Spectroscopy on a single trapped ^137Ba^+ ion for nuclear magnetic octupole moment determination

Abstract

We present precision measurements of the hyperfine intervals in the 5D 3/2 manifold of a single trapped Barium ion, 137 Ba + . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1 Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, Ω, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in 137 Ba + and the most accurately determined octupole moment to date. High precision measurements of the hyperfine structure provides stringent tests for state-of-the-art atomic structure calculations. These calculations play a crucial role in the interpretation of parity nonconservation (PNC) experiments which provide important tests of the standard model at low energy [1]. The accuracy of calculated PNC matrix elements can be assessed by comparing measured hyperfine structure constants with calculated values [2]. In addition, the hyperfine structure provides insight into the nuclear structure of atoms [3].In this paper we present precision measurements of the hyperfine intervals of the 5D 3/2 manifold of 137 Ba + . By combining high precision radio frequency (rf) spectroscopy with shelving techniques [4,5] on singly trapped ions, we measure the hyperfine intervals of the 5D 3/2 manifold to an accuracy below a few Hz. Together with theoretical calculations, this permits a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants and the first observation of the magnetic octupole moment in 137 Ba + . We determine the magnetic octupole moment, Ω, to an accuracy of 1% percent limited almost entirely by uncertainties in the theory. Ba + is an excellent candidate for magnetic octupole determination. Long lived metastable D states permit high precision spectroscopy measurements of the hyperfine levels, and high precision calculations are possible [6]. In [7] it was shown that the hyperfine intervals, δW F = W F − W F +1 , of the 5D 3/2 manifold can be written where C is the magnetic octupole hyperfine constant while η and ζ are the correction terms characterizing the mixing with the upper 5D 5/2 manifold. With measured values of the hyperfine intervals, δW k , and theoretical estimates for the correction terms we can solve the equations for the hyperfine constants. The octupole moment, Ω, can then be extracted from our theoretical result [8]using the CCSD(T) method described in [2,9], where µ N is the Bohr magneton and b is the barn unit of area. The procedure to measure the hyp...

Reliability test for the experimental results of electric-quadrupole hyperfine-structure constants and assessment of nuclear quadrupole moments in135Ba and137Ba

“…Recently the B value for this state has been measured to very high accuracy, 44.538 793 6(10) MHz [15], consistent with the value given in Table III. Combined with our calculated R e value given in Table I Table II, we find significant differences in the results.…”

“…It is also important for the extraction of higher-order nuclear * bijaya@prl.res.in moments [15]. Furthermore, studies of the hyperfine structure are also interesting for the investigation of the variation of the fine-structure constant [16] and for astrophysical studies [17].…”

Atomic properties ofLu+

“…The experiments are performed in a four-rod linear Paul trap with axial end caps, similar to the ones described in [17,18]. The trap consists of four stainless steel rods of diameter 1.0 mm whose centers are arranged on the vertices of a square with 3.6 mm length of the side.…”

Experimental determination of the nuclear magnetic octupole moment of137Ba+ion

“…The method for measuring the hyperfine intervals of the 5D 5/2 manifold is similar to one detailed in [10]. Briefly, the ion is first Doppler cooled and then optically pumped to the |F = 2, m F = 2 ground state.…”

“…The magnetic field for each rf resonance scan is measured in the 5D 3/2 manifold using the |F ′′ = 2, m F ′′ = 0 ↔ |F ′′ = 3, m F ′′ = ±1 transitions as in our previous work [10]. The time lapsed between taking the first magnetic field calibration measurement and measuring the hyperfine interval of interest is about 10 mins.…”