Lowest eigenvalue of the nuclear shell model Hamiltonian

Abstract

In this paper we investigate regular patterns of matrix elements of the nuclear shell model Hamiltonian $H$, by sorting the diagonal matrix elements from the smaller to larger values. By using simple plots of non-zero matrix elements and lowest eigenvalues of artificially constructed "sub-matrices" $h$ of $H$, we propose a new and simple formula which predicts the lowest eigenvalue with remarkable precisions.Comment: six pages, four figures, Physical Review C, in pres

Suppression of the High-pTCharged-HadronRAAat the LHC

“…As this Letter will deal solely with the spectra and azimuthal anisotropy at high p T (p T ≥ 6 GeV), we will only provide the most salient features of these simulations in the current paper and direct the reader to Refs. [12,13] for further details.…”

Regularity of nuclear structure under random interactions

“…Below we concentrate on the simple formula of the lowest eigenvalue [3]. i j (i, j = 1, 2, · · · , d).…”

“…The first result is on collective motion in sd-boson systems, and the second is on evaluation of eigenvalues [3].…”

“…Recently we made the following progresses [3] of evaluating eigenvalues of the nuclear shell model Hamiltonian: (1) By using simple plots of non-zero matrix elements and lowest eigenvalues of artificially constructed "sub-matrices" h of H, we propose a new and simple formula which predicts the lowest eigenvalue with remarkable precisions. (2) We investigate a few extrapolation methods for the nuclear shell model Hamiltonian, and predict energy levels and electromagnetic properties such as electric quadrupole moments, magnetic dipole moments and E2 transitions.…”

“…For random Hamiltonians, we studied relevance of generalized seniority under random interactions in single-closed shell nuclei in the sd and the p f shell [1], and the collective motions of sd bosons with random interactions [2]. Concerning the fourth topic, Prof. Arima, Mr. Shen (one of my graduate students), Prof. Yoshinaga, and I, have been working very hard to evaluate eigenvalues of the nuclear shell model Hamiltonian without diagonalizing the full matrices [3,4]. Prof. Arima is now the main engine in pushing forward the studies of the eigenvalue problem in this collaboration.…”