超短激光脉冲控制下光缔合反应的波包动力学过程
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摘要
量子波包理论可以应用于处理物理和化学领域中物质与外场相互作用的动力学过程。特别是飞秒激光技术的出现与发展,使人们能够从更快的时间尺度上来探测和研究分子内部的动力学行为。现在已经能够使用激光对原子进行某些控制,光缔合反应就是其中之一。
利用激光场实现分子的选择性激发是一项很有意义的课题,其基本思想是通过设计激光场参数将分子激发到目标态,从而实现对分子内和分子间选择性激发的有效控制。分子的选择性激发已经被广泛应用研究碰撞动力学、分子光谱以及激光化学等领域。
本文主要采用含时量子波包理论,模拟了激光场控制下HF分子和HD~+分子光缔合反应的一些基本动力学过程。首先以HF分子为例研究了光缔合反应中初始碰撞能与缔合几率及态选择性之间的关系,并重点探讨了激光场参数对振动选态的影响。通过调节优化激光参数,有效地控制了产物分子的振动选态。其中特别讨论了激光场强度对态选择性的影响,得出当连续态上布居向更低的振动态上转移时,需要更大的激光场能量。随着激光场强度的增加,缔合过程中会明显伴随多光子跃迁和解离过程。通过计算推导,得到了共振跃迁条件。同时,还分析了不同时刻动量表象下波函数中出现的多个峰值,发现相邻峰值之间相差一个光子的能量,这表明通过缔合反应形成的产物分子HF可以吸收一个或者多个光子再解离。针对HD~+分子缔合过程的研究得出:与单色光相比,双色光可以降低解离几率,提高分子的缔合产率,且缔合产物HD~+的几率也可以通过调节激光场参数得以控制;在反应中存在两个缔合通道,通过计算可以得出两个通道各自的缔合几率。
尽管本文采用了比较简单的理论模型,但其中的讨论结果和计算方法对激光控制光缔合反应产物具有一定的意义。
The time-dependent quantum wave packet method has been widely applied to the physical and chemical areas to study the interaction dynamics of molecules with laser fields. Especially, with the emergence and development of femtosecond laser techniques, the molecular dynamics can be detected and investigated on a faster time scale. Nowadays, many methods have been proposed for controlling chemical reactions including photoassociation reaction with laser pulse.
By making use of the laser field to implement the molecular state-selectivity is a significant project. The essence of this research is to excitated the molecule to the target state by adjusting the parameters of the laser pulse. Consequently, the control of state-selectivity in and between molecules can be carried out efficiently. The molecular state-selectivity has been widely used for studying collision dynamics, spectrum of molecules and laser chemistry.
In this thesis, the time-dependent quantum wave packet theory was mainly used to stimulate the basic dynamics of molecules, HF and HD~+, photoassociation reaction controlled by laser pulse. First, the relationship between the initial collision momentum and the association probability together with the state-selectivity is studied for the product HF. Then the effect of the laser parameters on the vibrational state-selectivity is discussed in detail. By optimizing the laser parameters, the control of the product molecule HF in a selective vibrational state can be achieved effectively. Meanwhile, the impact of the laser pulse intensity is analyzed particularly. It is shown that a stronger laser pulse can transfer the population of the continuum state to the lower vibrational state. However, with the increasing of the laser energy, the multiphoton transition and dissociation accompany the association process. The resonant transition condition can be obtained from the calculation. The wave packet dynamics in the momentum space representation is studied, and the peaks of the wave packets can be observed at different times. In the calculation, we find that the energy difference between two neighboring peaks equals one-photon energy. This indicates that the product HF of association reaction may be dissociated by absorbing more photons. From the photoassociation study of HD~+, we conclude that the two-color laser pulses can more efficiently lower the dissociation probability and therefore enhance the yield ratio of the product than the one-color laser pulse, and the populations of the products can be controlled with the laser pulse. There are two channels in the photoassociation reactions, and the reaction probability through each channel can be calculated.
Although the model employed is simple, the results may serve as a guideline for controlling the product of photoassociation reaction.
利用激光场实现分子的选择性激发是一项很有意义的课题,其基本思想是通过设计激光场参数将分子激发到目标态,从而实现对分子内和分子间选择性激发的有效控制。分子的选择性激发已经被广泛应用研究碰撞动力学、分子光谱以及激光化学等领域。
本文主要采用含时量子波包理论,模拟了激光场控制下HF分子和HD~+分子光缔合反应的一些基本动力学过程。首先以HF分子为例研究了光缔合反应中初始碰撞能与缔合几率及态选择性之间的关系,并重点探讨了激光场参数对振动选态的影响。通过调节优化激光参数,有效地控制了产物分子的振动选态。其中特别讨论了激光场强度对态选择性的影响,得出当连续态上布居向更低的振动态上转移时,需要更大的激光场能量。随着激光场强度的增加,缔合过程中会明显伴随多光子跃迁和解离过程。通过计算推导,得到了共振跃迁条件。同时,还分析了不同时刻动量表象下波函数中出现的多个峰值,发现相邻峰值之间相差一个光子的能量,这表明通过缔合反应形成的产物分子HF可以吸收一个或者多个光子再解离。针对HD~+分子缔合过程的研究得出:与单色光相比,双色光可以降低解离几率,提高分子的缔合产率,且缔合产物HD~+的几率也可以通过调节激光场参数得以控制;在反应中存在两个缔合通道,通过计算可以得出两个通道各自的缔合几率。
尽管本文采用了比较简单的理论模型,但其中的讨论结果和计算方法对激光控制光缔合反应产物具有一定的意义。
The time-dependent quantum wave packet method has been widely applied to the physical and chemical areas to study the interaction dynamics of molecules with laser fields. Especially, with the emergence and development of femtosecond laser techniques, the molecular dynamics can be detected and investigated on a faster time scale. Nowadays, many methods have been proposed for controlling chemical reactions including photoassociation reaction with laser pulse.
By making use of the laser field to implement the molecular state-selectivity is a significant project. The essence of this research is to excitated the molecule to the target state by adjusting the parameters of the laser pulse. Consequently, the control of state-selectivity in and between molecules can be carried out efficiently. The molecular state-selectivity has been widely used for studying collision dynamics, spectrum of molecules and laser chemistry.
In this thesis, the time-dependent quantum wave packet theory was mainly used to stimulate the basic dynamics of molecules, HF and HD~+, photoassociation reaction controlled by laser pulse. First, the relationship between the initial collision momentum and the association probability together with the state-selectivity is studied for the product HF. Then the effect of the laser parameters on the vibrational state-selectivity is discussed in detail. By optimizing the laser parameters, the control of the product molecule HF in a selective vibrational state can be achieved effectively. Meanwhile, the impact of the laser pulse intensity is analyzed particularly. It is shown that a stronger laser pulse can transfer the population of the continuum state to the lower vibrational state. However, with the increasing of the laser energy, the multiphoton transition and dissociation accompany the association process. The resonant transition condition can be obtained from the calculation. The wave packet dynamics in the momentum space representation is studied, and the peaks of the wave packets can be observed at different times. In the calculation, we find that the energy difference between two neighboring peaks equals one-photon energy. This indicates that the product HF of association reaction may be dissociated by absorbing more photons. From the photoassociation study of HD~+, we conclude that the two-color laser pulses can more efficiently lower the dissociation probability and therefore enhance the yield ratio of the product than the one-color laser pulse, and the populations of the products can be controlled with the laser pulse. There are two channels in the photoassociation reactions, and the reaction probability through each channel can be calculated.
Although the model employed is simple, the results may serve as a guideline for controlling the product of photoassociation reaction.
引文
[1]Schr(o|¨)dinger E. Naturwiss. 1926, 14:664.
[2]Ehrenfest P. Z. Physiz. 1927, 45: 455.
[3]Heller E J. Time-dependent approach to semiclassical dynamics. J. Chem. Phys. , 1975, 62 (4):1544-1555.
[4]Kosloff D and Kosloff R. A fourier method solution for the time dependent Schr(o|¨)dinge equation as a tool in molecular dynamics. J.Comput. Phys., 1983, 52(1):35-53.
[5]Kosloff D, and Kosloff R. Absorbing boundaries for wave propagation problems. J. Comput. Phys., 1986, 63(2):363-376.
[6] Kosloff R. Time dependent quantum-mechanical methods for molecular dynamics. J. Phys. Chem., 1988,92(8):2087-2100.
[7]Kosloff R. Propagation methods for quantum molecular dynamics. Ann. Rev. Phys.Chem.,1994,45:145-178.
[8]Feit M D, Fleck J A, Jr et al. Solution of the Schrodinger equation by a spectral method. J. Comput. Phys., 1982, 47(3):412-433.
[9]Light J C, Hamilton I P, Lill J V. Generalized discrete variable approximation in quantum mechanics. J. Chem. Phys., 1985, 82(3):1400-1409.
[10]Park T J, Light J C. Unitary quantum time evolution by Iterative lanczos reduction. J.Chem. Phys. , 1986, 85(10):5870-5876.
[11]Tal-Ener H, Kosloff R. An accurate and efficient scheme fir propagating the time dependent Schrodinger equation. J. Chem. Phys., 1984, 81(4):3967-3971.
[12]Sun Z G, Liu H P, Lou N Q et al. Selecting ionization path by dynamic stark shift with strong laser pulse. Chem. Phys. Lett., 2003,369:374-379.
[13]Stapelfeldt H, Sakai H, Constant E et al. Deflection of Neutral Molecules using the Nonresonant Dipole Force. Phys. Rev. Lett. , 1997,79:2787-2790.
[14]Zhang L D, Wei J, Jiang Y Y et al. Multiphoton ionization mass spectra of n-C_3H_7I and i-C_3H_7I at 532 nm. Chin. Phys. , 1998, 7(4):271-276.
[15]Niu D W, Li H Y, Luo X L et al. Cluster-assisted generation of multi-charged ions in nanosecond laser ionization of pulsed hydrogen sulf ide beam at 1064 and 532nm. Chin. Phys. , 2006,15(7):1511-1516.
[16]Wickenhauser M, Tong X M, Arbó D G et al. Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses. Phys. Rev. A, 2006,74:041402.
[17]Li G X, Huang G M, Peng J S. COHERENT POPULATION TRAPPING IN MULTILEVEL LASER-INDUCED CONTINUUM STRUCTURE SYSTEM INCLUDING CASCADE TW0-PH0TON PROCESSES. Chin. Phys.,1998,7(6):422-431.
[18]Eramo R, Cavalier S, Fini L et al. Observation of a laser-induced structure in ionization continuum of sodium atoms using photoelectrom energy spectroscopy. J. Phys. B, 1997,30(17):3789-3796.
[19]Faucher O, Hertz E, Lavorel B et al. Observation of laser-induced contimuum structure in the NO molecule. J. Phys. B, 1999,32(18):4485-4493.
[20]Magnier S, Persico M, Rahman N. Rabi Oscillations Between Dissociative Molecular States. Phys. Rev. Lett., 1999, 83:2159-2162.
[21]Sage J M, Sainis S, Bergeman T et al. Optical Production of Ultracold Polar Molecules. Phys. Rev. Lett., 2005, 94:203001.
[22]Fioretti A, Comparat D, Crubellier A et al. Formation of Cold C& Molecules through Photoassociation. Phys. Rev. Lett., 1998,80:4402-4405.
[23]Machholm M, Giusti-Suzor A, Mies F H. Photoassociation of atoms in ultracold collisions probed by wave-packet dynamics. Phys. Rev. A, 1994,50:5025-5036.
[24]Lett P D, Helmerson K, Phillips W D et al. Spectroscopy of Na_2 by photoassociation of laser-cooled Na. Phys. Rev. Lett., 1993,71:2200-2203.
[25]Miller J D, Cline R A, Heinzen D J. Photoassociation spectrum of ultracold Rb atoms. Phys. Rev. Lett., 1993,71:2204-2207.
[26]Yu J, Wang S M, Yuan K J et al. Photoionization of NaK molecule with a double-well potential in femtosecond pump-probe pulse laser fields. Chin. Phys., 2006,15(9):199.6-2001.
[27]Dai C J, Chen Z D. PHOTOEXCITATION OF ATOM WITH ULTRASHORT LASER PULSES. Chin. Phys., 2001, 10(5):403-406.
[28]Zheng L, Wang C, Li S H et al. Study on the interaction of intense femtosecond laser pulses with nanometre-sized hydrogen clusters. Chin. Phys., 2006, 15(4):697-701.
[29]Marvet U, Dantus M. Femtosecond photoassociation spectroscopy: coherent bond formation. Chem. Phys. Lett., 1995, 245(4-5):393-399.
[30]Vala J, Dulieu O, Masnou-Seeuws F et al. Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field Phys. Rev. A, 2000, 63(1):013412.
[31]Vatasescu M, Dulieu O, Kosloff R et al. Optimal control of photoassociation of cold atoms and photodissociation of long-range molecules: Characteristic times for wave-packet propagation. Phys. Rev. A, 2001, 63 (3):033407.
[32]Niu Y Y, Wang S M, Cong S L. Vibrational state-selectivity of product HI in photoassociation reaction I+H→HI. Chem. Phys. Lett., 2006, 428(1-3) :7-12.
[33]Javanainen J, Matt M. Probability of photoassociation from a quasicontinuum approach. Phys. Rev. A, 1998, 58(2):R789-R792.
[34]Matt M, Javanainen J. Quasicontinuum modeling of photoassociation. Phys. Rev. A, 1999,60(4):3174-3187.
[35]Korolkov M V, Manz J, Paramonov G K. Vibrationally state-selective photoassociation by infrared sub-picosecond laserr pulses: model simulations for O+H→OH(v). Chem. Phys. Lett. , 1996, 260(5-6):604-610.
[36]Backhaus P, Schmidt B. Femtosecond quantum dynamics of photoassociation reactions: the exciplex formation of mercury. Chem. Phys., 1996, 217(2-3):131-143.
[37]Korolkov M V, Schmidt B. Infrared picosecond laser control of acceleration of neutral atoms: model simulations for the collision pair O+H. Chem. Phys. Lett., 1997,272(1-2):96-102.
[38]Korolkov M V, Schmidt B. Vibrationally state-selective laser pulse control of electronic branching in OH (X~2∏/A~2∑~+ ) photoassociation. Chem.Phys., 1998, 237(1-2):123-138.
[39]Backhaus P, Manz J, Schmidt B. Effect of Rotations and Shape Resonances on Photoassociation and Photoacceleration by Short Infrared Laser Pulses. J. Phys. Chem. A, 1998,102(23):4118-4128.
[40]Korolkov M V, Schmidt B. Spin-orbit induced association under ultrafast laser pulse control. Chem. Phys. Lett., 2002, 361(5-6):432-438.
[41]Rickes T, Yatsenko LP, Steuerwald S. Efficient adiabatic population transfer by two-photon excitation assisted by a laser-induced Stark shift. J. Chem. Phys., 2000, 113(2):534-546.
[42]Dlorshagen G, Heller EJ. A time dependent wave packet approach to three-dimensional gas - surface scattering. J. Chem. Phys., 1983, 79(4):2072-2082
[43]Andrianov I V, Paramonov G K. Selective excitation of the rational-rotational states and dissociation of diatomic molecules by picosecond infrared laser pulses: Modeling for HF in the ground electronic state. Phys. Rev. A,1998,59(3) :2134-2138.
[44]Manz J, Paramonov G K. Laser control scheme for state-selective ultrafast vibrational excitation of the water-d molecule. J. Phys. Chem., 1993, 97(48):12625-12633.
[45]Tran P. Population transfer through the continuum: ir excitation of HeH~+. Phys. Rev. A, 1999, 59(2):1444-1450.
[46]Backhaus P,Schmidt B. Femtosecond quantum dynamics of photoassociation reactions: the exciplex formation of mercury. Chem. Phys., 1997, 217(2-3):131-143.
[47]Esry B D, Sadeghpour H R. Adiabatic formulation of heteronuclear hydrogen molecular ion. Phys. Rev. A, 1999,60 (5):3640-3617.
[48]Charron E, Giusti-Suzor A, Mies F H. Coherent control of isotope separation in HD~+ photoassociation by strong fields. Phys. Rev. Lett. , 1995,75(15):2815-2818.
[49]Ohmura H, Nakanaga T, Tachiya M. Coherent control of photofragment separation in the dissociative ionization of Ibr. Phys. Rev. Lett., 2004,92:113002.
[50]Datta B, Bhattacharyya S S, Resonant two photon dissociation dynamics of HD~+ in intense infrared laser field. J. Chem. Phys., 1991,94(12):7779-7787.
[2]Ehrenfest P. Z. Physiz. 1927, 45: 455.
[3]Heller E J. Time-dependent approach to semiclassical dynamics. J. Chem. Phys. , 1975, 62 (4):1544-1555.
[4]Kosloff D and Kosloff R. A fourier method solution for the time dependent Schr(o|¨)dinge equation as a tool in molecular dynamics. J.Comput. Phys., 1983, 52(1):35-53.
[5]Kosloff D, and Kosloff R. Absorbing boundaries for wave propagation problems. J. Comput. Phys., 1986, 63(2):363-376.
[6] Kosloff R. Time dependent quantum-mechanical methods for molecular dynamics. J. Phys. Chem., 1988,92(8):2087-2100.
[7]Kosloff R. Propagation methods for quantum molecular dynamics. Ann. Rev. Phys.Chem.,1994,45:145-178.
[8]Feit M D, Fleck J A, Jr et al. Solution of the Schrodinger equation by a spectral method. J. Comput. Phys., 1982, 47(3):412-433.
[9]Light J C, Hamilton I P, Lill J V. Generalized discrete variable approximation in quantum mechanics. J. Chem. Phys., 1985, 82(3):1400-1409.
[10]Park T J, Light J C. Unitary quantum time evolution by Iterative lanczos reduction. J.Chem. Phys. , 1986, 85(10):5870-5876.
[11]Tal-Ener H, Kosloff R. An accurate and efficient scheme fir propagating the time dependent Schrodinger equation. J. Chem. Phys., 1984, 81(4):3967-3971.
[12]Sun Z G, Liu H P, Lou N Q et al. Selecting ionization path by dynamic stark shift with strong laser pulse. Chem. Phys. Lett., 2003,369:374-379.
[13]Stapelfeldt H, Sakai H, Constant E et al. Deflection of Neutral Molecules using the Nonresonant Dipole Force. Phys. Rev. Lett. , 1997,79:2787-2790.
[14]Zhang L D, Wei J, Jiang Y Y et al. Multiphoton ionization mass spectra of n-C_3H_7I and i-C_3H_7I at 532 nm. Chin. Phys. , 1998, 7(4):271-276.
[15]Niu D W, Li H Y, Luo X L et al. Cluster-assisted generation of multi-charged ions in nanosecond laser ionization of pulsed hydrogen sulf ide beam at 1064 and 532nm. Chin. Phys. , 2006,15(7):1511-1516.
[16]Wickenhauser M, Tong X M, Arbó D G et al. Signatures of tunneling and multiphoton ionization in the electron-momentum distributions of atoms by intense few-cycle laser pulses. Phys. Rev. A, 2006,74:041402.
[17]Li G X, Huang G M, Peng J S. COHERENT POPULATION TRAPPING IN MULTILEVEL LASER-INDUCED CONTINUUM STRUCTURE SYSTEM INCLUDING CASCADE TW0-PH0TON PROCESSES. Chin. Phys.,1998,7(6):422-431.
[18]Eramo R, Cavalier S, Fini L et al. Observation of a laser-induced structure in ionization continuum of sodium atoms using photoelectrom energy spectroscopy. J. Phys. B, 1997,30(17):3789-3796.
[19]Faucher O, Hertz E, Lavorel B et al. Observation of laser-induced contimuum structure in the NO molecule. J. Phys. B, 1999,32(18):4485-4493.
[20]Magnier S, Persico M, Rahman N. Rabi Oscillations Between Dissociative Molecular States. Phys. Rev. Lett., 1999, 83:2159-2162.
[21]Sage J M, Sainis S, Bergeman T et al. Optical Production of Ultracold Polar Molecules. Phys. Rev. Lett., 2005, 94:203001.
[22]Fioretti A, Comparat D, Crubellier A et al. Formation of Cold C& Molecules through Photoassociation. Phys. Rev. Lett., 1998,80:4402-4405.
[23]Machholm M, Giusti-Suzor A, Mies F H. Photoassociation of atoms in ultracold collisions probed by wave-packet dynamics. Phys. Rev. A, 1994,50:5025-5036.
[24]Lett P D, Helmerson K, Phillips W D et al. Spectroscopy of Na_2 by photoassociation of laser-cooled Na. Phys. Rev. Lett., 1993,71:2200-2203.
[25]Miller J D, Cline R A, Heinzen D J. Photoassociation spectrum of ultracold Rb atoms. Phys. Rev. Lett., 1993,71:2204-2207.
[26]Yu J, Wang S M, Yuan K J et al. Photoionization of NaK molecule with a double-well potential in femtosecond pump-probe pulse laser fields. Chin. Phys., 2006,15(9):199.6-2001.
[27]Dai C J, Chen Z D. PHOTOEXCITATION OF ATOM WITH ULTRASHORT LASER PULSES. Chin. Phys., 2001, 10(5):403-406.
[28]Zheng L, Wang C, Li S H et al. Study on the interaction of intense femtosecond laser pulses with nanometre-sized hydrogen clusters. Chin. Phys., 2006, 15(4):697-701.
[29]Marvet U, Dantus M. Femtosecond photoassociation spectroscopy: coherent bond formation. Chem. Phys. Lett., 1995, 245(4-5):393-399.
[30]Vala J, Dulieu O, Masnou-Seeuws F et al. Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field Phys. Rev. A, 2000, 63(1):013412.
[31]Vatasescu M, Dulieu O, Kosloff R et al. Optimal control of photoassociation of cold atoms and photodissociation of long-range molecules: Characteristic times for wave-packet propagation. Phys. Rev. A, 2001, 63 (3):033407.
[32]Niu Y Y, Wang S M, Cong S L. Vibrational state-selectivity of product HI in photoassociation reaction I+H→HI. Chem. Phys. Lett., 2006, 428(1-3) :7-12.
[33]Javanainen J, Matt M. Probability of photoassociation from a quasicontinuum approach. Phys. Rev. A, 1998, 58(2):R789-R792.
[34]Matt M, Javanainen J. Quasicontinuum modeling of photoassociation. Phys. Rev. A, 1999,60(4):3174-3187.
[35]Korolkov M V, Manz J, Paramonov G K. Vibrationally state-selective photoassociation by infrared sub-picosecond laserr pulses: model simulations for O+H→OH(v). Chem. Phys. Lett. , 1996, 260(5-6):604-610.
[36]Backhaus P, Schmidt B. Femtosecond quantum dynamics of photoassociation reactions: the exciplex formation of mercury. Chem. Phys., 1996, 217(2-3):131-143.
[37]Korolkov M V, Schmidt B. Infrared picosecond laser control of acceleration of neutral atoms: model simulations for the collision pair O+H. Chem. Phys. Lett., 1997,272(1-2):96-102.
[38]Korolkov M V, Schmidt B. Vibrationally state-selective laser pulse control of electronic branching in OH (X~2∏/A~2∑~+ ) photoassociation. Chem.Phys., 1998, 237(1-2):123-138.
[39]Backhaus P, Manz J, Schmidt B. Effect of Rotations and Shape Resonances on Photoassociation and Photoacceleration by Short Infrared Laser Pulses. J. Phys. Chem. A, 1998,102(23):4118-4128.
[40]Korolkov M V, Schmidt B. Spin-orbit induced association under ultrafast laser pulse control. Chem. Phys. Lett., 2002, 361(5-6):432-438.
[41]Rickes T, Yatsenko LP, Steuerwald S. Efficient adiabatic population transfer by two-photon excitation assisted by a laser-induced Stark shift. J. Chem. Phys., 2000, 113(2):534-546.
[42]Dlorshagen G, Heller EJ. A time dependent wave packet approach to three-dimensional gas - surface scattering. J. Chem. Phys., 1983, 79(4):2072-2082
[43]Andrianov I V, Paramonov G K. Selective excitation of the rational-rotational states and dissociation of diatomic molecules by picosecond infrared laser pulses: Modeling for HF in the ground electronic state. Phys. Rev. A,1998,59(3) :2134-2138.
[44]Manz J, Paramonov G K. Laser control scheme for state-selective ultrafast vibrational excitation of the water-d molecule. J. Phys. Chem., 1993, 97(48):12625-12633.
[45]Tran P. Population transfer through the continuum: ir excitation of HeH~+. Phys. Rev. A, 1999, 59(2):1444-1450.
[46]Backhaus P,Schmidt B. Femtosecond quantum dynamics of photoassociation reactions: the exciplex formation of mercury. Chem. Phys., 1997, 217(2-3):131-143.
[47]Esry B D, Sadeghpour H R. Adiabatic formulation of heteronuclear hydrogen molecular ion. Phys. Rev. A, 1999,60 (5):3640-3617.
[48]Charron E, Giusti-Suzor A, Mies F H. Coherent control of isotope separation in HD~+ photoassociation by strong fields. Phys. Rev. Lett. , 1995,75(15):2815-2818.
[49]Ohmura H, Nakanaga T, Tachiya M. Coherent control of photofragment separation in the dissociative ionization of Ibr. Phys. Rev. Lett., 2004,92:113002.
[50]Datta B, Bhattacharyya S S, Resonant two photon dissociation dynamics of HD~+ in intense infrared laser field. J. Chem. Phys., 1991,94(12):7779-7787.