Two-photon energy distribution functions This is a set of six tables giving the photon energy distribution functions for two photon decay of the 2 1S0 states of heliumlike ions with Z=2...30. In the first four rows of each table, we list: Z = nuclear charge of the ion Omega = maximum photon energy (a.u.) lambda = wavelength associated with Omega in Angstrom rate = two photon rate (1/sec). In the remaining 51 rows of each table, we list: 1st column: y = omega/Omega (fraction of the maximum energy) 0.0 - 0.5 2nd-6th column: f(y) =(1/rate)*(d rate/dy)(y) The function f(y) is symmetric with wespect to y = 0.5. Note that Interal_0^(1/2) f(y) dy = 1 for all cases. Z = 2 3 4 5 6 Omega = 0.757481 2.23870 4.47052 7.45298 11.1864 lambda= 601.512 203.526 101.920 61.1344 40.7312 rate = 5.102[1] 1.940[3] 1.816[4] 9.211[4] 3.300[5] 0.000 0.00000 0.00000 0.00000 0.00000 0.00000 0.010 0.02034 0.02988 0.03916 0.04796 0.05615 0.020 0.09681 0.12882 0.15567 0.17833 0.19754 0.030 0.21242 0.26547 0.30590 0.33778 0.36344 0.040 0.34804 0.41655 0.46528 0.50199 0.53056 0.050 0.49162 0.57004 0.62293 0.66147 0.69076 0.060 0.63613 0.71996 0.77411 0.81255 0.84124 0.070 0.77764 0.86344 0.91688 0.95401 0.98133 0.080 0.91399 0.99923 1.05064 1.08572 1.11121 0.090 1.04410 1.12691 1.17543 1.20803 1.23145 0.100 1.16747 1.24653 1.29163 1.32148 1.34271 0.110 1.28401 1.35836 1.39971 1.42670 1.44572 0.120 1.39382 1.46281 1.50024 1.52433 1.54115 0.130 1.49713 1.56031 1.59375 1.61497 1.62964 0.140 1.59422 1.65134 1.68078 1.69919 1.71177 0.150 1.68542 1.73632 1.76183 1.77751 1.78808 0.160 1.77106 1.81569 1.83735 1.85040 1.85906 0.170 1.85147 1.88984 1.90777 1.91828 1.92512 0.180 1.92697 1.95915 1.97346 1.98157 1.98667 0.190 1.99784 2.02395 2.03479 2.04059 2.04405 0.200 2.06438 2.08456 2.09206 2.09568 2.09758 0.210 2.12685 2.14126 2.14558 2.14711 2.14754 0.220 2.18549 2.19431 2.19559 2.19515 2.19420 0.230 2.24053 2.24396 2.24234 2.24004 2.23777 0.240 2.29218 2.29041 2.28605 2.28197 2.27848 0.250 2.34064 2.33388 2.32690 2.32116 2.31650 0.260 2.38607 2.37454 2.36509 2.35777 2.35202 0.270 2.42864 2.41255 2.40076 2.39196 2.38518 0.280 2.46851 2.44807 2.43407 2.42388 2.41613 0.290 2.50581 2.48124 2.46515 2.45365 2.44499 0.300 2.54066 2.51218 2.49412 2.48139 2.47189 0.310 2.57320 2.54100 2.52110 2.50722 2.49693 0.320 2.60351 2.56781 2.54619 2.53123 2.52020 0.330 2.63170 2.59271 2.56947 2.55351 2.54179 0.340 2.65786 2.61578 2.59103 2.57414 2.56178 0.350 2.68207 2.63711 2.61095 2.59320 2.58024 0.360 2.70440 2.65675 2.62930 2.61074 2.59724 0.370 2.72492 2.67479 2.64614 2.62684 2.61284 0.380 2.74370 2.69127 2.66152 2.64155 2.62708 0.390 2.76078 2.70625 2.67550 2.65491 2.64003 0.400 2.77622 2.71978 2.68812 2.66698 2.65171 0.410 2.79006 2.73190 2.69942 2.67778 2.66217 0.420 2.80235 2.74265 2.70945 2.68735 2.67145 0.430 2.81310 2.75206 2.71822 2.69574 2.67956 0.440 2.82237 2.76016 2.72576 2.70295 2.68655 0.450 2.83017 2.76697 2.73211 2.70901 2.69242 0.460 2.83652 2.77252 2.73728 2.71395 2.69720 0.470 2.84144 2.77681 2.74128 2.71777 2.70090 0.480 2.84494 2.77987 2.74413 2.72050 2.70354 0.490 2.84704 2.78170 2.74584 2.72213 2.70512 0.500 2.84774 2.78231 2.74641 2.72267 2.70565 Z = 7 8 9 10 11 Omega = 15.6713 20.9082 26.8979 33.6412 41.1391 lambda= 29.0745 21.7921 16.9394 13.5439 11.0754 rate = 9.444[5] 2.310[6] 5.029[6] 1.001[7] 1.856[7] 0.000 0.00000 0.00000 0.00000 0.00000 0.00000 0.010 0.06370 0.07061 0.07687 0.08253 0.08761 0.020 0.21393 0.22794 0.23997 0.25030 0.25918 0.030 0.38444 0.40180 0.41628 0.42842 0.43865 0.040 0.55335 0.57180 0.58691 0.59941 0.60980 0.050 0.71370 0.73200 0.74682 0.75894 0.76892 0.060 0.86340 0.88089 0.89492 0.90631 0.91562 0.070 1.00219 1.01851 1.03151 1.04200 1.05051 0.080 1.13050 1.14548 1.15733 1.16683 1.17451 0.090 1.24903 1.26258 1.27324 1.28176 1.28860 0.100 1.35853 1.37065 1.38014 1.38767 1.39369 0.110 1.45978 1.47049 1.47882 1.48540 1.49064 0.120 1.55349 1.56282 1.57005 1.57573 1.58022 0.130 1.64031 1.64833 1.65450 1.65932 1.66311 0.140 1.72085 1.72762 1.73278 1.73679 1.73992 0.150 1.79564 1.80121 1.80543 1.80868 1.81118 0.160 1.86516 1.86961 1.87294 1.87546 1.87738 0.170 1.92985 1.93324 1.93572 1.93758 1.93895 0.180 1.99010 1.99248 1.99418 1.99540 1.99626 0.190 2.04625 2.04769 2.04864 2.04927 2.04966 0.200 2.09862 2.09917 2.09943 2.09951 2.09945 0.210 2.14749 2.14721 2.14681 2.14637 2.14590 0.220 2.19312 2.19205 2.19104 2.19011 2.18925 0.230 2.23573 2.23391 2.23233 2.23095 2.22973 0.240 2.27552 2.27302 2.27089 2.26909 2.26753 0.250 2.31269 2.30954 2.30691 2.30471 2.30284 0.260 2.34740 2.34364 2.34054 2.33797 2.33581 0.270 2.37981 2.37548 2.37194 2.36902 2.36658 0.280 2.41006 2.40519 2.40124 2.39800 2.39530 0.290 2.43826 2.43290 2.42856 2.42502 2.42208 0.300 2.46454 2.45871 2.45401 2.45019 2.44703 0.310 2.48900 2.48273 2.47770 2.47362 2.47026 0.320 2.51173 2.50506 2.49972 2.49539 2.49184 0.330 2.53282 2.52577 2.52014 2.51559 2.51186 0.340 2.55235 2.54495 2.53905 2.53429 2.53040 0.350 2.57038 2.56266 2.55652 2.55156 2.54752 0.360 2.58699 2.57897 2.57259 2.56746 2.56328 0.370 2.60222 2.59393 2.58734 2.58205 2.57774 0.380 2.61613 2.60759 2.60081 2.59537 2.59095 0.390 2.62877 2.62000 2.61305 2.60748 2.60295 0.400 2.64018 2.63121 2.62410 2.61840 2.61378 0.410 2.65040 2.64124 2.63399 2.62819 2.62348 0.420 2.65945 2.65013 2.64276 2.63686 2.63207 0.430 2.66738 2.65791 2.65043 2.64445 2.63960 0.440 2.67420 2.66461 2.65704 2.65098 2.64607 0.450 2.67993 2.67024 2.66259 2.65647 2.65151 0.460 2.68460 2.67483 2.66711 2.66094 2.65594 0.470 2.68821 2.67838 2.67061 2.66440 2.65938 0.480 2.69079 2.68090 2.67310 2.66686 2.66182 0.490 2.69233 2.68242 2.67459 2.66834 2.66328 0.500 2.69284 2.68292 2.67509 2.66883 2.66377 Z = 12 13 14 15 16 Omega = 49.3926 58.4029 68.1713 78.6993 89.9883 lambda= 9.22474 7.80156 6.68365 5.78955 5.06325 rate = 3.249[7] 5.421[7] 8.685[7] 1.344[8] 2.020[8] 0.000 0.00000 0.00000 0.00000 0.00000 0.00000 0.010 0.09214 0.09615 0.09967 0.10275 0.10540 0.020 0.26680 0.27332 0.27888 0.28358 0.28752 0.030 0.44726 0.45452 0.46060 0.46567 0.46984 0.040 0.61845 0.62566 0.63164 0.63656 0.64058 0.050 0.77717 0.78399 0.78960 0.79418 0.79788 0.060 0.92327 0.92954 0.93467 0.93882 0.94214 0.070 1.05746 1.06313 1.06774 1.07145 1.07438 0.080 1.18075 1.18580 1.18989 1.19315 1.19571 0.090 1.29412 1.29858 1.30216 1.30499 1.30719 0.100 1.39853 1.40241 1.40550 1.40793 1.40980 0.110 1.49482 1.49816 1.50081 1.50286 1.50442 0.120 1.58379 1.58661 1.58883 1.59053 1.59181 0.130 1.66609 1.66844 1.67027 1.67165 1.67266 0.140 1.74236 1.74426 1.74572 1.74680 1.74758 0.150 1.81311 1.81460 1.81572 1.81653 1.81709 0.160 1.87884 1.87994 1.88075 1.88131 1.88167 0.170 1.93997 1.94071 1.94123 1.94155 1.94173 0.180 1.99687 1.99728 1.99753 1.99764 1.99765 0.190 2.04988 2.04998 2.04998 2.04990 2.04976 0.200 2.09931 2.09912 2.09890 2.09863 2.09835 0.210 2.14543 2.14497 2.14453 2.14410 2.14369 0.220 2.18847 2.18777 2.18713 2.18654 2.18602 0.230 2.22866 2.22773 2.22691 2.22618 2.22555 0.240 2.26619 2.26504 2.26406 2.26320 2.26247 0.250 2.30125 2.29990 2.29876 2.29778 2.29696 0.260 2.33398 2.33245 2.33116 2.33007 2.32918 0.270 2.36454 2.36284 2.36142 2.36023 2.35926 0.280 2.39306 2.39119 2.38965 2.38837 2.38733 0.290 2.41965 2.41764 2.41598 2.41461 2.41352 0.300 2.44443 2.44228 2.44052 2.43907 2.43792 0.310 2.46749 2.46521 2.46335 2.46183 2.46063 0.320 2.48892 2.48653 2.48458 2.48299 2.48174 0.330 2.50880 2.50630 2.50427 2.50262 2.50133 0.340 2.52721 2.52461 2.52251 2.52080 2.51947 0.350 2.54421 2.54152 2.53935 2.53759 2.53623 0.360 2.55987 2.55709 2.55486 2.55305 2.55166 0.370 2.57423 2.57138 2.56908 2.56724 2.56581 0.380 2.58735 2.58443 2.58208 2.58020 2.57874 0.390 2.59926 2.59628 2.59389 2.59197 2.59050 0.400 2.61002 2.60698 2.60454 2.60260 2.60110 0.410 2.61965 2.61656 2.61409 2.61211 2.61060 0.420 2.62819 2.62506 2.62255 2.62055 2.61902 0.430 2.63566 2.63249 2.62995 2.62793 2.62639 0.440 2.64209 2.63889 2.63632 2.63429 2.63273 0.450 2.64750 2.64427 2.64168 2.63963 2.63807 0.460 2.65190 2.64864 2.64604 2.64398 2.64241 0.470 2.65531 2.65204 2.64942 2.64735 2.64577 0.480 2.65774 2.65445 2.65183 2.64975 2.64817 0.490 2.65919 2.65590 2.65327 2.65119 2.64960 0.500 2.65968 2.65638 2.65375 2.65166 2.65008 Z = 17 18 19 20 21 Omega = 102.040 114.856 128.439 142.789 157.911 lambda= 4.46524 3.96699 3.54748 3.19095 2.88538 rate = 2.957[8] 4.230[8] 5.930[8] 8.163[8] 1.108[9] 0.000 0.00000 0.00000 0.00000 0.00000 0.00000 0.010 0.10766 0.10955 0.11110 0.11234 0.11328 0.020 0.29077 0.29339 0.29546 0.29702 0.29812 0.030 0.47323 0.47592 0.47797 0.47946 0.48043 0.040 0.64380 0.64630 0.64817 0.64947 0.65025 0.050 0.80080 0.80304 0.80468 0.80576 0.80635 0.060 0.94474 0.94670 0.94808 0.94896 0.94937 0.070 1.07665 1.07833 1.07948 1.08016 1.08042 0.080 1.19766 1.19907 1.20001 1.20052 1.20064 0.090 1.30884 1.31001 1.31076 1.31111 1.31112 0.100 1.41118 1.41213 1.41270 1.41293 1.41284 0.110 1.50555 1.50630 1.50671 1.50683 1.50666 0.120 1.59271 1.59328 1.59356 1.59358 1.59336 0.130 1.67336 1.67377 1.67393 1.67386 1.67359 0.140 1.74809 1.74835 1.74841 1.74827 1.74797 0.150 1.81743 1.81756 1.81753 1.81734 1.81701 0.160 1.88185 1.88187 1.88176 1.88152 1.88117 0.170 1.94177 1.94169 1.94151 1.94124 1.94088 0.180 1.99757 1.99740 1.99716 1.99685 1.99649 0.190 2.04956 2.04931 2.04902 2.04870 2.04833 0.200 2.09805 2.09773 2.09740 2.09705 2.09670 0.210 2.14330 2.14292 2.14255 2.14219 2.14185 0.220 2.18554 2.18511 2.18471 2.18435 2.18401 0.230 2.22500 2.22451 2.22409 2.22372 2.22341 0.240 2.26185 2.26133 2.26088 2.26052 2.26022 0.250 2.29628 2.29572 2.29526 2.29489 2.29462 0.260 2.32844 2.32784 2.32737 2.32701 2.32675 0.270 2.35847 2.35784 2.35736 2.35701 2.35678 0.280 2.38650 2.38585 2.38536 2.38501 2.38480 0.290 2.41264 2.41197 2.41147 2.41114 2.41095 0.300 2.43701 2.43631 2.43582 2.43549 2.43533 0.310 2.45969 2.45898 2.45848 2.45817 2.45803 0.320 2.48077 2.48005 2.47955 2.47925 2.47913 0.330 2.50034 2.49960 2.49910 2.49881 2.49872 0.340 2.51845 2.51771 2.51721 2.51694 2.51687 0.350 2.53519 2.53443 2.53394 2.53368 2.53363 0.360 2.55060 2.54984 2.54934 2.54910 2.54907 0.370 2.56474 2.56397 2.56348 2.56325 2.56324 0.380 2.57766 2.57688 2.57640 2.57617 2.57619 0.390 2.58939 2.58862 2.58814 2.58792 2.58795 0.400 2.59999 2.59921 2.59873 2.59853 2.59858 0.410 2.60948 2.60870 2.60822 2.60803 2.60809 0.420 2.61789 2.61711 2.61664 2.61645 2.61653 0.430 2.62525 2.62447 2.62400 2.62382 2.62391 0.440 2.63159 2.63080 2.63034 2.63017 2.63027 0.450 2.63692 2.63613 2.63567 2.63550 2.63561 0.460 2.64126 2.64047 2.64001 2.63985 2.63996 0.470 2.64462 2.64383 2.64337 2.64321 2.64333 0.480 2.64701 2.64622 2.64576 2.64561 2.64574 0.490 2.64844 2.64765 2.64720 2.64704 2.64717 0.500 2.64892 2.64813 2.64767 2.64752 2.64765 Z = 22 23 24 25 26 Omega = 173.805 190.475 207.922 226.150 245.161 lambda= 2.62152 2.39209 2.19136 2.01474 1.85851 rate = 1.478[9] 1.946[9] 2.531[9] 3.249[9] 4.143[9] 0.000 0.00000 0.00000 0.00000 0.00000 0.00000 0.010 0.11396 0.11439 0.11460 0.11461 0.11442 0.020 0.29878 0.29907 0.29899 0.29859 0.29790 0.030 0.48093 0.48100 0.48067 0.47999 0.47897 0.040 0.65056 0.65045 0.64993 0.64905 0.64783 0.050 0.80649 0.80621 0.80556 0.80455 0.80322 0.060 0.94936 0.94896 0.94820 0.94712 0.94573 0.070 1.08028 1.07979 1.07897 1.07784 1.07643 0.080 1.20040 1.19985 1.19898 1.19785 1.19645 0.090 1.31081 1.31021 1.30933 1.30820 1.30683 0.100 1.41247 1.41184 1.41096 1.40986 1.40854 0.110 1.50625 1.50561 1.50474 1.50368 1.50242 0.120 1.59291 1.59227 1.59143 1.59042 1.58924 0.130 1.67313 1.67250 1.67169 1.67074 1.66965 0.140 1.74749 1.74688 1.74612 1.74524 1.74423 0.150 1.81653 1.81595 1.81524 1.81443 1.81351 0.160 1.88071 1.88016 1.87950 1.87877 1.87795 0.170 1.94043 1.93992 1.93932 1.93866 1.93794 0.180 1.99606 1.99559 1.99505 1.99448 1.99385 0.190 2.04793 2.04750 2.04703 2.04654 2.04601 0.200 2.09632 2.09594 2.09554 2.09512 2.09469 0.210 2.14150 2.14117 2.14083 2.14050 2.14017 0.220 2.18370 2.18342 2.18315 2.18290 2.18266 0.230 2.22312 2.22290 2.22269 2.22252 2.22238 0.240 2.25997 2.25979 2.25965 2.25957 2.25952 0.250 2.29440 2.29428 2.29420 2.29420 2.29424 0.260 2.32658 2.32651 2.32649 2.32656 2.32669 0.270 2.35664 2.35661 2.35667 2.35681 2.35703 0.280 2.38470 2.38473 2.38484 2.38506 2.38536 0.290 2.41089 2.41096 2.41114 2.41142 2.41180 0.300 2.43530 2.43542 2.43565 2.43601 2.43646 0.310 2.45803 2.45820 2.45849 2.45890 2.45943 0.320 2.47917 2.47939 2.47972 2.48020 2.48080 0.330 2.49880 2.49905 2.49944 2.49998 2.50064 0.340 2.51697 2.51727 2.51770 2.51830 2.51903 0.350 2.53376 2.53410 2.53458 2.53523 2.53602 0.360 2.54923 2.54960 2.55013 2.55083 2.55167 0.370 2.56343 2.56383 2.56440 2.56514 2.56604 0.380 2.57640 2.57684 2.57744 2.57823 2.57918 0.390 2.58819 2.58866 2.58930 2.59012 2.59112 0.400 2.59884 2.59933 2.60000 2.60086 2.60190 0.410 2.60837 2.60889 2.60959 2.61049 2.61156 0.420 2.61683 2.61737 2.61809 2.61902 2.62012 0.430 2.62423 2.62479 2.62554 2.62649 2.62762 0.440 2.63060 2.63117 2.63194 2.63292 2.63408 0.450 2.63595 2.63654 2.63733 2.63833 2.63951 0.460 2.64031 2.64092 2.64172 2.64273 2.64393 0.470 2.64369 2.64431 2.64512 2.64614 2.64735 0.480 2.64610 2.64672 2.64754 2.64857 2.64979 0.490 2.64754 2.64816 2.64899 2.65003 2.65125 0.500 2.64802 2.64864 2.64947 2.65051 2.65174 Z = 27 28 29 30 Omega = 264.958 285.544 306.923 329.097 lambda= 1.71964 1.59567 1.48452 1.38450 rate = 5.223[9] 6.517[9] 8.092[9] 9.938[9] 0.000 0.00000 0.00000 0.00000 0.00000 0.010 0.11408 0.11358 0.11294 0.11219 0.020 0.29693 0.29571 0.29426 0.29260 0.030 0.47764 0.47603 0.47415 0.47203 0.040 0.64630 0.64448 0.64238 0.64004 0.050 0.80158 0.79966 0.79747 0.79503 0.060 0.94405 0.94209 0.93989 0.93744 0.070 1.07475 1.07281 1.07064 1.06825 0.080 1.19480 1.19291 1.19081 1.18850 0.090 1.30523 1.30343 1.30142 1.29922 0.100 1.40702 1.40530 1.40341 1.40134 0.110 1.50099 1.49938 1.49761 1.49568 0.120 1.58790 1.58641 1.58477 1.58299 0.130 1.66841 1.66704 1.66554 1.66392 0.140 1.74310 1.74186 1.74050 1.73904 0.150 1.81249 1.81138 1.81017 1.80887 0.160 1.87704 1.87605 1.87499 1.87385 0.170 1.93715 1.93629 1.93538 1.93440 0.180 1.99317 1.99245 1.99168 1.99086 0.190 2.04544 2.04485 2.04423 2.04356 0.200 2.09424 2.09378 2.09330 2.09279 0.210 2.13983 2.13949 2.13915 2.13879 0.220 2.18243 2.18222 2.18201 2.18180 0.230 2.22226 2.22217 2.22209 2.22202 0.240 2.25950 2.25952 2.25958 2.25965 0.250 2.29433 2.29446 2.29464 2.29484 0.260 2.32688 2.32712 2.32742 2.32776 0.270 2.35731 2.35766 2.35807 2.35853 0.280 2.38573 2.38618 2.38671 2.38729 0.290 2.41227 2.41282 2.41345 2.41415 0.300 2.43701 2.43766 2.43839 2.43920 0.310 2.46007 2.46080 2.46163 2.46255 0.320 2.48151 2.48233 2.48326 2.48428 0.330 2.50143 2.50233 2.50334 2.50446 0.340 2.51988 2.52086 2.52196 2.52316 0.350 2.53694 2.53799 2.53917 2.54045 0.360 2.55266 2.55378 2.55502 2.55639 0.370 2.56708 2.56827 2.56958 2.57102 0.380 2.58027 2.58151 2.58289 2.58440 0.390 2.59226 2.59356 2.59500 2.59656 0.400 2.60309 2.60443 2.60593 2.60755 0.410 2.61279 2.61418 2.61572 2.61740 0.420 2.62139 2.62282 2.62441 2.62613 0.430 2.62892 2.63039 2.63201 2.63378 0.440 2.63541 2.63690 2.63856 2.64036 0.450 2.64086 2.64238 2.64407 2.64590 0.460 2.64530 2.64685 2.64855 2.65041 0.470 2.64874 2.65030 2.65203 2.65390 0.480 2.65119 2.65277 2.65450 2.65639 0.490 2.65266 2.65424 2.65599 2.65788 0.500 2.65315 2.65473 2.65648 2.65838