Ray Angular Distributions Research Articles

Observations on the cosmic ray angular distribution underground at 1500 hg/cm 2 (Kolar) and the question of muon production in the TeV energy region

Measurements on the angular distribution of cosmic ray muons at 1500 hgm̧ 2 (Kolar) are presented: these relate to muons with energies ⩾ 500 GeV. These observations are fully consistent with the picture that pions and kaons together are wholly responsible for the production of muons at these energies.

A correction to some experiments to measure the reorientation effect

The importance of the attenuation of the γ ray angular distribution on the interpretation of reorientation experiments is discussed. The attenuation which arises when the emitting nuclei recoil into vacuum leads to an appreciable uncertainty in some reported quadrupole moments.

Differential Cross Sections of theK39,41(n, n′γ)Reactions

Differential production cross sections of the $^{39,41}\mathrm{K}(n, {n}^{\ensuremath{'}}\ensuremath{\gamma})$ and $^{39}\mathrm{K}(n, p\ensuremath{\gamma})$ reactions have been measured at incident neutron energies of 1.82, 2.63, 3.42, and 3.96 MeV. $\ensuremath{\gamma}$ rays were detected with NaI(Tl) and Ge(Li) detectors using pulsed-beam techniques to eliminate backgrounds. Transition-energy measurements of the Ge(Li) detector fix the first excited state of $^{39}\mathrm{K}$ at 2.519\ifmmode\pm\else\textpm\fi{}0.003 MeV. Interpretation of the $\ensuremath{\gamma}$-ray angular distributions and production cross sections permitted spin assignments to $^{39,41}\mathrm{K}$ levels. The $^{39}\mathrm{K}$ levels assigned (excitation in MeV, spin) are 2.817, $\frac{7}{2}$; 3.021, $\frac{3}{2}$; 3.603, $\frac{9}{2}$. Those assigned in $^{41}\mathrm{K}$ are 0.978, \textonehalf{} or $\frac{3}{2}$; 1.291, $\frac{7}{2}$; 1.58, $\frac{9}{2}$ or $\frac{11}{2}$.

Scattering of Alpha Particles by Oxygen. II. Bombarding Energy Range 10 to 19 MeV

The ${\mathrm{O}}^{16}(\ensuremath{\alpha}, \ensuremath{\alpha}){\mathrm{O}}^{16}$ and ${\mathrm{O}}^{16}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\gamma}){\mathrm{O}}^{16}$ reactions have been studied in the bombarding energy range from 10.0 to 19.0 MeV. Elastic-scattering differential cross sections were measured at eight angles as a function of energy, and a total of thirty-five levels in the compound nucleus ${\mathrm{Ne}}^{20}$ have been observed in the excitation curves. Angular distributions of the elastically scattered $\ensuremath{\alpha}$ particles have been measured at seven energies and each shows a strong dependence of the differential cross section on angle. These were analyzed in terms of the Ackhiezer-Pomeranchuk-Blair-McIntyre (APBM) model and the nuclear optical model. Good theoretical fits to the experimental data were obtained only when contributions from resonances were included explicitly in the APBM-model calculations. Excitation curves for the $\ensuremath{\gamma}$ rays emitted from nuclei excited in inelastic-scattering events have been measured, and the ${\mathrm{Ne}}^{20}$ energy levels found in the $\ensuremath{\gamma}$-ray excitation curves confirm most of the levels found in the elastic-scattering experiment. Thin- and thick-target angular distributions for the 6.13-MeV $\ensuremath{\gamma}$ rays were measured at 15 energies. Thick-target $\ensuremath{\gamma}$-ray angular distributions which average over many resonances could not be simply interpreted in terms of broad levels in ${\mathrm{Ne}}^{20}$. Twenty spin-and-parity assignments to states in ${\mathrm{Ne}}^{20}$ have been made in the analysis of the elastic- and inelastic-scattering data, and of these, 14 are tentative. The levels in ${\mathrm{Ne}}^{20}$ observed here have broader widths, larger spacings, and greater spins than the majority of those reported in the literature for the same excitation energy range. These differences are discussed and a possible explanation is offered. The incorporation of several of the levels found in this work in ${\mathrm{Ne}}^{20}$ rotational bands has been included in Paper I.

Some Effects of Parity Nonconservation in Nuclear Electromagnetic Decays

The matrix elements for decay of a nucleus by $\ensuremath{\gamma}$ emission or electron conversion are considered with relaxation of the usual parity selection rules. Four types of pseudoscalar observables are calculated assuming, in particular, mixed $\mathrm{ML}$ and $\mathrm{EL}$ multipole matrix elements with arbitrary relative amplitude. These are (1) $\ensuremath{\gamma}$-ray nuclear polarization with unpolarized initial and final nuclei, (2) $\ensuremath{\gamma}$-ray angular distribution (terms odd in $cos\ensuremath{\theta}$) with polarized initial nucleus, (3) helicity of conversion electrons with unpolarized initial and final nuclei, and (4) circular polarization of the succeeding $\ensuremath{\gamma}$ ray relative to the direction of the first, mixedparity $\ensuremath{\gamma}$ ray in the two-photon cascade of an unpolarized nucleus. A proof is presented that the helicity of the conversion electron (3) approaches the circular polarization (1) in the mathematical limit of infinite transition energy. Numerical results are presented for $^{180}\mathrm{Hf}^{m}$ based on a recent conjecture of parity mixing in one of its transitions.

The gyromagnetic ratio of the first excited 2+ state of 182W and 184W

The gyromagnetic ratios of the 100 keV 2+ state of 182W and the 111 keV 2+ state of 184W have been measured by observing the time integrated precession of the gamma ray angular distribution following Coulomb excitation with a neutral hydrogen beam. Thick metallic targets of separated isotopes have been used. Particular attention is given to the effects of internal perturbations by a randomly oriented static quadrupole interaction. The values of the g factors are g = 0.249±0.024 for 182W and g = 0.282±0.018 for 184W.

Polarization of Silver Nuclei in Metallic Iron and Nickel

Nuclei of ${\mathrm{Ag}}^{104}$ and ${\mathrm{Ag}}^{110m}$ were polarized at temperatures between 0.0105 and 0.97\ifmmode^\circ\else\textdegree\fi{}K, employing the large hyperfine magnetic fields induced at the nuclei of silver atoms dissolved in iron and in nickel. The temperature and angular dependences of $\ensuremath{\gamma}$-ray angular distributions were used to determine the magnitudes of the hyperfine structure constants. Nonconservation of parity in beta decay was used to determine the signs of the internal fields, using germanium detectors to count positrons from ${\mathrm{Ag}}^{104}$ and electrons from ${\mathrm{Ag}}^{110m}$. The hyperfine fields were found to be negative in both iron and nickel. Analysis of the $\ensuremath{\gamma}$-ray data on one-hour ${\mathrm{Ag}}^{104}$ yielded approximate values for the internal fields: ${H}_{i}(\mathrm{Ag}\mathrm{in}\mathrm{Fe})=\ensuremath{-}350\ifmmode\pm\else\textpm\fi{}100$ kG, ${H}_{i}(\mathrm{Ag}\mathrm{in}\mathrm{Ni})=\ensuremath{-}108\ifmmode\pm\else\textpm\fi{}30$ kG. Cobalt-60 $\ensuremath{\gamma}$-ray thermometry was used, and the problems of thermometry at 0.01\ifmmode^\circ\else\textdegree\fi{}K are discussed. Nuclear spins of four levels in ${\mathrm{Cd}}^{110}$ were determined unambigously, confirming earlier work, which was re-interpreted where necessary. The energy levels (spins) are 2162 keV (3+), 2219 keV(4+), 2479 keV(6+), 2926 keV(5+). The 1384-keV $\ensuremath{\gamma}$ ray in ${\mathrm{Cd}}^{110}$ was found to be (91.7\ifmmode\pm\else\textpm\fi{}2.8)% magnetic dipole and (8.3\ifmmode\pm\else\textpm\fi{}2.8)% electric quadrupole. The 1505-keV $\ensuremath{\gamma}$ ray was (78.9\ifmmode\pm\else\textpm\fi{}4.8)% magnetic dipole and (21.1\ifmmode\pm\else\textpm\fi{}4.8)% electric quadrupole. An approximate value of +2.9\ifmmode\pm\else\textpm\fi{}1.3 nm was determined for the nuclear moment of ${\mathrm{Ag}}^{110m}$.

Angular Distribution ofγRadiation Following Direct Nuclear Reaction

The $\ensuremath{\gamma}$-ray angular distributions following the direct reaction ${\mathrm{C}}^{12}(p, {p}^{\ensuremath{'}}{\ensuremath{\gamma}}_{4.43\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V}}){\mathrm{C}}^{12}$ have been calculated for the cases of single-particle excitation and collective excitation using Glendenning's optical potential and the surface interaction model. In the case of particle excitation, the effective two-body potential has been assumed to have the form ${V}_{d}(|{\mathrm{r}}_{p}\ensuremath{-}{\mathrm{r}}_{n}|)[{a}_{0}+{a}_{1}\ensuremath{\sigma}(p)\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\sigma}(n)]$. Comparison with experiments at this laboratory for incident proton energies ${E}_{p}=6.69, 8.46, 8.71, \mathrm{and} 9.72$ MeV shows remarkably good fits for $\frac{{a}_{1}}{{a}_{0}}=\ifmmode\pm\else\textpm\fi{}0.67$. For the case of collective excitation, the agreement has been found to be poor. The plane-wave Born approximation for the incoming and outgoing waves does not yield satisfactory results for either mechanism.

Endothermic Deuteron Stripping Reactions. I. Stripping Near Threshold

Wilkinson's explanation of the good agreement between theory and experiment for low energy, low $Q$ value, ($d, p$) and ($d, n$) stripping reactions is restated from the point of view of the dispersion relations derivation of the Butler stripping formula. From this point of view, the kinematical conditions which should lead to the least distortion of the stripping pattern appear in a simple way. As a consequence of Wilkinson's arguments, it is proposed that the stripping mechanism should contribute significantly to endothermic ($d, p$) or ($d, n$) reactions near threshold. Some ($d, n$) threshold work is discussed, and it is concluded that this work gives some evidence that the stripping mechanism is important near threshold. The information on the reaction mechanism near threshold which can be obtained from $\ensuremath{\gamma}$-ray angular distribution measurements in ($d, p\ensuremath{\gamma}$) or ($d, n\ensuremath{\gamma}$) reactions is discussed and a general form for the angular distribution function for either plane-wave or distorted-wave stripping is developed. The ${\mathrm{B}}^{11}(d, n){\mathrm{C}}^{12}$ (15.1-Mev level) reaction is considered in some detail and it is concluded that the experimental evidence is consistent with this reaction proceeding via the stripping mechanism near threshold.