Simple approach to the angular momentum distribution in the ground states of many-body systems

Abstract

We propose a simple approach to predict the angular momentum I ground state (Ig.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be applicable to all cases that have been discussed: even and odd fermion systems (both in single-j and many-j shells), and boson (both sd and sdg) systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features.PACS number: 05.30. Fk, 21.60Cs, 24.60.Lz Typeset using REVT E X 1

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].…”

“…[74] shows that the results of this procedure are nor always right, even qualitatively. A hard problem for such an empirical approach emerges for the ensembles with different weights for different matrix elements.…”

“…The regular methods of boson expansion of fermion operators were introduced in nuclear physics long ago, [96] for a single-j level and [97] for a general level scheme, see the detailed review article [98]. The application of the boson picture to our problem seems promising, especially because numerous studies of the IBM with random interactions [61,62,63,64,65,75] found a similar pattern of the predominance of J = 0 ground states.…”

“…At the same time the probability of an "aligned" ground state with J 0 = J max is higher and for N ≪ 2j + 1 seem to stabilize at around 20-25%. Table 1, column (f), shows the predictions for ground state spins in a system of N = 6, j = 21/2 obtained with the use of the practical recipe suggested by Zhao, Arima and Yoshinaga [74]. The results here are produced by the consecutive choice of the realizations of the random ensemble with only one nonzero parameter V L < 0.…”

“…We usually try to avoid such systems which are exceptional, see for example [74], because of particle-hole symmetry that eliminates even-K multipole moments.…”