Total cross sections,real part of the amplitude,and slope of diffraction cones of the pp and ¯pp forward scattering

In the framework of the model described in [6], analytic expressions are obtained for the ratio of the real part of the forward scattering amplitude to its imaginary part, and for the total cross sections and the slopes of diffraction cones for hadron-hadron and hadron-antihadron interactions. A comparison with the existing experimental data for pp and pp interaction shows that that the computed values of parameters of the elastic scattering are in good qualitative and fair quantitative agreement with their observed values in a wide range of energies s = 5 to 546 GeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 65–70, May, 1990.     

Perturbation theory and Padé approximants in realistic large-matrix models of the nuclear effective interaction

Realistic extended shell-model calculations are used to construct exact effective Hamiltonians, the perturbation series for the effective Hamiltonian to any order, and the [N+1, N] Padé approximants to the series. It is found that the Padé approximants give reliable results even when the series diverge, but that for both convergent and divergent series reasonably accurate results can be obtained only in fifth, or even seventh order. In addition, the poles of the low-order Padé approximants are not always reliable indicators of singularities of the perturbation series. The perturbation series and Padé approximants for the Q-box (energy-dependent effective Hamiltonian) are no more accurate in low orders than those for the usual effective Hamiltonian. Explicit formulas for the matrix Padé approximants are given in an appendix.     

Two-particle ladder diagrams and double-counting in effective interaction calculations

It is shown that including the two-particle ladder diagrams, computed with the Barrett, Hewitt, McCarthy G matrix elements at a starting energy of 47 MeV and for intermediate excitations of 2?Ω, in the perturbation expansion for the effective two-body interaction in mass-18 nuclei involves a double-counting of roughly 42%. It is argued by comparison that the double-counting should be roughly the same when the Kuo G matrix elements are used.