The ability of the cosmic-ray neutron albedo mechanism to account for geomagnetically trapped electrons is investigated quantitatively. Injection as a function of energy, pitch angle, and altitude is computed from a reasonable neutron albedo model. Loss mechanisms (slowing down and pitch-angle diffusion) based on Coulomb interactions with the residual atmosphere are considered to act both independently and simultaneously. It is found that slowing down is generally dominant. The resulting electron belt has the following features: (a) an intensity whose energy spectrum shows a peak at ∼200 kev; (b) an angular distribution that is approximately ‘isotropic’ up to the loss cone; and (c) an omnidirectional, integral intensity in the geomagnetic equatorial plane that is approximately constant vs. altitude. The absolute intensities depend directly on the atmospheric model used in the calculation; namely, rv−2.7, where atmospheric density is taken as ρ0r−v. These results agree only poorly with spectrometer observations which show an energy spectrum with a peak at a much lower energy. However, the quantitative agreement as to intensity is good at energies ≳400 kev. It is concluded that only a small fraction of the trapped electrons can be accounted for in terms of neutron albedo, essentially all trapped electrons >400 kev. An ‘auroral’ component of low-energy electrons is also present. The energy of this low-energy component probably derives from local acceleration, and ultimately from the sun. The effect of the Capetown magnetic anomaly is investigated and shown to produce a ‘slot’ of only 2 per cent in the equatorial plane in the vicinity of 2.7 earth radii.

Geomagnetically trapped electrons from cosmic ray albedo neutrons

Energy-independent and energy-dependent analyses are given for the proton-proton scattering data from 1 to 500 MeV. These analyses are similar to those of the Livermore series, but a number of modifications have been made, particularly in the low-energy representation. First, the range of the analyses has been extended by 50 MeV (i.e., from 450 to 500 MeV) and provisions have been made to include total cross sections in the analyses. This and new data additions have resulted in a 20% expansion of the data base. The other modifications concern the low-energy data and the representation bases. To help alleviate normalization difficulties with the low-energy data, the normalization errors of all experiments in the 0- to 10-MeV energy range were floated. The $S$-wave scattering-length and effective-range parameters were adjusted to give the best fit to the data, and the energy-dependent representation was modified to account for low-energy Coulomb effects. A 28-parameter energy-dependent solution is obtained which is quite good, with ${\ensuremath{\chi}}^{2}=1052$ for 1233 data. This is a definite improvement over the Livermore result, but the phase shifts in the 50- to 400-MeV range are virtually unchanged (with the exception of the $^{3}F_{4}$ and $^{1}G_{4}$ phases) despite the modifications to the bases functions, a strong indication that the data place strong restrictions on the phases.[NUCLEAR STRUCTURE energy-dependent, energy-independent phase-shift analyses of 1-500-MeV $p\ensuremath{-}p$ scattering data.]

Nucleon-nucleon scattering analyses. I. Proton-proton scattering, from 1 to 500 MeV

The absolute differential cross-section for elastic p-p scattering has been measured for an energy of 0.97 GeV at 5‡, 20‡, 25‡, 30‡ and 35‡ in the laboratory system (LS). The data fit the curve $ \sigma \left( \theta \right) = \left\{ {(4.27 \pm 0.37)P_0 (\cos \theta ) + (10.13 \pm 1.44)P_2 (\cos \theta ) + (5.50 \pm 1.36)P_4 (\cos \theta ) + (1.50 \pm 0.64)P_6 (\cos \theta )} \right\} \cdot (1.000 \pm 0.016)mb/sr, $ where Σ(θ) is the unpolarized differential cross-section and 0 the scattering angle in the centre-of-mass system (c.m.s.). This gives a total elastic cross-section of (26.8±2.3) mb and a forward scattering cross-section of (21.4±0.5) mb/sr, which is considerably in excess of the optical theorem minimum of (16.3±0.2) mb/sr.

Absolute differential cross-section for elastic proton-proton scattering at 0.97 GeV

The author discusses the problem of the evaluation of the real parts of forward pp amplitudes directly from the data at small t. The expressions for d sigma /dt and for a number of polarisation parameters are derived in the limit of small t by means of an expansion of the non-singular parts of the amplitudes in powers of t. The analysis of the data at small t available in the energy range 330-800 MeV is performed and the real parts of forward mixed amplitudes are determined. A method suitable for calculation of the Bethe phases at low and medium energies is proposed, and the real parts of forward hadronic amplitudes are calculated. Comparison of these 'measured' real parts with those predicted by the forward dispersion relations reveals a rather satisfactory agreement for the real parts of all three forward hadronic amplitudes.

On the evaluation of the real parts of forward pp amplitudes from the data at small t

Measurements are reported of the difference ..delta..sigma/sub L/ between proton-proton total cross sections for parallel and antiparallel spin states and of the parameter C/sub L/L for proton-proton elastic scattering near 90/sup 0/, for thirteen energies between 300 and 800 MeV. The ..delta..sigma/sub L/ results agree well with previous ANL ZGS and SIN data, but disagree with recent results from TRIUMF. Attempts to understand the cause of the discrepancy have been unsuccessful, but possible sources are discussed. The ..delta..sigma/sub L/ and C/sub L/L results have been used with other experimental data to extract quantities which depend only on spin-singlet, coupled spin-triplet, and spin-triplet partial waves. Structure is found in these quantities, which appears to be associated with the resonantlike /sup 1/D/sub 2/ and /sup 3/F/sub 3/ partial waves. Additional similar structure is also found, which may be due either to the /sup 3/P/sub 0/ partial wave or the (/sup 3/P/sub 2/, /sup 3/F/sub 2/) partial-wave pair.

Measurement of. delta. sigma/sub L/ and C/sub L/L = (L,L; 0,0) in proton-proton scattering between 300 and 800 MeV

Measurements on the proton-proton differential elastic scattering cross section at 380 MeV have been made within the angular range 4° to 30° (c.m.). A target of liquid hydrogen was used and a threshold Cerenkov counter was included in the detecting telescope to eliminate particles from inelastic processes. The total cross section for deuteron production was found to be 0.57 ± 0.08 mbn.

The Elastic Scattering of 380 MeV Protons by Protons I: At Angles Greater than 30? (c.m.)

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The Elastic Scattering of 380 MeV Protons by Protons I: At Angles Greater than 30? (c.m.)