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At least 415 records · Page 23

Energy-dependent optimization of the prompt fission neutron spectrum with CGMF

Throughout the course of FY21, significant effort was put into investigating models within the LANL developed Hauser-Feshbach fission fragment decay code, CGMF, to understand and potentially solve the long-standing challenge of a too-soft prompt fission neutron spectrum, PFNS. Several inputs and models to CGMF were investigated, including the discrete nuclear levels, the optical model potential, level densities, and the fission fragment initial conditions. Some of the global models within CGMF led to a slight hardening of the neutron spectrum—particularly the likely incomplete discrete levels in through which γ-rays decay—but none of the changes where large enough for the tail of the PFNS to reproduce experimental data. A significant hardening of the spectrum tail was observed when the fission fragment initial conditions were optimized based on their sensitivities to the PFNS data for thermal incident neutrons. In this way, the parameters for the CGMF mass and total kinetic energy distributions, along with the spin cutoff factor were adjusted to better reproduce the experimental PFNS measurements. This optimization hardened the tail of the PFNS slightly but led to unphysical mass distributions for the fission fragments before neutron emission. It was clear from the above that we do not expect to be able to produce an evaluation-quality PFNS with CGMF in the near future. Challenges at thermal will persist–and possibly worsen–with increasing incident energy, where more models are needed to completely describe the fission. Basic-science research funding exceeding the amount available and scope of our NCSP funds would be needed to tackle this decade-long challenge impacting many fission-fragment event generator. And, in fact, Amy Lovell won LDRD ECR funding to do so over the next few years. Therefore, we focused in FY22 on extending evaluation capabilities beyond thermal incident neutrons, to take into account the incident energy dependence of the PFNS and fission fragment initial condition distributions in CGMF. We chose to set up the evaluation methodology to perform PFNS evaluations with CGMF across incident-neutron energies, in order to have it readily available for future NCSP evaluations when the PFNS from CGMF has improved. In this report, we outline the evaluation methodology, along with the results of the optimization, including full model calculations with CGMF using the evaluated parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

An introduction to Spent Nuclear Fuel decay heat for Light Water Reactors: a review from the NEA WPNCS

This paper summarized the efforts performed to understand decay heat estimation from existing spent nuclear fuel (SNF), under the auspices of the Working Party on Nuclear Criticality Safety (WPNCS) of the OECD Nuclear Energy Agency. Needs for precise estimations are related to safety, cost, and optimization of SNF handling, storage, and repository. The physical origins of decay heat (a more correct denomination would be decay power) are then introduced, to identify its main contributors (fission products and actinides) and time-dependent evolution. Due to limited absolute prediction capabilities, experimental information is crucial; measurement facilities and methods are then presented, highlighting both their relevance and our need for maintaining the unique current full-scale facility and developing new ones. The third part of this report is dedicated to the computational aspect of the decay heat estimation: calculation methods, codes, and validation. Different approaches and implementations currently exist for these three aspects, directly impacting our capabilities to predict decay heat and to inform decision-makers. Finally, recommendations from the expert community are proposed, potentially guiding future experimental and computational developments. One of the most important outcomes of this work is the consensus among participants on the need to reduce biases and uncertainties for the estimated SNF decay heat. If it is agreed that uncertainties (being one standard deviation) are on average small (less than a few percent), they still substantially impact various applications when one needs to consider up to three standard deviations, thus covering more than 95% of cases. The second main finding is the need of new decay heat measurements and validation for cases corresponding to more modern fuel characteristics: higher initial enrichment, higher average burnup, as well as shorter and longer cooling time. Similar needs exist for fuel types without public experimental data, such as MOX, VVER, or CANDU fuels. A third outcome is related to SNF assemblies for which no direct validation can be performed, representing the vast majority of cases (due to the large number of SNF assemblies currently stored, or too short or too long cooling periods of interest). A few solutions are possible, depending on the application. For the final repository, systematic measurements of quantities related to decay heat can be performed, such as neutron or gamma emission. This would provide indications of the SNF decay heat at the time of encapsulation. For other applications (short- or long-term cooling), the community would benefit from applying consistent and accepted recommendations on calculation methods, for both decay heat and uncertainties. This would improve the understanding of the results and make comparisons easier.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Multi-modal tomographic imaging system for poolside characterization of nuclear test fuels: Design considerations and studies

Testing and qualification of advanced nuclear fuels involves an iterative process of prototyping, in-pile irradiation testing, and in-situ or ex-situ examination. Fuel restructuring and fission product migration during burnup are among the most important aspects of fuel evolution that affect several important performance characteristics such as heat removal, accident tolerance, and fission product retention. Pool-side non-destructive characterization techniques provide fuel developers with tools to understand fuel evolution at different points of burnup. A design for a compact, submersible, and multi-modal gamma-ray tomography system for imaging irradiated nuclear fuel is presented here. Detector selection, collimator geometry and fabrication, mechanical design, imaging protocol and acquisition speed are discussed. Modeling calculations show that sub-millimeter resolution can be achieved in both transmission computed tomography images as well as in emission computed tomography images in a matter of hours. Several design compromises and fabrication challenges are discussed which should be taken into consideration for future submersible gamma-ray tomography instruments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Calculation Of Neutrino Flux

The CONFLUX software framework, Calculation Of Neutrino FLUX, is built with the goal to simplify and standardize the calculation. CONFLUX packages three methods to calculate neutrinos generated from reactor neutrinos or individual beta decays with common nuclear data and beta theories for direct cross-method comparison. The software prepacked the latest nuclear database, including ENDF.B/VIII, JEFF 3.3, and ENSDF, as well as methods to process the uncertainties. It also allows customized nuclear data and beta theories and user generated time dependent reactor models for convenient adjustment of fission products, theoretical corrections.

Zhang, Xianyi [Lawrence Livermore National Laborat↗

New, low-energy excitations in 107 Mo and 109 Mo

New ground-state level with spin-parity 1/2 + is established in 109 Mo, 69.8 keV below the previously reported 5/2(+) ground state in this nucleus, based on precise spectroscopy measurements of gamma radiation following spontaneous fission of 248 Cm performed using the Eurogam2 array of anti-Compton spectrometers. Analogous measurement of gamma radiation following spontaneous fission of 252 Cf, performed using the Gammasphere array, confirms the new 1/2 + ground state of 107 Mo, proposed recently and establishes the isomeric character of the 5/2 + first excited state in 107 Mo. Two beta-decaying isomers are suggested in 111 Mo nucleus based on regular energy systematics, supporting previous predictions. Low-energy excitations in Mo isotopes are interpreted and compared to calculations reported in the literature. The results suggest shape transition from prolate to oblate deformation at N >= 67.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effect of the Coulomb force on fission fragment angular momenta

Nuclear fission produces fragments endowed with typically half a dozen units of angular momentum. After scission has occurred, the fragments are still interacting via the Coulomb force which exerts a torque on deformed fragments, thereby accelerating their rotations. Here, the essential features of this effect can be understood by simple perturbative considerations from which the effect on the fragment spin distributions can be obtained. Complete dynamical calculations of the coupled evolution of the spins validate the perturbative treatment, which ignores the second-order terms, showing that the fragment spins evolve essentially independently in the presence of the Coulomb torques.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Development of Decay Heat Sensitivity Analysis Capability in SCALE/ORIGEN

In this work, a decay heat sensitivity analysis capability was developed and implemented in the ORIGEN code of the SCALE nuclear modeling and simulation suite. This capability introduces improved numerical integration schemes, which overcome the challenges associated with accurately modeling the behavior of adjoint nuclide amounts during coarse time steps for both nuclide amount and decay heat sensitivity calculations. This capability significantly improves the accuracy of calculations without compromising computational efficiency compared to the existing method. Extensive verification was conducted for various benchmark problems, including a 238 Pu decay and an irradiation problem involving 135 Xe, evaluated with both coarse and fine time grids. The results show excellent agreement with reference direct perturbation solutions, reaffirming the computational accuracy of the newly proposed numerical integration methods. Furthermore, sensitivity analyses were performed for fission product inventories ( 147 Sm, 150 Sm, 155 Gd) in pressurized water reactor UO 2 and MOX fuel assemblies. These analyses demonstrated that the ORIGEN sensitivity analysis capability can capture detailed sensitivity coefficients and underlying physics in real applications. Additionally, a decay heat sensitivity analysis for high-assay low-enriched uranium fuel, including various initial 235 U enrichment and burnup points, highlights the extended capabilities of SCALE/ORIGEN in comprehensively assessing the factors influencing total decay heat. These advancements in ORIGEN offer valuable insights for reactor analysis, fuel design, and safety assessments, especially in the context of advanced nuclear fuel development and design changes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantal diffusion approach for multinucleon transfer processes in the 58,64 Ni + 208 Pb reactions: Toward the production of unknown neutron-rich nuclei

In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power. Purpose: This article aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of 64 Ni + 208 Pb at E c.m. = 268 MeV and 58 Ni + 208 Pb at E c.m. = 270 MeV and are compared with available experimental data. Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from time evolution of occupied single-particle orbitals in TDHF. Secondary de-excitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus de-excitation model, gemini++. Dynamics of a fast isospin equilibration process followed by a slow drift toward the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond-mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, gemini++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed. The SMF approach is designed to describe the quantum many-body problem according to an ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool in the search for optimal reaction conditions to produce yet-unknown neutron-rich heavy nuclei through the multinucleon transfer reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Determination of Solar System R-Process Abundances using ENDF/B-VIII.0 and TENDL-2015 libraries

Recent multi-messenger detection of the binary neutron star merger (GW170817) energized the astrophysical community and encouraged further research for determination of nuclear physics observables. Comprehensive studies of atomic nuclei in the cosmos provide an opportunity for investigating these astrophysical phenomena and acquiring complementary information on stellar nucleosynthesis processes that can be verified using the latest nuclear data. Evaluated Nuclear Data File (ENDF) libraries contain complete collections of reaction cross sections over the energy range relevant to astrophysics, fission yields and decay data. These data collections have been used worldwide in nuclear science, industry and national security applications. There is great interest in exploring the ENDF/B-VIII.0 and TALYS Evaluated Nuclear Data Library (TENDL-2015) for nuclear astrophysics purposes and comparing findings with the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNiS). The Maxwellian-averaged cross sections (MACS) and astrophysical reaction rates have been calculated using the ENDF/B-VIII.0 and TENDL-2015 evaluated data sets. The calculated cross sections were combined with the solar system abundances and fitted using the classical model of stellar nucleosynthesis. Astrophysical rapid- and slow-neutron capture, r- and s-process, respectively, abundances were obtained from present data and compared with available values. Further analysis of MACS reveals potential evaluated libraries data deficiencies and a strong need for new measurements. The current results demonstrate a large nuclear astrophysics potential of evaluated libraries and mutually beneficial relations between nuclear industry and research e orts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Update of CEA DES Criticality-Safety Activities and Perspectives [Slides]

Neutronics staff at CEA DES are in charge of a whole set of modeling and simulation tools for neutronics: nuclear data evaluation and processing, transport codes development, calculation sequences edition, verification, validation and uncertainty analysis. Advanced user groups are in charge of specific nuclear analysis in reactor physics, fuel cycle, criticality-safety, radiation shielding and nuclear instrumentation for CEA and its partners, at all stages of nuclear facilities life cycle. CEA is willing to participate/collaborate on the following issues: detector design, experiments, analysis and evaluation, DH validation by combining TAGS measurements with Fission Yield variance-covariance matrices.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ORNL Neutron Cross Section Measurements of 90 Zr

Nuclear criticality modeling and simulations rely on the quality of the existing evaluated nuclear data libraries such as Evaluated Nuclear Data File (ENDF)/B, the Joint Evaluated Fission and Fusion (JEFF) nuclear data library, or the Japanese Evaluated Nuclear Data Library (JENDL). In some cases, the cross-section evaluations of those libraries were found to be deficient in describing criticality benchmarks accurately. More than two decades ago, the US Nuclear Criticality Safety Program (NCSP) established a Nuclear Data (ND) task which encompassed experiments and evaluations. In response to this, the Oak Ridge National Laboratory (ORNL) formed a Nuclear Criticality and Data group which performed ND experiments, data analysis, and evaluations to produce ENDF files for the ND libraries as identified in the NCSP Five-Year Plan. Before being submitted to the ENDF library, files were processed and tested for performance by running benchmark calculations. This procedure was centralized in the ORNL group and is now often referred to as the ND pipeline. NCSP collaborates with the Joint Research Center (JRC) of the European Commission in Geel, Belgium, to perform high-resolution neutron-induced cross section measurements at the Geel Linear Accelerator (GELINA). The objective is to address emerging ND problems in criticality calculations. Difficulties with ND include insufficient neutron energy range, missing covariances, and previously unrecognized inaccuracies with experiments. New neutron total and capture cross sections of 90 Zr in the neutron energy range from 100 eV to several hundred keV were recently performed. These measured data will be used, together with existing high-resolution transmission data from a metallic 90 Zr sample, to improve representation of the cross sections.

97 MATHEMATICS AND COMPUTING↗

Cross sections for neutron-induced reactions from surrogate data: Reexamining the Weisskopf-Ewing approximation for ( n , n ' ) and ( n , 2 n ) reactions

Background: Modeling nuclear reaction networks for nuclear science applications and for simulations of astrophysical environments relies on cross section data for a vast number of reactions, many of which have never been measured. Cross sections for neutron-induced reactions on unstable nuclei are particularly scarce, since they are the most difficult to measure. Consequently, we must rely on theoretical predictions or indirect measurements to obtain the requisite reaction data. For compound nuclear reactions, the surrogate reaction method can be used to determine many cross sections of interest. Purpose: Earlier work has demonstrated that cross sections for neutron-induced fission and radiative neutron capture can be determined from a combination of surrogate reaction data and theory. For the fission case, it was shown that the Weisskopf-Ewing approximation, which significantly simplifies the implementation of the surrogate method, can be employed. Capture cross sections cannot be obtained, and require a detailed description of the surrogate reaction process. Here, we examine the validity of the Weisskopf-Ewing approximation for determining unknown (n, n') and (n, 2n) cross sections from surrogate data. Methods: Using statistical reaction calculations with realistic parametrizations, we investigate first whether the assumptions underlying the Weisskopf-Ewing approximation are valid for (n, n') and (n, 2n) reactions on representative target nuclei. We then produce simulated surrogate reaction data and assess the impact of applying the Weisskopf-Ewing approximation when extracting (n, n') and (n, 2n) cross sections in situations where the approximation is not strictly justified. Results: We find that peak cross sections can be estimated using the Weisskopf-Ewing approximation, but the shape of the (n, n') and (n, 2n) cross sections, especially for low neutron energies, cannot be reliably determined without accounting for the angular-momentum differences between the neutron-induced and surrogate reaction. Conclusions: To obtain reliable (n, n') and (n, 2n) cross sections from surrogate reaction data, a detailed description of the surrogate reaction mechanisms is required. To do so for the compound-nucleus energies and decay channels relevant to these reactions, it becomes necessary to extend current modeling capabilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ab Initio Evaluation of Plutonium Dioxide $S(α,β)$ and Thermal Neutron Cross Sections

Plutonium Dioxide (PuO 2 ) is an advanced fuel-cycle nuclear fuel material for thermal and fast reactors, with a melting point at 3261.8 K and thermal conductivity above 3 Wm -1 K -1 for temperatures below 1500 K. Plutonium from spent UO 2 is reprocessed to form chemically stable mixed oxide (MOX) fuel. In contrast to metallic fuels, the low PuO 2 conductivity results in high thermal gradients between fuel center and surface, resulting in structural annealing and efficient fission product migration over burnup. Crystal binding affects the doppler broadening of epithermal resonances for nuclear fuels and scattering behavior of thermal neutrons. Currently, there is no ENDF/B Thermal Scattering Law, i.e., $S(α,β)$, evaluation for PuO 2 , only free atom cross sections for Plutonium and Oxygen, respectively, which neglect lattice contributions to total cross section. Herein, ab initio lattice dynamics (AILD) techniques are employed to calculate the phonon density of states (DOS) using spin-orbit-coupling density functional theory (DFT) to predict the PuO2 paramagnetic ground-state structure. These results highlight the evaluation of $S(α,β)$ for Plutonium and Oxygen, respectively in PuO 2 and consequential generation of thermal neutron scattering cross sections for high fidelity criticality safety analysis and reactor calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Nuclide inventory validation: radiochemical assay data quality and modeling challenges in benchmark models development

Oak Ridge National Laboratory is conducting radiochemical assay experiments, using high-precision analytical protocols validated with a comprehensive quality assurance plan, to expand the nuclide inventory validation basis for high burnup spent nuclear fuel. Preliminary measurement data for key actinides and fission products in two pressurized water reactor spent fuel samples are being used to investigate the impact of measurement data uncertainty on the sample burnup estimation. These measurement data are also being used to examine the impact of assumptions applied when developing best-estimate computational models to simulate fuel irradiation history. The simulations are being performed using depletion capabilities in the SCALE code system. Comparison of calculated and measured nuclide concentrations shows good agreement for the considered nuclides. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Performing a multi-unit level-3 PSA with MACCS

MACCS (MELCOR Accident Consequence Code System), WinMACCS, and MelMACCS now facilitate a multi-unit consequence analysis. MACCS evaluates the consequences of an atmospheric release of radioactive gases and aerosols into the atmosphere and is most commonly used to perform probabilistic safety assessments (PSAs) and related consequence analyses for nuclear power plants (NPPs). WinMACCS is a user-friendly preprocessor for MACCS. MelMACCS extracts source-term information from a MELCOR plot file. The current development can combine an arbitrary number of source terms, representing simultaneous releases from a multi-unit facility, into a single consequence analysis. The development supports different release signatures, fission product inventories, and accident initiation times for each unit. The treatment is completely general except that the model is currently limited to collocated units. A major practical consideration for performing a multi-unit PSA is that a comprehensive treatment for more than two units may involve an intractable number of combinations of source terms. This paper proposes and evaluates an approach for reducing the number of calculations to be tractable, even for sites with eight or ten units. The approximation error introduced by the approach is acceptable and is considerably less than other errors and uncertainties inherent in a Level 3 PSA.

42 ENGINEERING↗

Level structure of light neutron-rich La isotopes beyond the 𝑁 = 82 shell closure

Here, the high spin excited states of Lanthanum isotopes 140–143 La, above the 𝑁 = 82 closed shell, were populated in fission reactions. The prompt 𝛾-ray transitions were measured using two complementary methods: (a) in coincidence with the isotopically identified fragments produced in the fission of the 238 U + 9 Be system using the Variable Mode Spectrometer (VAMOS++) and the Advanced Gamma Tracking Array (AGATA) spectrometer, and (b) high statistics threefold 𝛾−𝛾−𝛾 and fourfold 𝛾−𝛾−𝛾−𝛾 coincidence data from the spontaneous fission of 252 Cf using the Gammasphere. This work reports the first identification of a pair of parity doublet structures in 143 La and the new high spin level structure in 140–142 La from prompt 𝛾-ray spectroscopy. The level structures are interpreted in terms of the systematics of neighboring odd-𝑍 nuclei above the 𝑍 = 50 shell closure and large-scale shell model calculations. The present results indicate the presence of stable octupole deformation in 143 La. The excitation energy pattern and their comparison with neighboring isotones, moving away from the 𝑁 = 82 closed shell, point towards a transition from single-particle structures to an alternating parity rotational band structure in the La isotopic chain.

Navin, A. [Centre National de la Recherche Scienti↗

Development of Accelerated Steady-state Test Capsule Experiments to Replicate EBR-II Fuel Behavior Using BISON Fuel Performance Analysis

Here in this work, BISON fuel performance calculations were performed to predict the fuel behavior of accelerated burnup U-Pu-Zr fuel, with temperature operation conditions of the fuel and the cladding mirroring conditions within EBR-II fuel pins. The temperature operating conditions within the FAST accelerated burnup rods were aimed at replicating EBR-II X447/X447A fuel surface and inner cladding surface temperatures. Due to the FAST capsule design, these temperatures can be replicated with fission rate densities being significantly increased. fuel performance modeling has not been assessed for novel experiments such as accelerated burnup utilizing the FAST capsule within ATR. This is an important step in understanding accelerated irradiation methods as many performance models are empirical models conforming to the results of PIE but do not always include physical models that would represent the changes in irradiation tests.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Probing C–I bond fission in the UV photochemistry of 2-iodothiophene with core-to-valence transient absorption spectroscopy

The UV photochemistry of small heteroaromatic molecules serves as a testbed for understanding fundamental photo-induced chemical transformations in moderately complex compounds, including isomerization, ring-opening, and molecular dissociation. Here, a combined experimental-theoretical study of 268 nm UV light-induced dynamics in 2-iodothiophene (C 4 H 3 IS) is performed. The dynamics are experimentally monitored with a femtosecond extreme ultraviolet (XUV) probe that measures iodine N-edge 4d core-to-valence transitions. Experiments are complemented by density functional theory calculations of both the pump-pulse induced valence excitations and the XUV probe-induced core-to-valence transitions. Possible intramolecular relaxation dynamics are investigated by ab initio molecular dynamics simulations. Furthermore, gradual absorption changes up to ~0.5 to 1 ps after excitation are observed for both the parent molecular species and emerging iodine fragments, with the latter appearing with a characteristic rise time of 160 ± 30 fs. Comparison of spectral intensities and energies with the calculations identifies an iodine dissociation pathway initiated by a predominant π → π* excitation. In contrast, initial excitation to a nearby n ⟂ → σ* state appears unlikely based on a significantly smaller oscillator strength and the absence of any corresponding XUV absorption signatures. Excitation to the π → π* state is followed by contraction of the C–I bond, enabling a nonadiabatic transition to a dissociative π→σ C-I * state. For the subsequent fragmentation, a relatively narrow bond-length region along the C–I stretch coordinate between 230 and 280 pm is identified, where the transition between the parent molecule and the thienyl radical + iodine atom products becomes prominent in the XUV spectrum due to rapid localization of two singly occupied molecular orbitals on the two fragments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗