Laser spectroscopy of fine-structure splittings in the 2$^{\mathrm{3}}$P$_{\mathrm{J}}$ levels of $^{\mathrm{4}}$He*

The fine-structure splittings of the 2$^{\mathrm{3}}$P$_{\mathrm{J}}$ (J$=$0, 1, 2) levels of $^{\mathrm{4}}$He is of great interest for tests of quantum electrodynamics and for the determination of the fine structure constant $\alpha $. Here we report our recent studies on the fine-structure splitting intervals. The metastable helium atoms are prepared by RF discharge and are collimated by transverse cooling. The laser spectroscopy is performed via 2$^{\mathrm{3}}$P$_{\mathrm{J\thinspace }}$- 2$^{\mathrm{3}}$S$_{\mathrm{1}}$ transitions at 1083nm. The 2$^{\mathrm{3}}$P$_{\mathrm{0\thinspace }}$- 2$^{\mathrm{3}}$P$_{\mathrm{2}}$ and2$^{\mathrm{3}}$P$_{\mathrm{1\thinspace }}$- 2$^{\mathrm{3}}$P$_{\mathrm{2}}$ intervals are determined to be 31 908 130.98(13) kHz and 2 291 177.56(19) kHz, respectively. Both intervals show good agreements with the theoretical calculations. Progress towards measurements on the absolute frequency of 2$^{\mathrm{3}}$P$_{\mathrm{J\thinspace }}$- 2$^{\mathrm{3}}$S$_{\mathrm{1}}$ on $^{\mathrm{4}}$He will be reported.