We report on a theoretical calculation and a new experimental determination of the 1s3p ^3P_J fine structure intervals in atomic ^4He. The values from the theoretical calculation of 8113.730(6) MHz and 658.801(6) MHz for the nu_{01} and nu_{12} intervals, respectively, disagree significantly with previous experimental results. However, the new laser spectroscopic measurement reported here yields values of 8113.714(28) MHz and 658.810(18) MHz for these intervals. These results show an excellent agreement with the theoretical values and resolve the apparent discrepancy between theory and experiment.
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