Collective nuclear model

The discoveries of Becquerel, Curie, and Rutherford and Rutherford s later development of the nuclear model of the atom (Section B) showed that radioactivity is produced by nuclear decay, the partial breakup of a nucleus. The change in the composition of a nucleus is called a nuclear reaction. Recall from Section B that nuclei are composed of protons and neutrons that are collectively called nucleons a specific nucleus with a given atomic number and mass number is called a nuclide. Thus, H, 2H, and lhO are three different nuclides the first two being isotopes of the same element. Nuclei that change their structure spontaneously and emit radiation are called radioactive. Often the result is a different nuclide. 

The GRECP errors in reproducing the results of the all-electron HFDB calculations with the Fermi nuclear model are collected into two groups. First, the GRECP errors for transitions without change in the occupation... 

The inequalities in Eq. [75] also define the condition for the generating function (Eq. [23]) to be analytic in the integration contour in Eq. [25]. This condition is equivalent to the linear connection between the diabatic free energy surfaces, Eq. [24]. The Q model solution thus explicitly indicates that the linear relation between the diabatic free energy surfaces is equivalent to the condition of thermodynamic stability of the collective nuclear mode driving ET. 

In Sect. 2.3.1 the shell model of spherical and deformed nuclei was discussed. The model gives a good description of various phenomena observed in the light (A < 80), near double-magic (e.g., around Pb) and well-deformed nuclei (e.g., in the regions 150 < A < 190, A > 220). The shell model is a microscopic nuclear model, i.e., it is formulated at the nucleonic level. At the same time, the application of the model far from magic nuclei leads sometimes to very complicated calculations. Furthermore, many observations clearly show the existence of collective behavior in nuclei (surface vibration, collective rotation), which can be treated in macroscopic framework much more simply. 

The failure description is the third part of the taxonomy structure and involves the modes, severities, and types of failures. These are based on models in the In-Plant Reliability Data Base for Nuclear Power Plant Components Data Collection and Methodology Report (IPRDS) and IEEE Std. 500-1984,2 which are discussed in Chapter 2. 

Infrared (IR) spectra were measured on a Beckmann Microlab 600 model spectrophotometer. Nuclear magnetic resonance (NMR) spectra were measured on a Varian EM360 spectrometer, with 19F-spectra collected using trifluoroacetic acid as a standard, or with H-spectra collected using tetramethylsilane as a standard. 

In the 1950s, many basic nuclear properties and phenomena were qualitatively understood in terms of single-particle and/or collective degrees of freedom. A hot topic was the study of collective excitations of nuclei such as giant dipole resonance or shape vibrations, and the state-of-the-art method was the nuclear shell model plus random phase approximation (RPA). With improved experimental precision and theoretical ambitions in the 1960s, the nuclear many-body problem was born. The importance of the ground-state correlations for the transition amplitudes to excited states was recognized. 

The carbon-13 nuclear magnetic resonance spectrum of a 4.7% (w/v) solution of dorzolamide hydrochloride was obtained in deuterated dimethyl sulfoxide, and is shown in Figure 9. The spectrum was recorded using a Brucker model AM-400 NMR spectrometer. The band assignments were referenced relative to dimethyl sulfoxide-ds (39.5 ppm), and the carbon atom assignments (using the same numbering system as just described) are collected in Table 5. 

As we have seen, the nucleons reside in well-defined orbitals in the nucleus that can be understood in a relatively simple quantum mechanical model, the shell model. In this model, the properties of the nucleus are dominated by the wave functions of the one or two unpaired nucleons. Notice that the bulk of the nucleons, which may even number in the hundreds, only contribute to the overall central potential. These core nucleons cannot be ignored in reality and they give rise to large-scale, macroscopic behavior of the nucleus that is very different from the behavior of single particles. There are two important collective motions of the nucleus that we have already mentioned that we should address collective or overall rotation of deformed nuclei and vibrations of the nuclear shape about a spherical ground-state shape. 

A Fermion dynamical symmetry model which can account for both the low as well as high spin nuclear collective phenomena is presented. 

In conclusion, just as the IBM, the FDSM contains, for each low energy collective mode, a dynamical symmetry. For no broken pairs, some of the FDSM symmetries correspond to those experimentally known and studied previouly by the IBM. Thus all the IBM dynamical symmetries are recovered. In addition, as a natural consequence of the Hamiltonian, the model describes also the coupling of unpaired particles to such modes. Furthermore, since the model is fully microscopic, its parameters are calculable from effective nucleon-nucleon interactions. The uncanny resemblance of these preliminary results to well-established phenomenology leads us to speculate that fermion dynamical symmetries in nuclear structure may be far more pervasive than has commonly been supposed. 

One of the most interesting aspects of the Interacting Boson Model concerns its connections with the underlying fermion space. The understanding of the mechanism through which bosonlike features arise from effective nuclear hamiltonians provides, in fact, a way to relate collective spectra to the fermion motion. 

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