A shell-model analysis of Λ binding energies for the p-shell hypernuclei. I. Basic formulas and matrix elements for ΛN and ΛNN forces

A uniform intermediate-coupling shell model is formulated for the p-shell Λ hypernuclei, those belonging to the configuration {(1s)_N⁴(1p)_N^Λ-5(1s)_Λ}, using NN parameters obtained from previous fits to the corresponding core nuclei. The physical origins of the ΛN forces are discussed, with special attention to the noncentral components, and the characteristics of the three-body double-OPE ΛNN interaction are reviewed briefly. Expressions are derived for all the ΛN and ΛNN matrix elements needed for the discussion of these configurations. Attention is drawn particularly to their qualitative characteristics. For the purpose of orientation, numerical estimates of them are given for all possible types of ΛN forces and for all the constituents of the double-OPE ΛNN interaction, using explicit forms for the radial wave functions, as a basis for the purely phenomenological analysis (now complete) of the data available on the p-shell hypernuclei to be discussed in Part II.