Shell modeling results

In fig. la-c the distribution function (14) is compared for isoscalar Ml-, E2- and E4-electromagnetic transition amplitudes with shell-model results for 20Ne(T s0,T2 0), calculated in the sd-conf iguration space. A surface delta interaction was used with strength parameters [BRU77] Aq Aj ... 

The approach adopted for the interpretation of the spectra of poorly crystalline calcium phosphates was to take the shell model of the crystalline phase having the greatest chemical similarity and progressively simplify and refine the model while maintaining a good fit to the observed spectrum. For the amorphous calcium phosphates, however, it was found that virtually identical shell models resulted from simplification and refinement of either the hydroxyapatite or brushite shell models to give the structure depicted in Fig. 18. 

The energy spectrum of the nucleus according to the semi-empirical shell model [23] appears not at zero ratio, but in two disjoint parts at ratios 0.22 and 0.18. This shift relates to the appearance of the symmetric arrangement at ratio 1.04 rather than 1. An Aufbau procedure based on this result fits the 8-period table derived from the number spiral, but like the observed periodic table, at ratio r, the shell-model result also has hidden symmetry. At ratio zero, the inferred energy spectrum not only fits the 8-period table but also... 

Among the microscopic models, the most accurate one for the presupernova and supernova calculations is the shell model. Over the years very large space shell model calculations for nuclei in the /p-shell were found to very successful and weak interaction rates have been calculated extensively using the shell model results [27,6]. 

The detailed shell model results in agreement with experiments led to better EC and /3-decay rates. The EC rates were often reduced compared to the FFN... 

In Table 10, CRYSTAL all-electron (AE) calculations at both HF and DFT level of theory (LDA and B3LYP) are compared with shell model results and ab initio PW calculations.G(HF) and G(B3LYP) refer to... 

Sir Ernest Rutherford (1871-1937 Nobel Prize for chemistry 1908, which as a physicist he puzzled over) was a brilliant experimentalist endowed with an equal genius of being able to interpret the results. He recognized three types of radiation (alpha, beta, and gamma). He used scattering experiments with alpha radiation, which consists of helium nuclei, to prove that the atom is almost empty. The diameter of the atomic nucleus is about 10 000 times smaller than the atom itself. Furthermore, he proved that atoms are not indivisible and that in addition to protons, there must also be neutrons present in their nucleus. With Niels Bohr he developed the core-shell model of the atom. 

This agrees with all previous results as far as the first term is concerned. The second constant term 0.3863 is very close to Broersma s 0.38 (73) and to the value 0.392 obtained by Broomfield et al. (76) from their shell-model theory, which is essentially a limiting case of the Kikwood-Riseman theory (77) for the bead model of flexible chains. However, these values are about 0.3 smaller than the corresponding term in Eq. (D-5). This implies that if the ellipsoid model and the continuous string model are applied to the same experimental data for as a function of M, the former should lead to a d value which is about i.35 times larger than that obtained by the latter. On the other hand, both models should give an identical value for ML. 

These are derived frum a. lensui force resulting from a coupling between individual pairs of nucleons and from the coupling between spin and orbital angular moments of the individual nucleus, as described by the shell model of the nucleus. 

Conventional spherical shell model calculations have been undertaken to describe 90 88zr and 90 88y in these large scale calculations valence orbitals included If5/2 2P3/2 2Pl/2 and 199/2 The d5/2 orbital was included for 98Y and for high-spin calculations in 98Zr. Restrictions were placed on orbital occupancy so that the basis set amounted to less than 2b,000 Slater determinants. Calculations were done with a local, state independent, two-body interaction with single Yukawa form factor. Predicted excitation energies and electromagnetic transition rates are compared with recent experimental results. 

Examples of large-basis shell-model calculations of Gamow-Teller 6-decay properties of specific interest in the astrophysical s-and r- processes are presented. Numerical results are given for i) the GT-matrix elements for the excited state decays of the unstable s-process nucleus "Tc and ii) the GT-strength function for the neutron-rich nucleus 130Cd, which lies on the r-process path. The results are discussed in conjunction with the astrophysics problems. 

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. 

These results demonstrate that a difference of only one neutron causes a considerable change of the nature of the nuclei at A 100 and that the study of the isotopes with odd nucleon numbers can provide insight into the details of the shape transition. The transition in the Y isotopes seems to be even more rapid than in the Sr and Zr chains where the N = 60 isotones still have coexisting shapes and where the shell-model character of the N 58 isotones at high excitation energies has not yet been tested.Further investigations are, however, needed in order to confirm in detail the proposed interpretation of the level schemes of the Y isotopes and to see whether similarly rapid structure changes occur in the Rb and Nb isotopes at N 60. 

For the positive parity states, the population of the 0+ 6+ states follows (2J+1) which indicates that these states are consistent with being an (f7/2)2 multiplet. As can be seen in Fig. 1, the spectrum of the (12C,11C) reaction leading to Nd enhances h9/2 transfer. Comparison of the (16q,15o) and (12C,nC) spectra clearly shows that the 8+ state at 2.709 MeV is primarily an f7/2 h9/2 configuration. Unfortunately, there are no extensive shell model calculations with..which to compare these results. 

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