在這篇論文裡, 我們考慮另一觀點並建立一數學模型來解釋從SGR 1806-20
和SGR 1900+14這兩個軟X射線復發源(Soft-Gamma Repeaters)所得到的準
週期振盪(Quasi-Periodic Oscillations)頻率.
我們只考慮星體的振盪是單純來自磁勞倫茲力(Lorentz Force in Magnetic
field)的作用, 而且假設整個星體的磁場分怖是依據Ferraro在1954所給
予的數學定義來作為我們在數學模型建立上的工具.
從以上的模型出發, 我們可以得到一個頻率公式並且發現和觀測上所得到
的QPO頻率幾乎吻合.因此我們得到一個結論: 對於內部磁場為非均勻
(Nonhomogeneous)的情況下, 磁勞倫茲張力(Lorentz Force of Magnetic
Field Stress)在準週期振盪的現象下扮演重要的角色.

In the thesis, several issues of asteroseimology of pulsars and magnetars are considered from the view point of a model of a solid star capable of
sustaining the quake-induced shear vibrations. A brief review is given of magneto-solid-mechanical theory of node-free torsional seismic vibrations of a quaking neutron star with homogeneous internal and dipolar external magnetic field. This theory has been developed to explain quasi-periodic
oscillations (QPOs) in the outburst X-ray flux from SGR 1806-20 and SGR 1900+14. The main task of presented work is to investigate the model of torsional nodeless vibrations of neutron star with inhomogeneous internal and dipolar external magnetic field which has been taken in Ferraro’s form. Based on the energy variational method. the frequency spectrum for the frequency of Alfv’en toroidal vibrational mode is obtained and applied
to modal identification of the QPOs in X-ray outburst of above magnetars. It is shown that the model provide fairly good description of detected frequencies and lead one’s to conclude that it is the Lorentz force of magnetic field stresses plays decisive part in post-quake vibrational relaxation of above magnetars in which the magnetic field is non-
homogeneous. The work is a part of running pro jects of Institute of Astronomy, National Tsing Hua University, on the study of sources of high-energy emission.

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