Shell effects correction approach

The TF and modified methods based on average shell effects does not reproduce fairly closely local properties like p(0). It diverges with TF and TFD and only after introducing gradient corrections, can we obtain at least a finite value. In the present work we have obtain results quite close to HFvalues (Table 1). As an example, in Table 2 we present the evolution of this value through the different theories in the case of Krypton. The improvement by the present approach is found to be large. 

Significant advances with respect to the quantitative theoretical description of spontaneous fission were achieved by the so-called shell-correction approach (Stru-tinsky, 1967) in which single-particle effects are combined with liquid-drop properties. This approach led to the prediction of a double potential barrier (Fig. 5.19) for some regions of Z and A. From the distorted state II the nuclei may pass much more easily over the fission barrier than from the ground state I. 

In the following, we will present jellium-related theoretical approaches (specifically the shell-correction method (SCM) and variants thereof) appropriate for describing shell effects, energetics and decay pathways of metal-cluster fragmentation processes (both the monomer/dimer dissociation and fission), which were inspired by the many similarities with the physics of shell effects in atomic nuclei (Section 4.2). In Section 4.3, we will compare the experimental trends with the resulting theoretical SCM interpretations, and in addition we will discuss theoretical results from first-principles MD simulations (Section 4.3.3.1). Section 4.4 will discuss some of the latest insights concerning the importance of electronic-entropy and finite-temperature effects. Finally, Section 4.5 will provide a summary. 

Brack, M., Damgaard, J., Jensen, A.S., Pauli, H.C., Strutinsky, V.M., Wong, C.Y. Funny hills the shell-correction approach to nuclear shell effects and its applications to the fission process. Rev. Mod. Phys. 44, 320-405 (1972)... 

Such a function exhibits peaks (Fig. 9C) that correspond to interatomic distances but are shifted to smaller values (recall the distance correction mentioned above). This finding was a major breakthrough in the analysis of EXAFS data since it allowed ready visualization. However, because of the shift to shorter distances and the effects of truncation, such an approach is generally not employed for accurate distance determination. This approach, however, allows for the use of Fourier filtering techniques which make possible the isolation of individual coordination shells (the dashed line in Fig. 9C represents a Fourier filtering window that isolates the first coordination shell). After Fourier filtering, the data is back-transformed to k space (Fig. 9D), where it is fitted for amplitude and phase. The basic principle behind the curve-fitting analysis is to employ a parameterized function that will model the... 

As a first application of a new analytical gradient method employing UHF reference functions, seven different methods for inclusion of correlation effects were employed to optimize the geometry and calculate the harmonic vibrational frequencies and dipole moments of the lowest open-shell states for three simple hydrides including 3Z i SiH2228. As the degree of correlation correction increased, results approached those from the best multiconfiguration SCF calculation. 

Relativistic effects in heavy atoms are most important for inner-shell electrons. In ab initio and DFT calculations these electrons are often treated through relativistic effective core potentials (RECP), also known as pseudopotentials. This approach is sometimes called quasirelativistic, because it accounts for relativity effects in a rather simplified scalar way. The use of pseudopotentials not only takes into account a significant part of the relativistic corrections, but also diminishes the computational cost. 

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