SU(3) in 3+1 dimensions: Run A, beta=3.0, xi=3, (15 x 15 x 15) x 45 as * at * sigma = 0.02827(65) 1 / (as * at * sigma) = 35.38(81) xi = 3 Zxi = 0.943(10) 1 / Zxi = 1.061(11) a_s * sqrt(sigma) = 0.2828(36) a_t * sqrt(sigma) = 0.1000(13) 1 / (a_s * sqrt(sigma)) = 3.537(44) 1 / (a_t * sqrt(sigma)) = 10.00(13) Energy gaps above the ground state. orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) A1g' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.023810 0.057502 (2,0,0) 0.565600 0.007161 1.768667 0.022225 3.239457 0.046417 (3,0,0) 0.848400 0.010741 1.179111 0.014817 2.849282 0.040204 (4,0,0) 1.131200 0.014321 0.884333 0.011113 2.614176 0.036659 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.438097 0.033797 (6,0,0) 1.696800 0.021482 0.589556 0.007408 2.288029 0.032533 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.172977 0.032799 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.061927 0.034729 (9,0,0) 2.545200 0.032222 0.393037 0.004939 1.953879 0.039616 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) A1g'' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.270921 0.101517 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.293931 0.073734 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.193886 0.063446 (4,0,0) 1.131200 0.014321 0.884333 0.011113 4.014806 0.064550 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.941773 0.063207 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.718673 0.060383 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.589615 0.065282 (8,0,0) 2.262400 0.028642 0.442167 0.005556 3.404531 0.061501 (9,0,0) 2.545200 0.032222 0.393037 0.004939 3.268470 0.061049 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) A1u / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.065278 0.084983 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.255914 0.065787 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.835725 0.057475 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.481566 0.056171 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.246460 0.050191 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.032364 0.048623 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.837276 0.050073 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.701215 0.051054 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.536141 0.060225 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) A2g / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.494021 0.061569 (2,0,0) 0.565600 0.007161 1.768667 0.022225 3.723675 0.050309 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.287479 0.046048 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.021359 0.044014 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.808263 0.042244 (6,0,0) 1.696800 0.021482 0.589556 0.007408 2.653193 0.042390 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.505127 0.051781 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.422089 0.052767 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.296033 0.066650 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) A2u / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 3.487569 0.044650 (2,0,0) 0.565600 0.007161 1.768667 0.022225 2.740533 0.035964 (3,0,0) 0.848400 0.010741 1.179111 0.014817 2.416587 0.031964 (4,0,0) 1.131200 0.014321 0.884333 0.011113 2.223000 0.030506 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.091941 0.031396 (6,0,0) 1.696800 0.021482 0.589556 0.007408 1.991896 0.035454 (7,0,0) 1.979600 0.025062 0.505333 0.006350 1.921864 0.044250 (8,0,0) 2.262400 0.028642 0.442167 0.005556 1.886849 0.043171 (9,0,0) 2.545200 0.032222 0.393037 0.004939 1.902856 0.044119 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) B1g / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.481016 0.064479 (2,0,0) 0.565600 0.007161 1.768667 0.022225 3.665649 0.051215 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.177429 0.046726 (4,0,0) 1.131200 0.014321 0.884333 0.011113 2.865289 0.041809 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.614176 0.043270 (6,0,0) 1.696800 0.021482 0.589556 0.007408 2.417087 0.040737 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.228002 0.044126 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.101945 0.042345 (9,0,0) 2.545200 0.032222 0.393037 0.004939 1.975889 0.046300 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) B1g' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.829622 0.093679 (2,0,0) 0.565600 0.007161 1.768667 0.022225 5.192335 0.088175 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.788154 0.081710 (4,0,0) 1.131200 0.014321 0.884333 0.011113 4.420989 0.091894 (5,0,0) 1.414000 0.017901 0.707467 0.008890 4.167875 0.082851 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.841728 0.127614 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.655644 0.104742 (8,0,0) 2.262400 0.028642 0.442167 0.005556 3.463558 0.123070 (9,0,0) 2.545200 0.032222 0.393037 0.004939 3.172427 0.155313 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) B1u / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.176328 0.079889 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.404981 0.074769 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.001800 0.073214 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.685658 0.066843 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.459556 0.059214 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.191435 0.065783 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.967335 0.070743 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.856285 0.066613 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.729228 0.070943 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) B2g / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.490020 0.061139 (2,0,0) 0.565600 0.007161 1.768667 0.022225 3.639637 0.051815 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.179430 0.044824 (4,0,0) 1.131200 0.014321 0.884333 0.011113 2.882296 0.038618 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.620179 0.037174 (6,0,0) 1.696800 0.021482 0.589556 0.007408 2.419088 0.034461 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.247011 0.035284 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.115952 0.033970 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.001900 0.034847 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) B2g' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.419438 0.340093 (2,0,0) 0.565600 0.007161 1.768667 0.022225 5.063277 0.145796 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.619078 0.120127 (4,0,0) 1.131200 0.014321 0.884333 0.011113 4.282926 0.129830 (5,0,0) 1.414000 0.017901 0.707467 0.008890 4.098844 0.093612 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.943774 0.066431 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.648641 0.085483 (8,0,0) 2.262400 0.028642 0.442167 0.005556 3.561602 0.061518 (9,0,0) 2.545200 0.032222 0.393037 0.004939 3.303486 0.091125 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) B2u / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.232353 0.077715 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.447000 0.064593 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.076834 0.066414 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.727677 0.061749 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.470561 0.055443 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.247461 0.055214 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.025361 0.056028 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.827272 0.060624 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.679205 0.062039 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eg / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.193886 0.055889 (2,0,0) 0.565600 0.007161 1.768667 0.022225 3.485568 0.046462 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.164423 0.042648 (4,0,0) 1.131200 0.014321 0.884333 0.011113 2.903306 0.038544 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.648191 0.036624 (6,0,0) 1.696800 0.021482 0.589556 0.007408 2.432094 0.035081 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.245010 0.031596 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.096943 0.030920 (9,0,0) 2.545200 0.032222 0.393037 0.004939 1.954879 0.028869 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eg' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 4.496022 0.059820 (2,0,0) 0.565600 0.007161 1.768667 0.022225 3.663648 0.049603 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.215446 0.044797 (4,0,0) 1.131200 0.014321 0.884333 0.011113 2.997348 0.043258 (5,0,0) 1.414000 0.017901 0.707467 0.008890 2.860287 0.041755 (6,0,0) 1.696800 0.021482 0.589556 0.007408 2.743234 0.042121 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.702215 0.042880 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.644189 0.044210 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.607173 0.048041 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eg'' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.745584 0.120325 (2,0,0) 0.565600 0.007161 1.768667 0.022225 5.061277 0.100056 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.732128 0.086089 (4,0,0) 1.131200 0.014321 0.884333 0.011113 4.412985 0.078982 (5,0,0) 1.414000 0.017901 0.707467 0.008890 4.238907 0.065612 (6,0,0) 1.696800 0.021482 0.589556 0.007408 4.012805 0.066433 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.897753 0.064680 (8,0,0) 2.262400 0.028642 0.442167 0.005556 3.639637 0.064305 (9,0,0) 2.545200 0.032222 0.393037 0.004939 3.598619 0.072110 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eu / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 3.412735 0.044178 (2,0,0) 0.565600 0.007161 1.768667 0.022225 2.563253 0.033289 (3,0,0) 0.848400 0.010741 1.179111 0.014817 2.124255 0.027358 (4,0,0) 1.131200 0.014321 0.884333 0.011113 1.823720 0.023752 (5,0,0) 1.414000 0.017901 0.707467 0.008890 1.603021 0.021039 (6,0,0) 1.696800 0.021482 0.589556 0.007408 1.432945 0.019280 (7,0,0) 1.979600 0.025062 0.505333 0.006350 1.294982 0.017978 (8,0,0) 2.262400 0.028642 0.442167 0.005556 1.188635 0.017190 (9,0,0) 2.545200 0.032222 0.393037 0.004939 1.078485 0.020256 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eu' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.057275 0.070939 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.218898 0.061600 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.818718 0.057295 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.550597 0.052307 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.323495 0.055930 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.166424 0.053785 (7,0,0) 1.979600 0.025062 0.505333 0.006350 2.993346 0.052880 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.848281 0.051589 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.706217 0.051845 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eu'' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.199339 0.081292 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.418988 0.069810 (3,0,0) 0.848400 0.010741 1.179111 0.014817 3.944774 0.057605 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.632634 0.057072 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.424540 0.053771 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.213445 0.052919 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.072382 0.054997 (8,0,0) 2.262400 0.028642 0.442167 0.005556 2.937321 0.052377 (9,0,0) 2.545200 0.032222 0.393037 0.004939 2.805262 0.058851 orientation r * sqrt(sigma) 1 / (r * sqrt(sigma)) Eu''' / sqrt(sigma) (1,0,0) 0.282800 0.003580 3.537333 0.044451 5.373417 0.075401 (2,0,0) 0.565600 0.007161 1.768667 0.022225 4.569055 0.063656 (3,0,0) 0.848400 0.010741 1.179111 0.014817 4.088839 0.060188 (4,0,0) 1.131200 0.014321 0.884333 0.011113 3.794707 0.057590 (5,0,0) 1.414000 0.017901 0.707467 0.008890 3.513580 0.056488 (6,0,0) 1.696800 0.021482 0.589556 0.007408 3.367515 0.053803 (7,0,0) 1.979600 0.025062 0.505333 0.006350 3.198439 0.060456 (8,0,0) 2.262400 0.028642 0.442167 0.005556 3.100395 0.058142 (9,0,0) 2.545200 0.032222 0.393037 0.004939 3.017357 0.062859