining channels. Possible improvement for future instrument calibration is also discussed.

Mo, Tsan↗

Rate Coefficients of C2H with C2H4, C2H6, and H2 from 150 to 359 K

Rate coefficients for the reactions C2H with C2H4, C2H6, and H2 are measured over the temperature range 150-359 K using transient infrared laser absorption spectroscopy. The ethynyl radical is formed by photolysis of C2H2 with a pulsed excimer laser at 193 nm, and its transient absorption is monitored with a color center laser on the Q(sub 11)(9) line of the A(sup 2) Pi-Chi(sup 2) Sigma transition at 3593.68 cm(exp -1). Over the experimental temperature range 150-359 K the rate constants of C2H with C2H4, C2H6, and H2 can be fitted to the Arrhenius expressions k(sub C2H4) = (7.8 +/- 0.6) x 10(exp -11) exp[(134 +/- 44)/T], k(sub C2H6) = (3.5 +/- 0.3) x 10(exp -11) exp[(2.9 +/- 16)/T], and k(sub H2) = (1.2 +/- 0.3) x 10(exp -11) exp[(-998 +/- 57)]/T cm(exp 3) molecule(exp -1) sec(exp -1). The data for C2H with C2H4 and C2H6 indicate a negligible activation energy to product formation shown by the mild negative temperature dependence of both reactions. When the H2 data are plotted together with the most recent high-temperature results from 295 to 854 K, a slight curvature is observed. The H2 data can be fit to the non-Arrhenius form k(sub H2) = 9.2 x 10(exp -18) T(sup 2.17 +/- 0.50) exp[(-478 +/- 165)/T] cm(exp 3) molecules(exp -1) sec(exp -1). The curvature in the Arrhenius plot is discussed in terms of both quantum mechanical tunneling of the H atom from H2 to the C2H radical and bending mode contributions to the partition function.

Opansky, Brian J.↗

No Compton Reflection In a Chandra/RXTE Observation of Mkn 509: Implications for the Fe-K Line Emission From Accreting X-Ray Sources

We report the results of simultaneous Chandra and RXTE observations of the Seyfert 1 galaxy Mkn 509. We deconvolve the broad and narrow Fe-K emission-line components for which we measure rest-frame equivalent widths of 119+/-18 eV and 57+/-13 eV respectively. The broad line has a FWHM of 57,600((sup 14,400)(sub -21,000)) km/s and the narrow line is unresolved, with an upper limit on the FWHM of 4,940 km/s. Both components must originate in cool matter since we measure rest-frame center energies of 6.36((sup +0.13)(sub -0.12)) keV and 6.42+/-0.01 keV for the broad and narrow line respectively. This rules out He-like and H-like Fe for the origin of both the broad and narrow lines. If, as is widely accepted, the broad Fe-K line originates in Thomson-thick matter (such as an accretion disk), then one expects to observe spectral curvature above approximately 10 keV, (commensurate with the observed broad line), characteristic of the Compton-reflection continuum. However our data sets very stringent limits on deviations of the observed continuum from a power law. Light travel-time delays cannot be invoked to explain anomalies in the relative strengths of the broad Ferry line and Compton-reflection continuum since they are supposed to originate in the same physical location. We are forced to conclude that both the broad and narrow Fe-K lines had to originate in Thomson-thin matter during our observation. This result, for a single observation of just one source, means that our understanding of Fe K line emission and Compton reflection from accreting X-ray sources in general needs to be re-examined. For example, if an irradiated accretion disk existed in Mkn 509 at the time of the observations, the lack of spectral curvature above approximately 10 keV suggests two possibilities. Either the disk was Thomson-thick and highly ionized, having negligible Fe-K line emission and photoelectric absorption or the disk was Thomson-thin producing some or all of the broad Fe-K line emission. In the former case, the broad Fe-K line had to have produced in a Thomson-thin region elsewhere. In both cases the predicted spectral curvature above approximately 10 keV is negligible. An additional implication of our results is that any putative obscuring torus in the system, required by unification models of active galaxies, must also be Thomson-thin. The same applies to the optical broad line region (BLR) if it has a substantial covering factor.

Yaqoob, Tahir↗

Photoionization Modeling of Oxygen K Absorption in the Interstellar Medium: The Chandra Grating Spectra of XTE J1817-330

We present detailed analyses of oxygen K absorption in the interstellar medium (ISM) using four high-resolution Chandra spectra towards the X-ray low-mass binary XTE J1817-330. The 11-25 A broadband is described with a simple absorption model that takes into account the pileup effect and results in an estimate of the hydrogen column density. The oxygen K-edge region (21-25 A) is fitted with the physical warmabs model, which is based on a photoionization model grid generated with the XSTAR code with the most up-to-date atomic database. This approach allows a benchmark of the atomic data which involves wavelength shifts of both the K lines and photoionization cross sections in order to fit the observed spectra accurately. As a result we obtain: a column density of N(sub H) = 1.38 +/- 0.01 x 10(exp 21) cm(exp -2); ionization parameter of log xi = .2.70 +/- 0.023; oxygen abundance of A(sub O) = 0.689(exp +0.015./-0.010); and ionization fractions of O I/O = 0.911, O II/O = 0.077, and O III/O = 0.012 that are in good agreement with previous studies. Since the oxygen abundance in warmabs is given relative to the solar standard of Grevesse and Sauval (1998), a rescaling with the revision by Asplund et al. (2009) yields A(sub O) = 0.952(exp +0.020/-0.013, a value close to solar that reinforces the new standard. We identify several atomic absorption lines.K-alpha , K-beta, and K-gamma in O I and O II; and K-alpha in O III, O VI, and O VII--last two probably residing in the neighborhood of the source rather than in the ISM. This is the first firm detection of oxygen K resonances with principal quantum numbers n greater than 2 associated to ISM cold absorption.

Gatuzz, E.↗

Commissioning of a 20 K Helium Refrigeration System for NASA-JSC Chamber A

A new 20 K helium refrigerator installed at NASA Johnson Space Center s Space Environment Simulation Laboratory (SESL) was successfully commissioned and tested in 2012. The refrigerator is used to create a deep space environment within SESL s Chamber A to perform ground testing of the James Webb Space Telescope (JWST). The chamber previously and currently still has helium cryo-pumping panels (CPP) and liquid nitrogen shrouds used to create low earth orbit environments. Now with the new refrigerator and new helium shrouds the chamber can create a deep space environment. The process design, system analysis, specification development, and commissioning oversight were performed by the cryogenics department at Jefferson Lab, while the contracts and system installation was performed by the ESC group at JSC. Commissioning data indicate an inverse coefficient of performance better than 70 W/W for a 18 kW load at 20 K (accounting for liquid nitrogen pre-cooling power) that remains essentially constant down to one third of this load. Even at 10 percent of the maximum capacity, the performance is better than 150 W/W at 20 K. The refrigerator exceeded all design goals and demonstrated the ability to support a wide load range from 10 kW at 15 K to 100 kW at 100 K. The refrigerator is capable of operating at any load temperature from 15 K to ambient with tight temperature stability. The new shroud (36 tons of aluminum) can be cooled from room temperature to 20 K in 24 hours. This paper will outline the process design and commissioning results.

Homan, J.↗

Recent Developments and Challenges Implementing New and Improved Stress Intensity Factor (K) Solutions in NASGRO for Damage Tolerance Analyses

Fatigue crack growth analysis software has been available to damage tolerance analysts for many years in either commercial products or via proprietary in-house codes. The NASGRO software has been publicly available since the mid-80s (known as NASA/FLAGRO up to 1999) and since 2000 has been sustained and further developed by a collaborative effort between Southwest Research Institute® (SwRI®), the NASA Johnson Space Center (JSC), and the members of the NASGRO Industrial Consortium. Since the stress intensity factor (K) is the foundation of fracture mechanics and damage tolerance analysis of aircraft structures, a significant focus of development efforts in the past fifteen years has been geared towards enhancing legacy K solutions and developing new and efficient numerical K solutions that can handle the complicated stress gradients computed by today’s analysts using detailed finite element models of fatigue critical locations. This paper provides an overview of K solutions that have been recently implemented or improved for the analysis of geometries such as two unequal through cracks at a hole and two unequal corner cracks at a hole, as well as state-of-the-art weight function models capable of computing K in the presence of univariant and/or bivariant stress gradients and complicated residual stress distributions. Some historical background is provided to review how common K solutions have evolved over the years, including selective examples from the literature and from new research. Challenges and progress in rectifying discrepancies between older legacy solutions and newer models are reviewed as well as approaches and challenges for verification and validation of K solutions. Finally, a summary of current challenges and future research and development needs is presented. A key theme throughout the presentation of this paper will be how members of the aerospace industry have collaborated with software developers to develop a practical analysis tool that is used world-wide to support new design as well as the ongoing sustainment and airworthiness of commercial and military aircraft.

Cardinal, Joseph W.↗

Experimental and Finite Element Modeling of Near-Threshold Fatigue Crack Growth for the K-Decreasing Test Method

The experimental methods to determine near-threshold fatigue crack growth rate data are prescribed in ASTM standard E647. To produce near-threshold data at a constant stress ratio (R), the applied stress-intensity factor (K) is decreased as the crack grows based on a specified K-gradient. Consequently, as the fatigue crack growth rate threshold is approached and the crack tip opening displacement decreases, remote crack wake contact may occur due to the plastically deformed crack wake surfaces and shield the growing crack tip resulting in a reduced crack tip driving force and non-representative crack growth rate data. If such data are used to life a component, the evaluation could yield highly non-conservative predictions. Although this anomalous behavior has been shown to be affected by K-gradient, starting K level, residual stresses, environmental assisted cracking, specimen geometry, and material type, the specifications within the standard to avoid this effect are limited to a maximum fatigue crack growth rate and a suggestion for the K-gradient value. This paper provides parallel experimental and computational simulations for the K-decreasing method for two materials (an aluminum alloy, AA 2024-T3 and a titanium alloy, Ti 6-2-2-2-2) to aid in establishing clear understanding of appropriate testing requirements. These simulations investigate the effect of K-gradient, the maximum value of stress-intensity factor applied, and material type. A material independent term is developed to guide in the selection of appropriate test conditions for most engineering alloys. With the use of such a term, near-threshold fatigue crack growth rate tests can be performed at accelerated rates, near-threshold data can be acquired in days instead of weeks without having to establish testing criteria through trial and error, and these data can be acquired for most engineering materials, even those that are produced in relatively small product forms.

Smith, Stephen W.↗

Development of a Flight-Worthy 10 to 4 K Continuous Adiabatic Demagnetization Refrigerator

The cryogenics and fluids branch at NASA's Goddard Space Flight Center is currently developing a high-efficiency, vibration-free, flight-worthy Continuous Adiabatic Demagnetization Refrigerator (CADR) that consist of two modular units: one that lifts ~6 microW at 50 mK while rejecting its heat to a 4 K thermal sink, and another unit that provides a constant 4 K cooling stage while rejecting its heat to a thermal sink at 10 K. The two units are linked together via a 4 K common platform. This paper discusses the status report on the thermodynamic performance of the 4 -10 K ADR. This ADR utilizes an Nb3Sn superconducting magnet and Gadolinium Gallium Garnet (GGG) as its refrigerant. Results show that an idealized cycle, one where its hold time at 4 K is equal to the recycle time, can lift 13 mW at 4 K with a hold time of 132 seconds.

CADR↗

Applications of the Dynamic N-Dimensional K-Vector

The n-dimensional k-vector (NDKV) is an appealing alternative to binary tress for resolving complex queries in large relational databases. The method has excelled in several applications involving static databases. The present paper extends the theory supporting the NDKV to handle dynamic databases, where the data is updated frequently. This includes deleting records, adding new entries, or editing existing elements. The merit of this new version of the NDKV, the dynamic n-dimensional k-vector (DNDKV), is that it is no longer necessary to recompute the entire k-vector (the main structure that indexes the data) every time a record changes. The algorithm updates the four constituents of the standard NDKV on the fly: the database, sorted database, index, and k-vector tables. As a result, the DNDKV becomes comparable in terms of capabilities and flexibility to stateof-the-art storage engines relying on structured query languages (SQL). The performance of the DNDKV is assessed by running typical read/write operations on a database that contains millions of pre-computed missions to celestial bodies. This database requires frequent updates whenever an orbit solution is refined or new bodies are discovered. The DNDKV is faster than rebuilding the k-vector tables completely, provided that the number of elements being added or removed is not excessively large. Direct runtime comparisons with MySQL suggest that the DNDKV is several times faster for reading but might be slower for writing and updating the database. One limit of the technique is the elements being added must be within the range of the current k-vector tables. If this is not the case, the technique cannot be used and the k-vector tables must be rebuilt from scratch.

Mortari, Daniele↗

Search for CP violation and measurement of branching fractions and decay asymmetry parameters for Λ$^+_c$ → Λ h + and Λ$^+_c$ → Σ 0 h + ( h = K, π )

Here, we report a study of Λ$^+_c$ → Λ h + and Λ$^+_c$ → Σ 0 h + ( h = K, π ) decays based on a data sample of 980 fb -1 collected with the Belle detector at the KEKB energy-asymmetric e + e - collider. The first results of direct CP asymmetry in two-body singly Cabibbo-suppressed (SCS) decays of charmed baryons are measured, A$^{dir}_{CP}(Λ^+_{c} → ΛK^{+})$ = +0.021 ± 0.026 ± 0.001 and A$^{dir}_{CP}(Λ^+_{c} → Σ^{0}K^{+})$ = +0.025 ± 0.054 ± 0.004. We also make the most precise measurement of the decay asymmetry parameters (α) for the four modes of interest and search for CP violation via the α-induced CP asymmetry (A$^α_{CP}$ ). We measure A$^α_{CP}$ ($Λ^+_{c} → ΛK^{+}$) = -0.023 ± 0.086 ± 0.071 and A$^α_{CP}$ ($Λ^+_{c} → Σ^{0}K^{+}$) = +0.08 ± 0.35 ± 0.14, which are the first A$^α_{CP}$ results for SCS decays of charmed baryons. We search for Λ -hyperon CP violation in $Λ^+_{c}$ → (Λ, Σ 0 )π + and find A$^α_{CP}$(Λ → pπ - ) = +0.013 ± 0.007 ± 0.011 . This is the first time that hyperon CP violation has been measured via Cabibbo-favored charm decays. No evidence of baryon CP violation is found. We also obtain the most precise branching fractions for two SCS Λ$^+_c$ decays, $\mathscr{B}$($Λ^+_{c} → ΛK^{+}$) = (6.57 ± 0.17 ± 0.11 ± 0.35) x 10 -4 and $\mathscr{B}$($Λ^+_{c} → Σ^{0}K^{+}$) = (3.58 ± 0.19 ±0.06 ±0.19) x 10 -4 . The first uncertainties are statistical and the second systematic, while the third uncertainties come from the uncertainties on the world average branching fractions of $Λ^+_{c}$ → (Λ, Σ 0 )π + .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗