臺灣博碩士論文加值系統

原子核殼模型(shell model，簡稱SM)在計算中、重原子核能譜時，會遇到下列兩大困難;1.能量矩陣元維度過大，使對角化過程難以進行;2.二體相互作用參數過多，不易決定。於是引入準軌道一準自旋(k-i)基底(basis)，來架構原子核殼模型(簡稱k-iSM)，以求解決上述兩大困難。
文中說明為何k-iSM有可能解決SM的困難，目前在架構k-i殼模型上所取得的進展，及我個人所作的工作。要架構k-i SM包含有五個部分的工作：1.讀取和存儲k-i 派生係數。2.按總角動量J排態並存儲相關的量子數。3.計算哈密頓量的矩陣元。4.對角化，計算出能譜及存儲波函數。5.讀取波函數，計算躍遷機率及磁矩、電四極矩等物理量。目前，由於時間關係只作到第三步。其中主要是建立了一套節省儲存空間和時間的壓縮與解壓縮的存儲和讀取數據的方法，編制了存儲和讀取k-i 派生係數及排態和讀取有關狀態量子數的程式並推導了計算包含兩個k-i殼層的矩陣元計算公式。

While shell model(SM) calculating,it will get two big problems as such: 1. The dimensionsof elements of energe matrix are too large and it make the process of diagonalization not easy to program. 2. The parammeter of interaction of two bodies are too many and they are not easy to be determined. So I take both quasiorbital angular momentum k and quasiispin i basis(k-i) to set up nucleus' shell model to overcome the two large
difficulties.My paper illustratess the reason why While shell model(SM) calculating,it will get two big problems which The dimensionsof elements of matrix are too large and the parammeters are too many .Find the ways to overcome them.The stops of my paper read as such: 1.The SM' elementary theory. 2.Introduction of Fermion Dynamical Symmetry Model(FDSM). 3. The steps of the structure of k-i shell model. 4. The conclusions of my paper.

§1 引言……………………..……………………………………….…….1
§2 費米子動力對稱模型之簡介………………………….…………4
2-1 k-i 基底……………………………….………….……….4
2-2 S對與D對截斷…………………………….…..………..7
2-3 FDSM的成就………………………………………..……8
§3 k-i SM的構想………………….……………………………….10
3-1 FDSM的局限…………..…….….…………………….….10
3-2 破對粒子數u….….………………….…………………….10
3-3 甚麼是k-iSM ?……………………………….…………….11
3-4 k-i 派生係數………………………………………….…13
§4 k-i SM的架構…………………………………….…..…………16
4-1 k-i 派生係數的讀取和存儲…………………………….16
4-2 按J排態及相關量子數的存取……….………..………19
4-3 哈密頓量矩陣元的計算……………..……….….….….20
4-3-1 符號的定義…………………………………..……20
4-3-2 全同粒子矩陣元的計算……………….………….22
4-3-3 n-p系統矩陣元的計算……………...…..……….25
§5 總結及展望……………………………………………..……….35
參考文獻……………………………………………………………….36
附錄：
A1、 k-i基底的c.f.p係數(The k-i Coupled CFPs)
A2、 k-i基底殼模型程式(A PROGRAM FOR k-i BASIS SHELL MODEL只完成c.f.p的輸入和排態部份)

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