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

Abstract

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = J max pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I ≤ 2j. For I = 0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.

Angular momentum distribution of the ground states in the presence of random interactions: Boson systems

“…Many works have been done in the context of this discovery [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For example, many efforts were made concerning the origin of this observation and generic properties of many-body systems in the presence of random interactions.…”

Companion problems in quasispin and isospin

“…This was shown by the above authors [17] simply by equating the left-hand side of eq. (2.11) with the right-hand side, and relying on the proof in ref.…”

Nuclear structure, random interactions and mesoscopic physics

“…[8] found a surprisingly large fraction of cases with the ground state spin J 0 = 0. Being later confirmed and studied by many authors for different ensembles and different fermion and boson single-particle spaces, the effect seems to be generic, see for example [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85].…”