Table 4: Coefficients $a^{(n)}_{j_2=1;j\alpha \leftarrow j'\alpha '}$ (n = 0 to 4) of the polynomial fit (Eq. (3)) to the effective de-excitation rate coefficients of ortho-water in Table 2. The effective excitation rate coefficients can be obtained by detailed balance. The first column gives the final state and the polynomial order n, the following columns give the fitting coefficients for various initial states. The levels are labelled with jK-1K1. We emphasize that these fits are only valid in the temperature range from 5 K to 20 K.
10,1 $a^{(n)}_{\leftarrow 1_{1,0}}$ $a^{(n)}_{\leftarrow 2_{1,2}}$ $a^{(n)}_{\leftarrow 2_{2,1}}$ $a^{(n)}_{\leftarrow 3_{0,3}}$ $a^{(n)}_{\leftarrow 3_{1,2}}$ $a^{(n)}_{\leftarrow 3_{2,1}}$ $a^{(n)}_{\leftarrow 4_{1,4}}$ $a^{(n)}_{\leftarrow 3_{3,0}}$ $a^{(n)}_{\leftarrow 4_{2,3}}$
0 -10.1876 -9.8101 -10.1703 -10.5424 -12.2931 -9.6483 -11.1640 -11.3694 -12.4494
1 6.5796 0.5647 -3.0277 -0.6399 9.2629 -13.2040 -3.0869 -5.0876 -0.7116
2 -22.7661 -5.9239 7.4800 0.5258 -29.2146 36.8854 9.9865 15.9120 6.3499
3 31.4597 9.9441 -9.2544 0.0215 37.5916 -46.7970 -14.0478 -22.1115 -13.6319
4 -15.6234 -5.1116 4.6355 0.0989 -17.6172 22.2593 7.1424 11.2390 8.6836
11,0                  $a^{(n)}_{\leftarrow 2_{1,2}}$ $a^{(n)}_{\leftarrow 2_{2,1}}$ $a^{(n)}_{\leftarrow 3_{0,3}}$ $a^{(n)}_{\leftarrow 3_{1,2}}$ $a^{(n)}_{\leftarrow 3_{2,1}}$ $a^{(n)}_{\leftarrow 4_{1,4}}$ $a^{(n)}_{\leftarrow 3_{3,0}}$ $a^{(n)}_{\leftarrow 4_{2,3}}$
0   -10.8118 -9.7732 -11.4567 -10.1456 -10.3113 -11.2115 -10.6512 -11.3165
1   7.4280 -3.1678 5.0975 -5.2141 -9.7549 -3.1187 -6.1335 -5.1081
2   -23.3047 8.0202 -13.7565 12.4640 27.6769 10.0179 18.9963 16.2240
3   30.0489 -10.1443 16.0631 -15.3446 -35.2199 -14.3942 -26.1038 -23.4875
4   -14.0322 5.0836 -6.6633 7.4845 16.6678 7.3682 13.1249 12.3566
21,2                                   $a^{(n)}_{\leftarrow 2_{2,1}}$ $a^{(n)}_{\leftarrow 3_{0,3}}$ $a^{(n)}_{\leftarrow 3_{1,2}}$ $a^{(n)}_{\leftarrow 3_{2,1}}$ $a^{(n)}_{\leftarrow 4_{1,4}}$ $a^{(n)}_{\leftarrow 3_{3,0}}$ $a^{(n)}_{\leftarrow 4_{2,3}}$
0     -10.1667 -10.2893 -10.2134 -9.8133 -10.3763 -10.6506 -11.6818
1     1.7849 3.5690 0.3910 -6.0796 -4.0238 -6.3023 -0.8441
2     -6.5466 -13.9411 -2.5257 16.9870 11.5290 19.7761 6.2154
3     7.6661 19.5139 2.9383 -22.4136 -16.0531 -28.3573 -12.1634
4     -2.9588 -9.3103 -0.9904 11.1376 8.3618 14.9054 7.5419
22,1                                                    $a^{(n)}_{\leftarrow 3_{0,3}}$ $a^{(n)}_{\leftarrow 3_{1,2}}$ $a^{(n)}_{\leftarrow 3_{2,1}}$ $a^{(n)}_{\leftarrow 4_{1,4}}$ $a^{(n)}_{\leftarrow 3_{3,0}}$ $a^{(n)}_{\leftarrow 4_{2,3}}$
0       -12.5143 -11.3874 -8.9216 -10.5847 -9.9467 -10.4404
1       16.9687 10.5262 -9.3767 -4.1839 -3.8886 -6.4087
2       -48.2815 -34.1153 23.6301 9.8197 12.2989 19.9189
3       56.9744 44.0339 -28.4478 -10.7217 -17.6984 -29.2215
4       -24.2411 -20.4615 13.0161 4.2197 9.2371 15.5988
30,3                                                                     $a^{(n)}_{\leftarrow 3_{1,2}}$ $a^{(n)}_{\leftarrow 3_{2,1}}$ $a^{(n)}_{\leftarrow 4_{1,4}}$ $a^{(n)}_{\leftarrow 3_{3,0}}$ $a^{(n)}_{\leftarrow 4_{2,3}}$
0         -10.1031 -10.2176 -9.6188 -12.0621 -10.2604
1         4.4953 -3.6094 -3.9802 1.4928 -4.3320
2         -16.4020 12.8009 10.3903 4.3519 13.7521
3         22.5214 -19.8468 -14.2019 -14.1974 -20.5819
4         -11.0314 10.9007 7.5242 10.0233 11.1931


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