J.R. Huizenga

Theoretical reaction cross sections for alpha particles with an optical model

Abstract The transmission coefficients T l and total reaction cross section σ R for alpha particles in the energy range 0–46 MeV interacting with 20 target nuclei with atomic numbers ranging from 10 to 92 are calculated with an optical model program in which a previously determined complex nuclear potential is utilized. The dependence of the T l values and hence σ R on the Woods-Saxon parameters is investigated as a function of projectile energy. The optical model reaction cross sections are compared to those derived from (1) a square well potential and (2) a model which approximates the real optical model potential barrier by a parabola and makes use of the Hill-Wheeler penetration formula for a parabolic potential.

Heavy-ion fusion: Comparison of experimental data with classical trajectory models

Abstract Currently available data on fusion excitation functions for heavy-ion induced reactions over a wide mass range are compared to results calculated with a classical dynamical model based on the proximity nuclear potential of Blocki et al., the Coulomb potential of Bondorf et al., and one-body nuclear friction in the proximity formalism of Randrup. With these conservative and dissipative forces and the radial parameters of Myers, overall good agreement is obtained between the theoretical excitation functions and most of the available data. Extensive calculations have been performed to test the sensitivity of the calculated fusion cross-sections to a number of parameters, including the radial dependence of the Coulomb and nuclear potentials, the radial and tangential friction form factors as well as the projectile and target radii. The theoretical excitation functions for the lighter heavy-ion systems are rather insensitive to changes in either the conservative or dissipative forces. The calculations show that tangential friction sufficient to produce the rolling condition is necessary to explain the magnitude of the fusion cross-sections at high energies, which are also sensitive to the magnitude of the radial friction component. This is in contrast to the fusion cross-sections at low energies which are determined by the nuclear potential at larger separations, and to a lesser extent by tangential friction. The low energy fusion data are most sensitive to the nuclear radii. The calculations reveal the importance of more experimental measurements of fusion cross-sections at high energies, especially for heavy systems where the magnitudes of the fusion cross-sections are the most sensitive to the assumed forces. However, even for these cases the effects of the conservative and dissipative forces are similar and difficult to separate. These studies indicate, however, that it is possible to construct a conservative potential that will give calculated fusion excitation functions which are in good agreement with all experimental data over the entire mass range. The maximum fusion cross-sections as defined here exceed considerably the liquid-drop limiting value for heavy systems.

Reaction parameters for heavy-ion collisions

Abstract These tables present reaction parameters for all combinations of 27 projectile and 16 target nuclei in a laboratory bombarding energy range of 1–50 MeV/u. The reaction parameters are derived from the Fresnel model of heavy-ion scattering, the droplet model, and the rotating liquid-drop model, or from systematics of experimental data.

Bismuth, thallium and mercury in stone meteorites by activation analysis☆

Abstract The radiochemical procedures for the assay of bismuth, thallium, and mercury in stone meteorites following neutron activation are described in detail. A Bi 209 abundance of 2.2 sx 10 −9 gramme/ gramme meteorite leading to a cosmic abundance of 0.0016 (per 10 6 Si atoms) was determined from the analysis of six stone meteorites. A T1 209 abundance of 0.40 sx 10 −9 g/g meteorite and a Hg 202 abundance of 30 sx 10 −9 g/g meteorite corresponding to cosmic abundances of 0.00030 and 0.023 (per 10 6 Si atoms), respectively, were determined from analysis of five stone meteorites. Implications of these data as pertaining to the life history of meteorites are discussed.

Interpretation of isomer ratios in nuclear reactions with Fermi-gas and superconductor models

Nuclear temperatures and isomer ratios are calculated on the basis of a recent semi-quantitative theory for a Fermi gas with pairing correlations analogous to those of a superconducting metal. Although the superconductor model predicts only a slight energy dependence of the nuclear temperature at low-excitation energies, in agreement with some, but not all experimental results, the single-particle level spacings required to reproduce the absolute values of the experimental nuclear temperatures are considerably smaller than expected. The superconductor model predicts a reduction from the rigid-body moment of inertia which is consistent with isomer ratios for nuclei with an odd number of nucleons. However, some evidence is presented to show that the superconductor model overestimates the reduction in the moment of inertia for odd nuclei†††. Nuclear temperatures and isomer ratios are calculated also with a shifted Fermi gas model. In this model the Fermi gas predictions are modified to compensate for pairing interactions by simply re-defining excitation energies relative to a characteristic level. In the present calculations we assume the characteristic level of an odd nucleus is identical with its ground state. For odd nuclei the experimental isomer ratios are in good agreement with predictions of the Fermi gas theory with a rigid body moment of inertia. The shifted Fermi gas model gives better agreement with nuclear temperatures than the superconductor model, but gives too large a moment of inertia for odd-mass nuclei. The degree of agreement between the predictions of the above superconductor theory and the various experimental data for all types of nuclei is unimproved over the simpler Fermi gas theory.

THORIUM IN STONE METEORITES BY NEUTRON ACTIVATION ANALYSIS

Radiochemical procedures for assay of Pa/sup 233/ following neutron activation of Th/sup 232/ in stone meteorites are described in detail. Eight analyses of five chondrites yielded an average concentration of (3.96 plus or minus 0.20) x 10/sup -8/g Th/g which with proper assumptions, leads to a cosmic atomic abundance of 0.026 for thorium (per 10/sup 6/ Si atoms). The thorium concentrations in two achondrites were found to differ by nearly two orders of maguitude. On comparison with uranium concentrations in stones determined by neutron activation analysis, the Th/U ratio in chondrites and achondrites agree to nearly 5 per cent, yielding an average weight ratio of about 3 to 6. (auth)

A study of the 232Th(3He, α)231Th reaction

The 232Th(3He, α)231Th reaction has been studied with a 30 MeV 3He beam. From a comparison of the experimental and theoretical (DWNA) angular distributions of the outgoing α-particles and a comparison of measured and calculated spectroscopic factors, the following Nilsson bands are assigned in 231Th: 52[633↓] at 0 keV, 32[631↑] at 75 keV, 52[752↑] at 185 keV and 72[743↑] at 380 keV. The bands 32[642↓] at 812 keV and 32[761↑] (only the 152 state is seen) are tentatively assigned. The spectroscopic factors and energy spacings of several bands are influenced by Coriolis coupling. From the published theoretical expression of the spectroscopic factor for one-nucleon transfer reactions, the differential pick-up cross section for a deformed target with spin zero is developed.

Abundances of ruthenium, osmium and uranium in some cosmic and terrestrial sources

Determinations of ruthenium and osmium in ten chondrites by neutron activation analysis give average concentrations of 0.89 × 10−6gRug meteorite and 0.91 × 10−6gOsg meteorite. With proper assumptions these values lead in turn to cosmic abundances (per 106 Si atoms) of 1.3 for Ru and 0.73 for Os. The averages cited include Ru and Os concentrations for a carbonaceous chondrite, which, though below average, fall within the range of concentrations found for the non-carbonaceous chondrites. The range in both the Ru and Os concentrations from about 0.6 × 10−6 g/g to 1.4 × 10−6 g/g reflects not only the variable amount of metal content in the chondrites, but also the variation in Ru and Os concentrations in the metal phase. Analyses of the separated metal and siliceous phases of two chondrites show a marked enrichment of Ru and Os in the metal phase, and they further show that significant amounts of these elements are present in the siliceous phase. Ruthenium and osmium concentrations in Canyon Diablo troilite are found to be suppressed approximately two orders of magnitude below the chondritic averages, which makes it difficult to attribute the presence of Ru and Os in the siliceous phase of chondrites to sulfide inclusion. The isotopic ratio Os184Os190 for osmium in meteorites agrees with that in terrestrial material to about 1 per cent, within the limits of experimental error. The experimental uncertainty in determining the ratio Ru96Ru102 is greater, and as a consequence the agreement of Ru96Ru102 for ruthenium in meteoritic and terrestrial sources cannot be established to much better than 2–3 per cent. With these limits of experimental accuracy, no conclusive evidence for anomalous isotopic composition of ruthenium or osmium has been found in the samples analysed in this work. For samples in which the uranium concentration approaches that of ruthenium, the corrections necessary to account for fission-produced ruthenium permit incidentally the measurement of the uranium present. Uranium concentrations determined in this manner are reported for a few samples

Scandium, chromium and europium in stone meteorites by simultaneous neutron activation analysis☆

ncluding the standard rocks G-1 and W-1. Two achondrites, a tektite and several terrestrial samples are found to have ruthenium and osmium concentrations 2–3 orders of magnitude below those in chondrites, giving evidence of the marked depletion of these elements in differentiated silicate matter.

Collective states of Gd isotopes from (p, t) reactions

Analyses of five chondrites by simultaneous neutron activation yielded average concentrations of (9·4 ± 0·3) × 10−6gSc/g meteorite, (2.2 ± 0.1) × 10−3gCr/g meteorite and (7.8 ± 0.3) x 10−8 g Eu/g meteorite. Following the assumptions of Urey, these results lead to cosmic abundances of 32,6400 and 0.078 (per 106 Si atoms) for Sc, Cr and Eu, respectively. Except for lowering the europium abundance by a factor of 2, the Suess-Urey abundances based on chondrite analyses are not materially altered. The present results are consistently lower than the solar abundances reported by Aller, approaching nearly an order of magnitude in the case of europium. The concentrations of the three elements in two achondrites varied markedly; the Sc/Eu atom ratio, for example, decreased from an average of 410 for the chondrites to 190 for Nuevo Laredo but increased to 5700 for Johnstown, Colorado.