Nilsson model

Nanocarbon emitters behave like variants of carbon nanotube emitters. The nanocarbons can be made by a range of techniques. Often this is a form of plasma deposition which is forming nanocrystalline diamond with very small grain sizes. Or it can be deposition on pyrolytic carbon or DLC run on the borderline of forming diamond grains. A third way is to run a vacuum arc system with ballast gas so that it deposits a porous sp2 rich material. In each case, the material has a moderate to high fraction of sp2 carbon, but is structurally very inhomogeneous [29]. The material is moderately conductive. The result is that the field emission is determined by the field enhancement distribution, and not by the sp2/sp3 ratio. The enhancement distribution is broad due to the disorder, so that it follows the Nilsson model [26] of emission site distributions. The disorder on nanocarbons makes the distribution broader. Effectively, this means that emission site density tends to be lower than for a CNT array, and is less controllable. Thus, while it is lower cost to produce nanocarbon films, they tend to have lower performance. 

The Nilsson model is able to predict the ground state and low-lying states of deformed odd A nuclei. Figure 6.18 is a more detailed picture of how the energies of the Nilsson levels vary as a function of the deformation parameter 32 for the... 

Analyze the following level schemes in terms of the collective and Nilsson models ... 

We discuss some features of a model for calculation of p-strength functions, in particular some recent improvements. An essential feature of the model is that it takes the microscopic structure of the nucleus into account. The initial version of the model used Nilsson model wave functions as the starting point for determining the wave functions of the mother and daughter nuclei, and added a pairing interaction treated in the BCS approximation and a residual GT interaction treated in the RPA-approximation. We have developed a version of the code that uses Woods-Saxon wave functions as input. We have also improved the treatment of the odd-A Av=0 transitions, so that the singularities that occured in the old theory are now avoided. 

Since most nuclei in the region of deformation at A 100 can only be produced with rather low yields which makes detailed spectroscopic studies difficult, we have examined possibilities of extracting nuclear structure information from easily measurable gross 13-decav properties. As examples, comparisons of recent experimental results on Rb-Y and 101Rb-Y to RPA shell model calculations using Nilsson-model wave functions are presented and discussed. 

Fig.l. Single-particle levels for protons and neutrons in the A=100 region for the modified oscillator potential of the Nilsson model as a function of prolate deformation. 

The properties of 99Y suggest that this nucleus is a classical symmetric rotor. Thus, configurations can be assigned to all the bands in accordance with the predictions of the Nilsson model for A 100 and a deformation of e - 0.3. Also the mixing ratios 6 for the AI = 1 members of the bands can be accounted for in the classical picture of rotational nuclei. The half-life of the isomer at 2142 keV is obviously due to K forbiddenness. 

Choice of the Q30 Hamiltonian and comparison with the Nilsson model... 

Recently it has been shown [21] that the spectrum of this g-deformed, 3-dimensional harmonic oscillator (Q30) reproduces very well that of the modified harmonic oscillator introduced by Nilsson [12, 15] without the spin-orbit coupling term. Since the Nilsson model without spin-orbit coupling is essentially the Nilsson-Clemenger model used for the description of metal clusters [11], it is worth examining whether the Q30 model can be used to reproduce the magic numbers and some other properties of simple metal clusters. 

Figure 4 The energy spectrum of the -deformed, 3-dimensional harmonic oscillator as a function of the deformation parameter r. As in Nilsson model pictures, one observes level bunching areas at certain values of r, separated by larger energy gaps.

The nuclear spins and moments of the strongly deformed rare-earth nuclides have been discussed in detail previously within die Nilsson model in connection with the ABMR experiments mentioned above [79]. The addition of the data fiom coUinear fast-beam laser spectroscopy [48, 50, 71], the new reference values on spectroscopic quadrupole moments from muonic and pionic hfs [1], and the refined calculations within the partice-rotor model, including a number of orbitals close to the Fermi surface, have however resulted in a more complete picture and a better understanding of tiie nuclear single-particle stmcture in this region. 

The shell model of deformed nuclei was elaborated by Nilsson (1955) and others. The basic assumptions of the Nilsson model are as follows ... 

With the wave functions of the Nilsson model, it is also possible to calculate the electromagnetic moments and the gamma and beta transition probabilities between single-particle... 

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