Hyperfine Structure of the Metastable(1s22s2p) P3States ofBe94and the Nuclear Electric Quadrupole Moment

The hyperfine structure (hfs) of ${}_4{}^{}{}_{}{}^{}{\mathrm{Be}}^9(I=\frac{3}{2})$ in its metastable $\left(1\mathrm{}{s}^{2}2s2p\right) {}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ atomic states has been measured by the atomic-beam magnetic-resonance method. The zero-field hfs intervals in the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state are $\left\{\Delta \nu \right(\frac{1}{2},\frac{3}{2}),=187.6157\mathrm{}\pm 0.0042 \frac{\mathrm{Mc}}{sec},\}\left\{\Delta \nu \right(\frac{3}{2},\frac{5}{2}),=312.0226\mathrm{}\pm 0.0021 \frac{\mathrm{Mc}}{sec},\}\left\{\Delta \nu \right(\frac{5}{2},\frac{7}{2}),=435.4773\mathrm{}\pm 0.0021 \frac{\mathrm{Mc}}{sec}.\}$ The zero-field hfs intervals in the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state are $\left\{\Delta \nu \right(\frac{1}{2},\frac{3}{2}),=202.9529\mathrm{}\pm 0.0015 \frac{\mathrm{Mc}}{sec},\}\left\{\Delta \nu \right(\frac{3}{2},\frac{5}{2}),=354.4365\mathrm{}\pm 0.0027 \frac{\mathrm{Mc}}{sec}.\}$ In order to obtain the dipole and quadrupole coupling constants from the hfs separations, second- and third-order corrections arising from off-diagonal matrix elements of the hyperfine interaction between the ${}_{}{}^3{}_{}{}^{}P$ fine-structure levels must be included. The values of the hfs interaction constants before and after secondand third-order corrections are: The individual-electron interaction constants, calculated from the corrected values of $A$ and $B$, are $\{a_s,=-460.2\mathrm{}\pm 1.6 \frac{\mathrm{Mc}}{sec},\}\{a_{\frac{3}{2}},=-12.65\mathrm{}\pm 0.54 \frac{\mathrm{Mc}}{sec},\}\{b_{\frac{3}{2}},=1.467\mathrm{}\pm 0.042 \frac{\mathrm{Mc}}{sec}.\}$ The reason for the larger error limits in the corrected, compared with the uncorrected, numbers is discussed and the experimental values of $a_s$ and $a_{\frac{3}{2}}$ are compared with theory. Measurements of the magnetic field dependence of the hfs lead to the following estimate for the ${}_{}{}^3{}_{}{}^{}P$ fine-structure separations: $\left\{W\right({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{})-W({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}),=71.86\mathrm{}\pm 0.24 \frac{\mathrm{Gc}}{sec},\}\left\{W\right({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{})-W({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}),=19.41\mathrm{}\pm 0.19 \frac{\mathrm{Gc}}{sec}.\}$ From the ratio $\frac{b_{\frac{3}{2}}}{a_{\frac{3}{2}}}$ the quadrupole moment, without Sternheimer polarization corrections, is $Q=+0.049\mathrm{}\pm 0.003$ b. Expressions for the third-order corrections to the zero-field hyperfine energies are given, and estimates of the intermediate coupling coefficients $c_1$ and $c_2$ are discussed.