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PNPI IN THE MATS PROJECT AT FAIR
PNPI participants of the MATS collaboration:
S.A. Eliseev, Yu.I. Gusev, P.A. Kravtsov, A.Kh. Khusainov, D.A. Nesterenko, Yu.N. Novikov,
A.V. Popov, A.K. Pustovoit, D.M. Seliverstov, M.D. Seliverstov, S.V. Tchenmarev, V.A. Trofimov,
A.A. Vasiliev, G.K. Vorobjev, and M.E. Vznuzdaev
1. Introduction
Ion traps occupy a weighty place among methods of modern physics experiments. These traps make it
possible to study the problems of physics in a wide range: from the cosmological scale to atomic and nuclear
dimensions and from astrophysics to nuclear, atomic, and molecular physics, working with particles in
a wide range of mass from the atoms of superheavy elements to elementary particles, including a tiny
neutrino [1]. The Penning Trap Mass Spectrometry (PTMS) relates to the low energy region and
complements ultra-high energy experiments performed with particle colliders. Both ultra-low and ultra-high
energy approaches may provide a complete picture of the properties of matter in Nature.
Ion traps have come into use in nuclear physics recently. Ions can be confined for a long time in traps,
making it possible to study their atomic and nuclear structure. Traps can be installed directly in beams of
short-lived nuclides in the on-line regime, thus investigating exotic nuclides. The MATS project (precision
Measurements of very short-lived nuclides using an Advanced Trapping System for highly-charged ions) [2]
is one of the projects combined by the association of scientists NuSTAR (Nuclear STructure, Astrophysics,
and Reactions). The objective of this scientific collaboration is to study the structure of nuclei under extreme
conditions, nuclear reactions, and nuclear astrophysics. The MATS project presupposes PTMS of very shortlived nuclides in a wide range of mass numbers with the use of the FAIR accelerator complex, which can
produce nuclides in the “inverse fragmentation” reaction, almost completely covering the Periodic Table of
elements. The expected intensity of the FAIR radioactive beams can be many orders of magnitude higher
than that in the currently functioning facilities. Thus, FAIR can provide an unprecedented variety of
radioactive samples for investigations by means of PTMS with the proposed MATS facility. The MATS
project incorporates about 20 laboratories from 10 countries.
This paper has a goal to present the MATS project at FAIR (Darmstadt) with the emphasis on the PNPI
contribution.
2. MATS tasks
Precision measurements of nuclear masses (i.e., the total binding energy) that are basic characteristics of
nuclei pose the following problems of physics:
 Construction of a precise mass surface (landscape) of the nuclear chart,
 Determination of the limits of proton and neutron stability of nuclei,
 Construction of the isomeric states landscape,
 Determination of the pathway of the astrophysical processes (r and rp) under high temperature
conditions in stars,
 Checking the hypothesis of the vector current conservation and the unitarity of the CabibboKobayashi-Maskawa matrix.
The PTMS at MATS can solve each of these problems by precise measurements of a large number of
nuclides, including exotic ones whose masses are still unknown. Indeed:
 The mass landscape for ground and isomeric states of nuclides can be determined only after
the masses of a large number of nuclides have been measured,
 The determination of the boundaries of the nucleon stability (the so called “drip-lines”) presupposes
the knowledge of the separation energy of nucleons (i.e., the corresponding mass differences) along
the expected boundary,
 The pathways of the astrophysical explosive processes (rapid proton capture “rp”, and rapid neutron
capture “r”) fully depend on the proton and neutron separation energies, respectively, that is,
on the corresponding mass differences, which should be known along the expected lengthy process
paths on the chart of the nuclides. Such a pathway for the r process is shown in Fig. 1, which
represents the nuclear chart of interest. As can be seen in Fig. 1, the r-process pathway largely passes
along the regions of extremely neutron-rich nuclides which have yet to be discovered. For this
reason, the task of the MATS project will be not only to measure the mass of these nuclides but at
first to discover them. The knowledge of the right position of the r-process pathway in combination
with the known solar element abundances, shown in Fig. 1 [3], paves the way for determination of
the astrophysical temperature and neutron density giving rise to the fast multipole capture. It is
expected that the masses of the most nuclides participating in the r process can be determined with
MATS. There are also a plenty of nuclides from the valley of stability towards the r-process path
whose masses also should be determined.
Астрофизический r-процесс (красные квадраты) проходит по «целинной» области неизвестных
нейтронно-избыточных нуклидов, массы которых предполагается измерить на установке MATS
Fig. 1. Chart of nuclides. The expected pathway for the astrophysical rapid neutron capture process (r process) is shown by red
colour [3]. The valley of stability is shown by black colour. The known solar abundances for the r-process nuclides are also shown in
relative units
Aside from direct measurements of nuclear masses, the MATS project is also tasked with a precision
spectroscopic exploration. Since the ion trap is a precision mass spectrometer, it makes possible to have ions
of definite nuclide at the exit of the system and to perform measurements under ideal background conditions
by means of in- and post-trap spectroscopy [2].
3. MATS experimental complex
The main measuring instrument is a series of Penning ion traps in tandem. Therefore, the ions directed
into the traps should have low energy. However, the primary ion beam of the SIS-100 synchrotron
bombarding the target will have an energy of about 2A GeV. The products of the inverse fragmentation
reaction which pass through the SuperFRS separator will also have a relativistic energy. For spectrometry
with traps, these products should be moderated to an acceptable energy less than 1 keV. This is supposed to
be done using a solid state moderator, which is followed by a large cryogenic He-gas cell where the ions are
stopped. This absorber should make it possible to obtain thermolysed singly charged ions and after their
extraction to form the low-energy branch (LEB) of beams of radioactive products which should be used in
different NuSTAR experiments including MATS. The ion-optical channel for transporting ions into
the measurement apparatus was calculated and designed by Russian specialists. The part A3 of this channel,
bending the beam in the required direction, is shown schematically in Fig. 2. The MATS facility consists of
an electronic source of highly charged ions EBIT (Electron Beam Ion Trap) indicated as B1 in Fig. 2, a mass
calibrator B2 using ion sources of different types, and Penning ion traps themselves: a preparatory trap B3
and a precise one B4.
Fig. 2. Schematics of the principal units of the MATS complex [2]: A3 – electrostatic system for bending the ion beam towards
the set-up; B1 – EBIT system to produce highly charged ions, B2 – mass calibration unit, B3 – preparatory trap, B4 – measuring trap
for precise mass measurements performed in the second stage
An ion in a Penning trap is confined by a combination of magnetic and electric fields in a very small
volume with the radius r < 100 μm. The ion motion is limited in three spatial dimensions with a certain
combination of a strong uniform magnetic and week electrostatic fields. A confined particle with the chargeto-mass ratio q/m circulates in a plane perpendicular to the magnetic field B with the cyclotron frequency
ωc = q/mB. A magnetic field directed along the Z axis confines the ion to the radial plane. If a quadrupole
electrostatic field is added, then the ion motion in the radial plane will consist of two harmonic motions:
a fast modified cyclotron motion and a slow magnetron one. The two motions are coupled by the relation of
the angular frequencies ω+ + ω–  ωc. An axial harmonic motion along the Z axis will also be present. Thus,
the motion of the charged particle in the trap is a superposition of three independent harmonic motions – one
axial motion and two radial ones [4]. An additional rf field applied between the segments of an annular
electrode gives rise to a quadrupole excitation which couples the motion in the radial plane.
This excitation applied at a frequency ωc couples two radial motions. It makes possible to determine the
cyclotron frequency ωc and, therefore, the desired ratio q/m if the applied field is under conditions of
a resonance. The resonance frequency can be determined more accurately with the octupole excitation, as it
was accomplished in Ref. [5]. In order to achieve high precision in the mass measurement, the magnetic field
should have high homogeneity of δB/B < 10–7 /cm3. It is necessary also to provide vacuum of ~10–8 Pa and to
cool ions to the liquid-helium temperature [1]. Before entering the precision measuring trap, the ions are
directed into the preparatory trap B3 (see Fig. 2). This trap should be used to separate ions by mass using
the buffer gas and to prepare the cooled ions for the precision trap B4 or for a detector trap placed in
the second uniform part of the same magnet as the preparatory trap. The task of the detector trap should be
in-trap spectroscopy. In order to increase considerably the precision of measurements, a use of highly
charged ions was proposed. Increasing the value of q/m, and hence of ωc, makes it possible to decrease
δωc/ωc by the same factor. Since after the He gas chamber of LEB the ions fly out predominantly singly
charged and enter the MATS system with the same charge, it is proposed to use the electron gun EBIT to
produce high-charge ions right up to completely ionized atoms (bare nuclei). This unit is presented
schematically by the block B1 in Fig. 2. The schematic of the precision measurement Penning trap proposed
for the MATS project is presented in Fig. 3 [2]. Since it is the frequency that is measured in the trap system,
and it can be measured much more accurately than, for example, the potentials, it makes PTMS
unprecedented with respect to the precision with which the nuclear masses can be determined. Thus,
the expected precision of PTMS in MATS will exceed all other known methods of measuring nuclear masses
by factors of 10–100.
Fig. 3. Scheme of the precision Penning trap proposed for the MATS system. The measurement trap is placed in a magnetic field of
7 T produced by a superconducting solenoid. The Micro Channel Plate (MCP) and the channeltron detector are shown
The cyclotron frequency will be determined by two methods: using the time-of-flight ion cyclotron
resonance (ToF–ICR) and the Fourier frequency transformation method (FT–ICR). In the ToF–ICR method,
the cyclotron frequency is determined from the resonance in the time-of-flight curve for the ions releasing
the trap and detected by the MCP. If the scanned external rf coincides with the characteristic cyclotron
frequency, dependent on the ratio q/m, the ions will have the maximal energy and therefore will reach
the detector (MCP) ahead of those at the non-resonance frequency. A typical experimental resonance timeof-flight curve for this destructive method, in which ions are lost, is shown in Fig. 4a [6]. Recently, a novel
approach based on the projection of the Penning trap ion motion onto a position-sensitive MCP detector has
been proposed and checked at the SHIPTRAP system at GSI [7]. This new approach opens the door to very
precise mass measurements on the sub-ppb level even for short-lived nuclides with half-lives well below
a second. In addition to increasing the precision in the mass determination, the new method provides
a superior resolving power by which low-lying isomeric states with the excitation energy on the 10-keV level
can be easily separated from the ground state. All these advantages just suit the MATS requirements.
The precision of the mass determination will reach in the absolute values a level of 100 eV, or even better for
light nuclides.
In the nondestructive method, the ion moves inside the trap with the oscillation frequency and produces
an induced charge in the resonance circuit. A single ion induces a very weak current (less than one
picoampere), which is amplified. The Fourier transformation permits identification of the resonance
frequency (see Fig. 4b). This method is appropriate for nuclides whose production yields are very small and
thus is relevant for the MATS project. However, the FT–ICR requires strict fulfilment of several conditions,
among which is the presence of ideal mechanical and thermal characteristics of the material of the trap and
the magnetic field, whose homogeneity should be as high as possible. Moreover, the trap should be cooled to
the liquid-helium temperature. Note that the FT–ICR method has not yet been implemented in any existing
trap systems for radioactive nuclides.
Fig. 4. Determination of the cyclotron frequency in the ion trap: (a) dependence of the time-of-flight of singly charged ions (from
the trap to the outside detector MCP) on the external rf field, and fragments of the time-of-flight spectrum [6]; (b) principle for
determination of the resonance frequency in the Fourier transformation method (FT–ICR) [1]
The principle of mass determination is the same for these two methods of measurements. The mass of
an ion with the known charge can be easily found if the magnetic field is known. The latter can be
determined in similar measurements with the ions of nuclides whose mass is well known. The atomic mass
M is determined from the expression:
M = (ωcal / ω)(Mcal – me) + me,
where ωcal and ω are the measured cyclotron frequencies of the calibrant and investigated singly charged
ions, respectively; Mcal is the mass of the calibration ion, and me stands for the electron mass.
4. Individual units of the MATS Complex (with the responsibility of PNPI)
4.1. Ion-optical channel
After the LEB cryogenic gas cell, the ions should be collected into a beam and transported over
a distance of about ten metres to the MATS installation. For these purposes, thermal ions are accelerated to
several keV, and the ion beam is bent by a dipole magnet for additional mass separation and for guiding in
the required direction. Next, the focused ion beam, assembled into ion groups by means of a gas-filled rf
quadrupole, is bent again electrostatically and forwarded towards the MATS set-up. In the MATS set-up,
the ion guide starts with an electrostatic deflection. A gas-filled rf quadrupole, which is placed directly in
front of the deflector, forms an ion beam at the exit with the emittance of 50 π·mm and with the energy of
about 100 eV. In order to avoid substantial losses, the beam should be accelerated. A scheme with two
doublets of electrostatic quadrupoles, placed symmetrically with respect to the bending dipole magnet, was
Fig. 5. Simulated arrangement of the ion-optical guide for bending and passage of the ion beam towards the MATS set-up [9]
Fig. 6. System of cylindrical lenses for stopping and focusing the ion beam at the entrance of the Penning trap, and the dependence of
the electrostatic potential on the focal distance d [9, 10]
chosen to transport the beam. Simulations with the SIMION code [8] showed that the optimal acceleration
energy should be ~5 keV with the beam diameter increased to 14 mm and with the angular divergence
approximately of ± 1 mrad. The overall scheme of this part of the set-up is shown in Fig. 5 (see also
Ref. [9]). In order to trap ions, the energy of the entrance beam should not exceed several hundred eV.
Therefore, it is necessary to stop the accelerated beam just in front of the ion trap. To do this, six cylindrical
electrostatic lenses are proposed. The scheme was simulated by the SIMION code and is shown in Fig. 6.
4.2. Mass calibrator
High precision experiments for mass determination require careful calibration of the precision ion trap.
Besides the necessity to eliminate temporal effects of magnetic field instabilities caused by different reasons
[11], an important component of the experiments is the accuracy of the calibration mass. The relative
accuracy of the masses of nuclides 23Na, 85-87Rb, and 133Cs most often used for calibration is δm/m =
= (1–2)·10–10, which could be insufficient for ultraprecise measurements for nuclides far from the mass
number of the calibration nuclides. For this reason, 12C was proposed for calibration. This mass standard can
be used in cluster compounds (of the fullerene type) to cover the extensive mass ranges of the chart of
nuclides [12]. As can be seen in Fig. 2, the mass calibrator B2 can be used in coupled operations of both
traps (B3 and B4). A scheme of the unit proposed by PNPI is shown in Fig. 7, which includes different types
of ionizers (laser, surface, and electron impact). This versatile unit will cover different mass regions of
the calibrants, and thus can be used for calibration of broad unknown mass regions.
Fig. 7. Schematic diagram of the mass calibrator proposed by PNPI for the PTMS at MATS. Ions can be produced by ion sources
of different type, then extracted and forwarded to the ion trap for mass measurements
4.3. Post- and in-trap spectroscopy
An ion trap is a very precision mass separator which confines nuclides of only one mass- and Z-number.
The ions extracted from the trap fly in a magnetic field gradient and strike the substrate, which can be
installed instead of MCP (usually used for PTMS). The particle and gamma radiation of the implanted
nuclides with the specific values of Z and A then can be measured. Another important advantage is
the possibility to use a trap for the in-trap spectroscopy. The ions in a trap are held at rest without any
corresponding carrier, which is a necessary component of any conventional radioactive source. The presence
of a carrier leads to the problem of accurate determination of the energy of the very low-energy charge
radiation (α, p, or e), which passes through the thickness of the substrate and therefore unavoidably loses
energy. The α decay particles can be detected with silicon strip detectors surrounding the trap that
simultaneously acts as a trap ring electrode to confine the decaying nuclei. This will allow to detect
the momentum vector of α decay particles without energy losses. Thus, the properties of the excited states of
exotic nuclides can be firstly investigated. The ion-optical simulations for the in-trap spectroscopy were
performed at PNPI [12].
5. Conclusion
The MATS project is dedicated to precision mass measurements of exotic nuclides very far from
the stability line. A dramatic increase of the production yields, which can be provided by the FAIR
accelerator, makes it possible to measure masses of hundreds of new nuclides, some of which are still
unknown. These global measurements will pave the way for the mass mapping and investigation of
the landscape of exotic nuclides, which is very important for nuclear physics and astrophysics. A novel
method of measurements of highly charged ions in combination with an advanced approaches in detection of
single ions will allow one to reach the mass precision on the level of 10–9 for the nuclides with the half-lives
even well below 1 s. MATS will be superior to all other existing and planned experimental installations for
mass-spectrometry of radioactive nuclides. The Penning traps of the MATS project can in addition be used
for post- and in-trap spectroscopy of very clean radioactive samples. PNPI is responsible for ion-optics
simulations of the MATS system, for building of the mass calibration unit and for production of thin
Si-detectors.
We would like to thank the members of the MATS-project for very fruitful collaboration.
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