Fluctuation properties of states in26Al

Abstract

The fluctuation properties of the energy levels of 26A1 from the ground state to excitation energies of about 8 MeV have been examined. Several statistics have been employed, and particular attention has been given to the suitability of these statistics for small sample sizes. The results show, for a variety of states, behavior intermediate between GOE and Poisson but apparently favoring GOE. The results are consistent with the fluctuations' being independent of isospin.

Statistical behavior and symmetry tests

“…Experimentally the distribution is intermediate between the one-GOE and two-GOE distributions [7,8,10]. This agrees with predictions, fi rst by Dyson [18] and later by Pandey [19] There are no other direct tests in nuclei, but there are extensive results in " analog" systems: acoustic resonances in quartz blocks [21] and electromagnetic resonances in in superconducting microwave billiards [22].…”

“…We have performed a series of measurements on the effect of isospin symmetry breaking on level statistics [7,8] and on electromagnetic transitions [9,10]. The most striking feature is that a small symmetry breaking can have a large impact on the level statistics and on the transition distributions.…”

Influence of symmetry breaking on the fluctuation properties of spectra

“…For a finite number of sequences, the fluctuation properties are intermediate between the Poisson and GOE statistics. In the following, we shall restrict our consideration to the case when the symmetry under investigation is represented by an operator that has two possible eigenvalues, such as parity, or isospin 0 and 1 as considered in Refs [3,4,5,6,7]. The NNS distribution of a spectrum resulting from a random superposition of n independent sequences is calculated, e.g., by Berry and Robnik [9] and in Mehta's book [10].…”

“…Crystalline quartz exhibits D 3 point-group symmetry about the crystal's Z (optical) axis, and three two-fold rotation symmetries about the three X (piezoelectric) axes; the latter three axes lie in a plane orthogonal to the Z axis and sustain angles of 120 degrees with respect to each other. Ellegaard et al used rectangular blocks of dimensions 14 × 25 × 40 mm 3 , cut in such a way that all symmetries are fully broken except a two-fold "flip" symmetry about one of the three X axes. A gradual breaking of this symmetry is then achieved by removing successively bigger octants of a sphere from one corner, thereby creating a three-dimensional Sinai billiard.…”

“…Impressive are the studies of isospin mixing in light nuclei [2]. Shriner et al [3] measured a "complete" spectrum of low-lying states of 26 Al involving states with isospins T = 0 and 1 throughout the energy range covered by the data. These data offered a testing ground for studying the influence of isospin-symmetry breaking on the fluctuation properties of energy spectra (see, e.g., [4,5,6,7]).…”