This paper presented an clear a beautiful way on measuring highly charged state decay by the Schottky Mass Spectrometry.

The synchrotron frequency is related to mass by:

\frac{\delta f}{f } = - \frac{1}{\gamma^2} \frac{ \Delta m/q }{m/q}

For electron capture of ^{140}_{59}Pr^{58+} :

p + e^- \rightarrow n + \mu_e

The charge state does not change. Thus the frequency different is due to the mass different between parent and daught nucleus. that give an increase in frequency by 270Hz.

While for β+ decay:

p \rightarrow n + e^+ + \mu_e

both the charge state and mass changed after the decay. this make the frequency decrease alot. by this mean, we can observe the decay in a very clear detail.

By using the area of the Schottky frequency peak, They can identify the number of ion inside and the charge or it. because the peak is proportional to the number of stored ions and the square of charge.

the synchrotron frequency is about 2MHz. the data is analysed by FFT. each FFT frame has bandwidth 5kHz and was collected for 128ms. in this period, the ions will have 256,000 revolutions. This set of data will be FFT analysed and plot with time.

the half life of the ion is about 3.39min, thus, the time resolution is very good to give precise measurement on decay time.

the measured decay curve has an oscillation with about 7s period. they pointed out 3 possible reason for that:

  1. instability of the storage ring
  2. quantum beat between 2 hyperfine structure F=1/2 and F=3/2, where the nuclear spin is 1. but they also concluded that the quantum beat frequency is still 2 large for accounting it.
  3. an oscillation of neutrino mass state.
Note: since the half-life is 3.39 min, is there other way to measure the electron capture and verify the 7s oscillation??