本論文研究單球及二維球形陣列的電子激發性質、方法是利用自洽場的方法去計算介電函數,再利用介電函數倒數的虛部得到能量損失函數去研究電漿子激發的性質。內容分成兩部份研究:一是研究單一球狀系統外加弱磁場,討論原簡併能階因為外磁場分裂,討論角動量量子數差L= l-l′時,系統激發模的變化,對於較大的L會造成較多的激發模;而l越大時,會使電漿子激發模的能量往較高能量位移,而得到較高的電漿子激發能量;另一方面,我們討論許多碳六十的小球以週期性的方式排列成一個二維陣列系統,討論在各種不同L的躍遷過程中電漿子的激發模的差別,對於較高L的躍遷也有較多的激發模;其中,都有一相對極大的激發模能量。而在二維陣列系統中,介電函數不僅與L有關,也與q有關,當q變小時,激發模能量會較偏向單球的系統。

In this thesis, we study electronic excitations in a single-sphere and 2D sphere-array systems. In the former system, a uniform magnetic field is considered to apply on the sphere. The dielectric function is calculated by using self-consistent field (SCF) method and the energy loss function is obtained from the imaginary part of the reciprocal of dielectric function. The energy loss function is then used to study behavior of the plasma excitation. The degeneracy energy levels split due to the applying of an external magnetic field is also discussed. The properties of excitation modes in various L's (L= l-l') is studied.Our result shows that there are more excitation modes for large L; and the excitation modes is shifted to higher energy for larger l's. We also study the 2D sphere array system.It is found that the dielectric function of 2D sphere array is related to L and q. The properties of excitation modes for various L is studied and we find that the excitation modes of various L all have the dominant peak. The excitation modes is shifted to higher energy for larger l's. As neglect the sphere-sphere interaction, the excitation energy of 2D sphere array approaches that of a single-sphere in small q.

1 Introduction 1
2 Formulation 4
2.1 Dielectric function within self-consistent field approach 4
2.2 The formulation of the dielectric function 7
2.3 Electron energy loss function
11
3 Dielectric function of the sphere within magnetic and 2D sphere-array
system 12
3.1 Dielectric function of the electron gas distributed over a spherical surface
acting under an external magnetic field 12
3.2 Dielectric function of 2D sphere-array system 20
3.3 Summary
25
4 Results and discussions 26
4.1 The excitation properties of the single-sphere shell acting under an external
magnetic field 26
4.2 The excitation properties of the 2D sphere-array system 27
5 Conclusions 29
Reference 31

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