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Authors: Keechiprath, Rhine Kumar Arayakkandi
Keywords: Nuclear Many-Body Problem
Adequate Phenomenological Inputs
Most Dominant Mode
Various Theoretical
Issue Date: Jul-2015
Publisher: Dept. of Physics iit Roorkee
Abstract: The theoretical understanding of nuclear many-body problem is built upon the models with adequate phenomenological inputs. Such models representing the nature of ever-intriguing nuclear force can be robust if they render applicability over various domains, including the extremes of temperature (T), spin (I), isospin and density. Hence, extending the nuclear models to study nuclei at these extremes also gains significance, especially in the light of recent developments in the experimental facilities with which these nuclear states are becoming more accessible. Another important task in this regard is to identify the relevant phenomena for which the observables can be calculated reliably in all the considered domains. Giant resonances (GR) in nuclei is one such fundamental mode of excitation which can be built on any nuclear state. In a simplistic view, the GR are due to collective oscillations of protons and neutrons under the influence of the electromagnetic field induced by the emitted/absorbed photons, which results in a large peak in the emission/absorption spectrum of g -rays. Among the various possible modes of the GR, the most dominant mode is the isovector giant dipole resonance which is commonly termed as GDR. Constructing a theoretical framework to study the GDR built on various nuclear states so as to unravel the underlying nuclear structure, is the broad aim of this thesis work. Various theoretical approaches have been introduced to investigate the GDR. In a macroscopic approach, GDR is a collective mode of excitation of nuclei caused by the out-of-phase oscillations between the proton and neutron fluids under the influence of the electromagnetic field induced by an emitted/absorbed photon. The GDR couples directly to the shape of the nucleus, hence providing corresponding structure information. This link is not so straight-forward especially in hot nuclei where thermal v fluctuations are expected to be large since the nucleus is a tiny finite system. The thermal shape fluctuation model (TSFM) is based on the macroscopic approach for GDR and takes into account the thermal fluctuations over the possible degrees of freedom, in a simple case, the shape parameters. This is achieved through a weighted average of the observable over the considered degrees of freedom. The weights are given by the Boltzmann factor [exp(−F/T)] where the free energy (F) is calculated within the Nilsson-Strutinsky (microscopic-macroscopic) approach. The theoretical framework developed in this thesis work is built upon such a TSFM. In an alternative approach, the GDR observables can be calculated utilizing a linear response theory incorporating the thermal shape fluctuation within the static path approximation. Other rigorous microscopic approaches exist but are mostly limited to the study of low-lying states. In microscopic approaches, such as the phonon-damping model (PDM), GDR damping is explained through coupling of the GDR phonon to particle-hole, particle-particle, and hole-hole excitations. Apart from the above discussed models, a few phenomenological parametrizations have been reported, which are very successful in explaining the global trend of the GDR width as a function of T and I. Several earlier works on GDR focussed on the high-I regime whereas the recent studies at extreme isospins have potential astrophysical implications. Apart from the higher limits of T, I and isospin, the properties of atomic nuclei are intriguing and less explored at the limits of lowest but finite temperatures. Such studies have gained acceleration in recent times. At very low temperatures there is a strong interplay between the shell (quantal fluctuations), statistical (thermal fluctuations), and residual pairing effects. At high-I, the pairing collapses but still the other two effects are strong and so is their interplay. In these cases, conclusive experimental results are scarce. This thesis work is an attempt to understand such warm nuclei both in the rotating and nonrotating cases, by studying the GDR observables. As the physics cases we have chosen the following: 1. Warm nuclei (a) Role of pairing and its fluctuations (b) Role of the choice of mean-field 2. Warm and rotating nuclei: Shape transitions at higher spins. Several properties of nuclei at low T are still not clear, for example, the existence of pairing phase transition, the order of it if it exists, the role of fluctuations, etc. The success of pairing approach at low T and that of the TSFMelsewhere have motivated us to vi consider a combination of pairing correlations within the TSFM. Thermal shape fluctuations and fluctuations in the pairing field are the dominating fluctuations and they have been so far studied separately within different models. Both of these fluctuations are expected to be present at low temperatures. However, the interplay between them has not been investigated so far and forms a motivation for our above case 1(a). The availability of GDR data for nuclei away from stability like the case of 179Au demands a careful introspection of the choice of the mean-field because a simple potential like that of Nilsson could not be a reliable choice for such cases. The case 2 above is motivated by the fact that most of the earlier GDR studies of rotating nuclei were at sufficiently larger T. With dominant thermal fluctuations, and melting of shell effects, the features of such nuclei can be explained even by a liquid drop model. More interesting shape transitions driven by the shell effects can be studied only at lower T and hence considered in this work. More details of the content of the thesis is presented below in a chapter-wise breakup. Chapter 1: In this chapter, we start by introducing giant resonances and their importance in understanding several nuclear properties. More emphasis is given to the GDR studies at different domains such as low T, high T and high I. The different theoretical models and the experimental efforts to understand the GDR are reviewed. A brief description of general behaviour of GDR observables such as GDR width and GDR cross sections are presented. With this essential background, the motivation for the present work is justified along with the layout of the thesis goals. Chapter 2: In chapter 2, we discuss the details of the microscopic-macroscopic approach to calculate the energy of the nucleus as a function of deformations. The macroscopic part is calculated with the liquid drop model, and the microscopic part is obtained either with Nilsson or Woods-Saxon potential. Some of the important details about calculating the Woods-Saxon potential for triaxial shapes are presented. While developing the codes for calculating shell corrections with Woods-Saxon potential, we observed that the problems in obtaining proper plateau conditions can be solved by optimizing the choice of the basis states. These details are presented in this chapter along with some relevant discussions on the pairing calculations which are done within the BCS and the Lipkin-Nogami approaches. Chapter 3: This chapter deals with the formalism developed to study the nuclear properties at finite excitations. Essentially this comprises the extension of the formalism discussed in the previous chapter to finite T and I. The complexities while evaluating the shell corrections with (i) T, (ii) T and I, and (iii) T and pairing, are vii elucidated with adequate explanations. The methodology to consider thermal fluctuations under various conditions is presented. In this thesis work, we have constructed for the first time a theoretical framework to study the hot nuclei with proper treatment of pairing and its fluctuations along with the thermal shape fluctuations. Chapter 4: Here we discuss the GDR model which relates the GDR cross sections with the nuclear shapes and angular momentum through a macroscopic approach considering an rotating anisotropic harmonic oscillator potential with a separable dipoledipole interaction. The complete derivations of the GDR energies and the role of pairing in modifying them are presented. We have presented an analysis of GDR as a probe for features like shape-coexistence and gamma softness. Chapter 5: In this chapter, we discuss the results for warm nuclei. We start with the study of pairing phase transitions as depicted by the GDR measurements in 97Tc, 120Sn, 179Au, and 208Pb. Our study reveals that the observed quenching of GDR width at low temperature in the open-shell nuclei can be understood in terms of simple shape effects caused by the pairing correlations. For a precise match with the experimental data, the consideration of pairing fluctuations is crucial. Our results clearly demonstrate that the TSFM can be quite successful if the shell effects (with explicit temperature dependence) and the pairing ones are properly incorporated in the free energy. We observe that more measurements with better precision could yield rich information about several phase transitions that can happen in warm nuclei. These studies are revisited with the Woods-Saxon potential and its implications in the chosen nuclei are discussed. Chapter 6: Our results for the GDR properties and the shape transitions in hot and rotating nuclei are discussed in this chapter. Our theoretical predictions in the case of 144Sm are confirmed by the experimental results, and explained the temperature and angular momentum dependence on GDR properties very well. The GDR properties of 152Gd and 113Sb at two different excitation energies are also studied with our formalism and the important results are discussed in this chapter. Chapter 7: A succinct summary of this thesis is presented in chapter 7 along with the outlook of this work, highlighting the most important conclusions and the future aspects.
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