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We investigate Hamiltonians with attractive interactions between pairs offermions coupled to angular momentum J. We show that pairs with spin J arereasonable building blocks for the low-lying states. For systems with only a J= Jmax pairing interaction, eigenvalues are found to be approximately integersfor a large array of states, in particular for those with total angular momentaI le 2j. For I=0 eigenstates of four fermions in a single-j shell we show thatthere is only one non-zero eigenvalue. We address these observations using thenucleon pair approximation of the shell model and relate our results with anumber of currently interesting problems.Comment: a latex text file and 2 figures, to be publishe

physical review. c. nuclear physics/physical review. c, nuclear physics

General pairing interactions and pair truncation approximations for fermions in a single-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math>shell

General pairing interactions and pair truncation approximations for fermions in a single-jshell