Table 5: 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 para-water in Table 3. 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.
00,0 $a^{(n)}_{\leftarrow 1_{1,1}}$ $a^{(n)}_{\leftarrow 2_{0,2}}$ $a^{(n)}_{\leftarrow 2_{1,1}}$ $a^{(n)}_{\leftarrow 2_{2,0}}$ $a^{(n)}_{\leftarrow 3_{1,3}}$ $a^{(n)}_{\leftarrow 3_{2,2}}$ $a^{(n)}_{\leftarrow 4_{0,4}}$ $a^{(n)}_{\leftarrow 4_{1,3}}$ $a^{(n)}_{\leftarrow 3_{3,1}}$
0 -9.2196 -10.5644 -12.5365 -10.0061 -11.2977 -12.8447 -11.8093 -13.6415 -11.9075
1 -4.8077 0.7471 12.0237 -8.0560 -2.6392 -2.7402 -1.2909 8.9455 -3.8667
2 11.9283 -3.1298 -35.7592 21.1002 7.1789 21.6079 3.4620 -27.4139 11.8491
3 -14.3880 3.7884 42.8885 -25.0268 -9.1812 -42.8813 -5.1317 35.4918 -16.4370
4 6.6227 -1.2576 -18.3335 11.5425 4.7295 26.0394 2.9875 -17.0599 8.5438
11,1                  $a^{(n)}_{\leftarrow 2_{0,2}}$ $a^{(n)}_{\leftarrow 2_{1,1}}$ $a^{(n)}_{\leftarrow 2_{2,0}}$ $a^{(n)}_{\leftarrow 3_{1,3}}$ $a^{(n)}_{\leftarrow 3_{2,2}}$ $a^{(n)}_{\leftarrow 4_{0,4}}$ $a^{(n)}_{\leftarrow 4_{1,3}}$ $a^{(n)}_{\leftarrow 3_{3,1}}$
0   -10.7363 -10.2653 -9.6180 -10.4682 -10.7198 -11.4634 -11.8217 -10.8323
1   8.0746 3.6744 -4.8781 -1.8012 -6.4847 0.2937 -1.4055 -4.8412
2   -23.9005 -14.1624 12.0389 4.8826 22.0777 -1.7585 4.6025 14.1863
3   29.1820 19.2240 -13.8634 -6.9287 -32.6194 3.5667 -6.8634 -18.9250
4   -12.8709 -8.9750 6.4187 3.9533 17.1533 -2.2181 3.4001 9.4947
20,2                                   $a^{(n)}_{\leftarrow 2_{1,1}}$ $a^{(n)}_{\leftarrow 2_{2,0}}$ $a^{(n)}_{\leftarrow 3_{1,3}}$ $a^{(n)}_{\leftarrow 3_{2,2}}$ $a^{(n)}_{\leftarrow 4_{0,4}}$ $a^{(n)}_{\leftarrow 4_{1,3}}$ $a^{(n)}_{\leftarrow 3_{3,1}}$
0     -9.9342 -9.9715 -9.6593 -9.8947 -10.4306 -12.7925 -11.9214
1     3.6405 -4.4341 -2.2514 -6.6853 -3.3175 11.1765 0.9281
2     -14.0091 12.7021 4.0588 21.2566 7.8651 -36.0036 -1.5458
3     20.0353 -15.6973 -5.0059 -31.0300 -9.0122 48.1492 -0.1500
4     -10.0308 7.2244 3.0100 16.2566 4.1399 -23.6727 1.1650
21,1                                                    $a^{(n)}_{\leftarrow 2_{2,0}}$ $a^{(n)}_{\leftarrow 3_{1,3}}$ $a^{(n)}_{\leftarrow 3_{2,2}}$ $a^{(n)}_{\leftarrow 4_{0,4}}$ $a^{(n)}_{\leftarrow 4_{1,3}}$ $a^{(n)}_{\leftarrow 3_{3,1}}$
0       -9.9108 -10.8548 -9.6450 -11.3711 -10.4960 -10.6282
1       1.9280 5.2417 -6.4971 3.0639 -4.6407 -4.4253
2       -8.2382 -16.2733 19.3304 -11.7300 11.9976 12.6545
3       11.5316 20.3823 -27.1327 17.7318 -15.2811 -17.0611
4       -5.3817 -9.0809 13.8905 -9.4384 7.3365 8.7126
22,0                                                                     $a^{(n)}_{\leftarrow 3_{1,3}}$ $a^{(n)}_{\leftarrow 3_{2,2}}$ $a^{(n)}_{\leftarrow 4_{0,4}}$ $a^{(n)}_{\leftarrow 4_{1,3}}$ $a^{(n)}_{\leftarrow 3_{3,1}}$
0         -10.8154 -9.5935 -12.7240 -11.3048 -10.0644
1         2.7559 -4.2012 15.0927 1.0408 -2.7224
2         -7.3990 10.5606 -54.6129 -1.1575 8.4156
3         4.4787 -14.5285 81.0160 -0.3876 -12.0942
4         -3.4467 7.3934 -43.1518 0.5005 6.4608


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