Decay Of Nuclides Research Articles

Validation of decay heat calculation results of ORIGEN2.2 and CASMO5 for light water reactor fuel

ABSTRACTComparing with the fission product nuclide (FP) decay heat summation calculation result in MeV/sec/fission based on the JENDL FP decay and yield data files 2011 for the burst fission, FP decay heat calculated by ORIGEN2.2 coupled with JENDL-4.0 base library ORLIBJ40 was verified at the cooling time from 1 sec to 108 sec for 235U (thermal), 238U (fast), 239Pu (thermal) and 241Pu (thermal). For these fission nuclides, FP decay heat calculated by CASMO5 at the same cooling time after a short irradiation (104 sec) was also compared with that of ORIGEN2.2. In the analysis of decay heat measurements at the cooling time from 2.3 years to 27 years consisting of four data sets on the fuel assemblies discharged from the US PWRs and BWRs, and the Swedish PWRs and BWRs, the average values of the ratios of the calculated to measured results (C/E's) were from 0.972 to 1.031 for ORIGEN2.2, and from 0.977 to 1.016 for CASMO5. The standard deviations of C/E's for the four data sets were from 0.02 to 0.03 for the both codes except for those of the US BWR fuel assemblies which were from 0.11 to 0.12. The obtained C/E's were similar to those in the precedent study.

Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

The Chebyshev rational approximation method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant substeps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the lower-upper decompositions for the linear solutions required in CRAM need to be formed only on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. With substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.

Chondrules in CK carbonaceous chondrites and thermal history of the CV–CK parent body

AbstractCK chondrites are the only group of carbonaceous chondrites with petrologic types ranging from 3 to 6. It is commonly reported than ~15 vol% of CK4–6 samples are composed of chondrules. The modal abundance of chondrules estimated here for 18 CK3–6 (including five CK3s) ranges from zero (totally recrystallized) to 50.5%. Although almost all chemically re‐equilibrated with the host matrix, we recognized in CK3s and Tanezrouft (Tnz) 057 (CK4) up to 85% of chondrules as former type I chondrules. Mean diameters of chondrules range from 0.22 to 1.05 mm for Karoonda (CK4) and Tnz 057 (CK4), respectively. Up to ~60% of chondrules in CK3–4 are surrounded by igneous rims (from ~20 μm to 2 mm width). Zoned olivines were found in unequilibrated chondrules from DaG 431 (CK3‐an), NWA 4724 (CK3.8), NWA 4423 (CK3.9), and Tnz 057 (CK4). We modeled Fe/Mg interdiffusion profiles measured in zoned olivines to evaluate the peak metamorphic temperatures and time scales of the CK parent body metamorphism, and proposed a two‐stage diffusion process in order to account for the position of inflection points situated within chondrules. Time scales inferred from Fe/Mg interdiffusion in olivine from unequilibrated chondrules are on the order of tens to a hundred thousand years (from 50 to 70,000 years for peak metamorphic temperatures of 1140 and 920 K, respectively). These durations are longer than what is commonly accepted for shock metamorphism and shorter than what is required for nuclide decay. Using the concept of a continuous CV–CK metamorphic series, which is reinforced by this study, we estimated peak metamorphic temperatures <850 K for CV, 850–920 K for CK3, and 920–1140 K for CK4–6 chondrites considering a duration of 70,000 years.

Statistical Research of Nuclide’s Shell Structure

This thesis, after a systematic and in-depth analysis of known nuclides, pro-poses a new model of nuclides’ shell structure and offers a table of shell structures of 935 nuclides. With this theoretic approach, thesis studies shell combination with a bias towards statistical analysis of nuclide structures. This thesis distinguishes between basic models of nuclides and gives 7criteria for nuclide binding, maximal nucleonic of each shell (Δ ), combination of proton and neutron (p/n) and graphs of nuclide growth. Based on magnetic moment, it also conducts a quantitative analysis of p/n on shell. The nuclide structure has characteristic of a shell and on every shell combination of proton and neutron features clear regularity. Among 106 elements from H to Sg serial of most outside s hell in structure is 7, and nuclides Ha and Sg are respectively even A and odd A 7 shells. It is not a coincidence but a reflection of nuclide shell structure. The thesis uses result of a statistical analysis to confirm existence of the magic Number and reveals fact that magic number is a reflection of p/n on nuclide shell, particularly on outer shells. The statistical analysis reveals that nuclide stability and its way of decay are dependent on nucleonic combination on most outside shell and matching between full-filled and semi-full filled p/n, thus unveiling general law governing stability and decay of nuclides.

Hidden Variable Theory Supports Variability in Decay Rates of Nuclides

PROBLEM- The orthodox expectation is for decay rates to be strictly constant for all types of decay (β+, β-, EC, α). However empirical results show strong evidence for nuclides having variable decay rates, typically evident as periodicity. The volume of data available suggests this is a real phenomenon, not merely a spurious outcome of measurement errors. However the problem is complex because the data are conflicted for different decays. Consequently it is a significant challenge to explain how the variability might arise, what factors could be involved, and how the underlying mechanisms of causality might operate. PURPOSE- This paper develops a theoretical explanation of the variability of nuclide decay rates. APPROACH- The non-local hidden-variable solution provided by the Cordus theory was used, specifically its mechanics for neutrino-species interactions with nucleons. FINDINGS- It is predicted that the β-, β+ and electron capture processes are induced by pre-supply of neutrino-species, and that the effects are asymmetrical for those species. Also predicted is that different input energies are required, i.e. that a threshold effect exists. Four simple non-contentious lemmas are proposed with which it is straightforward to explain why β- and EC would be enhanced and correlate to solar neutrino flux (proximity & activity), and α emission unaffected. It is shown that the concept of a neutrino-species asymmetry makes sense of the broad patterns evident in the empirical data. IMPLICATIONS- The results support the variability of decay rates, on theoretical grounds. The type of decay (β+, β-, EC, α) is found to be a key variable in this theory, as is the type of neutrino species and its energy. ORIGINALITY- The novel contribution is the provision of a theoretical explanation for why decay rates would be variable. A detailed mechanism is presented for neutrino-species induced decay. Also novel is the prediction that the interaction is asymmetrical, and that the energy requirements are different for the various types of decay.

The Radionuclide Pollutant Dispersion Simulation in Nuclear Accident of Liaoning Hongyanhe Nuclear Power Plant

In order to simulate the nuclear proliferation model of power plant accident, the objective factors of the nuclide dry deposition, wet deposition and radioactive decay are considered and studied based on Gauss diffusion model. With the model modified, the nuclear proliferation simulation of power plant accident is implemented. The simulation system of radionuclide nuclear proliferation is designed and realized with the application of information technology such as GIS and so on. In light of variations in such things as geography, climate and working, the nuclear proliferation of power plant accident emergency is simulated. The results showed that the system can effectively realize the simulation of radionuclide nuclear proliferation including the instantaneous point source, continuous point source, which provides decision support for nuclear accident emergency treatment.

Asymmetrical Neutrino Induced Decay of Nucleons

Problem- The operation of neutrino detectors shows that nuclide decay rates can be affected by loading of neutrino species. However the underlying principles of this are poorly understood. Purpose- This paper develops a conceptual solution for the neutrino-species interactions with single nucleon decay processes. Approach- The starting point was the non-local hidden-variable (NLHV) solution provided by the Cordus theory, specifically its mechanics for the manipulation of discrete forces and the remanufacture of particle identities. This mechanics was applied to the inverse beta decays and electron capture processes for nucleons. These are situations where the neutrino or antineutrino is supplied as an input, as opposed to being an output as in the conventional decays. Findings- Inverse decays are predicted to be differentially susceptible to inducement by neutrino-species. The inverse β- neutron decay is predicted to be susceptible to neutrino inducement (but not to the antineutrino). Correspondingly β+ proton decay is predicted to be induced by input of energetic antineutrinos, but not neutrinos. Hence a species asymmetry is predicted. The inverse electron capture is predicted to be induced by pre-supply of either a neutrino or antineutrino, with different energy threshold requirements in each situation. The neutrino induced channel is predicted to have the greater energy barrier than the antineutrino channels. All the nucleon decay processes (forward, inverse, and induced) may be represented in a single unified decay equation, with transfers across the decay equality resulting in inversion of the matter-antimatter species (hand). Implications- The theory predicts the existence of a number of induced decays with asymmetrical susceptibility to neutrino-species. The results imply that detectors that measure β- outcomes are measuring neutrinos, and β+ antineutrinos. Originality- A new methodology is demonstrated for predicting the outcomes of decays and particle transformations. A unified decay relationship is proposed, that expresses all the conventional and induced decay processes. A novel prediction is made, that neutrino-species induce decay of nucleons, and that the interaction is asymmetrical. Hence also, that different decay types are affected differently by the input of energy and neutrino-species. A detailed explanation is provided of how this occurs at the level of the internal structures of the particules. This is an unorthodox outcome and is testable and falsifiable.

Np-237在AP1000首循环堆芯中的嬗变研究

核电站所产生的乏燃料中含有大量的放射性核素，主要包括长寿命裂变产物(LLFP)和少量锕系元素(MA)，这些核素要通过上万年的衰变才能消除放射性危害。分离嬗变技术(P&T)是将这些放射性核素从乏燃料中分离出来，放入特定装置中，对其进行中子照射，使其转变成低放射性核素或稳定核素。镎(Np)作为一种最主要的MA核素，其含量高，半衰期长。本文利用MCNP程序搭建AP1000反应堆堆芯模型，以二氧化镎(NpO2)嬗变棒为引入方式，设计出在首循环堆芯中添加嬗变材料的10种方案。通过计算比较各种方案中有效增殖因子(keff)、二氧化镎的添加质量和使堆芯重新达到临界所需要改变堆芯的程度，结果显示在堆芯燃料富集度为4.45%区域添加二氧化镎涂层的方案具有优势，本文对该方案进行了分析并进行了优化。 The spent fuel generated by nuclear power plants contains large quantities of radionuclides, in-cluding long-lived fission products (LLFP) and minor actinides (MA). These nuclides decay to no harm through thousands of years. Partitioning and transmutation technology (P&T) is to separate these nuclides from the spent fuel into specific device for neutron irradiation, making it into a low-level radioactive nuclides or stable nuclides. As a major MA nuclide, neptunium (Np) has a high productivity and long half-time. In this paper, MCNP code is used to build the AP1000 reactor core model, and neptunium dioxide (NpO2) transmutation rod is introduced to design 10 schemes where transmutation material is putted into the first cycle core. By calculation and comparing the effective multiplication factor (keff), the added quality of neptunium dioxide and the changing extent to make the core reach the critical again, the result shows that the scheme where neptunium dioxide coating is putted in the fuel enrichment 4.45% of the core has advantages. This paper analyzes the scheme and optimized.

Radioisotope studies of the farmville meteorite using γγ-coincidence spectrometry

Radionuclides are cosmogenically produced in meteorites before they fall to the surface of the Earth. Measurement of the radioactive decay of such nuclides provides a wealth of information on the irradiation conditions of the meteorite fragment, the intensity of cosmic rays in the inner solar system, and the magnetic activity of the Sun. We report here on the detection of 26Al using a sophisticated spectrometer consisting of a HPGe detector and a NaI(Tl) annulus. It is shown that modern γ-ray spectrometers represent an interesting alternative to other detection techniques. Data are obtained for a fragment of the Farmville meteorite and compared to results from Geant4 simulations. In particular, we report on optimizing the detection sensitivity by using suitable coincidence gates for deposited energy and event multiplicity. We measured an 26Al activity of 48.5±3.5dpm/kg for the Farmville meteorite, in agreement with previously reported values for other H chondrites.

A background simulation method for cosmogenic nuclides inside HPGe detectors for rare event experiments

Cosmogenic nuclides inside germanium detectors contribute background noise spectra quite different from ordinary external sources. We propose and discuss a nuclide decay and level transition model based on graph theory to understand the background contribution of the decay of cosmogenic nuclides inside a germanium crystal. In this work, not only the level transition process, but the detector response time was also taken into consideration to decide whether or not to apply coincidence summing-up. We simulated the background spectrum of the internal cosmogenic nuclides in a germanium detector, and found some unique phenomena caused by the coincidence summing-up effect in the simulated spectrum. Thus, the background spectrum of each cosmogenic nuclide can be quantitatively obtained.

A method for determining the extent of bulk 210Po and 210Pb adsorption and retardation in aquifers

The naturally-occurring radionuclides 210Po and 210Pb are normally found in very low concentrations in the environment. However, under some conditions 210Po contributes significantly to the radioactivity in ground waters and can constitute a health risk. Naturally-occurring 210Pb can be used in predicting the behavior of contaminant Pb. While studies have identified the processes controlling 210Po and 210Pb behavior, the extent of adsorption and rates of removal in an aquifer cannot be determined without quantifying the rates of supply of these isotopes from decay of parent nuclides on and within aquifer solids. This study demonstrates how the isotope systematics of the 238U decay series, which includes 210Po and 210Pb, can be used to quantify the adsorption and retardation factors of 210Po and 210Pb in aquifers. The rates of 210Po and 210Pb supply to ground waters are determined from the concentrations of other radionuclides in the series, especially 222Rn, and so the distribution coefficients between aquifer solids and groundwater can be calculated. The effects of different supply rates due to different distributions of parent radionuclides in the aquifer can then be separated from differences in adsorption, which is controlled by aquifer water chemistry. A review of groundwaters where 210Po, 210Pb, and 222Rn data are available indicates that systematic variations can be found in bulk effective adsorption coefficients and retardation factors. Overall, a method is provided for future studies of 210Po and 210Pb behavior, and greater understanding of the occurrence and migration of these radionuclides.

The Electron Capture $$^{163}$$ 163 Ho Experiment ECHo

The determination of the absolute scale of the neutrino masses is one of the most challenging present questions in particle physics. The most stringent limit, $m(\bar{\nu}_{\mathrm{e}})<2$eV, was achieved for the electron anti-neutrino mass \cite{numass}. Different approaches are followed to achieve a sensitivity on neutrino masses in the sub-eV range. Among them, experiments exploring the beta decay or electron capture of suitable nuclides can provide information on the electron neutrino mass value. We present the Electron Capture $^{163}$Ho experiment ECHo, which aims to investigate the electron neutrino mass in the sub-eV range by means of the analysis of the calorimetrically measured energy spectrum following electron capture of $^{163}$Ho. A high precision and high statistics spectrum will be measured with arrays of metallic magnetic calorimeters. We discuss some of the essential aspects of ECHo to reach the proposed sensitivity: detector optimization and performance, multiplexed readout, $^{163}$Ho source production and purification, as well as a precise theoretical and experimental parameterization of the calorimetric EC spectrum including in particular the value of $Q_{\mathrm{EC}}$. We present preliminary results obtained with a first prototype of single channel detectors as well as a first 64-pixel chip with integrated micro-wave SQUID multiplexer, which will already allow to investigate $m(\nu_{\mathrm{e}})$ in the eV range.

188W/188Re Generator System and Its Therapeutic Applications

The188Re radioisotope represents a useful radioisotope for the preparation of radiopharmaceuticals for therapeutic applications, particularly because of its favorable nuclear properties. The nuclide decay pattern is through the emission of a principle beta particle having 2.12 MeV maximum energy, which is enough to penetrate and destroy abnormal tissues, and principle gamma rays (Eγ=155 keV), which can efficiently be used for imaging and calculations of radiation dose.188Re may be conveniently produced by188W/188Re generator systems. The challenges related to the double neutron capture reaction route to provide only modest yield of the parent188W radionuclide indeed have been one of the major issues about the use of188Re in nuclear medicine. Since the specific activity of188W used in the generator is relatively low (&lt;185 GBq/g), the elutedRe188O4-can have a low radioactive concentration, often ineffective for radiopharmaceutical preparation. However, several efficient postelution concentration techniques have been developed, which yield clinically usefulRe188O4-solutions. This review summarizes the technologies developed for the preparation of188W/188Re generators, postelution concentration of the188Re perrhenate eluate, and a brief discussion of new chemical strategies available for the very high yield preparation of188Re radiopharmaceuticals.

A re-evaluation of the Mn–Cr systematics of olivine from the angrite meteorite D’Orbigny using Secondary Ion Mass Spectrometry

‘Quenched’ angrite meteorites are among the best time markers of igneous activity in early formed planetesimals of the Solar System. They can be precisely dated by the Mn–Cr extinct nuclide decay system because they contain olivine with high Mn/Cr. Nevertheless, there is disagreement between various determinations of the initial 53Mn/55Mn for this meteorite, hindering their use for cross-calibration between chronometric systems and between Secondary Ion Mass Spectrometry (SIMS) and bulk measurement techniques. Here we re-evaluate the Mn–Cr systematics of olivine from the quenched angrite D’Orbigny using Sensitive High-mass Resolution Ion Micro Probe Reverse Geometry (SHRIMP-RG) to search for heterogeneity in isotope systematics and check for inter-laboratory bias. We investigated possible bias arising due to different data reduction methods and have paid careful attention to the relative sensitivities of Mn and Cr by utilising a three-component mixing model to correct for matrix effects associated with Mg, Fe and Ca zoning in angrite olivine. We have determined an initial 53Mn/55Mn of 3.60 (±0.39)×10−6 and 3.44 (±0.29)×10−6 (2σ errors) for D’Orbigny olivine by the Mean of Ratios and Ratio of Total Counts data reduction methods. These values are in agreement with those found by some previous bulk and mineral-scale determinations, and with the generally accepted initial 53Mn/55Mn of this meteorite, but not with previous SIMS work on this material. The source of this discrepancy remains unclear. We can exclude heterogeneity in D’Orbigny as a source of discrepancy because we used the same sample and the meteorite appears to have consistent initial 53Mn/55Mn over both micro- and macro-scales. The discrepancy between this and the previous SIMS study probably reflects an unrecognised systematic analytical bias, possibly associated with relative sensitivities of Mn and Cr or with mass spectrometric backgrounds (isobaric interferences or scattered ions) which may become significant at very low Cr count rates.

Development of a MCNP–ORIGEN burn-up calculation code system and its accuracy assessment

An MCNP–ORIGEN burn-up calculation code system, named MCORE (MCNP and ORIGEN burn-up Evaluation code), is developed in this work. MCORE makes use of the Monte Carlo neutron and photon transport code MCNP4C and nuclides depletion and decay calculation code ORIGEN2.1. MCNP and ORIGEN are coupled by data processing and linking subroutines. In MCORE, a so called “modified predictor corrector” approach is used. MCORE provides the capability of using different depletion calculation schemes and simulating fuel shuffling. Total nuclide density changes in active cells are considered in MCORE. The validity and applicability of the developed code are tested by investigating and predicting the neutronic and isotopic behavior of a “VVER-1000 LEU Assembly Computational Benchmark” at lattice level and a “Physics of Plutonium Recycling” fast reactor at core level (OECD-NEA).The comparison results show that the MCORE code predicts the nuclide composition within 5% accuracy and k∞ within 800pcm at the end of the burn-up for LEU assembly (40MWD/kg HM). For a fast reactor, the results obtained by MCORE are in the range of reported results except for 243Am. In general, MCORE results show a good agreement with the benchmark values.

Hard X-ray continuum from lunar surface: Results from High Energy X-ray spectrometer (HEX) onboard Chandrayaan-1

The High Energy X-ray spectrometer (HEX) on Chandrayaan-1 was designed to study the photon emission in the range of 30–270keV from naturally occurring radioactive decay of 238U and 232Th series nuclides from the lunar surface. The primary objective of HEX was to study the transport of volatiles on the lunar surface using radon as a tracer and mapping the 46.5keV line from 210Pb, a decay product of 222Rn. HEX was tested for two days during the commissioning phase of Chandrayaan-1 and performance of all sub systems was found to be as expected. HEX started collecting science data during the first non-prime imaging season (February–April, 2009) of Chandrayaan-1. Certain anomalies persisted in this data set and the early curtailment of Chandrayaan-1 mission in August, 2009, did not allow any further operation of HEX. Despite these issues, HEX provided the first data set for 30–270keV continuum emission, averaged over a significant portion of the lunar surface, including the polar region.

Surface Ionization of Radioactive Nuclides - Numerical Simulations

The Monte Carlo method based model of the ionization in the hot cavity taking into account radioactive decay of nuclides is presented. The code upgraded compared to the previous version enables calculation of the ion source ionization e ciency not only for di erent geometries and temperatures of the ionizer, extraction voltages etc. but also gives opportunity of setting di erent values of the nuclide half-life and its sticking time, which may be considered as the main factor determining the time that a particle spends in the ion source. The results of calculations are presented together with the discussion of the radioactive decay on the ion source performance.

On the Time Scales of Magma Genesis, Melt Evolution, Crystal Growth Rates and Magma Degassing in the Erebus Volcano Magmatic System Using the 238U, 235U and 232Th Decay Series

We investigate the time scales of magma genesis, melt evolution, crystal growth rates and magma degassing in the Erebus volcano magmatic system using measurements of 238U–230Th–226Ra–210Pb–210Po, 232Th–228Ra–228Th and 235U–231Pa–227Ac. These are the first measurements of 231Pa–227Ac in volcanic samples and represent the first set of data in a volcanic system to examine the entire suite of relevant 238U, 235U and 232Th decay series nuclides. Our sample suite consists of 22 phonolite volcanic bombs, erupted between 1972 and 2005, and five anorthoclase megacrysts separated from bombs erupted in 1984, 1989, 1993, 2004 and 2005. The 238U–230Th, 230Th–226Ra and 235U–231Pa systems are uniform over the 34 years examined. The anorthoclase megacrysts and phonolite glasses show complementary 226Ra/230Th disequilibria with (226Ra/230Th) ∼40 in the anorthoclase and ∼0·75 in the phonolite glass. In all samples, (210Pb/226Ra) is in radioactive equilibrium for both phases. In two phonolite glass samples (227Ac/231Pa) is unity. For the phonolite glasses (228Ra/232Th) is in equilibrium, whereas in the anorthoclase megacrysts it is significantly greater than unity. Instantaneous crystal fractionation, with magma residence times greater than 100 years and less than 10 kyr, can account for the measured 238U–230Th–226Ra–210Pb and 235U–231Pa–227Ac. However, the significant 228Ra/232Th disequilibria in the anorthoclase megacrysts preclude this simple interpretation. To account for this apparent discrepancy we therefore developed an open-system, continuous crystallization model that incorporates both nuclide ingrowth and decay during crystallization. This open-system model successfully reproduces all of the measured 238U and 232Th disequilibria and suggests that the shallow magma reservoir at Erebus is growing. The implication of this modeling is that when the time scale of crystallization is comparable with the half-life of the daughter nuclide of interest (e.g. 226Ra) the simple isochron techniques typically used in most U-series studies can provide erroneous ages. The observation that (210Pb/226Ra) and (227Ac/231Pa) are in radioactive equilibrium suggests that the residence time of the magmas is >100 years. When considering the effect of 222Rn degassing on 210Pb/226Ra, the data indicate that the majority of magma degassing is deep and long before eruption, consistent with melt inclusion data. Additionally, for the 2005 lava bomb, whose eruption date (16 December 2005) is known explicitly, 210Po was not completely degassed from the magma at the time of eruption. Incomplete degassing of 210Po is atypical for subaerially erupted lavas and suggests that the Erebus shallow magma degasses about 1% of its Po per day. The combined 238U and 232Th data further indicate that the pyroclasts ejected by Strombolian eruptions at Erebus have compositions that are close to what would be expected for a near-steady-state system, reflecting inmixing of degassed magmas, crystal fractionation, and aging.

THE DUAL ORIGIN OF THE NITROGEN DEFICIENCY IN COMETS: SELECTIVE VOLATILE TRAPPING IN THE NEBULA AND POSTACCRETION RADIOGENIC HEATING

We propose a scenario that explains the apparent nitrogen deficiency in comets in a way consistent with the fact that the surfaces of Pluto and Triton are dominated by nitrogen-rich ice. We use a statistical thermodynamic model to investigate the composition of the successive multiple guest clathrates that may have formed during the cooling of the primordial nebula from the most abundant volatiles present in the gas phase. These clathrates agglomerated with the other ices (pure condensates or stoichiometric hydrates) and formed the building blocks of comets. We report that molecular nitrogen is a poor clathrate former, when we consider a plausible gas phase composition of the primordial nebula. This implies that its trapping into cometesimals requires a low disk temperature ($\sim$20 K) in order to allow the formation of its pure condensate. We find that it is possible to explain the lack of molecular nitrogen in comets as a consequence of their postformation internal heating engendered by the decay of short-lived radiogenic nuclides. This scenario is found consistent with the presence of nitrogen-rich ice covers on Pluto and Triton. Our model predicts that comets should present xenon-to-water and krypton-to-water ratios close to solar xenon-to-oxygen and krypton-to-oxygen ratios, respectively. In contrast, the argon-to-water ratio is predicted to be depleted by a factor of $\sim$300 in comets compared to solar argon-to-oxygen, as a consequence of poor trapping efficiency and radiogenic heating.

The development of a through-diffusion model with a parent–daughter decay chain

A valid performance assessment of radioactive waste repositories strongly depends on the reliability of nuclide transport parameters, including distribution and diffusion coefficients. To reduce the waste produced and time spent conducting diffusion experiments, a robust model is required to accurately interpret the experiment results. Therefore, we developed a through-diffusion model with parent–daughter nuclide decay chain. We validated our model through comparisons with the Moridis model (Moridis, 1999) and Bharat model (Bharat et al., 2009), assessing our model and these two models using the distribution of parent nuclide concentrations. This strongly supports the rationality and functionality of extending our proposed model to daughter nuclides. In this study, we derived analytical solutions for the parent nuclides of the through-diffusion experiment using the multicompartment (MC) model. We also propose a simplified formula for estimating the apparent diffusion coefficient of parent nuclides based on the analytical solutions. Through numerical experiments, we verified the feasibility of the formula. Our models are useful for determining the apparent diffusion coefficient of daughter nuclides when conducting through-diffusion experiments with parent–daughter nuclide decay chains. Additionally, the proposed models offer the advantages of saving time and reducing experimental waste.