Spectral statistics of energy levels of 152 Dy
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000151-y
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Spectral statistics of energy levels of
152
Dy
Nishchal Dwivedi1 , Bijay Agarwal2,4 , and Sudhir R. Jain3,4,5,a 1
2 3 4 5
Department of Physics, Indian Institute of Technology Bombay, Mumbai 400071, India Saha Institute of Nuclear Physics, Kolkata 700064, India Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India Homi Bhabha National Institute, Mumbai 400094, India UM-DAE Centre for Excellence in Basic Sciences, Kalina, Mumbai 400098, India Received 7 July 2020 / Accepted 28 August 2020 Published online 23 October 2020 Abstract. We carry out a study on various configurations admissible in a superdeformed nucleus, 152 Dy. Our interest is in extracting the nature of spectral fluctuations and compare with those of random matrix theory. In particular, we study the distribution functions of ratios of the nearest-neighbor spacing of the energy levels. This does not require usage for the average level density. For several variations of shapes, the energy levels have been calculated in a self-consistent manner, and their fluctuations show that the energy levels are correlated in a manner expected for the eigenvalues of quantum systems which are classically non-integrable. Due to limited size of level sequences in each symmetry class, our results may be termed only indicative.
1 Introduction Nuclei are rather complex quantum systems. The nucleons are bound by central and tensor interactions [1]. The tensor interaction spoils the planetary description which follows from a central potential. The resulting non-integrability is expressed in the fluctuation properties of the energy levels and the corresponding eigenfunctions [2]. And this holds for all nuclei, from deuteron to superheavy nuclei. The ground state eigenfunction of deuteron is non-symmetric [3,4], leading to a non-zero quadrupole moment [5]. Apart from a few exact solutions [3,4] for deuteron and triton by employing ~-expansions, to all orders of ~, all studies involve numerical solutions of spectra or analyzing their statistical properties. The statistical theory for energy spectra of nuclei was born in the hands of Wigner and Landau, it has emerged as a major field in the area of mathematical physics [6–9]. A given quantum system is characterized by a set of commuting observables which subsume symmetries of the system. We classify the states corresponding to the energy levels in accordance with the symmetries of the quantum system. For example, the states of a quadrupole deformed nucleus are labeled by angular momentum and parity. However, when octupole deformation comes into play, parity is no more a good symmetry. In this paper, we consider only one nucleus, 152 Dy. This is a classic case of a
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2620
The European Physical Journal Special Topics
a superdeformed nucleus possessing different energy levels corresponding to different set of states corresponding to symmetr
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