《碰撞能量为20-70.9ev时he+(2s)+ne(2p6,1s)→he+(2s)+ne(2p53s1p)的横截面积和经典路径的计算》由会员分享，可在线阅读，更多相关《碰撞能量为20-70.9ev时he+(2s)+ne(2p6,1s)→he+(2s)+ne(2p53s1p)的横截面积和经典路径的计算（7页珍藏版）》请在金锄头文库上搜索。
1、THEO CHEM ELSEVIER Journal of Molecular Structure (Thcochem) 341 ( 1995) 149- 155 Quantum and classical path calculations of the total cross section for Hec(2S) + Ne(2p6,S) -+ H, Of1 I 20.0 0.7002 0 7350 25.0 0.7855 O.SlO3 30.0 0.8222 0.8247 35.0 0.81 I9 0.8256 40.0 0.7YX8 0.8105 45.0 0.7847 lJ.7892
2、 50.0 0 7703 0.771 7 55.0 0.7470 0.757X 60.0 0.7301 0.732 65.0 0.7117 0.7170 70.9 0.6936 0.6979 Cross sections arc m (I,. %I flill 71 / 0 6520 0.6985 I).6071 0.7677 0.7891 0 7 165 0.7992 08117 0 7492 0.7972 08113 0 7537 11.790? 0. X01)4 0 7462 077X7 0.7840 (I 7377 13.7564 0.764 I II 71x3 0.7440 0.75
3、09 0 7074 Il.7225 0.7177 0 6860 0.7067 0 71 I9 0 6712 II.6899 0.6939 0 6537 damping procedure in the Liouville equations was applied 16 for this system. However. they have found no oscillations at all for low collision energy. Thus, using the system described by Eq. (l), one can test the validity of
4、 the CP approxi- mation close to the threshold by comparing its results with quantum calculations. This paper aims to compare transition probabil- ities and total quantum cross sections over the range of 20 eV (the threshold energy, Eth = 16.8 eV) to 70.9 eV with the CP approximation and Landau-Zene
5、r (LZ) method. A more critical analysis of damping functions introduced to semi- classical approximations can therefore be made. 2. Theory For details of the quantum and LZ methods the reader is addressed to Refs. 1.181. For the CP approach we follow Billing 191. Our calculations were made on a diab
6、atic basis using the potential 12 in atomic units. WI, = 21.1R exp(,-R/0.678) I, = 27l 0 f,.,(b)bdb - (11) where b is the impact parameter. Two initial conditions were used to calculate the CP transition probabilities: (a) starting on the upper curve rl, = 0, dz = 1 or (b) starting on the lower curv
7、e. ti, = 1. d: = 0. One can approach the CP total cross section for a specified initial condition as 1,18 (12) where N is the number of channels energetically available. Following such an approach we will show that for a two state system one can obtain accurate results compared with close coupling (
8、CC) calculations. For that we calculate CP total cross sections with the initial condition a. 0.8 15 20 25 30 35 40 45 50 55 60 65 70 75 Energy(eV) Fig. 2. Comparison between total quantum cross sectlon (1 - I (*) and arithmetic mean total classical path cross section 0 - l(e). Energy(eV) Fig. 3. Co
9、mparison betcen total quantum cross section 0 - I (* j and Landau-Zener total cross section (A). Therefore Eq. (12) becomes The cross sections for the LZ model were obtained in the usual way 1,18, c7 = 7 = I. full line) transition probabilities at EC = 20 eV (Eth = I6 8 eV). that the CP method still
10、 provides transition when probabilities that are always proportional to the the kinetic energy becomes imaginary as is the case for quantum probabilities. The oscillations in the interference between the real and imaginary coeffr- cients in the CP equations. CP approximation are due to treating the
11、internal states quantically. Different initial conditions lead to different oscillations for the CP transition The CP transition probabilities (d, = 1 and d2 = 0) and quantum probabilities at 70.9 eV are shown in Fig. 5 and we have obtained the same 154 Fig. 5. Quantum (broken lint) and CP (mltial c
12、ondition 1, : I and dz = 0. full line) transition probabilities at E, = 70.9 eV. results as reported in Ref. 161. However, at low produce eigenstates of the electronic Hamiltonian energies. they have found no oscillations at all in in the final states. the CP probabilities. They have argued that the
13、 Fig. 6 shows the transition probability with damping functions should be introduced to initial condition dr = 0 and d2 = 1 at 17 eV I I 0.6 - Fig. 6. Quantum (broken line) and CP (initial condition d, = 0 and 1 = I. full line) transition probabilities at E, = 17.0 eV (Eth = 16.8 ev). (0.2 eV above
14、the threshold). .4s can be seen there are several oscillations both in CP and in quantum calculations. in disagreement with the previous damping analysis. 4. Conclusions Although it is recognized that the damping pro- cedure works well at high energies, this work shows that one does not need to intr
15、oduce it even close to the threshold for the two state model system (1). Furthermore our calculations show that the CP approximation works well for such a model and the symmetrizations in the total CP cross sections yield results identical to the exact values. References l M.S. Child. Molecular Coll
16、iston Theory. .Acadcmc Press. London. 1974. 2 G.D. Bilhng. J. Chem. Phys. 62 (1975) 14X0. 3 G.D. Billing. Chem. Phys Len. 30 (1975) 359. 4 G.D. Bilhng and L.L. Paulsen. Chem. Phys. 70 (19821 119. S J.T. Muckerman, R.D. Gilbert and G.D. Billing, J. Chem. Phys., 88 (1988) 4779. 6 R.L. McKenzie, J. Chem. Phys. 63 (1975) 1655. 7 J T. Muckerman, 1. Rusinek. R.E. Roberts and M. Alexander. J. Chem. Phys. 65
