Dipole Moment of ${\mathrm{PH}}^{+}$ and the Atomic Masses of $^{28}\mathrm{Si}$, $^{31}\mathrm{P}$ by Comparing Cyclotron Frequencies of Two Ions Simultaneously Trapped in a Penning Trap

Dipole Moment of ${PH}^{+}$ and the Atomic Masses of ${}^{28}{Si}$ , ${}^{31}P$ by Comparing Cyclotron Frequencies of Two Ions Simultaneously Trapped in a Penning Trap

Matthew Redshaw, Joseph McDaniel, and Edmund G. Myers

Phys. Rev. Lett. 100, 093002 – Published 5 March 2008

Abstract

By trapping pairs of ions in a Penning trap, alternating each ion between large and small cyclotron orbits, we have measured the cyclotron frequency ratios ${}^{12}C_{2} H_{4}^{+} / {}^{28}{Si}^{+}$ , ${}^{13}C_{2} H_{2}^{+} / {}^{28}{Si}^{+}$ , ${}^{28}{SiH}_{3}^{+} / {}^{31}P^{+}$ , and ${}^{16}O_{2}^{+} /^{31} {PH}^{+}$ , all to $< 30 ppt$ precision. The ${}^{16}O_{2}^{+} /^{31} {PH}^{+}$ data exhibit a bimodal distribution due to the polarizability of the $Λ$ -doubling components of the ${PH}^{+}$ ground state, from which we obtain the electric dipole moment of ${}^{31}{PH}^{+}$ , 0.331(8) $e a_{0}$ . Combined with other atomic mass measurements we also obtain improved values for $m ({}^{28}{Si})$ , 27.976 926 535 0(6) u, and $m ({}^{31}P)$ , 30.973 761 998 9(9) u.