飞秒泵浦-探测实验动力学数据处理

类别:    标签: 编程 matlab   阅读次数:   版权: (CC) BY-NC-SA

2013-11-09 15:00:10

基本过程

基态分子S0吸收266 nm的泵浦光子被激发到S2态, 然后吸收800 nm的探测光子被电离形成母体离子. S2激发态分子可能的弛豫过程是通过内转换到S0和S1态. 通过内转换弛豫到S1激发态的分子可以通过内转换弛豫到S0态, 也可以继续吸收探测光子被电离, 形成母体离子. 而根据Franc-Condon原理, 基态S0分子由于电离需要很高的能量, 不能被探测光子直接电离. 因此, 总的母体离子来源于激发态S1和S2的电离.

动力学方程

其中[Ion], [S2], [S1]和[S0]分别表示总的母体离子, 第二激发态, 第一激发态和基态高振动态的相对布局数, I(t)为检测到的信号. $\sigma_i$ 和 $\sigma_a$ 表示光电离截面和光吸收截面. 和 $I_{prob}(t)$ 分别对应泵浦光和探测光的强度. $\alpha_1={1 \over \tau_1}, \alpha_2={1 \over \tau_2}$ 和 $\alpha_3={1\over \tau_3}$ 分别表示S2->S1, S1->S0 和S2->S0的内转换速率. 由于S2和S1激发态的光电离截面与它们本身和对应离子态的电子构型有关, 因此这两个态的光电离截面的相对比例是一个未知量, 设其为k.

特例

若忽略 $\sigma_a I_{pump}(t)[S_0]$ 这一项, 则动力学方程简化为:

此为线性微分方程组, 可求得通解

设初始条件为 $[S_2]_0=C_0, [S_1]_0=0$, 则特解为

探测光检测的是S2与S1电离的总信号, 检测信号 $I(t)$ 是[S2], [S1]之和与仪器响应函数 $G(t)$ 的卷积(其计算参看另一篇博文)

设仪器函数 $G(t)=\sigma e^{-\kappa t^2}$, 则

此种情形下, 对 $I(t)$ 进行非线性拟合, 可得到 $\alpha_{13}, \alpha_2, \kappa, I_0, P$, 但无法分别求得 $\alpha_1, \alpha_3$ 和 $k$, 除非假定 $\alpha_3$ 远小于 $\alpha_1$.

数据示例与拟合结果

t Yexp Yfit Y1 Y2 Yfit-Yexp
-0.300 0.00937 0.00000 0.00000 0.00000 -0.00937
-0.250 0.01503 0.00204 0.00000 0.00190 -0.01299
-0.200 0.03345 0.02056 0.00005 0.01919 -0.01289
-0.150 0.13349 0.12306 0.00036 0.11482 -0.01043
-0.100 0.41596 0.42532 0.00171 0.39638 0.00936
-0.050 0.80750 0.80468 0.00498 0.74817 -0.00282
0.000 0.95882 0.97642 0.00971 0.90420 0.01760
0.050 0.96463 1.00000 0.01480 0.92117 0.03537
0.100 1.00000 0.98852 0.01982 0.90542 -0.01148
0.150 0.99241 0.97115 0.02467 0.88431 -0.02126
0.200 0.96059 0.95273 0.02935 0.86239 -0.00786
0.250 0.88052 0.93431 0.03385 0.84064 0.05379
0.300 0.82304 0.91620 0.03818 0.81936 0.09316
0.350 0.82319 0.89847 0.04235 0.79860 0.07528
0.400 0.87304 0.88114 0.04635 0.77837 0.00810
0.450 0.88735 0.86418 0.05020 0.75865 -0.02317
0.500 0.87892 0.84760 0.05390 0.73943 -0.03132
0.550 0.85825 0.83138 0.05745 0.72070 -0.02687
0.600 0.86426 0.81551 0.06085 0.70244 -0.04875
0.650 0.85882 0.79999 0.06412 0.68465 -0.05883
0.700 0.82704 0.78481 0.06726 0.66730 -0.04223
0.750 0.83614 0.76995 0.07026 0.65040 -0.06619
0.800 0.79509 0.75542 0.07313 0.63392 -0.03967
0.850 0.73578 0.74120 0.07588 0.61786 0.00542
0.900 0.72928 0.72729 0.07852 0.60221 -0.00199
0.950 0.70738 0.71368 0.08103 0.58695 0.00630
1.000 0.69390 0.70036 0.08344 0.57208 0.00646
1.050 0.66723 0.68733 0.08573 0.55759 0.02010
1.100 0.64108 0.67458 0.08792 0.54346 0.03350
1.150 0.62586 0.66210 0.09001 0.52970 0.03624
1.200 0.62946 0.64988 0.09199 0.51628 0.02042
1.250 0.60026 0.63793 0.09389 0.50320 0.03767
1.300 0.60033 0.62623 0.09568 0.49045 0.02590
1.350 0.59572 0.61478 0.09739 0.47803 0.01906
1.400 0.59461 0.60357 0.09901 0.46592 0.00896
1.450 0.55393 0.59259 0.10054 0.45411 0.03866
1.500 0.56845 0.58185 0.10199 0.44261 0.01340
1.550 0.54063 0.57134 0.10336 0.43140 0.03071
1.600 0.54543 0.56104 0.10465 0.42047 0.01561
1.650 0.53860 0.55096 0.10587 0.40982 0.01236
1.700 0.53482 0.54109 0.10702 0.39943 0.00627
1.750 0.49968 0.53143 0.10809 0.38931 0.03175
1.800 0.47553 0.52197 0.10910 0.37945 0.04644
1.850 0.49586 0.51271 0.11004 0.36984 0.01685
1.900 0.49663 0.50363 0.11092 0.36047 0.00700
1.950 0.50203 0.49475 0.11173 0.35134 -0.00728
2.000 0.50134 0.48604 0.11249 0.34244 -0.01530
2.050 0.49525 0.47752 0.11319 0.33376 -0.01773
2.100 0.46992 0.46917 0.11383 0.32531 -0.00075
2.150 0.43286 0.46099 0.11441 0.31707 0.02813
2.200 0.41583 0.45298 0.11495 0.30903 0.03715
2.250 0.41480 0.44514 0.11543 0.30120 0.03034
2.300 0.43082 0.43745 0.11587 0.29357 0.00663
2.350 0.45134 0.42992 0.11626 0.28614 -0.02142
2.400 0.44063 0.42254 0.11660 0.27889 -0.01809
2.450 0.44999 0.41531 0.11690 0.27182 -0.03468
2.500 0.44135 0.40822 0.11715 0.26494 -0.03313
2.550 0.43267 0.40128 0.11736 0.25822 -0.03139
2.600 0.41335 0.39448 0.11754 0.25168 -0.01887
2.650 0.40019 0.38781 0.11767 0.24531 -0.01238
2.700 0.38663 0.38128 0.11777 0.23909 -0.00535
2.750 0.41059 0.37487 0.11783 0.23303 -0.03572
2.800 0.40330 0.36859 0.11786 0.22713 -0.03471
2.850 0.38133 0.36244 0.11786 0.22138 -0.01889
2.900 0.38358 0.35641 0.11782 0.21577 -0.02717
2.950 0.38627 0.35050 0.11775 0.21030 -0.03577
3.000 0.38779 0.34470 0.11765 0.20498 -0.04309
3.050 0.36934 0.33902 0.11753 0.19978 -0.03032
3.100 0.31651 0.33344 0.11737 0.19472 0.01693
3.150 0.29785 0.32798 0.11719 0.18979 0.03013
3.200 0.29857 0.32262 0.11699 0.18498 0.02405
3.250 0.28143 0.31737 0.11675 0.18029 0.03594
3.300 0.28016 0.31222 0.11650 0.17573 0.03206
3.350 0.28532 0.30716 0.11622 0.17127 0.02184
3.400 0.29552 0.30221 0.11592 0.16694 0.00669
3.450 0.28343 0.29735 0.11560 0.16271 0.01392
3.500 0.29952 0.29258 0.11526 0.15858 -0.00694
3.550 0.29948 0.28790 0.11490 0.15457 -0.01158
3.600 0.30616 0.28331 0.11452 0.15065 -0.02285
3.650 0.30108 0.27881 0.11413 0.14684 -0.02227
3.700 0.29272 0.27439 0.11371 0.14312 -0.01833
3.750 0.26723 0.27006 0.11328 0.13949 0.00283
3.800 0.24359 0.26581 0.11284 0.13596 0.02222
3.850 0.24166 0.26164 0.11238 0.13251 0.01998
3.900 0.24907 0.25755 0.11190 0.12915 0.00848
3.950 0.25931 0.25353 0.11141 0.12588 -0.00578
4.000 0.26799 0.24959 0.11091 0.12269 -0.01840
4.050 0.26302 0.24572 0.11040 0.11959 -0.01730
4.100 0.26923 0.24192 0.10987 0.11656 -0.02731
4.150 0.26356 0.23819 0.10934 0.11360 -0.02537
4.200 0.25328 0.23453 0.10879 0.11073 -0.01875
4.250 0.25164 0.23094 0.10823 0.10792 -0.02070
4.300 0.25456 0.22741 0.10766 0.10519 -0.02715
4.350 0.26258 0.22395 0.10709 0.10252 -0.03863
4.400 0.25118 0.22055 0.10650 0.09992 -0.03063
4.450 0.23190 0.21721 0.10591 0.09739 -0.01469
4.500 0.20579 0.21393 0.10531 0.09493 0.00814
4.550 0.20165 0.21071 0.10470 0.09252 0.00906
4.600 0.21981 0.20755 0.10408 0.09018 -0.01226
4.650 0.21785 0.20444 0.10346 0.08789 -0.01341
4.700 0.20096 0.20140 0.10284 0.08567 0.00044
4.750 0.20797 0.19840 0.10220 0.08350 -0.00957
4.800 0.19697 0.19546 0.10156 0.08138 -0.00151
4.850 0.16766 0.19257 0.10092 0.07932 0.02491
4.900 0.16617 0.18973 0.10027 0.07731 0.02356
4.950 0.17180 0.18694 0.09962 0.07535 0.01514
5.000 0.15996 0.18420 0.09896 0.07344 0.02424
5.050 0.15389 0.18151 0.09830 0.07158 0.02762
5.100 0.16079 0.17886 0.09764 0.06977 0.01807
5.150 0.14808 0.17626 0.09697 0.06800 0.02818
5.200 0.16003 0.17371 0.09631 0.06628 0.01368
5.250 0.18182 0.17119 0.09563 0.06460 -0.01063
5.300 0.18168 0.16873 0.09496 0.06296 -0.01295
5.350 0.17881 0.16630 0.09429 0.06137 -0.01251
5.400 0.17427 0.16392 0.09361 0.05981 -0.01035
5.450 0.14703 0.16157 0.09293 0.05830 0.01454
5.500 0.14863 0.15927 0.09225 0.05682 0.01064
5.550 0.15422 0.15701 0.09157 0.05538 0.00279
5.600 0.14638 0.15478 0.09089 0.05398 0.00840
5.650 0.15389 0.15259 0.09021 0.05261 -0.00130
5.700 0.14746 0.15044 0.08953 0.05128 0.00298
5.750 0.13622 0.14832 0.08885 0.04998 0.01210
5.800 0.14449 0.14624 0.08817 0.04871 0.00175
5.850 0.16297 0.14420 0.08749 0.04748 -0.01877
5.900 0.16867 0.14218 0.08680 0.04628 -0.02649
5.950 0.15738 0.14020 0.08612 0.04510 -0.01718
6.000 0.15317 0.13826 0.08544 0.04396 -0.01491
6.050 0.15429 0.13634 0.08477 0.04285 -0.01795
6.100 0.13095 0.13446 0.08409 0.04176 0.00351
6.150 0.14387 0.13261 0.08341 0.04070 -0.01126
6.200 0.14833 0.13078 0.08274 0.03967 -0.01755
6.250 0.14318 0.12899 0.08207 0.03867 -0.01419
6.300 0.14677 0.12723 0.08139 0.03769 -0.01954
6.350 0.13270 0.12549 0.08073 0.03673 -0.00721
6.400 0.11875 0.12379 0.08006 0.03580 0.00504
6.450 0.11719 0.12210 0.07939 0.03490 0.00491
6.500 0.12202 0.12045 0.07873 0.03401 -0.00157
6.550 0.12383 0.11882 0.07807 0.03315 -0.00501
6.600 0.11715 0.11722 0.07741 0.03231 0.00007
6.650 0.11493 0.11565 0.07675 0.03149 0.00072
6.700 0.10953 0.11410 0.07610 0.03069 0.00457
6.750 0.11446 0.11257 0.07545 0.02992 -0.00189
6.800 0.11773 0.11107 0.07480 0.02916 -0.00666
6.850 0.11533 0.10959 0.07415 0.02842 -0.00574
6.900 0.10858 0.10813 0.07351 0.02770 -0.00045
6.950 0.10451 0.10670 0.07287 0.02700 0.00219
7.000 0.09213 0.10529 0.07223 0.02631 0.01316
7.050 0.08973 0.10390 0.07160 0.02565 0.01417
7.100 0.08733 0.10253 0.07097 0.02500 0.01520
7.150 0.07789 0.10118 0.07034 0.02436 0.02329
7.200 0.07691 0.09985 0.06971 0.02375 0.02294
7.250 0.07335 0.09855 0.06909 0.02315 0.02520
7.300 0.08029 0.09726 0.06848 0.02256 0.01697
7.350 0.09380 0.09599 0.06786 0.02199 0.00219
7.400 0.09173 0.09475 0.06725 0.02143 0.00302
7.450 0.08983 0.09352 0.06664 0.02089 0.00369
7.500 0.08279 0.09231 0.06604 0.02036 0.00952
7.550 0.09049 0.09111 0.06544 0.01984 0.00062
7.600 0.09885 0.08994 0.06484 0.01934 -0.00891
7.650 0.08592 0.08878 0.06425 0.01885 0.00286
7.700 0.08403 0.08764 0.06366 0.01837 0.00361
7.750 0.08606 0.08652 0.06307 0.01791 0.00046
7.800 0.09090 0.08541 0.06249 0.01745 -0.00549
7.850 0.10041 0.08432 0.06191 0.01701 -0.01609
7.900 0.08850 0.08325 0.06134 0.01658 -0.00525
7.950 0.07738 0.08219 0.06077 0.01616 0.00481
8.000 0.08399 0.08115 0.06020 0.01575 -0.00284
8.050 0.08086 0.08012 0.05964 0.01535 -0.00074
8.100 0.06863 0.07911 0.05908 0.01496 0.01048
8.150 0.06296 0.07811 0.05852 0.01458 0.01515
8.200 0.05970 0.07712 0.05797 0.01421 0.01742
8.250 0.06503 0.07615 0.05742 0.01385 0.01112
8.300 0.07252 0.07520 0.05688 0.01350 0.00268
8.350 0.06576 0.07426 0.05634 0.01316 0.00850
8.400 0.05821 0.07333 0.05581 0.01283 0.01512
8.450 0.05636 0.07241 0.05527 0.01250 0.01605
8.500 0.07124 0.07151 0.05475 0.01219 0.00027
8.550 0.06906 0.07062 0.05422 0.01188 0.00156
8.600 0.05359 0.06974 0.05370 0.01158 0.01615
8.650 0.05766 0.06888 0.05319 0.01128 0.01122
8.700 0.05752 0.06803 0.05267 0.01100 0.01051
8.750 0.06173 0.06719 0.05217 0.01072 0.00546
8.800 0.06805 0.06636 0.05166 0.01045 -0.00169
8.850 0.07201 0.06554 0.05116 0.01018 -0.00647
8.900 0.07695 0.06473 0.05067 0.00992 -0.01222
8.950 0.07513 0.06394 0.05017 0.00967 -0.01119
9.000 0.07041 0.06316 0.04968 0.00943 -0.00725
9.050 0.06994 0.06238 0.04920 0.00919 -0.00756
9.100 0.05574 0.06162 0.04872 0.00896 0.00588
9.150 0.06344 0.06087 0.04824 0.00873 -0.00257
9.200 0.06246 0.06013 0.04777 0.00851 -0.00233
9.250 0.06162 0.05940 0.04730 0.00829 -0.00222
9.300 0.05000 0.05867 0.04683 0.00808 0.00867
9.350 0.04572 0.05796 0.04637 0.00788 0.01224
9.400 0.05094 0.05726 0.04592 0.00768 0.00632
9.450 0.04529 0.05657 0.04546 0.00748 0.01128
9.500 0.03679 0.05589 0.04501 0.00729 0.01910
9.550 0.03356 0.05521 0.04457 0.00711 0.02165
9.600 0.03599 0.05455 0.04412 0.00693 0.01856
9.650 0.04452 0.05389 0.04369 0.00675 0.00937
9.700 0.04935 0.05324 0.04325 0.00658 0.00389
9.750 0.05479 0.05260 0.04282 0.00642 -0.00219
9.800 0.05218 0.05197 0.04239 0.00625 -0.00021
9.850 0.05214 0.05135 0.04197 0.00610 -0.00079
9.900 0.05726 0.05074 0.04155 0.00594 -0.00652
9.950 0.06126 0.05013 0.04113 0.00579 -0.01113
10.000 0.05276 0.04954 0.04072 0.00564 -0.00322
10.050 0.05181 0.04895 0.04031 0.00550 -0.00286
10.100 0.05047 0.04837 0.03991 0.00536 -0.00210
10.150 0.04793 0.04779 0.03951 0.00523 -0.00014
10.200 0.05817 0.04722 0.03911 0.00509 -0.01095
10.250 0.05044 0.04667 0.03871 0.00496 -0.00377
10.300 0.04195 0.04611 0.03832 0.00484 0.00416
10.350 0.03399 0.04557 0.03794 0.00472 0.01158
10.400 0.03719 0.04503 0.03755 0.00460 0.00784
10.450 0.04173 0.04450 0.03717 0.00448 0.00277
10.500 0.03853 0.04398 0.03679 0.00437 0.00545
10.550 0.03163 0.04346 0.03642 0.00426 0.01183
10.600 0.04329 0.04295 0.03605 0.00415 -0.00034
10.650 0.03367 0.04244 0.03568 0.00404 0.00877
10.700 0.03443 0.04195 0.03532 0.00394 0.00752
10.750 0.02150 0.04146 0.03496 0.00384 0.01996
10.800 0.02825 0.04097 0.03460 0.00374 0.01272
10.850 0.03468 0.04049 0.03425 0.00365 0.00581
10.900 0.01892 0.04002 0.03390 0.00356 0.02110
10.950 0.02767 0.03955 0.03355 0.00347 0.01188
11.000 0.02996 0.03909 0.03321 0.00338 0.00913
11.050 0.02953 0.03864 0.03287 0.00329 0.00911
11.100 0.04354 0.03819 0.03253 0.00321 -0.00535
11.150 0.04423 0.03774 0.03220 0.00313 -0.00649
11.200 0.05465 0.03731 0.03187 0.00305 -0.01734
11.250 0.05519 0.03687 0.03154 0.00297 -0.01832
11.300 0.04500 0.03645 0.03122 0.00290 -0.00855
11.350 0.02800 0.03602 0.03090 0.00282 0.00802
11.400 0.02677 0.03561 0.03058 0.00275 0.00884
11.450 0.02187 0.03520 0.03026 0.00268 0.01333
11.500 0.02847 0.03479 0.02995 0.00261 0.00632
11.550 0.03047 0.03439 0.02964 0.00255 0.00392
11.600 0.02989 0.03399 0.02933 0.00248 0.00410
11.650 0.02520 0.03360 0.02903 0.00242 0.00840
11.700 0.01623 0.03322 0.02873 0.00236 0.01699
11.750 0.02052 0.03283 0.02843 0.00230 0.01231
11.800 0.01721 0.03246 0.02814 0.00224 0.01525
11.850 0.01456 0.03208 0.02785 0.00218 0.01752
11.900 0.01075 0.03172 0.02756 0.00213 0.02097
11.950 0.01206 0.03135 0.02727 0.00207 0.01929
12.000 0.02455 0.03099 0.02699 0.00202 0.00644
12.050 0.03298 0.03064 0.02671 0.00197 -0.00234
12.100 0.03290 0.03029 0.02643 0.00192 -0.00261
12.150 0.04318 0.02994 0.02615 0.00187 -0.01324
12.200 0.04173 0.02960 0.02588 0.00182 -0.01213
12.250 0.03759 0.02926 0.02561 0.00178 -0.00833
12.300 0.03026 0.02893 0.02535 0.00173 -0.00133
12.350 0.03025 0.02860 0.02508 0.00169 -0.00165
12.400 0.02706 0.02828 0.02482 0.00165 0.00122
12.450 0.02281 0.02795 0.02456 0.00161 0.00514
12.500 0.01943 0.02764 0.02430 0.00156 0.00821
12.550 0.02295 0.02732 0.02405 0.00152 0.00437
12.600 0.02132 0.02701 0.02380 0.00149 0.00569
12.650 0.03054 0.02671 0.02355 0.00145 -0.00383
12.700 0.03588 0.02640 0.02330 0.00141 -0.00948
12.750 0.03766 0.02611 0.02306 0.00138 -0.01155
12.800 0.03334 0.02581 0.02282 0.00134 -0.00753
12.850 0.03784 0.02552 0.02258 0.00131 -0.01232
12.900 0.02916 0.02523 0.02234 0.00127 -0.00393
12.950 0.02909 0.02494 0.02211 0.00124 -0.00415
13.000 0.03548 0.02466 0.02187 0.00121 -0.01082
13.050 0.03802 0.02438 0.02164 0.00118 -0.01364
13.100 0.03014 0.02411 0.02142 0.00115 -0.00603
13.150 0.03704 0.02384 0.02119 0.00112 -0.01320
13.200 0.03246 0.02357 0.02097 0.00109 -0.00889
13.250 0.01856 0.02330 0.02075 0.00106 0.00474
13.300 0.01750 0.02304 0.02053 0.00104 0.00554
13.350 0.01493 0.02278 0.02031 0.00101 0.00785
13.400 0.01271 0.02253 0.02010 0.00099 0.00982
13.450 0.01576 0.02227 0.01989 0.00096 0.00651
13.500 0.01827 0.02202 0.01968 0.00094 0.00375
13.550 0.01554 0.02178 0.01947 0.00091 0.00624
13.600 0.02386 0.02153 0.01926 0.00089 -0.00233
13.650 0.02600 0.02129 0.01906 0.00087 -0.00471
13.700 0.02310 0.02105 0.01886 0.00085 -0.00205
13.750 0.01830 0.02082 0.01866 0.00082 0.00252
13.800 0.02531 0.02058 0.01846 0.00080 -0.00473
13.850 0.02560 0.02035 0.01827 0.00078 -0.00525
13.900 0.02110 0.02013 0.01808 0.00076 -0.00097
13.950 0.02161 0.01990 0.01788 0.00074 -0.00171
14.000 0.02510 0.01968 0.01769 0.00072 -0.00542
14.050 0.02658 0.01946 0.01751 0.00071 -0.00712
14.100 0.02448 0.01924 0.01732 0.00069 -0.00524
14.150 0.01787 0.01903 0.01714 0.00067 0.00116
14.200 0.02063 0.01882 0.01696 0.00065 -0.00181
14.250 0.01689 0.01861 0.01678 0.00064 0.00172
14.300 0.02756 0.01840 0.01660 0.00062 -0.00916
14.350 0.03257 0.01819 0.01642 0.00061 -0.01438
14.400 0.03603 0.01799 0.01625 0.00059 -0.01804
14.450 0.02716 0.01779 0.01608 0.00058 -0.00937
14.500 0.02168 0.01759 0.01591 0.00056 -0.00409
14.550 0.01743 0.01740 0.01574 0.00055 -0.00003
14.600 0.02096 0.01720 0.01557 0.00053 -0.00376
14.650 0.02103 0.01701 0.01540 0.00052 -0.00402
14.700 0.02836 0.01682 0.01524 0.00051 -0.01154
14.750 0.02313 0.01664 0.01508 0.00049 -0.00649
14.800 0.02408 0.01645 0.01492 0.00048 -0.00763
14.850 0.02219 0.01627 0.01476 0.00047 -0.00592
14.900 0.01856 0.01609 0.01460 0.00046 -0.00247
14.950 0.01653 0.01591 0.01445 0.00044 -0.00062
15.000 0.02281 0.01573 0.01429 0.00043 -0.00708
15.050 0.02720 0.01556 0.01414 0.00042 -0.01164
15.100 0.02575 0.01539 0.01399 0.00041 -0.01036
15.150 0.03036 0.01522 0.01384 0.00040 -0.01514
15.200 0.02945 0.01505 0.01369 0.00039 -0.01440
15.250 0.02796 0.01488 0.01355 0.00038 -0.01308
15.300 0.01860 0.01472 0.01340 0.00037 -0.00388
15.350 0.01547 0.01456 0.01326 0.00036 -0.00091
15.400 0.01718 0.01439 0.01312 0.00035 -0.00279
15.450 0.01474 0.01424 0.01298 0.00034 -0.00050
15.500 0.01137 0.01408 0.01284 0.00034 0.00271
15.550 0.00759 0.01392 0.01270 0.00033 0.00633
15.600 0.00966 0.01377 0.01257 0.00032 0.00411
15.650 0.01540 0.01362 0.01244 0.00031 -0.00178
15.700 0.01485 0.01347 0.01230 0.00030 -0.00138
15.750 0.01155 0.01332 0.01217 0.00030 0.00177
15.800 0.00581 0.01317 0.01204 0.00029 0.00736
15.850 0.00650 0.01303 0.01191 0.00028 0.00653
15.900 0.01398 0.01288 0.01179 0.00027 -0.00110
15.950 0.01903 0.01274 0.01166 0.00027 -0.00629
16.000 0.01838 0.01260 0.01153 0.00026 -0.00578
16.050 0.02328 0.01246 0.01141 0.00025 -0.01082
16.100 0.02317 0.01233 0.01129 0.00025 -0.01084
16.150 0.01997 0.01219 0.01117 0.00024 -0.00778
16.200 0.01674 0.01206 0.01105 0.00023 -0.00468
16.250 0.01765 0.01192 0.01093 0.00023 -0.00573
16.300 0.01046 0.01179 0.01081 0.00022 0.00133
16.350 0.00479 0.01166 0.01070 0.00022 0.00687
16.400 0.00500 0.01153 0.01058 0.00021 0.00653
16.450 0.00567 0.01141 0.01047 0.00021 0.00574
16.500 0.00635 0.01128 0.01036 0.00020 0.00493
16.550 0.00843 0.01116 0.01025 0.00020 0.00273
16.600 0.01805 0.01104 0.01014 0.00019 -0.00701
16.650 0.01402 0.01091 0.01003 0.00019 -0.00311
16.700 0.01402 0.01079 0.00992 0.00018 -0.00323
16.750 0.01573 0.01068 0.00982 0.00018 -0.00505
16.800 0.02215 0.01056 0.00971 0.00017 -0.01159
16.850 0.01866 0.01044 0.00961 0.00017 -0.00822
16.900 0.01391 0.01033 0.00950 0.00016 -0.00358
16.950 0.00984 0.01022 0.00940 0.00016 0.00038
17.000 0.01376 0.01010 0.00930 0.00016 -0.00366
17.050 0.02019 0.00999 0.00920 0.00015 -0.01020
17.100 0.02531 0.00988 0.00910 0.00015 -0.01543
17.150 0.01983 0.00977 0.00900 0.00014 -0.01006
17.200 0.02067 0.00967 0.00891 0.00014 -0.01100
17.250 0.02099 0.00956 0.00881 0.00014 -0.01143
17.300 0.01678 0.00946 0.00872 0.00013 -0.00732
17.350 0.01776 0.00935 0.00862 0.00013 -0.00841
17.400 0.01209 0.00925 0.00853 0.00013 -0.00284
17.450 0.00578 0.00915 0.00844 0.00012 0.00337
17.500 0.01010 0.00905 0.00835 0.00012 -0.00105
17.550 0.00672 0.00895 0.00826 0.00012 0.00223
17.600 0.00948 0.00885 0.00817 0.00011 -0.00063
17.650 0.01071 0.00876 0.00808 0.00011 -0.00195
17.700 0.01402 0.00866 0.00800 0.00011 -0.00536
17.750 0.01809 0.00857 0.00791 0.00011 -0.00952
17.800 0.01674 0.00847 0.00783 0.00010 -0.00827
17.850 0.01954 0.00838 0.00774 0.00010 -0.01116
17.900 0.02553 0.00829 0.00766 0.00010 -0.01724
17.950 0.01950 0.00820 0.00758 0.00010 -0.01130
18.000 0.02023 0.00811 0.00750 0.00009 -0.01212
19.000 0.01420 0.00651 0.00604 0.00006 -0.00769
20.000 0.01932 0.00523 0.00486 0.00003 -0.01409
21.000 0.01885 0.00420 0.00391 0.00002 -0.01465
22.000 0.01493 0.00338 0.00315 0.00001 -0.01155
23.000 0.01122 0.00272 0.00254 0.00001 -0.00850
24.000 0.00298 0.00219 0.00204 0.00000 -0.00079
25.000 0.00058 0.00176 0.00164 0.00000 0.00118
26.000 0.00730 0.00141 0.00132 0.00000 -0.00589
27.000 0.01235 0.00114 0.00106 0.00000 -0.01121
28.000 0.01427 0.00091 0.00086 0.00000 -0.01336
29.000 0.01395 0.00074 0.00069 0.00000 -0.01321
30.000 0.01819 0.00059 0.00055 0.00000 -0.01760

参考

  1. 张蓉蓉, 秦朝朝, 龙金友, 杨明晖, 张冰. “丙烯酸分子的激发态超快预解离动力学”, 物理化学学报, 28(3):522-527, 2012
  2. Bumaliya Abulimiti, Rongshu Zhu, Jinyou Long, Yanqi Xu, Yuzhu Liu, Ahmed Yousif Ghazal, Minghui Yang, Bing Zhang. “Study of ultrafast dynamics of 2-picoline by time-resolved photoelectron imaging”, J. Chem. Phys. 134, 234301, 2011
  3. Ying Tang, Yoshi-ichi Suzuki, Huan Shen, Kentaro Sekiguchi, Naoya Kurahashi, Kiyoshi Nishizawa, Peng Zuo, Toshinori Suzuki. “Time-resolved photoelectron spectroscopy of bulk liquids at ultra-low kinetic energy”, Chem. Phys. Lett., 494:111-116, 2010

代码

# Language: clike
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Jicun LI: Jerkwin@gmail.com
% 2013-11-09: Demo !!! Convolution NOT used !!!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function PumpProb
	clc;

	[texp, Yexp] = textread('exp.dat', '%f %f');
	Ndat = size(texp);
	Yexp = Yexp/max(Yexp);

	LB = [0,   0,   0,   0,   0,   0  ];
	UB = [inf, inf, inf, inf, inf, inf];
	lsqoptions = optimset('lsqnonlin');
	lsqoptions.LM = 'on';
	lsqoptions.MaxFunEvals = 1000;
	lsqoptions.Tolx = 1e-6;                   % default is 1e-6
	lsqoptions.TolFun = 1e-6;                 % default is 1e-6
	lsqoptions.Display = 'iter';              % 'off' or 'final'
	lsqoptions.LineSearchType = 'cubicpoly';  % or 'quadcubic'

	a1 = 1; a2 = 1; a3 = 0; k = 1;
	Apump = 1; Spump= 70;

	fileID = fopen('exp_fit.dat', 'w');
	P0 = [ a1 a2 a3  k  Apump Spump ];
	Pfit = lsqnonlin(@(P)ObjFun(P, texp, Yexp), P0, LB, UB, lsqoptions);

	Pfit
	a1 = Pfit(1); a2 = Pfit(2); a3 = Pfit(3);
	k = Pfit(4); Apump = Pfit(5); Spump = Pfit(6);

	fprintf('T1= %f\nT2= %f\nT3= %f\n', 1/a1, 1/a2, 1/a3);
	fprintf('k = %f\n', k);
	fprintf('Apump= %f Spump= %f\n', Apump, Spump);

	Y0 = [0 0 1];
	options = odeset('RelTol',1e-6, 'AbsTol',[1e-6 1e-6 1e-6]);
	[t, Y] = ode45(@dY, texp, Y0, options, a1, a2, a3, Apump, Spump);
	Yfit = k*Y(:,1)+Y(:,2);
	Yfit = Yfit/max(Yfit);
	Y = Y/max(Yfit);

	fprintf(fileID,'%8s%12s%12s%12s%12s%12s\n', ...
		't','Yexp', 'Yfit', 'Y1','Y2', 'Yfit-Yexp');
	for i=1:Ndat;
		fprintf(fileID, '%8.3f%12.5f%12.5f%12.5f%12.5f%12.5f\n', ...
			t(i), Yexp(i), Yfit(i), k*Y(i,1), Y(i,2), Yfit(i)-Yexp(i));
	end
end
%%
function ObjFun = ObjFun(P, texp, Yexp)
	a1 = P(1); a2 = P(2); a3 = P(3);
	k = P(4); Apump = P(5); Spump = P(6);

	Y0 = [0 0 1];
	options = odeset('RelTol',1e-6, 'AbsTol',[1e-6 1e-6 1e-6]);
	[t, Y] = ode45(@dY, texp, Y0, options, a1, a2, a3, Apump, Spump);
	Yfit = k*Y(:,1)+Y(:,2);
	Yfit = Yfit/max(Yfit);

	ObjFun = Yexp-Yfit;
end
%%
function dY = dY(t, Y, a1, a2, a3, Apump, Spump)
	dY = zeros(3,1);
	Ipump = Apump*exp(-Spump*t^2);
	dY(1) = a1*Y(2) - a2*Y(1);
	dY(2) = -(a1+a3)*Y(2) + Ipump*Y(3);
	dY(3) = a3*Y(2) + a2*Y(1) - Ipump*Y(3);
end
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