Optical phase shifts from low-energy neutron cross sections

The Lorentz-weighted average of the S-matrix introduced by G.E. Brown is used in the Feshbach theory of the generalized optical potential to show that the average many-body S-matrix for elastic scattering is exactly equal to the two-body S-matrix of an optical potential. However, the optical potential S-matrix must be evaluated at the complex energy $\text{E}\text{= E + iI,}\text{where}\text{I}$ is the half-width of the lorentzian. The resulting equation for the optical phase shifts (OPS) δ_c, exp $\text{[2iδ}{}_{\mathrm{c}}\text{(}\text{E}\text{)] = 〈S}{}_{\mathrm{cc}}\text{(E)〉}$, holds even when the level spacing D forces the use of an averaging half-width I > D which is comparable to the energy E, providing that the OPS are also evaluated at the complex $\text{E}$ instead of being approximated by their values on the real energy axis at E. An appendix discusses briefly the conditions on a potential necessary for the result obtained by Brown that $\text{〈S}{}_{\mathrm{cc}}\text{(E)〉 = S}{}_{\mathrm{cc}}\text{(}\text{E}\text{)}$ when Lorentz-weighted averaging is used.     

Ion current surface for a double focusing mass spectrometer of reversed geometry

Ion currents obtained for fragmentations in a mass spectrometer of reversed geometry have been represented as three-dimensional surfaces, which are termed ‘ion current surfaces’. In addition to ion current, useful dimensions of the ion current surfaces are a parameter ln(|ρ|) where ρ = (V₀/V)(E/E₀) and a parameter ln(|m*|) where m* = (V₀/V)m_B. Each ion reaction occurring in the source and flight path gives rise to a pattern of peaks and ridges on the surface. If the major features of the surface corresponding to each ion reaction are projected onto the zero ion current plane, they are disposed in a characteristic trapezoidal pattern. All simple and linked modes of scanning correspond to cross-sections of the surfaces, and representing the scanning modes in this light facilitates the identification of ‘cross-talk’.     

A study of the reaction p+d → 3He+π0 in the resonance region

The reaction $\text{p}\text{+}\text{d}\text{→}{}^3\text{He}\text{+ π}{}^0$ was studied at incident proton energies of 377, 462 and 576 MeV. A comparison of our data with others suggests the existence of a sharp forward peak in θ_He at 377 and 462 MeV, which is unexplained by the theory and disappears at higher energies.