††thanks: This work is supported by the National Key R&D Program of China
(Grants No. 2016YFA0400504, No. 2018YFA0404401), the Strategic Priority
Research Program of Chinese Academy of Sciences (Grant No. XDB34000000), the
NSFC (Grants No. 11905261, No. 11805032, No. 11975280, No. 11605248), Y.M.Xing
thanks for support from CAS ”Light of West China” Program, X.X. acknowledge
support from China Postdoctoral Science Foundation (Contract NO. 2019M660250).
X.Y. acknowledge partial support by the FRIB-CSC Fellow-ship, China under
Grant No. 201704910964, R.J. Chen is supported by the International
Postdoctoral Exchange Fellowship Program 2017 by the Office of China
Postdoctoral Council (No.60 Document of OCPC, 2017), Y.A.L. receives support
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement No 682841 “ASTRUm”).

# Charge resolution in the Isochronous Mass Spectrometry and the mass of 51Co

Xu Zhou  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  School of Nuclear Science and Technology, University of Chinese
Academy of Sciences, Beijing 100049, People’s Republic of China  Meng Wang
<EMAIL_ADDRESS>Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  School of Nuclear Science and Technology, University of
Chinese Academy of Sciences, Beijing 100049, People’s Republic of China  Yu-Hu
Zhang<EMAIL_ADDRESS>Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China  Hu-Shan Xu  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China  You-Jin Yuan  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China  Jian-Cheng Yang  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic
of China  Yu. A. Litvinov  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  GSI Helmholtzzentrum für
Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany  S. A. Litvinov
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291
Darmstadt, Germany  Bo Mei  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  Sino-French Institute of Nuclear Engineering
and Technology, Sun Yat-sen University, Zhuhai 519082, China  Xin-Liang Yan
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA
Xing Xu  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  School of Science, Xi’an Jiaotong University, Xi’an 710049,
China  Peng Shuai  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  Yuan-Ming Xing  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  Rui-Jiu Chen  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  GSI
Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt,
Germany  Xiang-Cheng Chen  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  Chao-Yi Fu  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  Qi Zeng  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of
nuclear science and engineering, East China University of Technology, Nanchang
330013, China  Ming-Ze Sun  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  Hong-Fu Li  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science
and Technology, University of Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China  Qian Wang  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science and
Technology, University of Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China  Tong Bao  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  Min Zhang  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, People’s Republic of China  Min Si  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  Université Paris-Saclay,
CNRS/IN2P3, IJCLab, F-91405 Orsay, France  Han-Yu Deng  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, People’s Republic of China  Ming-Zheng Liu  Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, People’s Republic of China  Ting Liao  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science
and Technology, University of Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China  Jin-Yang Shi  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science and
Technology, University of Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China  Yu-Nan Song  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  School of Nuclear Science and
Technology, University of Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China

###### Abstract

Isochronous mass spectrometry (IMS) at heavy-ion storage rings is a powerful
tool for mass measurements of short-lived nuclei. In IMS experiments, masses
are determined through precision measurements of the revolution times of the
ions stored in the ring. However, the revolution times can not be resolved for
the particles with nearly the same mass-to-charge ($m/q$) ratios. In order to
overcome this limitation and to extract the accurate revolution times for such
pairs of ion species with very close $m/q$ ratios, the amplitudes of timing
signals from the detector, based on the emission of secondary electrons, have
been analyzed in our early work on the particle identification. Here, the
previous data analysis method is further improved by taking into account the
signal amplitudes, the detection efficiencies, as well as the number of stored
ions in the ring. A sensitive $Z$-dependent parameter is introduced in the
data analysis, leading to a better resolution of 34Ar18+ and 51Co27+ with
$A/Z=17/9$. The mean revolution times of 34Ar18+ and 51Co27+ are deduced
although their time difference is merely 1.8 ps. The uncorrected, overlapped
peak of these ions has FWHM=7.7 ps. The mass excess of 51Co is re-determined
to be $-27332(41)$ keV in agreement with the previous value of $-27342(48)$
keV.

Isochronous mass spectrometry, Charge resolution, Signal amplitude, Micro-
channel plate, 51Co

##  I Introduction

Isochronous mass spectrometry (IMS) at heavy-ion storage rings plays an
important role in mass measurements of short-lived nuclei 1 ; 1_1 . There are
three storage ring facilities conducting such experiments worldwide 2_1 ; 2_2
; 2 ; Steck , namely the experimental cooler-storage ring (CSRe) in Lanzhou,
the experimental storage ring (ESR) in Darmstadt and the Rare-RI Ring (R3) in
Saitama. In the IMS experiments, nuclei of interest are produced in projectile
fragmentation (PF) or in-flight fission nuclear reactions, where the
production cross sections are related to the binding energies of the fragments
3_1 ; 3_2 ; 3_3 . The reaction products of interest are selected with a
fragment separator and injected into the storage ring for mass measurements.
The revolution times of the stored nuclides are directly related to their
mass-to-charge ($m/q$) ratios. The revolution times are typically measured by
using dedicated timing detectors 8_1 ; 8 ; TOF ; 8_2 . It is obvious that only
those revolution times which could unambiguously be assigned to a specific ion
species can be used 9 ; 10 .

Particle identification (PID) is a prerequisite in experiments with
radioactive ion beams (RIB) produced in a nuclear reaction, and is routinely
accomplished along a RIB beam-line by measuring the time-of-flight (TOF),
energy loss ($\Delta$E), and magnetic rigidity (B$\rho$) for each particle
Liang ; Sun . In particular, the atomic number $Z$ is mainly determined by
using the $\Delta$E value which is usually measured with various ionisation-
type detectors placed along the beam-line.

Among the storage-ring based facilities, PID within a beam-line can only be
done at the R3 in RIKEN r3 ; yamaguchi , where the quasi-DC beam from the
superconducting cyclotron is employed. Thus, the RIBs can indeed be identified
on the event-by-event basis prior to their injection into the R3 . It is very
different in the cases of the CSRe and ESR. The driver accelerator at the
facility in Lanzhou is the heavy-ion synchrotron CSRm CSRm . The primary beams
are fast extracted from the CSRm within $\sim$300 ns. Correspondingly the
produced RIBs have a similar bunched structure. Therefore, the event-by-event
PID is not feasible in the radioactive-ion beam line RIBLL2 connecting the
CSRm and the CSRe. Similar situation is at GSI in Darmstadt, where the ions
are fast-extracted from the heavy-ion synchrotron SIS-18, analyzed in flight
with the fragment separator FRS and injected for isochronous mass measurements
into the experimental storage ring ESR 1_5 . In this work we examine the
sensitivity of the timing detectors to the charge of the stored ions for the
purpose of the in-ring PID.

By using IMS at the CSRe, masses of more than 30 short-lived nuclei have been
measured Fu20 ; 3 ; 4 ; 5 ; 6 ; 7 ; 52Co ; Xu15 ; 9_1 ; add1 ; add2 . For a
recent review the reader is referred to Refs. 2 ; Steck ; 7  and references
cited therein. In these experiments, the ions are identified almost solely
through their $m/q$ ratios by comparing the revolution time spectrum obtained
experimentally with the simulated one 9 ; 10 . The $m/q$ resolving power of
$\sim 3\times 10^{5}$ has been achieved at the CSRe, which e.g. is sufficient
to identify the isomeric states in 101In and 52Co 4 ; 52Co . However, for some
pairs of ions with very similar $m/q$ ratios, such as 51Co27+ and 34Ar18+, the
revolution times are too close to each other to be resolved clearly. The
charge determination can provide crucial information for PID in these cases.
The charge-resolved IMS was developed by analyzing the average amplitudes of
signals from the timing detector induced by stored ions 11 . This method was
used successfully to determine for the first time the mass of 51Co. Although
the charge difference ($\Delta Z$) of 51Co27+ and 34Ar18+ is relatively large,
some events could not be unambiguously identified due to the limited charge
resolution in that work 11 .

A higher charge resolution is desired. For example, masses of 54,56Ti nuclides
have been measured in an earlier experiment at the CSRe 3 ; Xu15 . The 55Ti
nuclide must have been produced with a significant amount in this experiment
according to the yields of neighbouring nuclei, but it could not be separated
from 50Ca. To measure the mass of 55Ti, it is necessary to resolve 55Ti22+ and
50Ca20+ by charge, where $\Delta Z$ is merely 2. Such high charge resolution
was not realized in that experiment. Due to the limited charge resolution,
mass measurements of $N=Z$ nuclides with conventional IMS at the CSRe or ESR
are usually regarded to be unfeasible. The $N=Z$ nuclides with $\Delta Z=2$
have to be resolved by charge, while the neighbouring $N=Z$ ($\Delta Z=1$)
nuclides can be resolved by their revolution times because the difference of
their $m/q$ ratios is sufficiently large, thanks to the odd-even staggering of
binding energies. If ions with $\Delta Z=2$ can be resolved by charge then, in
principle, all nuclides can be identified and measured in IMS experiments.

In this work, we describe a new method, in which detailed characteristics of
the timing detector are considered in the data analysis. The charge resolution
of IMS is improved significantly, leading to a complete separation of 34Ar and
51Co. Possible future developments are discussed as well.

##  II Experiment and the timing detector

The following discussions are based on the same experimental data that were
analyzed in the earlier work 11 . More details about the experiment can be
found in Refs. 11 ; 12 ; 13 . This experiment aimed to measure the masses of
$T_{z}=-3/2$ nuclei in the $pf$-shell. The nuclei of interest were produced by
using projectile fragmentation of 463 MeV/u 58Ni19+ primary beams in a $\sim
15$ mm 9Be production target. At this energy the fragments emerged from the
target predominantly as bare ions. Therefore, in the following we assume the
atomic charge $q$ to be equal to atomic number $Z$. The RIBLL2 and CSRe were
set to a fixed magnetic rigidity of $B\rho=5.677$ Tm. All fragments within the
$B\rho$-acceptance of $\sim\pm$0.2$\%$ were injected into the CSRe.

Figure 1: (Colour online) Two-dimensional plot of average signal amplitudes
$A_{0}$ (a) and detection efficiencies $\eta$ (b) as a function of revolution
time $T$, for $T_{z}=-1/2$ (black labels), $T_{z}=-1$ (red labels) and
$T_{z}=-3/2$ (blue labels) ions.

Figure 2:  The scatter plot of the revolution times $T$ as a function of
$A_{0}$ (a), $A_{1}$ (b), $A_{2}$ (c) with their projected histogram for 34Ar
and 51Co ions.

The revolution times of the stored ions were measured by using a timing
detector equipped with a carbon foil of $19~{}\mu\rm{g/cm^{2}}$ in thickness
and $40$ mm in diameter 8 . The foil was positioned in the circulation path of
the stored ions. When an ion passed through the carbon foil, secondary
electrons were released from the foil surface and guided isochronously to a
set of micro-channel plates (MCP) in the Chevron configuration 15 . The MCP
had the same diameter as the carbon foil and the micro-channels were 5 $\mu$m
in diameter. When an electron hits a channel of the MCP, an avalanche of
further secondary electrons propagated through the channel. The bunch of
electrons exiting from the rear side of that channel was collected by a
conical anode. A signal can be generated with the activation of one or more
channels. The negative-voltage signal was directly transmitted from the anode
to a digital oscilloscope for data acquisition. The recording time was
$200~{}\mu$s for each injection in this experiment.

The amount of electrons from the carbon foil induced by an ion is roughly
proportional to the energy loss, which scales with $q^{2}=Z^{2}$ 8 .
Consequently, both the average signal amplitude ($A_{0}$) and the detection
efficiency ($\eta$) for an ion depend strongly on its atomic number $Z$.

Figure 1 (a) shows the two-dimensional plot of revolution times $T$ and
$A_{0}$ obtained in the experiment, similar as Fig. 3 given in the earlier
work 11 . The 51Co27+ and 34Ar18+ ions can be resolved by using the $A_{0}$
value, albeit not completely separated. Figure 1 (a) is an analogue of the
typical PID plots at an in-flight separator Liang ; Sun , though with a lower
charge resolution but a higher $m/q$ resolution. Figure 1 (b) shows the two-
dimensional plot of $T$ versus $\eta$. The two plots in Fig. 1 are quite
similar. It seems that $A_{0}$ provides a better charge resolution for heavier
ions while $\eta$ does better for lighter ones.

##  III Analysis of the signal amplitudes

In the earlier work, the average signal amplitude ($A_{0}$) was used to
resolve the 51Co27+ and 34Ar18+ ions 11 . Figure 2 (a) shows the scatter plot
of revolution times $T$ versus $A_{0}$ and its projected histogram for 34Ar
and 51Co. Although two ion species can be well resolved, there still exists an
overlap between the two Gaussian-like distributions.

Assuming each micro-channel is fully discharged after the electron impact and
thus provides the same contribution to the signal, $A_{0}$ is roughly
proportional to the average number of the activated micro-channels and in turn
to the number of released secondary electrons from the foil surface. However,
there were ion passages through the detector which did not generate signals.
This reflects the finite detection efficiency $\eta$ 11 , which includes
electron hits in between the channels (geometrical efficiency) and the hits
into the already discharged channels (dynamic efficiency). We define an
average signal amplitude corrected by the total efficiency as $A_{1}$

$A_{1}=A_{0}\times\eta.$ (1)

It is clear that $A_{1}$ is proportional to the total number of micro-channels
activated by an ion. Figure 2(b) shows the scatter plot of revolution times
$T$ versus $A_{1}$ and the projected histogram for 34Ar and 51Co. It can
directly be seen that the separation of these two ions became better.

After a micro-channel was activated to output the avalanche electrons, it took
$\sim 10$ ms to recharge the channel. During this period, the channel did not
respond to other coming electrons. Since the measurement time is much shorter
than the recharging time, each micro-channel could be used at most once during
the measurement ps . If the number of stored ions was too large in one
injection into the CSRe, the total number of activated micro-channels would be
large and the chance for each electron to activate a micro-channel would be
reduced, leading to the reduced $A_{0}$ and $\eta$ values. This dynamic
efficiency obviously depends on the number of stored ions and their charge.
The sum amplitude of all signals ($A_{s}$) was a direct measure of the total
number of activated channels in one injection. It is thus expected that
$A_{1}$ values have a negative correlation with $A_{s}$ values for one ion
species.

Figure 3: (Colour online) For 36K (blue empty circles) and 53Ni (red solid
circles) ions, plot of the constructed parameter $A_{1}$ values divided by the
mean value $\overline{A}_{1}$ for such ion specie, as a function of the sum
amplitude of all signals in one injection ($A_{s}$).

In the present experiment, the number of stored ions ranged from 2 to 46 in
various injections with the most probable value of 21. The $A_{s}$ values
ranged from $50$ to $300$ V. The relationship between $A_{1}$ and $A_{s}$
values is similar for all ion species, and is demonstrated in Fig. 3 on the
example of 36K and 53Ni ions, which can be clearly identified by using their
revolution times. The mean $\bar{A}_{1}$ values are calculated for these two
ion species. The $A_{1}/\bar{A}_{1}$ ratios are calculated for each individual
ion and the scatter plot of $A_{1}/\bar{A}_{1}$ versus $A_{s}$ is shown in
Fig. 3. The $A_{1}/\bar{A}_{1}$ values for both ion species are described by a
linear function of $A_{s}$. The obtained two slopes are very similar
indicating a constant slope for all ion species. If the observed correlation
of $A_{1}$ and $A_{s}$ values is taken into account, the charge resolution can
be improved.

A new parameter $A_{2}$ is defined as an estimate of the $A_{1}$ value at
$A_{s}=0$ V. The $A_{2}$ value is proportional to the number of channels that
should be activated by the ion if all micro-channels are available. It is thus
directly related to the number of released electrons from the detector foil
due to this ion. Considering the constant slope for different ion species as
shown in Fig. 3, the $A_{2}$ value can be calculated as

$A_{2}=A_{1}\times(1-B\times A_{s}).$ (2)

The $B$ parameter represents the slope in Fig. 3 and is determined by using
all ion species with proton number $Z>8$ and more than 100 counts. It is equal
to $B=-9.05(7)\times 10^{-4}\rm{~{}V^{-1}}$. Figure 2(c) shows the scatter
plot of revolution times $T$ versus $A_{2}$ and the projected histogram for
34Ar and 51Co ions. It can be seen that the two ions are completely separated.

Since the revolution time $T$ is $B\rho$ dependent for ions of 34Ar and 51Co
2_1 ; 2_2 , the $T$ values should depend on the ions’ average passage position
through the detector. As show in Fig. 2, there is no correlation of $A_{0}$,
$A_{1}$ and $A_{2}$ values with the revolution time $T$, proving position
independence of $A_{0}$, $A_{1}$ and $A_{2}$ in this experiment.

By using $A_{2}$ for particle identification, the mass excess of 51Co is re-
determined to be $-27332(41)$ keV, in agreement with the value $-27342(48)$
keV obtained previously 11 . The smaller mass uncertainty in this analysis is
mainly due to larger statistics obtained to less strict constraints. In the
earlier work only the particles that were stored for more than 300 revolutions
in the CSRe were used in the analysis. Based on the since then improved data
analysis methods, the threshold could be lowered in the present work to 80
revolutions, thus increasing the statistics.

##  IV Charge resolution

Figure 4:  (Colour online) For ions with same proton number $Z$, plot of
average (a) and standard deviations (b) of $A_{0}$ (black solid squares),
$A_{1}$ (red solid circles) and $A_{2}$ (blue empty squares) as a function of
$Z$.

The $A_{0}$, $A_{1}$ and $A_{2}$ values are calculated for all ions. Figure 4
(a) shows the average values of these three parameters for ions with the same
proton number $Z$. As can be seen, the $A_{1}$ and $A_{2}$ values are very
similar, while $A_{0}$ is larger than the other two parameters for light ions.
$A_{2}$ increases rapidly with proton number and approaches $A_{0}$. It is
evident that $A_{2}$ is more sensitive to proton number $Z$. The standard
deviations of these three parameters are shown in Fig. 4(b) as a function of
$Z$. For heavy ions ($Z\sim 20$) they are similar for all three parameters,
while for lighter ions the standard deviation of $A_{0}$ is considerably
larger.

The charge resolution ratio $R$ is introduced to represent the separation of
two ion species. $R$ is defined as

$R(A;Z,\Delta_{Z})=\frac{A_{Z}-A_{Z-\Delta
Z}}{\sigma_{A_{Z}}+\sigma_{A_{Z-\Delta Z}}},$ (3)

where $A$ indicates the parameters used in the charge identification, $Z$ is
the proton number and $\Delta Z$ is the proton number difference of two ion
species. For the normal distribution, two peaks can be resolved if $R\geq 2$,
corresponding to less than $2.5\%$ of events from one peak to overlap with
another peak. In the case of $R=1$, two peaks can be identified with $\sim
16\%$ overlapping events.

Figure 5:  (Colour online) For groups of ions with proton number difference
$\Delta Z=2$, plot of charge resolution ratios $R$ by using $A_{0}$ (black
solid block), $A_{1}$ (red solid dot) and $A_{2}$ (blue hollow block) as a
function of proton number $Z$.

Figure 5 shows the charge resolution ratios for different pairs of ions with
$\Delta Z=2$. The charge resolution ratios for $A_{2}$ ($R(A_{2})$) are the
largest for all ions, with an increase by $10\%-650\%$ as comparing with those
for $A_{0}$. The $A_{2}$ parameter provides the highest charge resolution.
Using $A_{2}$ values in the calculation, Figure 6 shows $R(A_{2})$ for pairs
of ions with various $\Delta Z$ as a function of $Z$. The $R$ values are
directly related to $\Delta Z/Z$. In this experiment, pairs of ions with
$\Delta Z/Z>0.22$ can clearly be resolved.

Only a moderate charge resolution was achieved in this experiment since the
charge resolution was not specially optimized. A better charge resolution can
be realized with several technical improvements. The charge resolution can be
improved by extending the recording time for each injection, namely from the
present 200 $\mu$s to 400-600 $\mu$s. A lower number of stored ions in an
individual injection will also lead to a higher resolution. Two timing
detectors, a new IMS method which is under development and will be applied in
future experiments at CSRe Xu15(IMS) ; TOF ; Xing ; add3 ; Yan , could also
increase the charge resolution. Last but not least, the MCP plates with 2
$\mu$m pore size will be adopted thus boosting the number of micro-channels.

Figure 6: (Colour online) Using the constructed parameter $A_{2}$ in
calculation, plot of charge resolution ratios $R$ as a function of proton
number $Z$, for groups of ions with $\Delta Z=2$ (black solid block), $\Delta
Z=4$ (green solid dot), $\Delta Z=6$ (red hollow dot),$\Delta Z=8$ (blue
hollow block).

##  V Summary

In the IMS experiments, charge resolution provides crucial information for
particle identification of ion pairs with $m/q$ ratios too similar to be
resolved by their revolution times. In an earlier work, the charge-resolved
IMS was developed at the CSRe to resolve the 51Co27+ and 34Ar18+ ions.
However, the two ion types were not separated completely due to the limited
charge resolution. In this work a new analysis method is presented, which
explicitly considers in the data analysis the average signal amplitudes, the
detection efficiencies, and the number of stored ions. The charge resolution
of IMS is significantly improved for ions with $Z<22$, leading to a complete
separation of 34Ar and 51Co. The mass excess of 51Co is re-determined to be
$-27332(41)$ keV, in agreement with the previous value 11 . The developed
analysis method may be of a broader interest for storage-ring-based atomic and
nuclear physics experiments using similar type of detectors.

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