Level repulsion in the ground-state region of nuclei

Cota, E.; Flores, J.; Mello, Pier A.; Yépez, Eduardo Cabal

doi:10.1016/0370-2693(74)90336-0

Cited by 16 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They showed that the widths of the positions of individual eigenvalues were much larger for the TBRE than for the GOE. Cota et al [15] fitted the nearest-neighbour spacing distribution to a Brody distribution, P (s, ω) = α(ω+1)s ω exp[−αs ω+1 ] with α = {Γ[(ω + 2)/(ω + 1)]} ω+1 , obtaining for the Brody parameter the value ω ≈ 0.80 ± 0.05. More recent results by Flores et al [17] show that the semi-Poisson distribution, P (s) = 4s exp[−2s], gives a better fit than the Brody distribution, if the levels of each member of the ensemble are normalized first according to an individual Gaussian distribution (spectral unfolding).…”

Section: Fermionic Systemsmentioning

confidence: 99%

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

2001

View full text Add to dashboard Cite

We consider m spinless Fermions in l > m degenerate single-particle levels interacting via a kbody random interaction with Gaussian probability distribution and k ≤ m in the limit l → ∞ (the embedded k-body random ensembles). We address the cases of orthogonal and unitary symmetry. We derive a novel eigenvalue expansion for the second moment of the Hilbert-space matrix elements of these ensembles. Using properties of the expansion and the supersymmetry technique, we show that for 2k > m, the average spectrum has the shape of a semicircle, and the spectral fluctuations are of Wigner-Dyson type. Using a generalization of the binary correlation approximation, we show that for k m l, the spectral fluctuations are Poissonian. This is consistent with the case k = 1 which can be solved explicitly. We construct limiting ensembles which are either fully integrable or fully chaotic and show that the k-body random ensembles lie between these two extremes. Combining all these results we find that the spectral correlations for the embedded ensembles gradually change from Wigner-Dyson for 2k > m to Poissonian for k m l. C

show abstract

Section: Fermionic Systemsmentioning

confidence: 99%

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

2001

View full text Add to dashboard Cite

show abstract

“…In the first one the nuclear levels observed in experiments were analysed [8][9][10][11]. Typically, these investigations are rather scarce in the recent literature, they are usually concerned with the superpositions of levels from several nuclei, and only exceptionally include also the low-energy part of the spectrum.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos forN=79 nuclei in the IBFM model

Lopac

Brant

Paar

1990

Z. Physik A - Atomic Nuclei

View full text Add to dashboard Cite

show abstract

“…4 The added statistics obtained by relaxing this requirement on the average spacing allows for the first time (see however ref. 8) an analysis of level spacings for near yrast configurations -see e.g. Figure 4.…”

Section: Discussionmentioning

confidence: 99%

The distribution of nuclear quantum states in ‘‘cold’’ rotating nuclei

Garrett¹,

German

Courtney

et al. 1992

AIP Conference Proceedings

View full text Add to dashboard Cite

A statistical analysis of the distribution of level spacings for states with the same spin and parity is described in which the average spacing is calculated for the total ensemble. The resulting distribution of level spacings for states of deformed nuclei with A = 155 -185 and Z = 62 -77 is the closest to that of a Poisson distribution yet obtained for nuclear levels. However, when only the even-spin, positive-parity data for even-even nuclei are considered, the level-spacing distribution becomes double peaked. The anomalously-large separations are shown to be the result of the low energy of the strongly-correlated, completely-paired yrast configuration of even-even nuclei. Average values of the level spacings also are discussed as a function of spin, parity, and nuclear type (even-even, even-Z--odd-N, etc.). Likewise, deviations from a Poisson distribution for several spacings (s) less than about 60 keV are compared with similar values for 116 Sn on an absolute scale. Such discrepancies are attributed to interactions (level repulsions) which become increasingly significant for s < 60 keV. BACKGROUND INFORMATION

show abstract

Level repulsion in the ground-state region of nuclei

Cited by 16 publications

References 6 publications

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices

Quantum chaos forN=79 nuclei in the IBFM model

The distribution of nuclear quantum states in ‘‘cold’’ rotating nuclei

Contact Info

Product

Resources

About