What is the Jellium Model? Magic Numbers Explained

[Fearless]

I am calculating some energylevels on the jellium model. But what is the jellium model (sorry to say, but google has failed me).

I understand that it's some kind of electron gas/electron sea model of atomclusters. Like for example sodium. Maybe it's correlated to magic numbers. If someone could explain what magic numbers is (or at least how you find out if like 40 sodium atoms together is a magic number-constellation).

(I have used the searchfunction and the newest thread with jellium in it was somewhat of a zombie).

 

[Cthugha]

I don't know, whether that helps you much, but the basic idea of the jellium model of solids is to first distinguish between conduction electrons and core ions. Then you do not consider the core ions as localized, but simply use a constant background charge density to describe them.

However afaik this model is only sensible for weakly interacting metals or surfaces and clusters.

 

[charng]

The Jellium Model is a simplified theoretical model used to describe the electronic structure of metals and metal clusters. It is based on the assumption that the positive ions in a metal are uniformly distributed in a "jellium" of positive charge, while the electrons are free to move within this background. This model allows for a simpler and more tractable way to calculate the electronic properties of metals, such as energy levels and electronic density, compared to more complex quantum mechanical models.

The concept of magic numbers, in the context of the Jellium Model, refers to the observation that certain numbers of electrons in a metal cluster exhibit particularly stable electronic structures. This can be seen in the form of sharp peaks in the calculated energy levels, which correspond to filled electronic shells. These stable configurations are often referred to as "magic number" clusters, and are believed to play a role in the stability and properties of metal clusters.

Determining if a specific number of atoms in a cluster is a magic number configuration can be done through theoretical calculations using the Jellium Model, as well as experimental techniques such as mass spectrometry. Overall, the Jellium Model and the concept of magic numbers provide a useful framework for understanding the electronic structure of metal clusters and their properties.