Interference term between the spin and orbital contributions to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi><mml:mn>1</mml:mn><mml:mn /></mml:math>transitions

Fayache, M. S.; Zamick, Larry; Sharon, Y. Y.; Devi, Y. D.

doi:10.1103/physrevc.61.024308

Cited by 3 publications

(4 citation statements)

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“…The mean value (8) of the isoscalar magnetic moment is large (relative to a typical off-diagonal element) and leads to the observed deviation from a Porter-Thomas distribution. In the case of the isovector M1 matrix elements, the relative phase of the orbital and spin contributions is more random [25], and the corresponding statistics are Porter-Thomas even when diagonal elements are included.…”

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confidence: 99%

Statistical fluctuations of electromagnetic transition intensities and electromagnetic moments inpf-shell nuclei

et al. 2002

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We study the fluctuation properties of ⌬Tϭ0 electromagnetic transition intensities and electromagnetic moments in Aϳ60 nuclei within the framework of the interacting shell model, using a realistic effective interaction for p f -shell nuclei with a 56 Ni core. The distributions of the transition intensities and of the electromagnetic moments are well described by the Gaussian orthogonal ensemble of random matrices. In particular, the transition intensity distributions follow a Porter-Thomas distribution. When diagonal matrix elements ͑i.e., moments͒ are included in the analysis of transition intensities, the distributions remain PorterThomas except for the isoscalar M 1. This deviation is explained in terms of the structure of the isoscalar M 1 operator.Random matrix theory ͑RMT͒ ͓1͔ was originally introduced to explain the statistical fluctuations of neutron resonances in compound nuclei ͓2͔. The theory assumes that the nuclear Hamiltonian belongs to an ensemble of random matrices that are consistent with the fundamental symmetries of the system. In particular, since the nuclear interaction preserves time-reversal symmetry, the relevant ensemble is the Gaussian orthogonal ensemble ͑GOE͒. The use of RMT in the compound nucleus was justified by the complexity of the nuclear system. Bohigas et al. ͓3͔ conjectured that RMT describes the statistical fluctuations of a quantum system whose associated classical dynamics is chaotic. RMT has become a standard tool for analyzing the universal statistical fluctuations in chaotic systems ͓4 -6͔.The chaotic nature of the single-particle dynamics in the nucleus can be studied in the mean-field approximation. The interplay between shell structure and fluctuations in the single-particle spectrum has been understood in terms of the classical dynamics of the nucleons in the corresponding deformed mean-field potential ͓7,8͔. However, the residual nuclear interaction mixes different mean-field configurations and affects the statistical fluctuations of the many-particle spectrum and wave functions. These fluctuations can be studied using various nuclear structure models. The statistics of the low-lying collective part of the nuclear spectrum have been studied in the framework of the interacting boson model ͓9,10͔, in which the nuclear fermionic space is mapped onto a much smaller space of bosonic degrees of freedom. Because of the relatively small number of degrees of freedom in this model, it was also possible to relate the statistics to the underlying mean-field collective dynamics. At higher excitations, additional degrees of freedom ͑such as broken pairs͒ become important ͓11͔, and the effects of interactions on the statistics must be studied in larger model spaces. The interacting shell model offers an attractive framework for such studies. In this model, realistic effective interactions are available, and the basis states are labeled by exact quantum numbers of angular momentum, isospin, and parity ͓12͔.RMT makes definite predictions for the statistical fluctuations of both the ...

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Section: Mostmentioning

confidence: 99%

Statistical fluctuations of electromagnetic transition intensities and electromagnetic moments inpf-shell nuclei

et al. 2002

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“…While the different models agree in relating the presence of the uncoupled nucleon with the * Electronic address: vargas@ganil.fr † Electronic address: hirsch@nuclecu.unam.mx ‡ Electronic address: draayer@lsu.edu observed fragmentation, the detailed description of this mode, with a nearly flat spectrum in some nuclei and has well-defined peaks in others is still not understood. Recently, the interplay between the spin and orbital M1 channels was examined [16] in the energy range between 4-10 MeV [17].…”

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“…strength of 0.483 µ 2 in the scissors energy region.The 'angle' between the orbital and spin channels, as defined by Fayache et al[16] is 110 o for 163 Dy. For 157 Gd, this angle has a value of 83 o and for 169 Tm it is 96 o .…”

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“…In the case of 163 Dy, there is an almost null contribution from the orbital part of the transition operator (0.103 µ 2 ), which in fact interferes destructively with the spin channel (0.543 µ 2 ) to produce a summed M1 strength of 0.483 µ 2 in the scissors energy region. The 'angle' between the orbital and spin channels, as defined by Fayache et al [16] is 110 o for 163 Dy. For 157 Gd, this angle has a value of 83 o and for 169 Tm it is 96 o .…”

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Microscopic description of the scissors mode in odd-mass heavy deformed nuclei

2003

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Pseudo-SU(3) shell-model results are reported for M1 excitation strengths in 157 Gd, 163 Dy and 169 Tm in the energy range between 2 and 4 MeV. Non-zero pseudo-spin couplings between the configurations play a very important role in determining the M1 strength distribution, especially its rapidly changing fragmentation pattern which differs significantly from what has been found in neighboring even-even systems. The results suggest one should examine contributions from intruder levels.

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