Thermonuclear reaction rates V

Energy levels of light nuclei A=8,9,10

A new critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}\ensuremath{\beta}$ decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references, either because they have been superseded by much more precise modern results or because there are now reasons to consider them fatally flawed; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections, which were motivated by these new Penning-trap results. Third, our calculation of the statistical rate function $f$ now accounts for possible excitation in the daughter atom, a small effect but one that merits inclusion at the present level of experimental precision. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new ``corrected'' $\mathcal{F}t$ values are impressively constant and their average, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, ${V}_{\mathit{ud}}=0.97425\ifmmode\pm\else\textpm\fi{}0.00022$. The unitarity test on the top row of the matrix becomes $|{V}_{\mathit{ud}}|{}^{2}+|{V}_{\mathit{us}}|{}^{2}+|{V}_{\mathit{ub}}|{}^{2}=0.99995\ifmmode\pm\else\textpm\fi{}0.00061$. Both ${V}_{\mathit{ud}}$ and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of ${V}_{\mathit{ud}}$ is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents, and extra $Z$ bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.

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Superallowed 0 + →0 + nuclear β decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model

Primary radiation damage: A review of current understanding and models

We present calculations of fission properties for heavy elements. The calculations are based on the macroscopic-microscopic finite-range liquid-drop model with a 2002 parameter set. For each nucleus we have calculated the potential energy in three different shape parametrizations: (1) for 5 009 325 different shapes in a five-dimensional deformation space given by the three-quadratic-surface parametrization, (2) for 10 850 different shapes in a three-dimensional deformation space spanned by epsilon(2), epsilon(4), and gamma in the Nilsson perturbed-spheroid parametrization, supplemented by a densely spaced grid in epsilon(2), epsilon(3), epsilon(4), and epsilon(6) for axially symmetric deformations in the neighborhood of the ground state, and (3) an axially symmetric multipole expansion of the shape of the nuclear surface using beta(2), beta(3), beta(4), and beta(6) for intermediate deformations. For a fissioning system, it is always possible to define uniquely one saddle or fission threshold on the optimum trajectory between the ground state and separated fission fragments. We present such calculated barrier heights for 1585 nuclei from Z=78 to Z=125. Traditionally, actinide barriers have been characterized in terms of a "double-humped" structure. Following this custom we present calculated energies of the first peak, second minimum, and second peak in the barrier for 135 actinide nuclei from Th to Es. However, for some of these nuclei which exhibit a more complex barrier structure, there is no unique way to extract a double-humped structure from the calculations. We give examples of such more complex structures, in particular the structure of the outer barrier region near Th-232 and the occurrence of multiple fission modes. Because our complete results are too extensive to present in a paper of this type, our aim here is limited: (1) to fully present our model and the methods for determining the structure of the potential-energy surface, (2) to present fission thresholds for a large number of heavy elements, (3) to compare our results with the two-humped barrier structure deduced from experiment for actinide nuclei, and (4) to compare to additional fission-related data and other fission models. . (Less)

Heavy-element fission barriers

The total $^{7}\mathrm{Be}$(n,p${)}^{7}$Li cross section has been measured from 25 meV to 13.5 keV. These energies correspond to temperatures of T=2.9\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ to 0.16 GK. For thermal neutrons the cross sections to the ground state (${p}_{0}$) and the first excited state (${\mathit{p}}_{1}$) of $^{7}\mathrm{BLi}$ are 38 400\ifmmode\pm\else\textpm\fi{}800 b and 420\ifmmode\pm\else\textpm\fi{}120 b, respectively. This result for the total $^{7}\mathrm{Be}$(n,p${)}^{7}$Li thermal cross section is about 25% lower, and is approximately a factor of 10 more precise than previous published measurements. For energies above 100 eV, a significant departure from a 1/v shape for the total cross section is observed. The data were analyzed using a single-level approximation, and were also analyzed together with other data using multilevel-multichannel R-matrix theory. Results are presented for the properties of the ${2}^{\mathrm{\ensuremath{-}}}$ threshold state and for a possible nearby ${2}^{\mathrm{\ensuremath{-}}}$ state. The astrophysical reaction rate, ${N}_{A}$〈\ensuremath{\sigma}v〉, was calculated from the measured cross sections for the combined ${p}_{0}$ and ${p}_{1}$ transitions. The resulting reaction rate is approximately 60--80 % of the rate currently in use. This reduction in the $^{7}\mathrm{Be}$(n,p${)}^{7}$Li reaction rate could result in a calculated increase in the production of $^{7}\mathrm{Li}$ during the big bang by as much as 20%.

7Be(n,p)7Li total cross section from 25 meV to 13.5 keV.

We have studied primary and secondary \ensuremath{\gamma} rays (46 in $^{29}\mathrm{Si}$, 107 in $^{30}\mathrm{Si}$, and 33 in $^{31}\mathrm{Si}$) following thermal-neutron capture by the stable $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, and $^{30}\mathrm{Si}$ isotopes. Almost all of these \ensuremath{\gamma} rays have been incorporated into corresponding level schemes consisting of 12 excited levels in $^{29}\mathrm{Si}$, 28 in $^{30}\mathrm{Si}$, and 9 in $^{31}\mathrm{Si}$. In each case, the observed \ensuremath{\gamma} rays account for nearly 100% of all captures. The measured neutron separation energies for $^{29}\mathrm{Si}$, $^{30}\mathrm{Si}$, and $^{31}\mathrm{Si}$ are 8473.56\ifmmode\pm\else\textpm\fi{}0.04, 10609.24\ifmmode\pm\else\textpm\fi{}0.05, and 6587.40\ifmmode\pm\else\textpm\fi{}0.05 keV, respectively. The measured thermal-neutron capture cross sections for $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, and $^{30}\mathrm{Si}$ are 169\ifmmode\pm\else\textpm\fi{}4, 119\ifmmode\pm\else\textpm\fi{}3, and 107\ifmmode\pm\else\textpm\fi{}3 mb, respectively. In all three cases, primary electric-dipole (E1) transitions account for the bulk of the total capture cross section. We have calculated these E1 partial cross sections using direct-capture theory. The agreement between theory and experiment is satisfactory.

Thermal-neutron capture by silicon isotopes

The 76-h isotope /sup 256/Es/sup m/ was produced from a 25-mug/cm/sup 2/ target of /sup 254/Es by the (t,p) reaction The reaction products were separated radiochemically, and the decay properties of /sup 256/Es/sup m/ were determined via beta-gamma, gamma-gamma, and beta-fission correlation techniques From these measurements we were able to assign 57 gamma rays to 26 levels in the daughter /sup 256/Fm An isomeric level was observed at 1425 keV and assigned a spin and parity of 7/sup -/ This level has a t/sub 1/2/ of (70 +- 5) ns and we observed two beta-delayed fissions with delay times in the proper time range to be associated with fission from this level This gives a beta-delayed fission probability of 2 x 10/sup -5/ for this level and a partial fission half-life of 08/sub -07//sup +88/ ms at the 95% confidence level

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beta -delayed fission from 256Esm and the level scheme of 256Fm.

The energies and intensities of 58 \ensuremath{\gamma} rays emitted in thermal-neutron capture by nitrogen (99.63% ${}^{14}\mathrm{N}$) have been measured accurately. A major reason was to establish this reaction as a standard for similar measurements on other nuclides. These \ensuremath{\gamma} rays have been placed between 19 known levels (including the ground state and the capturing state) in ${}^{15}\mathrm{N}.$ The primary \ensuremath{\gamma} rays of both electric dipole $(E1)$ and magnetic dipole $(M1)$ types have been analyzed with existing theories of slow-neutron capture. Unlike many other light nuclides, the cross sections for $E1$ transitions in ${}^{15}\mathrm{N}$ differ drastically from the calculations of pure direct-capture theory. The role of the resonance-capture contribution from the proton-unbound, neutron-bound level at $29\ifmmode\pm\else\textpm\fi{}2\mathrm{keV}$ below the neutron separation energy was considered. Some of the properties of this level are quite well known from the ${}^{14}\mathrm{C}(p,\ensuremath{\gamma})$ reaction, and others can be derived from an R-matrix analysis of the total cross section as a function of neutron energy. The thermal-neutron capture \ensuremath{\gamma}-ray spectrum is different from the proton-capture \ensuremath{\gamma}-ray spectrum, but if proper account is taken of the interference among the compound-nuclear processes, the valence-neutron mechanism, and potential capture, the data can be satisfactorily explained. In the thermal-neutron reaction, compound-nuclear $E1$ and direct-capture $E1$ contributions are of comparable magnitude. Valence-neutron capture forms a significant component of capture by the neutron-bound level at $\ensuremath{-}29\mathrm{keV}.$ Largely destructive interference between compound-nuclear and valence processes in a few transitions in thermal-neutron capture gives rise to a much smaller total cross section than would be obtained from the compound-nuclear process alone. The $M1$ transitions also show some evidence of a direct process but not a dominant one. The magnitudes of the compound-nuclear transitions, both $E1$ and $M1,$ are largely consistent with the values implied by giant resonance theories. The resonance parameters deduced for the $\ensuremath{-}29\ensuremath{-}\mathrm{keV}$ level are: total radiation $\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=565\ifmmode\pm\else\textpm\fi{}24\mathrm{}\mathrm{meV},$ $\mathrm{reduced}\mathrm{}\mathrm{neutron}\mathrm{}\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=51.6\ifmmode\pm\else\textpm\fi{}0.3\mathrm{}\mathrm{keV}$ (for a channel radius of 3.5 fm), and proton $\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=160\ifmmode\pm\else\textpm\fi{}30\mathrm{}\mathrm{meV}.$

Thermal-neutron capture by 14 N

Nuclear levels of ${\mathrm{Dy}}^{163}$ have been investigated, combining the following experimental techniques: the measurement of low-energy ($n, \ensuremath{\gamma}$) radiation between 30 keV and \ensuremath{\approx}1.2 MeV using a curved-crystal spectrometer, the measurement of ($n, {e}^{\ensuremath{-}}$) conversion electrons in the energy range between 113 and 950 keV with a double-focusing $\ensuremath{\beta}$ spectrometer, the investigation of high-energy ($n, \ensuremath{\gamma}$) transitions between 4 and 6.4 MeV using a Ge(Li) spectrometer, and the study of ($d, p$) and ($d, t$) reactions utilizing 12-MeV deutrons and a broad range magnetic spectrograph. The observed levels are: the [523\ensuremath{\downarrow}] ground-state rotational band, including the rotational states ${\frac{7}{2}}^{\ensuremath{-}}$, ${\frac{9}{2}}^{\ensuremath{-}}$, and $\frac{11}{{2}^{\ensuremath{-}}}$; the first 4 members of the [642\ensuremath{\uparrow}] band, with the ${\frac{5}{2}}^{+}$ band head at 250.9 keV; the [521\ensuremath{\downarrow}] band, including the members ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ (at 351.1 keV), ${\frac{3}{2}}^{\ensuremath{-}}$, ${\frac{5}{2}}^{\ensuremath{-}}$, and ${\frac{7}{2}}^{\ensuremath{-}}$; the lowest 4 members of the [521\ensuremath{\uparrow}] band, with the ${\frac{3}{2}}^{\ensuremath{-}}$ state at 421.8 keV; the ${\mathrm{\textonehalf{}}}^{+}$, ${\frac{3}{2}}^{+}$, and ${\frac{5}{2}}^{+}$ levels of a ${K}^{\ensuremath{\pi}}={\frac{1}{2}}^{+}$ band based at 737.6 keV, believed to be mainly a mixture of the vibrational configuration {[642\ensuremath{\uparrow}], $K\ensuremath{-}2$} and [660]; another ${K}^{\ensuremath{\pi}}={\frac{1}{2}}^{+}$ band based at 884.3 keV, including the ${\mathrm{\textonehalf{}}}^{+}$, ${\frac{3}{2}}^{+}$, and ${\frac{5}{2}}^{+}$ states, assigned as mainly a three-quasiparticle configuration; a state at 820.8 keV, assigned as the head of a ${K}^{\ensuremath{\pi}}={\frac{3}{2}}^{\ensuremath{-}}$ band, probably of vibrational character; a state at 859.3 keV, assigned as the head of a ${K}^{\ensuremath{\pi}}={\frac{3}{2}}^{+}$ band; an ${I}^{\ensuremath{\pi}}={\frac{3}{2}}^{\ensuremath{-}}$ level at 1049.1 keV; and an ${I}^{\ensuremath{\pi}}={\frac{1}{2}}^{\ensuremath{-}}$ state at 1055.7 keV. In addition, the ${\frac{7}{2}}^{\ensuremath{-}}$ rotational level of the [512\ensuremath{\uparrow}] band is probably at 799.5 keV, the ${\frac{3}{2}}^{\ensuremath{-}}$ state of the [510] band is indicated at 1200 keV, and a further state, probably of low spin, has been observed at 1058 keV. A number of other unassigned levels have been found in the ($d, p$), ($d, t$), and high-energy ($n, \ensuremath{\gamma}$) experiments. Essentially all states above 350 keV appear to be of mixed character, and several of the indicated "single-particle" bands are believed to have sizable vibrational components. Many of the $\ensuremath{\gamma}$-ray branching ratios among the three lowest negative-parity bands are anomalous, and the extent to which these deviations can be explained in terms of Coriolis coupling has been investigated.

J.W. Starner

Papers

7Be(n,p)7Li total cross section from 25 meV to 13.5 keV.

Thermal-neutron capture by silicon isotopes

beta -delayed fission from 256Esm and the level scheme of 256Fm.

Thermal-neutron capture by 14 N

Nuclear Levels in Dy 163