本實驗利用雙光子共振法(Optical-Optical Double Resonance, OODR)來偵測雙原子鈉分子的g（gerade）對稱單重態（singlet state）。利用氬離子雷射將雙原子鈉分子由基態（X1Σ+g）激發到B1Πu電子態，再使用含鈦藍寶石（Ti:sapphire）雷射與染料（DCM）雷射將雙原子鈉分子由B1Πu電子態激發到欲偵測之上態。而偵測方法，則是偵測被激發到上態的鈉分子經由碰撞後到三重態，再躍遷回a3Σ+u電子態的螢光訊號。
　　實驗中，共偵測到31Δg電子態65個振轉能階，其中包含36個e-level和29個f-level，振動量子數v=0~9，轉動態分布於J=11~100。另偵測到41Δg電子態223個振轉能階，包括126個e-level，97個f-level，振動量子數v=3~22，轉動態分布於J=11~65。同時在這兩個電子態中我們都觀測到 雙重簡併態分裂（Λ-doubling）的現象。將偵測所得的實驗數據經計算得到一組包含 雙重簡併態分裂的分子常數，建立其RKR位能曲線，並計算這兩個電子態與B1Πu電子態之間的法蘭克-康登因數（Franck-Condon factor）。
在計算分子常數的過程中，我們並沒有考慮31Δg和41Δg之間的交互作用，在第五章我們分析了Magnier [21]的理論計算中所使用的無相交法則(non-crossing rule)，來討論我們實驗中所觀測到的現象。

The 31Δg and 41Δg Rydberg states of Na2, which dissociate to Na(3s)+ Na(4d) and Na(3s)+ Na(4f), has been observed by using the high resolution cw optical-optical double resonance (OODR) spectroscopy. The splitting ofΛ -doubling in these two states were also measured under the experimental resolution. In this experiment the Na2 molecules were pumped from the thermally populated ground state X1Σ+g to the intermediate B1Πu state by a single line Ar+ laser (total of 9 lines). Then, a single-mode tunable ring laser (with gain media Ti:Sapphire and DCM dye) was used to probe the 31Δg and 41Δg Rydberg states from the intermediate state. The transitions can be described as:
B1Πu(v',J')←X1Σ+g(v",J")+hv1
31Δg,41Δg(v,J)←B1Πu(v',J')+hv2
UV fluorescence emitted from the highly excited triplet gerade states, which are transferred from 31Δg and 41Δg states via collision, to the a3Σ+u state was monitored by a filtered photomultiplier tube.
A total of 65 rovibrational levels of 31Δg state, including 36 e -levels and 29 f-levels ,were observed and assigned to the vibrational and rotational quantum numbers in
the range of 0≦ v ≦9 and 11≦ J ≦100, respectively; and a total of 223 rovibrational levels of 41Δg state, including 126 e -levels and 97 f -levels, were observed and assigned to the vibrational and rotational quantum numbers in the range of 3≦ v ≦22 and 11≦ J ≦ 65, respectively. The sets of Dunham coefficients with Λ -doubling constants and the RKR potential curves of the 31Δg and 41Δg states were deduced from all the observed rovibrational levels. Also the Franck-Condon Factors of 31Δg ← B1Πu and 41Δg ← B1Πu transitions were calculated.
With the Dunham-fitting of the 31Δg and 41Δg states, we did not include the interactions between these two states causing the potential crosses. In chapter 5 we analyze the ab initio calculation from Magnier [21]. There is an avoided crossing between 31Δg and 41Δg states at the potential bottom around 35500 cm-1. This avoided crossing point switches the molecular wavefunctions at the bottom of 31Δg state to the atomic properties of s+f and the 41Δg state to the atomic properties of s+d. If this is the case, then the assignment of this work may be reversed, ie. 31Δg → 41Δg and 41Δg →31Δg state.

[1] H. E. Roscoe and A. Schuster, “Note on the absorption-spectra of potassium and sodium at low temperatures”, Proc. R. Soc. London 22, 362 (1874).
[2] H. Knckel, T. Johr, H. Richter and E. Tiemann, “The influence of the spin-orbit and the hyperfine interaction on the asymptotic behaviour of the state of Na2”, Chem. Phys. 152, 399 (1991).
[3] H. Wang, T. J. Whang, A. M. Lyyra, L. Li, and W. C. Stwalley, “Study of the “shelf” state of Na2 by optical–optical double resonance spectroscopy”, J. Chem. Phys. 94, 4756 (1991).
[4] C. C. Tsai, J. T. Bahns, T. J. Whang, H. Wang, W. C. Stwalley, and A. M. Lyyra, “Optical-optical double resonance spectroscopy of the ‘‘shelf’’ states and states of Na2 using an ultrasensitive ionization detector”, Phys. Rev. Lett. 71, 1152 (1993).
[5] D. L. Cooper, R. F. Barrow, J. Vergs, C. Effantin and J. D'Incan, “Laser-excited fluorescence of the double-minimum state of sodium dimer studied by Fourier transform spectrometry”, Can. J. Phys. 62, 1543 (1984).
[6] L. P. Ratliff, M. E. Wagshul, P. D. Lett, S. L. Rolston, and W. D. Phillips, “Photoassociative spectroscopy of , , and states of Na2”, J. Chem. Phys. 101, 2638 (1994).
[7] C. C. Tsai, J. T. Bahns, and W. C. Stwalley, “First observation of the quasibound levels and tunneling line broadening in the state of Na2 using an ultrasensitive ionization detector”, J. Chem. Phys. 99, 7417 (1993).
[8] K. K. Verma, J. T. Bahns, A. R. Rajaei-Rizi, W. C. Stwalley and W. T. Zemke, “First observation of bound-continuum transitions in the laser-induced - fluorescence of Na2”, J. Chem. Phys. 78, 3599 (1983).
[9] G. Herzberg, “Molecules Spectra and Molecular Structure I. Spectra of Diatomic Molecules”, 2nd ed., Krieger Pub Co; Malabar, Florida 1989.
[10] W. C. Martin and R. Zalubas, “Energy levels of sodium Na i through Na xi”, J. Phys. Chem. Ref. Data 10, 153 (1981).
[11] W. Demtrder, M. McClintock, and R. N. Zare, “Spectroscopy of Na2 using laser-induced fluorescence”, J. Chem. Phys. 51, 5495 (1969).
[12] P. Kusch and M. M. Hessel, “An analysis of the band system of Na2”, J. Chem. Phys. 68, 2591 (1978).
[13] J. J. Camacho, A. Pardo, and J. M. L. Poyato, “A study of the system of Na2”, J. Phys. B 38, 1935 (2005).
[14] K. M. Jones, S. Maleki, S. Bize, P. D. Lett, C. J. Williams, H. Richling, H. Knckel, E. Tiemann, H. Wang, P. L. Gould, and W. C. Stwalley, “Direct measurement of the ground-state dissociation energy of Na2”, Phys. Rev. A 54, R1006 (1996).
[15] G.. W. King and J. H. van Vleck, “Dipole-dipole resonance forces”, Phys. Rev. 55, 1165 (1939).
[16] R. S. Mulliken, “The interaction of differently excited like atoms at large distances”, Phys. Rev. 120, 1674 (1960).
[17] H. Richter, H. Knckel, and E. Tiemann, “The potential of the Na2 state”, Chem. Phys. 157, 217 (1991).
[18] N. W. Carlson, A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Two-step polarization-labeling spectroscopy of excited states of Na2”, Phys. Rev. A 24, 822 (1981).
[19] Y. L. Pan, L. S. Ma, L. E. Ding, and D. P. Sun, “Optical-optical double-resonance excitation spectra of the high-lying Rydberg state in Na2”, J. Mol. Spectrosc. 162, 178 (1993).
[20] Y. L. Pan, S. Dianping, L. S. Ma, D. Liangen, and Z. G. Wang, “Optical-optical double-resonance excitation spectra of the and Rydberg states in Na2”, J. Mol. Spectrosc. 169, 534 (1995).
[21] S. Magnier, Ph. Milli, O. Dulieu, and F. Masnou-Seeuws, “Potential curves for the ground and excited states of the Na2 molecule up to the (3s+5p) dissociation limit: Results of two different effective potential calculations”, J. Chem. Phys. 98, 7113 (1993).
[22] L. Li, Y. Liu, and A. M. Lyyra, “Rydberg and doubly excited states of Na2 and Li2”, J. Chin. Chem. Soc. 48, 291 (2001).
[23] M. Tamanis, M. Auzinsh, I. Klincare, O. Nikolayeva, R. Ferber, E. A. Pazyuk, A. V. Stolyarov, and A. Zaitsevskii, “NaK Λ doubling and permanent electric dipoles in low-lying 1Π states: Experiment and theory”, Phys. Rev. A 58, 1932 (1998).
[24] M. M. Hessel and C. R. Vidal, “The band system of the 7Li2 molecule”, J. Chem. Phys. 70, 4439 (1979).
[25] C. C. Tsai, R. Y. Chang, and T. J. Whang, “ -doubling investigation of the Rydberg state of Na2 using optical-optical double resonance spectroscopy”, J. Mol. Spectrosc. 234, 264 (2005).
[26] R. Y. Chang, C. C. Tsai, T. J. Whang, and C. P. Cheng, “Observation of L uncoupling in the Rydberg state of Na2”, J. Chem. Phys. 123, 224303 (2005).
[27] B. H. Bransden and C. J. Joachain, “Physics of Atoms and Molecules”, 2nd ed., Prentice Hall; Harlow, England 2003.
[28] J. L. Dunham, “The energy levels of a rotating vibrator”, Phys. Rev. 41, 721 (1932).
[29] F. Hund, “The interpretation of some phenomena in the molecular spectra”, Z. Phys. 36, 657 (1926).
[30] R. Rydberg, “Graphische Darstellung einiger bandenspektroskopischer Ergebnisse”, Z. Phys. A 73, 376 (1931).
[31] O. Klein, “Zur Berechnung von Potentialkurven fr zweiatomige Molekle mit hilfe von Spektraltermen”, Z. Phys. A 76, 226 (1932).
[32] A. L. G. Rees, “The calculation of potential-energy curves from band-spectroscopic data”, Proc. R. Soc. London 59, 998 (1947).
[33] J. v. Neumann and E. Wigner, “er das Verhalten von Eigenwerten bei adiabatischen Prozessen”, Physik. Z. 30, 467 (1929).
[34] L. Li and R. W. Field, “CW optical-optical double resonance studies of the , , , and Rydberg states of Na2”, J. Mol. Spectrosc. 117, 245 (1986).
[35] G. M. Grover, T. P. Cotter, and G. F. Erickson, “Structures of very high thermal conductance”, J. Appl. Phys. 35, 1990 (1964).
[36] C. R. Vidal and J. Cooper, “Heat-pipe oven: a new, well-defined metal vapor device for spectroscopic measurements”, J. Appl. Phys. 40, 3370 (1969).
[37] C. R. Vidal and M. M. Hessel, “Heat-pipe oven for homogeneous mixtures of saturated and unsaturated vapors; application to NaLi”, 43, 2776 (1972).
[38] A. S. King, “An electric furnace for spectroscopic investigations, with results for the spectra of titanium and vanadium”, Astrophys. J. 28, 300 (1908).
[39] J. T. Bahns, “Laser Excitation Studies of Alkali Metal Vapors”, Ph. D. Dissertation, University of Iowa, Iowa City, 1985.
[40] A. J. Taylor, K. M. Jones, and A. L. Schawlow, “Scanning pulsed-polarization spectrometer applied to Na2”, J. Opt. Soc. Am. 73, 994 (1983).
[41] W. Demtrder and M. Stock, “Molecular constants and potential curves of Na2 from laser-induced fluorescence”, J. Mol. Spectrosc. 55, 476 (1975).
[42] W. Demtrder, W. Stetzenbach, M. Stock and J. Witt, “Lifetimes and Franck-Condon factors for the system of Na2”, J. Mol. Spectrosc. 61, 382 (1976).