Storage-ring measurement of the hyperfine-induced $2s2p$ ${}^3{P}_0\to 2s^2$ ${}^1{S}_0$ transition rate in berylliumlike sulfur

The hyperfine-induced $2s2p{}^3{P}_0\to 2s^2{}^1{S}_0$ transition rate in Be-like sulfur was measured by monitoring the decay of isotopically pure beams of ${}^{32}$S${}^{12+}$ and ${}^{33}$S${}^{12+}$ ions in a heavy-ion storage ring. Within the 4$\%$ experimental uncertainty the experimental value of $0.096\left(4\right)$ s${}^{-1}$ agrees with the most recent theoretical results of [Cheng et al. Phys. Rev. A 77, 052504 (2008)] and [Andersson et al. Phys. Rev. A 79, 032501 (2009)]. Repeated experiments with different magnetic fields in the storage-ring bending magnets demonstrate that artificial quenching of the $2s2p{}^3{P}_0$ state by these magnetic fields is negligible.

Figure 1

Simplified level diagram for berylliumlike S${}^{12+}$. The level energies [2] are given in eV on top of the horizontal lines which are not drawn to scale. The level lifetimes (in s) labeling the excited levels on the right side of the horizontal lines were calculated from theoretical one-photon transition rates [3] that do not account for hyperfine effects. The one-photon transitions are labeled $E$1 (electric dipole), $M$2 (magnetic quadrupole), and HFI (hyperfine induced). Numbers in square brackets denote powers of 10. In case of nonzero nuclear spin the hyperfine-induced ${}^3{P}_0\to {}^1{S}_0$ transition rate $A_{\mathrm{HFI}}$ acquires a finite value.

Figure 2

Sketch of the heavy-ion storage-ring TSR. The eight bending dipole magnets with 1.15-m bending radius together cover 13$\%$ of the closed orbit of the ions which has a circumference of 55.4 m. Both the electron target (Target) and the electron cooler (Cooler) were used for the present electron-ion recombination measurement. The locations of the recombination detectors are indicated by the thick curved arrows in the top left and bottom left corners of the ring which represent the paths of recombined ions. The labels PG1–PG4 denote the approximate locations of the pressure gauges that were monitored by the data acquisition system.

Figure 3

Measured DR spectra of ${}^{32}$S${}^{12+}$ (solid symbols, top curve, offset by $+{10}^{-9}$ cm${}^3$ s${}^{-1}$) and ${}^{33}$S${}^{12+}$ (open symbols, bottom curve). For these measurements the Target was used as electron target and the Cooler was used to continuously cool the ion beam during recombination data taking. The vertical arrow marks the position of a resonance which is associated with primary ions in the $2s2p{}^3{P}_0$ state (see discussion in the text).

Figure 4

(Large panels) Measured resonance-decay curves (symbols) and fits of Eq. (12) to the data (solid curves). (Small panels) Residuals from the fits.

Figure 5

Vacuum pressures at different locations (labels PG1–4 in Fig. 2) in the TSR storage ring recorded during the lifetime measurements which contributed to data set A with a single photocathode. Time zero is October 1st, 2010 at 16:14. During the gap between 12 and 16 h the isotope was changed from ${}^{33}$S to ${}^{32}$S. The pressures remained nearly constant over the entire measurement time of data set A. It should be noted that the absolute pressure values bear rather large (unknown) uncertainties.

Figure 6

Dependence of the fit parameters ${\tau }_m$ (solid symbols) and ${\tau }_g$ (open symbols) on the time of the first data point that is used in the fit of Eq. (12) to the measured decay curves of data set A [Figs. 4a and 4b]. The arrows mark the data that were used in the calculation of ${\tau }_{\mathrm{HFI}}$. (Note that all values shown here scatter by less than the one-sigma error bars since they are statistically not independent; see text.)

Figure 7

Correlations between the fit parameters ${\tau }_m$ and ${\tau }_g$ for data set A from the covariance matrices of the least-squares fits to the experimental resonance-decay curve [Figs. 4a and 4b]. The ellipses denote the one-sigma confidence limits for both ${\tau }_m$ and ${\tau }_g$ jointly. The dash-dotted horizontal and vertical lines represent the projections of the ellipses onto the parameter axes.