臺灣博碩士論文加值系統

我們以複數座標旋轉(B-spline-based complex rotation, BSCR)方法計算Ca和Sr原子的基態光游離，顯示出當能量慢慢增加並跨越幾個游離門檻(threshold)時，與自旋有關的交互作用和組態交互作用對Ca和Sr的雙激發之自游離系列之不同自旋狀態混合程度的影響。 更有趣的是，我們的研究已經確認某些多重態的能階會反轉，例如，因為受到某些重疊的共振態系列之擾動而不遵守Hund’s rules。我們的研究也顯示出具有高軌道角動量共振態之電子組態系列，其LS耦合將會開始不適用，這些都出現在第三游離門檻之上。接著，也使用Stabilization方法結合B-spline-based configuration interaction (BSCI)方法探討Be 2pns 和2pnd (1Po 及 3Po) 雙激發態之共振態能量，然後將這項結果和BSCR方法及其他實驗測量和理論計算做一比較，發現這些結果相當吻合。

We present a joint theoretical and experimental investigation to demonstrate explicitly how the combined spin-dependent interaction and the configuration interaction may affect the mixing of different spin states along various doubly excited autoionization series for Ca and Sr as energy increases across several ionization thresholds. In particular, our study has identi_ed the inversion of energy levels between members of a number of multiplets, i.e., in contrast to the Hund's rules, due to the presence of perturber from other overlapping resonance series. We are also able to demonstrate the beginning of the breakdown of the LS coupling for resonance series corresponding to electron configurations with higher orbital angular momenta and those above the third ionization threshold. Then, the resonance energies and widths of the Be 2pns and 2pnd (1Po and 3Po) doubly excited states are determined. The densities of the resonance states are calculated by using the stabilization method along with the B-spline-based configuration interaction (BSCI) approach. The results obtained from the stabilization method are in good agreement with those obtained from the B-spline-based complex rotation (BSCR) calculation, and other theoretical and experimental results.

目 錄
摘要
致謝
序言

第一章 BSCR方法之基本理論

§1-1簡介………………………………………………………………………………………. 1
§1-2基本理論程序……………………………………………………………………………. 1
§1-3 BSCR方法……………………………………………………………………………….. 6

第二章 BSCR方法中的最佳β值

§2-1簡介…………………………………………………………………………………………. 9
§2-2 最佳β值之尋找…………………………………………………………………………… 9
§2-3 基底數對最佳β值之影響……………………………………………………………….. 20
§2-4 基底數相同時1Po 和3Po系列之最佳β值……………………………………………….. 29
§2-5結論

第三章 BSCR方法中θ和β之關係

§3-1簡介………………………………………………………………………………………….. 37
§3-2 計算的過程和結果…………………………………………………………………………. 37
§3-3 結論………………………………………………………………………………………….. .. 59

第四章 用BSCR方法計算Ca+(3d) ~Ca+(5s) 和Sr+(5s)-Sr+(4d)之間的共振態能量和寬度

§4-1前言…………………………………………………………………………………………….. 60
§4-2 Ca+(3d)- Ca+(4p)threshold…………………………………………………………………….. 60
§4-3 Ca+(4p)- Ca+(5s)threshold…………………………………………………………………….... 68
§4-4 Sr+(5s)-Sr+(4d) threshold的1Po和3Po之共振態能量………………………………………….. 74
§4-5 結論……………………………………………………………………………………………. 83

第五章 利用Stabilization 方法和BSCR方法之比較

§5-1 簡介……………………………………………………………………………………………. 84
§5-2 Stabilization 方法原理……………………………………………………………………….. . 84
§5-3 Be原子之共振態能量和寬度………………………………………………………………..... 86
§5-4 Ca原子之共振態能量和寬度……………………………………………………………….. .. 97

第六章 考慮跟自旋有關的交互作用之後的BSCR方法及其應用

§6-1 簡介…………………………………………………………………………………………... 109
§6-2 理論和實驗…. ………………………………………………………………………………. 110
§6-3 結果和討論…………………………………………………………………………………... 112

第七章 結論……………………………………………………………………………. 128

參考資料…………………………………………………………………………………………………. 129

[1] T. N. Chang. in “Many-body Theory of Atomic Structure and Photoioniation.”edited by T. N. Chang (World Scientific. Singapore. 1993), p. 213.
[2] T. K. Fang and T. N. Chang, Phys. Rev. A 61, 062704 (2000).
[3] T. K. Fang. Y. K. Ho, and Y. C. Lin, in Proceedings of the Intenational Seminar on Photoionization in Atoms, edited by Y. Azuma et al. (Kyoto University Press. Kyoto. 2002). p. 12
[4] H. A. Bethe and E. E. Salpeter, in Quantum Mechanics of One- and Two- electron Atoms, (Springer-Verlag, Berlin, 1957).
[5] T. N. Chang and E. T. Bryan, Phys. Rev. A38, 645 (1988).
[6] T. N. Chang and Y. S. Kim, Phys. Rev. A36, 2609 (1986)
[7] T. N. Chang and K. T. Chung, Chinese .J. Phys. 27, 425 (1989).
[8] T. N. Chang, Phys. Rev. A39, 4946 (1989).
[9] C. Laughlin and G. A. Victor, in Atomic Physics, edited by S. J. Smith and G. K. Walters, (Plenum, New York, 1973), p. 247.
[10] C. H. Greene and L. Kim, Phys. Rev. A30, 2706 (1987).
[11] W. R. Johnson, S. A. B1undell, and J. Sapirstein, Phys. Rev. A37, 307 (l988)
[12]C. deBoor, A Pratica1 Guide to Splines, (Springer, NY, 1978).
[13] T. N. Chang, in Relativistic, Quantum Electrodynamics, and Weak Interaction Effects in Atoms, edited by W. Johnson, P. Mohr, and J. Sucher, AIP Conf. Proc. No. 189, (American Institute of Physics, New York, 1989), p. 217.
[14] T. N. Chang and X. Tang, Phys. Rev. A44, 232 (1991).
[15] Y. K. Ho, Phys. Rep. 99, 1 (1983).
[16] Thomas N. Rescigno and Vincent McKoy, Phys. Rev. A 12, 522 (1975).
[17] T. N. Rescigno, C. W. McCurdy, Jr., and A. E. Orel, Phys. Rev. A 17, 1931 (1978).
[18] T. N. Rescigno and C. W. McCurdy, Phys. Rev. A 31, 624 (1985).
[19] D. Delande, A. Bommier, and J. C. Gay, Phys. Rev. Lett. 66, 141 (1991).
[20] T. K.. Fang and Y. K. Ho, Phys. Rev. A 60, 2145 (1999); Y. K. Ho and T. K. Fang, J. Chin. Chem. Soc. 48. 539 (2001).
[21] Kwong T. Chung, T. K. Fang, and Y. K. Ho, J. Phys. B 34, 165 (2001).
[22] T. N. Rescigno, Phys. Rev. A 31, 607 (1985).
[23] Chris H.Greene.,Longhuan Kim, Phys. Rev. A36,2706(1987)
[24] R. Wehlitz, D. Lukic and J. B. Bluettl, Phys. Rev. A 68, 052708 (2003).
[25] T. N. Chang, Phys. Rev. A 48, 3, R1725 (1993).
[26] A. E. Kramida, W. C. Martin, J. Phys. Chem. Ref. Data 26, 1185 (1997).
[27] W. J. Pong, Y. K. Ho, Physica Scripta 61, 690 (2000).
[28] Bin Zhou and C.D.Lin, Phys. Rev. A51, 1286 (1995).
[29] J. H. Chen, “The optimized β value of 1P and 3P for Calcium photoionization in BSCR method” Journal of St. John's University, Vol.24, 205(2007)
[30] J. H. Chen, Journal of Chin-Min College Vol. 14, 59(2008)
[31] T. K. Fang. , Y. K. Ho ,Chinese J. Phys, p37, 37(1999)
[32] V. A. Mandelshtam, T. R. Ravuri and H. S. Taylor, Phys. Rev. Lett. 70, 1932 (1993)
[33] S. S. Tanand Y. K. Ho, Chinese J. Phys. 35, 701 (1997).
[34] H. Bachau and F. Martin, J. Phys. B29, 1451 (1996).
[35] J. Miller, X. Yang, and J. Burgdijrfer, Phys. Rev. A49, 2470 (1994).
[36] W. J. Pong and Y. K. Ho, J. Phys. B31, 2177 (1998).
[37] T. N. Chang and L. Zhu, Phys. Rev. A51, 374 (1995).
[38] T. K. Fang, et al., Phys. Rev. A55, 433 (1997).
[39] G. Mehlman-Balloffet and J. M. Esteva, Astrophys. J. 157, 945 (1969).
[40] J. M. Esteva, G. Mebiman-Balloffet, and J. Romand, J. Quant. Spectiosc. Radiat. Transf. 12, 1291 (1972).
[41] D. S. Kim et al., Phys. Rev. A 61, 06271 (2000).
[42] J. A. Tully, M.J. Seaton, and K.A. Bemngton, J. Phys. B 23, 3811 (1990).
[43] C.H. Greene, Phys. Rev. A23, 661 (1981).
[44] A. E. Kramida, W. C. Martin, J. Phys. Chem. Ref. Data 26, 1185 (1997).
[45] L. R. Wang. et al., J. Phys. B: At. Mol. Opt. Phys. , L217-L224 (2006).
[46] C.D. Lin, J. Phys. B: At. Mol. Phys.16, 723 (1983).
[47] Sugar J and Corliss C 1979 J. Phys. Chem. Ref. Data 8 865
[48] Claire McKenna and HugoW van der Hart, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 1627–1643
[49] Griesmann U, Shen N, Connerade J P. Sommer K, and Hormes J 1988 J. Phys. B 31 L83
[50] Griesmann U, Esser B, and Hormes J 1994 J. Phys. B 27 3939
[51] Chu C C, Fung H S, Wu H H, and Yih T S 1998 J. Phys. B 20 3843
[52] Hudson R D, Carter V L, and Young P A 1969 Phys. Rev. 180 77
[53] Fang T K and Chang T N 2007 Phys. Rev. A76 012721
[54] Garton W R S and Codling K 1960 Proc. Phys. Soc. 75 87; 1965 Proc. Phys. Soc. 86 1067; 1968 J. Phys. B 1 106
[55] Kim L and Greene C H 1987 Phys. Rev. A36 4272; Kim L and Greene C H 1988 Phys. Rev.A38 2361
[56] Aymar M 1987 J. Phys. B 20 6507
[57] Greene C H and Aymar M 1991 Phys. Rev. A44 1773
[58] Aymar M, Greene C H, and Luc-Koenig E 1996 Rev. Mod. Phys. 68 1015
[59] Aymar M, Lecomte J-M, Chu C C. Fung H S, Wu H H, and Yih T S 1998 J. Phys. B 31 5135
[60] Fano U and Cooper J W 1968 Rev. Mod. Phys. 40 441
[61] Kelly H P and Ron A 1972 Phys. Rev. A5 168
[62] Scott P, Kingston A E, and Hibbert A 1983 J. Phys. B 16 3945