Search NASA⌕ Search

SEARCH · Search NASA

Results for “Low Energy Nuclear Reactions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Negative components in the representation $\frac{𝑑^{2}⁡(𝜎⁢𝐸)}{𝑑⁡𝐸^2}$ of heavy-ion fusion cross sections

Negative components are observed in the representation $\frac{𝑑^{2}⁡(𝜎⁢𝐸)}{𝑑⁡𝐸^2}$ in heavy-ion fusions related to recent studies of noticeable oscillations in the high-energy region of the fusion excitation functions. A modified multiGaussian model has been developed, which includes contributions for both positive and negative components in the $\frac{𝑑^{2}⁡(𝜎⁢𝐸)}{𝑑⁡𝐸^2}$ representation. The model reproduces the heavy-ion fusion excitation functions very well, including oscillations. The property of these negative components in the $\frac{𝑑^{2}⁡(𝜎⁢𝐸)}{𝑑⁡𝐸^2}$ spectrum and the reaction mechanism of fusion at energies above the Coulomb barrier are investigated. Finally, the model also reproduces well light heavy-ion fusion reactions between 12 C and 16 O at high energy; results imply that the compound nucleus channel effect may have an important contribution at the high energy region for all fusion systems.

low & intermediate energy heavy-ion reactions↗

Universal function for heavy-ion fusion cross sections

A universal function for heavy-ion fusion cross sections, Y = $\sqrt{π}$ Xerfc (- X ) + exp(- X 2 ) is proposed. By scaling both the cross section σ(E) and the energy E, heavy-ion fusion cross section data are found to follow closely a universal function over the whole energy range. The scaling is developed from either a simple, empirical single-Gaussian barrier distribution model for the representation d 2 (σE)/dE 2 , or the modified Siwek-Wilczynski model. The cross section expressions of these models are analytical, and can be easily used for all heavy-ion fusion excitation functions. Thus a bench marking of heavy-ion fusion excitation functions has been achieved. Finally, a general discussion regarding the universal function is given.

low & intermediate energy heavy-ion reactions↗

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Steady Nuclear Combustion in Rockets

The astrophysical theory of stationary nuclear reactions in stars is applied to the conditions that would be met in the practical engineering cases that would differ from the former, particularly with respect to the much lower combustion pressures, dimensions of the reacting volume, and burnup times. This application yields maximum rates of hear production per unit volume of reacting gas occurring at about 10(exp 8) K in the cases of reactions between the hydrogen isotopes, but yields higher rates for heavier atoms. For the former, with chamber pressures of the order of 100 atmospheres, the energy production for nuclear combustion reaches values of about 10(exp 4) kilocalories per cubic meter per second, which approaches the magnitude for the familiar chemical fuels. The values are substantially lower for heavier atoms, and increase with the square of the combustion pressure. The half-life of the burnup in the fastest reactions may drop to values as low as those for chemical fuels so that, despite the high temperature, the radiated energy can remain smaller than the energy produced, particularly if an inefficiently radiating (i.e., easily completely ionized reacting material like hydrogen), is used. On the other hand, the fraction of completely ionized particles in the gases undergoing nuclear combustion must not exceed a certain upper limit because the densities (approximately 10(exp -10) grams per cubic centimeter)) lie in the range of high vacua and only for the previously mentioned fraction of nonionized particles can mean free paths be retained small enough so that the chamber diameters of several dozen meters will suffice. Under these conditions it appears that continuously maintained stable nuclear reactions at practical pressures and dimensions are fundamentally possible and their application can be visualized as energy sources for power plants and propulsion units.

Saenger, E.↗

16 O ⁡(𝑒,𝑒′⁢𝛼)⁢ 12 C measurements and the 12 C ⁡(𝛼,𝛾)⁢ 16 O astrophysical reaction rate

The 12 C ⁡(𝛼,𝛾)⁢ 16 O reaction, an important component of stellar helium burning, has a key role in nuclear astrophysics. It has significant impact on the evolution and final state of heavy to low mass stars, maximum mass of stellar formed black holes and also shapes the elemental abundances resulting from nucleosynthesis in such stars. Providing a reliable estimate for the energy dependence of this reaction at stellar helium burning temperatures has been a longstanding and important goal. In this work, we study the role of potential new 𝐸⁢1 and 𝐸⁢2 measurements of the 16 O ⁡(𝑒,𝑒′⁢𝛼)⁢ 12 C reaction in reducing the overall uncertainty in the astrophysical 𝑆 factor for the 12 C ⁡(𝛼,𝛾)⁢ 16 O 𝐸⁢1 and 𝐸⁢2 ground state capture extrapolated to a stellar energy of 300 keV. A multilevel 𝑅-matrix analysis is used to make extrapolations of the 𝑆 𝐸⁢1 (300 keV) and 𝑆 𝐸⁢2 (300 keV) factors for the 12 C ⁡(𝛼,𝛾)⁢ 16 O reaction from existing ground state capture data. Bayesian analysis is used to quantify the uncertainties in the extrapolations for both the existing data alone and also when possible new experimental data are included. In particular, we consider a new experiment that would make use of a high-intensity low-energy electron beam that impinges on a windowless oxygen gas target as a means to determine the total 𝐸⁢1 and 𝐸⁢2 ground state cross sections for this reaction. Here we find that the new data could significantly reduce the 𝑆⁡(300) uncertainties. Splitting the new data into high and low energy regions shows that both low and high energy data are effective in reducing the uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

H-2, H-3, He-3 production in solar flares

The production of deuterium, tritium, and helium-3 from nuclear reactions of accelerated charged particles is evaluated with the ambient solar atmosphere. Updated cross sections and kinematics are used, calculations are extended to very low energies (approximates 0.1 MeV/nucleon), and the angular distribution of the secondary particles is calculated. The calculations are compared with data on accelerated isotopes from solar flares. In particular, the August 1972 events are considered for which both He-3 and nuclear gamma rays were observed. An explanation for He-3-rich events is provided in terms of the angular distributions of secondary isotopes, and the flux of 2.2 MeV gamma rays from such flares are also predicted.

Ramaty, R.↗

Gas Stopper Developments for Improved Purity and Intensity of Low-Energy, Rare Isotope Ion Beams (Final Technical Report)

This final technical report summarizes the work of the Michigan State University (MSU) team supported by grant # DE-SC0021423 awarded by the Office of Nuclear Physics, Department of Energy. Objectives: The successful fulfillment of the FRIB science mission hinges on ensuring the availability of fast, stopped, and reaccelerated beams consisting of rare isotopes. This project's research and development focus was dedicated to supporting the advancement and creation of a cutting-edge linear gas stopper. The primary aim is to efficiently convert the high-intensity fast beams of rare isotopes provided by FRIB into high-quality, low-energy beams. These beams are essential for conducting stopped beam experiments or for subsequent reacceleration. The overarching goal is to advance technology, aiming to increase the beam rate capability of the linear gas stopper for medium-to-heavy-mass rare isotopes by more than tenfold compared to the currently most effective gas stopper in operation, and to improve the purity of the delivered beams. Project Description: The existing technology employed in gas stopping devices designed for low-energy, rare-isotope beams presents limitations in both the purity of extracted beams and the intensities of injected beams. These limitations are incompatible with the requirements of the recently commissioned rare isotope beam facility, FRIB. Our research and development efforts, aligned with the previously outlined objectives, focused on addressing the most critical aspects for enhancing beam-rate capability and purity. Specifically, advanced particle-in-cell simulations were developed and integrated into a simulation pipeline to explore the efficacy of multi-layer RF carpets on increasing ion transport efficiency with high incoming beam rates that generate space charge fields which can limit it. We also explored the possibility of using a collision-induced-dissociation (CID) gas cell to break up molecular contaminant ions that are generated during the stopping process. A prototype CID gas cell was constructed and tested with beams from an offline ion source, validating the concept with the successful demonstration of breaking of molecular ions. The outcome of this research enabled the formulation a conceptual design for a next-generation linear gas stopping device specifically tailored for FRIB. This device is envisioned to deliver rare-isotope-ion beams at a rate of 10 8 particles per second or higher, accompanied by advancements in purity. Methods employed: This project leverages advancements in technologies initially designed for the Advanced Cryogenic Gas Stopper (ACGS), the current state-of-the-art linear gas stopper, through the use of new simulations and beam purification via collision-induced-dissociation. The methods include: 1. Development of a prototype low-energy, low-pressure CID gas stopper. This prototype features a thin, approximately 20 nm, Si 3 N 4 entrance window designed for dissociating stable and rare-isotope molecular ions. The goal is to enhance beam purification and overall efficiency. 2. Creation of Particle-in-cell (PIC) simulations to assess the advantages of multi-layer RF carpets and multi-point extraction for ion transport efficiency. These simulations rely on the 3DCylPIC package, specifically designed for studying devices of this nature. The goal is to quantify and mitigate ion transport losses due to space charge generated in the stopping process of large numbers of ions. 3. Perform ion transport simulations across an RF carpet using an 8-phase travelling wave and evaluate its performance. Compared to the 4-phase RF carpets used in ACGS, the 8-phase carpets will double the wavelength of the generated traveling wave allowing for larger maximum RF amplitudes that could result in improved ion transport efficiency for high-intensity incoming beams when large space charge fields are present. Impact: Tackling the primary challenges associated with transforming high-energy projectile fragment beams into low-energy beams—specifically, addressing efficiency and purity—holds significant promise for advancing FRIB science. This advancement will particularly impact precision mass measurements, laser spectroscopy of short-lived nuclei, and studies in astrophysics and nuclear reactions using reaccelerated beams. These domains play a crucial role in addressing key questions outlined in the 2023 NSAC long-range plan, spanning nuclear structure, nuclear astrophysics, and fundamental symmetries. Additionally, they contribute to addressing 10 out of the 17 benchmarks identified by the NRC RISAC. The development of a next-generation gas stopping device capable of delivering low-energy, rare-isotope beams at a rate of 10 8 particles per second, or more, with high purity holds the potential to unlock experiments that would otherwise be unfeasible. Furthermore, it is expected to reduce the time required for experiments at FRIB, thereby maximizing scientific output. The research and development activities performed as part of this project bolstered essential competencies at FRIB in beam physics and ion source technologies, provided valuable training opportunities for junior scientists.

43 PARTICLE ACCELERATORS↗

Sustainable production of radionuclidically pure antimony-119

Background Radiopharmaceutical therapy (RPT) uses radionuclides that decay via one of three therapeutically relevant decay modes (alpha, beta, and internal conversion (IC) / Auger electron (AE) emission) to deliver short range, highly damaging radiation inside of diseased cells, maintaining localized dose distribution and sparing healthy cells. Antimony-119 ( 119 Sb, t 1/2 = 38.19 h, EC = 100%) is one such IC/AE emitting radionuclide, previously limited to in silico computational investigation due to barriers in production, chemical separation, and chelation. A theranostic (therapeutic/diagnostic) pair can be formed with 119 Sb’s radioisotopic imaging analogue 117 Sb (t 1/2 = 2.80 h, E γ = 158.6 keV, I γ = 85.9%, β + = 262.4 keV, I β+ = 1.81%). Results Within, we report techniques for sustainable and cost-effective production of pre-clinical quality and quantity, radionuclidically pure 119 Sb and 117 Sb, novel low energy photon measurement techniques for 119 Sb activity determination, and physical yields for various tin target isotopic enrichments and thicknesses using (p, n) and (d, n) nuclear reactions. Additionally, we present a two-column separation providing a radioantimony yield of 73.1% ± 6.9% (N = 3) and tin separation factor of (6.8 ± 5.5) x 10 5 (N = 3). Apparent molar activity measurements for deuteron produced 117 Sb using the chelator TREN-CAM were measured at 42.4 ± 25 MBq 117 Sb/µmol (1.14 ± 0.68 mCi/µmol), and we recovered enriched 119 Sn target material at a recycling efficiency of 80.2% ± 5.5% (N = 6) with losses of 11.6 mg ± 0.8 mg (N = 6) per production. Conclusion We report significant steps in overcoming barriers in 119 Sb production, chemical isolation and purification, enriched target material recycling, and chelation, helping promote accessibility and application of this promising therapeutic radionuclide. We describe a method for 119 Sb activity measurement using its low energy gamma (23.87 keV), negating the need for attenuation correction. Finally, we report the largest yet-measured 119 Sb production yields using proton and deuteron irradiation of natural and enriched targets and radioisotopic purity > 99.8% at end of purification.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Abrasion-fission reactions at intermediate energies

The availability of high-intensity, heavy-ion beams coupled to sensitive, large solid-angle acceptance spectrometers has enabled a detailed examination of the fission fragments produced in induced-fission reactions. The abrasion fission process involves the formation of projectile-like prefragments in violent nuclear collisions at relative energies in excess of 100 MeV/u. At intermediate energies below this threshold, experiments suggest a change in the prefragment kinematic qualities. Information regarding the influence of this transitional phase upon the evolution of nuclei approaching the point of scission is scarce. In this article, data are presented for over 200 nuclei from nickel to palladium produced in abrasion-fission reactions of a 80 MeV/u 238 U beam. Cross sections were obtained following yield measurements performed for the principal charge states of the identified fission fragments and a detailed analysis of the ion transmission. A full kinematic analysis of the fission fragments has been performed using the LISE ++ software package, where the trajectory of an ion passing through a spectrometer can be reconstructed based upon measurements at the focal plane. Furthermore, the results obtained at the S800 spectrograph are compared with predictions obtained with a three-fission progenitor (3EER) model. Systematic studies of fission-fragment properties continue to provide a valuable experimental benchmark for theoretical efforts directed toward describing this complex decay channel, that is important in the context of planning experiments to explore the neutron-rich region of the nuclear chart at rare-isotope beam facilities.

59 ≤ A ≤ 8990 ≤ A ≤ 149↗

Multinucleon transfer mechanism in Cf 250 + Th 232 collisions using the quantal transport description based on the stochastic mean-field approach

Production cross sections of heavy neutron-rich isotopes are calculated by employing quantal transport description in 250 Cf + 232 Th collisions. This quantal transport description is based on the stochastic mean-field approach, and it provides a microscopic approach beyond time-dependent Hartree-Fock theory to include mean-field fluctuations. Deexcitation of primary fragments is determined by employing the statistical GEMINI++ code. Here, calculations provide predictions for production cross sections of neutron rich transfermium isotopes without any adjustable parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Deblurring for nuclei: 3D characteristics of heavy-ion collisions

Observables from nuclear and high-energy experiments can be degraded by detector performance and/or methodology in extracting the observables, such as of the final-state characteristics of heavy-ion collisions in relation to a coarsely estimated reaction-plane direction. We propose the use of deblurring methods, such as in optics, to correct for observable degradation. Our main focus is the restoration of triple-differential particle distributions in heavy-ion collisions. We demonstrate that these could be extracted from collision measurements following the Richardson-Lucy deblurring method from optics. We illustrate basic features of the restoration methodology in a schematic model assuming either ideal or more realistic particle detection. Here, the inferred three-dimensional (3D) distributions for collisions may be easier to interpret in terms of collision dynamics and sought properties of bulk matter than the currently employed Fourier coefficients, that combine information from different azimuthal angles relative to the reaction plane.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Neutral-current neutrino cross section and expected supernova signals for 40 Ar from a three-fold increase in the magnetic dipole strength

In view of the great interest in liquid argon neutrino detectors, the 40 Ar(γ,γ') 40 Ar reaction was revisited to guide a calculation of the neutral current neutrino cross section at supernova energies. Using the nuclear resonance fluorescence technique with a monoenergetic, 99% linearly polarized photon beam, in this work we report a three-fold increase in magnetic dipole strength at around 10 MeV in 40 Ar. Based on shell-model calculations, and using the experimentally identified transitions, the neutral current neutrino cross sections for low-energy reactions on 40 Ar are calculated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Probing the neutron-proton asymmetry dependence of the nuclear source temperature with light charged particles

The dependence of the nuclear temperature on the source neutron-proton (N/Z) asymmetry was experimentally investigated with the light charged particles (LCPs) generated from thirteen reaction systems with different N/Z asymmetries, 64 Zn on 112 Sn and 70 Zn, 64 Ni on 112,124 Sn, 58,64 Ni, 197 Au, 232 Th at 40 MeV/u. A rather weak N/Z asymmetry dependence of the source temperature was qualitatively inferred from the extracted N/Z asymmetry dependence of the apparent temperature and that of the relative temperature change by the sequential decay effects with the help of the theoretical simulations. Comparing the present result with those from our previous work and other available experimental results, a weak N/Z asymmetry dependence of nuclear temperature is commonly observed in different independent experiments and with different thermometers, except for the result reported by McIntosh et al. [Phys. Lett. B 719, 337 (2013)]. Here, the origin of the difference between the conclusion of the former group and that of McIntosh et al. was addressed, using statistical multifragmentation model (SMM) simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A portable and monoenergetic 24 keV neutron source based on 124Sb-9Be photoneutrons and an iron filter

A portable monoenergetic 24 keV neutron source based on the 124Sb-9Be photoneutron reaction and an iron filter has been constructed and characterized. The coincidence of the neutron energy from SbBe and the low interaction cross-section with iron (mean free path up to 29 cm) makes pure iron specially suited to shield against gamma rays from 124Sb decays while letting through the neutrons. To increase the 124Sb activity and thus the neutron flux, a >1 GBq 124Sb source was produced by irradiating a natural Sb metal pellet with a high flux of thermal neutrons in a nuclear reactor. The design of the source shielding structure makes for easy transportation and deployment. A hydrogen gas proportional counter is used to characterize the neutrons emitted by the source and a NaI detector is used for gamma background characterization. At the exit opening of the neutron beam, the characterization determined the neutron flux in the energy range 20–25 keV to be 6.00±0.30 neutrons per cm2 per second and the total gamma flux to be 245±8 gammas per cm2 per second (numbers scaled to 1 GBq activity of the 124Sb source). A liquid scintillator detector is demonstrated to be sensitive to neutrons with incident kinetic energies from 8 to 17 keV, so it can be paired with the source as a backing detector for neutron scattering calibration experiments. This photoneutron source provides a good tool for in-situ low energy nuclear recoil calibration for dark matter experiments and coherent elastic neutrino-nucleus scattering experiments.

Dark Matter detectors (WIMPs, axions, etc.)↗

Assessment and Requirements of Nuclear Reaction Databases for GCR Transport in the Atmosphere and Structures

The transport properties of galactic cosmic rays (GCR) in the atmosphere, material structures, and human body (self-shielding) am of interest in risk assessment for supersonic and subsonic aircraft and for space travel in low-Earth orbit and on interplanetary missions. Nuclear reactions, such as knockout and fragmentation, present large modifications of particle type and energies of the galactic cosmic rays in penetrating materials. We make an assessment of the current nuclear reaction models and improvements in these model for developing required transport code data bases. A new fragmentation data base (QMSFRG) based on microscopic models is compared to the NUCFRG2 model and implications for shield assessment made using the HZETRN radiation transport code. For deep penetration problems, the build-up of light particles, such as nucleons, light clusters and mesons from nuclear reactions in conjunction with the absorption of the heavy ions, leads to the dominance of the charge Z = 0, 1, and 2 hadrons in the exposures at large penetration depths. Light particles are produced through nuclear or cluster knockout and in evaporation events with characteristically distinct spectra which play unique roles in the build-up of secondary radiation's in shielding. We describe models of light particle production in nucleon and heavy ion induced reactions and make an assessment of the importance of light particle multiplicity and spectral parameters in these exposures.

Cucinotta, F. A.↗

Incorporating new evaluation on angular distributions and energy spectra of neutron-induced charged particle reactions into the next ENDF library release (Technical Progress Report)

This project aims to provide the improved Evaluated Nuclear Data File (ENDF) using the newly measured data as well as the latest nuclear reaction model for calculating angular distributions and energy spectra on neutron-induced charged particle reactions through the collaboration of Korea Atomic Energy Research Institute (KAERI) and Los Alamos National Laboratory (LANL). The LANL group will provide the experimental data for angular distributions and spectra of (n,p) and (n,α) on several structural materials such as Fe, Ni and Zn isotopes using the Low Energy Neutron-induced Charged-particle (Z) Chamber (LENZ) instrument at Los Alamos Neutron Science Center (LANSCE). The KAERI group will provide the improved evaluated nuclear library which is based on the LANL experimental data, and further will predict angular distributions and spectra of (n,p) and (n,α) reactions on unmeasured nuclides, such as Cr, Mn, Co, Cu and so on. For the first year of this project, we planned to analyze (n,p) and (n,α) reactions for 54,56 Fe and perform new measurements on those reactions for 58,60 Ni isotopes with the LENZ instrument at LANSCE. For improving our evaluation quality, we have studied reaction models to reproduce LANL’s experimental angular distributions and energy spectra using the full Hauser-Feshbach model code, CoH3 with no approximations used. As the first year’s deliverables, we provided the experimental (n,p) and (n,α) reaction cross sections for 54,56 Fe and incorporate new evaluation on angular distributions and energy spectra of neutron-induced charged particle reactions into the current ENDF/B-VIII.0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

An alternative viewpoint on the nuclear structure towards 100 Sn: Lifetime measurements in 105 Sn

This work aims at presenting an alternative approach to the long standing problem of the B(E2) values in Sn isotopes in the vicinity of the N=Z double-magic nucleus 100 Sn, until now predominantly measured with relativistic and intermediate-energy Coulomb excitation reactions. The direct measurement of the lifetime of low-lying excited states in odd-even Sn isotopes provides a new and precise guidance for the theoretical description of the nuclear structure in this region. Lifetime measurements have been performed in 105 Sn for the first time with the coincidence Recoil Distance Doppler Shift technique. The lifetime results for the $7/2^+_1$ first excited state and the $11/2^+_1$ state, $2^+ (^{104}$Sn) Ⓧ $v1g_{7/2}$ multiplet member, are discussed in comparison with state-of-the-art shell model and mean field calculations, highlighting the crucial contribution of proton excitation across the core of 100 Sn. The reduced transition probability B(E2) of the $11/2^+_1$ core-coupled state points out an enhanced staggering with respect to the B(E2; $2^+_1$ → $0^+_1$) in the even-mass 104 Sn and 106 Sn isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dipole response in Te 128 , 130 below the neutron threshold

Numerous studies of the ground-state decay of the pygmy dipole resonance (PDR) have been carried out in the past. However, data on the decay of the PDR to low-lying excited states is still very scarce due to limitations of the sensitivity to weak branching transitions of experimental setups. Here, we present a detailed examination of the low-energy dipole response of 128 Te and 130 Te below their neutron separation thresholds of 8.8 and 8.5 MeV, respectively. Photonuclear reactions with the subsequent γ-ray spectroscopy of the decay channel with continuous-energy bremsstrahlung at varying endpoint energies and linearly polarized quasimonochromatic γ-ray beams with energies ranging from 2.7 to 8.9 MeV in steps of roughly 250 keV were used for probing the decay behavior of the low-energy dipole response in 128Te and 130Te. In addition, (γ,γ' γ") reactions were used to study the population of low-lying states of 128 Te. Spin-parity quantum numbers and reduced transition probabilities are determined for individual photo-excited states. The analysis of average decay properties for nuclear levels in narrow excitation-energy bins enable the extraction of photoabsorption cross sections, average branching ratios to the $2$$^{+}_{1}$ state, and the distinction between E1 and M1 transitions to the ground state and to the $2$$^{+}_{1}$ state accounting for resolved and unresolved transitions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗