Ryan P. Fitzgerald

Charged-Particle Thermonuclear Reaction Rates: II. Tables and Graphs of Reaction Rates and Probability Density Functions

Abstract Numerical values of charged-particle thermonuclear reaction rates for nuclei in the A = 14 to 40 region are tabulated. The results are obtained using a method, based on Monte Carlo techniques, that has been described in the preceding paper of this issue (Paper I). We present a low rate, median rate and high rate which correspond to the 0.16, 0.50 and 0.84 quantiles, respectively, of the cumulative reaction rate distribution. The meaning of these quantities is in general different from the commonly reported, but statistically meaningless expressions, “lower limit”, “nominal value” and “upper limit” of the total reaction rate. In addition, we approximate the Monte Carlo probability density function of the total reaction rate by a lognormal distribution and tabulate the lognormal parameters μ and σ at each temperature. We also provide a quantitative measure (Anderson–Darling test statistic) for the reliability of the lognormal approximation. The user can implement the approximate lognormal reaction rate probability density functions directly in a stellar model code for studies of stellar energy generation and nucleosynthesis. For each reaction, the Monte Carlo reaction rate probability density functions, together with their lognormal approximations, are displayed graphically for selected temperatures in order to provide a visual impression. Our new reaction rates are appropriate for bare nuclei in the laboratory. The nuclear physics input used to derive our reaction rates is presented in the subsequent paper of this issue (Paper III). In the fourth paper of this issue (Paper IV) we compare our new reaction rates to previous results.

Measurement of radon and xenon binding to a cryptophane molecular host

Xenon and radon have many similar properties, a difference being that all 35 isotopes of radon (195Rn–229Rn) are radioactive. Radon is a pervasive indoor air pollutant believed to cause significant incidence of lung cancer in many geographic regions, yet radon affinity for a discrete molecular species has never been determined. By comparison, the chemistry of xenon has been widely studied and applied in science and technology. Here, both noble gases were found to bind with exceptional affinity to tris-(triazole ethylamine) cryptophane, a previously unsynthesized water-soluble organic host molecule. The cryptophane–xenon association constant, Ka = 42,000 ± 2,000 M-1 at 293 K, was determined by isothermal titration calorimetry. This value represents the highest measured xenon affinity for a host molecule. The partitioning of radon between air and aqueous cryptophane solutions of varying concentration was determined radiometrically to give the cryptophane–radon association constant Ka = 49,000 ± 12,000 M-1 at 293 K.

Charged-particle thermonuclear reaction rates: I. Monte Carlo method and statistical distributions

Abstract A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability density function, including Gaussian, lognormal and chi-squared distributions. Based on these probability density functions the total reaction rate is randomly sampled many times until the required statistical precision is achieved. This procedure results in a median (Monte Carlo) rate which agrees under certain conditions with the commonly reported recommended “classical” rate. In addition, we present at each temperature a low rate and a high rate, corresponding to the 0.16 and 0.84 quantiles of the cumulative reaction rate distribution. These quantities are in general different from the statistically meaningless “minimum” (or “lower limit”) and “maximum” (or “upper limit”) reaction rates which are commonly reported. Furthermore, we approximate the output reaction rate probability density function by a lognormal distribution and present, at each temperature, the lognormal parameters μ and σ . The values of these quantities will be crucial for future Monte Carlo nucleosynthesis studies. Our new reaction rates, appropriate for bare nuclei in the laboratory , are tabulated in the second paper of this issue (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this issue (Paper III). In the fourth paper of this issue (Paper IV) we compare our new reaction rates to previous results.

Standardization of 68Ge/68Ga using three liquid scintillation counting-based methods

A solution containing 68Ge in equilibrium with its daughter, 68Ga, has been standardized for the first time at the National Institute of Standards and Technology (NIST) using 3 liquid scintillation-based techniques: live-timed 4πβ -γ anticoincidence (LTAC) counting, the Triple-to-Double Coincidence Ratio (TDCR) method, and 3H-standard efficiency tracing with the CIEMAT1/NIST (CNET) method. The LTAC technique is much less dependent on level scheme data and model-dependent parameters and was thus able to provide a reference activity concentration value for the master solution with a combined standard uncertainty of about 0.3 %. The other two methods gave activity concentration values with respective differences from the reference value of +1.2 % and −1.5 %, which were still within the experimental uncertainties. Measurements made on the NIST “4π”γ secondary standard ionization chamber allowed for the determination of calibration factors for that instrument, allowing future calibrations to be made for 68Ge/68Ga without the need for a primary measurement. The ability to produce standardized solutions of 68Ge presents opportunities for the development of a number of NIST-traceable calibration sources with very low (<1 %) relative standard uncertainties that can be used in diagnostic medical imaging.

Revision of the NIST Standard for (223)Ra: New Measurements and Review of 2008 Data.

After discovering a discrepancy in the transfer standard currently being disseminated by the National Institute of Standards and Technology (NIST), we have performed a new primary standardization of the alpha-emitter 223Ra using Live-timed Anticoincidence Counting (LTAC) and the Triple-to-Double Coincidence Ratio Method (TDCR). Additional confirmatory measurements were made with the CIEMAT-NIST efficiency tracing method (CNET) of liquid scintillation counting, integral γ-ray counting using a NaI(Tl) well counter, and several High Purity Germanium (HPGe) detectors in an attempt to understand the origin of the discrepancy and to provide a correction. The results indicate that a −9.5 % difference exists between activity values obtained using the former transfer standard relative to the new primary standardization. During one of the experiments, a 2 % difference in activity was observed between dilutions of the 223Ra master solution prepared using the composition used in the original standardization and those prepared using 1 mol·L−1 HCl. This effect appeared to be dependent on the number of dilutions or the total dilution factor to the master solution, but the magnitude was not reproducible. A new calibration factor (“K-value”) has been determined for the NIST Secondary Standard Ionization Chamber (IC “A”), thereby correcting the discrepancy between the primary and secondary standards.

Update of NIST half-life results corrected for ionization chamber source-holder instability.

As reported at the ICRM 2011, it was discovered that the source holder used for calibrations in the NIST 4πγ ionization chamber (IC) was not stable. This has affected a large number of half-life measurement results previously reported and used in compilations of nuclear data. Corrections have been made on all of the half-life data based on the assumption that the changes to the ionization chamber response were gradual. The corrections are energy dependent and therefore radionuclide specific. This presentation will review our results and present the recommended changes in half-life values and/or uncertainties.

NIST Ionization Chamber "A" Sample-Height Corrections.

For over 30 years scientists in the NIST radioactivity group have been using their pressurized ionization chamber “A” (PIC “A”) to make measurements of radioactivity and radioactive half-lives. We now have evidence that some of those reported measurements were incorrect due to slippage of the source positioning ring over time. The temporal change in the holder caused an error in the source-height within the chamber, which was thought to be invariant. This unaccounted-for height change caused a change in the detector response and thus a relative error in measured activity on the order of 10−5 to 10−3 per year, depending on the radionuclide. The drifting detector response affected calibration factors and half-life determinations. After discovering the problem, we carried out historic research and new sensitivity tests. As a result, we have created a quantitative model of the effect and have used that model to estimate corrections to some of the past measurement results from PIC “A”. In this paper we report the details and results of that model. Meanwhile, we have fixed the positioning ring and are recalibrating the detector using primary measurement methods and enhanced quality control measures.

Uncertainty of nuclear counting

Nuclear counting is affected by pulse pileup and system dead time, which induce rate-related count loss and alter the statistical properties of the counting process. Fundamental equations are presented to predict deviations from Poisson statistics due to non-random count loss in nuclear counters and spectrometers. Throughput and dispersion of counts are studied for systems with pileup, extending and non-extending dead time, before and also after compensation for count loss. Equations are provided for random fractions of the output events, applicable to spectrometry applications. Methods for loss compensation are discussed, including inversion of the throughput equation, live-time counting and loss-free counting. Secondary effects in live-time counting are addressed: residual interference from pileup in systems with imposed dead times and errors due to varying count rate when measuring short-lived radionuclides.

Liquid-scintillation-based anticoincidence counting of Co-60 and Pb-210

The method of liquid-scintillation-based 4pibeta-gamma anticoincidence counting was employed to assay the radioactivity concentration of acid solutions containing radionuclides (60)Co and (210)Pb (in equilibrium with its daughters). The limiting factors on the accuracy for such activity measurements and suggestions for minimizing such factors are reported.

Uncertainties in 4πβ–γ coincidence counting

The 4πβ-γ coincidence counting method and its close relatives are widely used for the primary standardization of radioactivity. Both the general formalism and specific implementation of these methods have been well-documented. In particular, previous papers contain the extrapolation equations used for various decay schemes, methods for determining model parameters and, in some cases, tabulated uncertainty budgets. Two things often lacking from experimental reports are both the rationale for estimating uncertainties in a specific way and the details of exactly how a specific component of uncertainty was estimated. Furthermore, correlations among the components of uncertainty are rarely mentioned. To fill in these gaps, the present article shares the best-practices from a few practitioners of this craft. We explain and demonstrate with examples of how these approaches can be used to estimate the uncertainty of the reported massic activity. We describe uncertainties due to measurement variability, extrapolation functions, dead-time and resolving-time effects, gravimetric links, and nuclear and atomic data. Most importantly, a thorough understanding of the measurement system and its response to the decay under study can be used to derive a robust estimate of the measurement uncertainty.