Eur. Phys. J. A (2016) 52: 278
DOI 10.1140/epja/i2016-16278-7
THE EUROPEAN
PHYSICAL JOURNAL A
Regular Article – Experimental Physics
Synthesis of new transuranium isotopes in multinucleon transfer
reactions using a velocity filter
S. Heinz1,2,a , H.M. Devaraja3 , O. Beliuskina1,2 , V. Comas1 , S. Hofmann1 , C. Hornung2 , G. Münzenberg1 ,
D. Ackermann1 , M. Gupta3 , R.A. Henderson4 , F.P. Heßberger1,5 , B. Kindler1 , B. Lommel1 , R. Mann1 , J. Maurer1 ,
K.J. Moody4 , K. Nishio6 , A.G. Popeko7 , D.A. Shaughnessy4 , M.A. Stoyer4 , and A.V. Yeremin7
1
2
3
4
5
6
7
GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
Justus-Liebig-Universität Gießen, II. Physikalisches Institut, 35392 Gießen, Germany
Manipal Centre for Natural Sciences, Manipal University, Manipal 576014, Karnataka, India
Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
Helmholtz-Institut Mainz, 55099 Mainz, Germany
Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
Joint Institute for Nuclear Research, 141980 Dubna, Russia
Received: 31 May 2016 / Revised: 20 July 2016
c Società Italiana di Fisica / Springer-Verlag 2016
Published online: 13 September 2016 – Abstract. Recently, we reported the observation of several new isotopes with proton numbers Z ≥ 92 in
low-energy collisions of 48 Ca + 248 Cm. The peculiarity is that the nuclei were produced in multinucleon
transfer reactions, a method which is presently discussed as a possible new way to enter so far unknown
regions in the upper part of the Chart of Nuclides. For separation of the transfer products we used a velocity
filter, the Separator for Heavy Ion Reaction Products SHIP at GSI. The resulting strong background
suppression allowed us to detect nuclei with cross-sections down to the sub-nanobarn scale. Beside the new
isotopes we identified about 100 further target-like transfer products and determined their cross-sections.
The results together with previous measurements strongly indicate that multinucleon transfer reactions
are a viable pathway to the production of new transuranium isotopes.
1 Introduction
Heavy exotic nuclei are usually produced in fragmentation reactions at relativistic energies or in complete fusion
reactions at Coulomb barrier energies. Projectile fragmentation allows to reach nuclei up to Z = 92. This limit is
given by the available beam materials which are limited to
uranium. To enter the transuranium region, fusion reactions are applied. However, they lead to relatively neutrondeficient isotopes. In particular, neutron-rich superheavy
nuclei cannot be synthesized in fusion reactions due to
the lack of sufficiently neutron-rich projectile-target combinations. This causes the necessity for novel methods.
Multinucleon transfer (MNT) reactions are discussed as a
possible appropriate solution. They allow, in principle, to
produce neutron-rich as well as neutron-deficient isotopes
with proton numbers reaching far beyond uranium.
Experimental and theoretical studies on the synthesis of heavy nuclei in MNT reactions were already
performed in the 1970s–1990s where either very heavy
projectile-target combinations like 238 U + 248 Cm or intermediate heavy projectiles and heavy target nuclei like
a
e-mail: [email protected]
48
Ca + 248 Cm were used. Beam energies were typically up
to 15% above the Coulomb barrier. Two different experimental techniques were used. In one approach the nuclear
charge number Z of the reaction products was determined
by measuring their energy loss ΔE and total kinetic energy E with ionization chambers and surface barrier detectors [1]. No separation techniques were applied before
the detection system. The Z resolution was about 3 charge
units (FWHM) in the region of uranium. An isotopic identification of single nuclei was not possible. Cross-section
limits on the order of 10 μb were reached with this method.
Additionally, in some of the experiments the α and spontaneous fission decays of nuclei implanted in the surface
barrier detectors were recorded during beam-off periods
which allowed isotope identification. Cross-section limits
of 20 nb were reached in those experiments. No new isotopes and no nuclei with Z > 92 were observed. Another
experimental approach was the application of chemical
separation methods with subsequent isotope identification
via radioactive decays. The fastest radiochemical separation techniques proceeded on a time scale of 10 s which allowed the detection of correspondingly long-living nuclei.
With this, transfer products up to Z = 101, N = 157 were
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identified in reactions of 48 Ca or 238 U beams on 248 Cm
targets [2–4]. No new isotopes were observed.
A revival of the topic was initiated about 10 years ago
by new calculations (see e.g. [5,6]) and measurements [7] of
reaction cross-sections and by the above described necessity to find methods different from the established fusion
and fragmentation reactions. Meanwhile, the possible application of MNT for synthesis of new heavy nuclei has
become a topical subject in various laboratories and appropriate separation and detection techniques are being
developed. Here one has to keep in mind that the expected
production cross-sections for new heavy and superheavy
isotopes are small and reach far to the sub-microbarn
range. As a consequence, efficient separation and detection techniques have to be applied, similar to those which
have been developed for the identification of single atoms
from fusion-evaporation reactions in superheavy element
experiments. Fast separation is indispensable due to the
short half-lives of exotic nuclei. Presently, no dedicated experimental setup for the study of heavy MNT products is
available, but for first pioneering experiments the existing
separators for superheavy fusion products can be used. In
particular velocity filters are very sensitive to the reaction
kinematics and can equally be applied to separate heavy
MNT products which are emitted to forward angles.
At GSI Darmstadt we use the velocity filter SHIP [8]
and its detection system to study MNT reactions in heavy
collision systems with the aim to apply them for synthesis
of new heavy isotopes. This method turned out to be significantly more sensitive than the techniques used in previous experiments. It allowed us to reach cross-sections
on the sub-nanobarn scale. Recently, this high sensitivity enabled the observation of several new isotopes in
the transuranium region produced in MNT reactions in
48
Ca + 248 Cm at the Coulomb barrier [9]. Beside the new
isotopes we populated a wide region of nuclei and identified about 100 further target-like transfer products. In the
following we will discuss their production cross-sections
and excitation energies and compare them with previous
experimental data. The results allow for a discussion if
MNT reactions are a practical way to access new heavy
and superheavy isotopes.
2 Experimental setup and method
2.1 Beam and targets
The 48 Ca beam was provided by the UNILAC accelerator of GSI with an energy of 5.63 MeV/u and an average
intensity of 2 × 1012 projectiles/s. The targets consisted
of 460 μg/cm2 thick layers of 248 Cm oxide which were
deposited on titanium backing foils with a thickness of
(2.2–2.4) μm (for details concerning the targets see [10]).
The beam had first to penetrate the Ti backing before
entering the Cm layer. Mainly influenced by the energy
loss and straggling in the Ti foil, the beam energy within
the Cm target covered the range Elab = (252–256) MeV
(5.3 MeV/u). This relatively low energy, 5% above the
Bass interaction barrier [11], is suggested by model calculations in ref. [6] as optimum energy for production of
Eur. Phys. J. A (2016) 52: 278
Fig. 1. Sketch of the experimental setup: the velocity filter
SHIP and the detection system. For details see text and [8].
heavy target-like nuclei in collisions of 48 Ca + 248 Cm. Theoretical as well as experimental studies revealed that beam
energies up to few percent above the barrier are already
sufficient to achieve a large flow of nucleons and allow
the production of isotopes far from the original projectile
and target nuclei. At the same time, the transfer products
are created with moderate excitation energies which keeps
their losses due to fission small.
The 48 Ca beam had a pulsed macro structure which
consisted of 5 ms long beam pulses followed by 15 ms long
beam-off periods. We used this time structure in combination with the electronic signal processing for recording
nearly background free α spectra during the beam-off periods. The total irradiation time was 43 hours. After the
irradiation we ran the data acquisition for two more weeks
which allowed us to register also decays of more long-lived
isotopes.
2.2 Separation and isotope identification
A sketch of the velocity filter SHIP and its detection system is shown in fig. 1. Reaction products which leave the
target at angles up to ±2 degree with respect to the beam
direction are accepted by the entrance aperture of SHIP.
All nuclei which enter SHIP are separated according to
their velocities. The ratio of the electric and magnetic field
values, E/B, determines the velocity at which an ion can
pass through SHIP. The accepted velocity window at a
given setting is Δv/v = 0.1 (FWHM).
All reaction products which pass the velocity filter are
implanted in a position sensitive 16 strip silicon detector
(stop detector) where their time of implantation, position,
kinetic energy and radioactive decays (α, β and fission decays) are registered. This allows reconstruction of the decay properties and decay chains of the nuclei and with this,
the identification of the isotopes. Each strip of the stop detector has a width of 5 mm and a length of 35 mm, where
the position sensitivity along the strip is continuous. Six
further Si detectors are installed in a box-like arrangement
(box detector) in front of the stop detector and cover 85%
of the backward hemisphere in order to register α particles and fission fragments escaping from the stop detector.
Two time-of-flight (TOF) detectors are installed in front
Eur. Phys. J. A (2016) 52: 278
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48
248
Fig. 2. Alpha spectrum measured in collisions of Ca+ Cm
at 5.3 MeV/u. The spectrum was recorded with the silicon stop
detector in the focal plane of SHIP during beam-off periods.
The α lines originate from decays of reaction products implanted in the stop detector and their daughter nuclei.
of the silicon detectors. They distinguish nuclei which were
produced in the reaction from products of radioactive decays of implanted nuclei in the stop detector. In addition,
a germanium clover detector was installed behind the stop
detector to measure γ-rays emitted in prompt or delayed
coincidence with particle registration in the stop or box
detectors.
For identification of the reaction products we used
their α-decay properties. The α spectrum measured during beam-off periods is shown in fig. 2. Many of the lines
contain contributions from more than one isotope with
α energies within the detector resolution. To disentangle
them, we reconstructed their α-decay chains and correlations with preceding recoil nuclei, where possible. The
reconstruction of α-decay chains is a very sensitive method
and enables in the utmost case the unambiguous identification of single isotopes.
The fast in-flight separation allows, in principle, to detect short-lived nuclei with half-lives down to microseconds. This limit is given by the flight time of the reaction
products through the 11 m long SHIP which is about 1 μs.
In the present experiment, the shortest accessible halflives were 20 μs given by the conversion time plus dead
time of the data acquisition system while the longest accessible half-lives are determined by the data recording
time and the yield of a specific isotope.
2.3 Transfer reaction studies with a velocity filter
Velocity filters are very sensitive to the reaction kinematics. They can separate fusion products from αxn and
transfer channels and even distinguish transfer products
with close lying proton numbers [12,13]. Therefore, in the
same way as SHIP is usually used to separate heavy and
superheavy fusion-evaporation residues, it can equally be
applied to separate heavy transfer products. In our experiment we set the E and B values such that targetlike transfer products could pass through SHIP while the
Fig. 3. Velocity spectrum of 225 Pa nuclei measured at SHIP
in reactions of 48 Ca + 248 Cm at 5.3 MeV/u. The velocities are
normalized to the compound nucleus velocity vCN . The width
of the peak is given by the velocity acceptance of SHIP which
is Δv/v = 10% (FWHM). The cross-sections were calculated
from the number of detected 225 Pa α-decays at the respective
velocity setting.
much faster projectiles and projectile-like reaction products were deflected to the beam stop. The average count
rate in the focal plane stop detector was 100 Hz in the
present experiment. It was mainly composed of scattered
projectiles and projectile-like nuclei and of elastically scattered target and target-like nuclei.
Usually, a broad variety of transfer products is created
in the reactions where each of the nuclei has a characteristic velocity depending on its A, Z, the scattering angle
and the energy dissipation during the reaction. In order to
cover this range of different velocities, we varied stepwise
the E and B values of the velocity filter and recorded at
each setting the α-decays of the implanted reaction products and their daughter nuclei. In this way, we obtain a
velocity spectrum for each individual isotope. Typically,
the target-like transfer products which are scattered into
the acceptance angle of SHIP of ±2 degrees have velocities close to two times the compound nucleus velocity
vCN (the velocity of elastically scattered target nuclei at
zero degrees is 2.0 vCN ). We applied five different field settings of SHIP to transmit reaction products with velocities
of 1.70 vCN , 1.80 vCN , 1.85 vCN , 1.90 vCN and 1.95 vCN .
In this range we expected the largest yields of target-like
transfer products. As an example we show in fig. 3 the
measured velocity spectrum for 225 Pa nuclei.
In MNT reactions at the Coulomb barrier the created
nuclei have broad angular distributions. But due to the
narrow acceptance angle only reaction products which are
emitted to forward angles are accepted by SHIP. Experimental data for the angular acceptance of SHIP for MNT
products are not available. Therefore we denote here the
value obtained from calculations with the dinuclear system model [14] for a scenario where the MNT products
are emitted isotropically in the centre-of-mass frame. The
target-like transfer products below uranium are then emitted to a cone with an opening angle of ±60 degrees in the
laboratory system. The resulting angular acceptance for
this case is 0.3%.
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Eur. Phys. J. A (2016) 52: 278
Fig. 4. Survey of all nuclei which we identified in multinucleon transfer reactions of 48 Ca + 248 Cm at 5.3 MeV/u (grey squares).
Beside 248 Cm with a contribution of 96.85% (black square), the target contained also the isotopes 244–247 Cm with contributions
of 0.0007%, 0.031%, 3.10% and 0.015% (black triangles). The five new isotopes which we published in [9] are marked by dots.
The selection of reaction products at forward angles
means at the same time selection of products from central
collisions with very small angular momenta, typically up
to ∼ 25 h̄ [15]. Consequently, the detected nuclei originate
from collisions where projectile and target nucleus reach
maximum possible overlap and sticking time at the given
beam energy. This is the most favourable configuration for
the exchange of large numbers of nucleons leading to the
creation of isotopes far from the original projectile and
target nuclei. Reaction products from collisions at larger
impact parameter are scattered to larger angles and do
not enter SHIP.
3 Experimental results and discussion
3.1 Isotopic distributions
The grey squares in fig. 4 represent all transfer products
which we identified in our experiment via their α-decay
properties. The five new isotopes [9] are marked by dots.
Usually, a contiguous region around the target and projectile nucleus is populated in MNT reactions. Therefore, we
can expect that most of the isotopes which are represented
by blank squares in fig. 4 were also populated in our experiment but could not be identified due to their too short
or too long half-lives and/or unfavourable decay channels. Many nuclei in this region are β emitters or undergo
electron-capture decay which makes them undetectable
with our method. The remaining α emitters have too long
half-lives and too short decay chains for an unambiguous
identification. This is also reflected by the small number
of only two trans-target nuclei which we could identify unambiguously. The nucleus with the longest half-life among
the observed isotopes is 242 Cm with T1/2 = 163 d. It can
easily be produced by stripping of few neutrons from the
target isotopes. The resulting large yields of 242 Cm enable
its observation despite the long half-life.
The cross-sections of the observed isotopes for elements Z = 84–95 are shown in fig. 5 as a function of
Fig. 5. Isotopic distributions of multinucleon transfer products with Z = 84–95 measured in collisions of 48 Ca + 248 Cm
at 5.3 MeV/u. The cross-sections are related to the cumulative
number of α-decays which comprise decays of directly populated nuclei and of nuclei populated by precursor decays. Upper
figure: distributions for even-Z nuclei; lower figure: odd-Z nuclei. The new isotopes are framed. The lines are drawn to guide
the eye.
their mass number —in the following called isotopic distributions. The cross-sections are related to the cumulative
number of α-decays detected at (0 ± 2) degrees, i.e. they
comprise for each isotope nuclei which were directly produced in the reaction as evaporation residues as well as
Eur. Phys. J. A (2016) 52: 278
Fig. 6. The same as fig. 5 but only for isotopes which were directly produced in the reaction, i.e. not populated by precursor
decays.
nuclei populated by precursor decays. The distributions
do not include all isotopes shown in the chart in fig. 4.
Nuclei for which the cross-sections could not be determined reliably were omitted. This concerns in particular
very short-lived isotopes or those which have short-lived
daughter nuclei. In these cases pileup events or event losses
occur if the half-lives are below 20 μs. The lowest measured
cross-sections were on the level of 10 pb/sr, which corresponds to an average event rate of one nucleus per day in
the stop detector at the given beam intensity and target
thickness. For comparison, we show in fig. 6 the isotopic
distributions comprising only MNT products which were
directly produced as evaporation residues. To determine
them, we required that their α-decays were directly preceded by an implanted recoil nucleus. Thus, nuclei which
are populated by precursor decays are excluded in fig. 6.
To minimize random correlations with recoil-like nuclei,
the distributions in fig. 6 comprise only isotopes with halflives up to 1 s. The maximum possible correlation times
in the search for recoil-alpha correlations are given by the
rate of target-like nuclei in the stop detector which are
potential recoil candidates. Their average event rate was
65 Hz. In the search for recoil-alpha correlations we required that the position difference between an implanted
recoil nucleus and its emitted α particle is at most ±1 mm.
Within this position window the rate of target-like nuclei
was 0.24 Hz, resulting in an average time difference between successive recoil candidates of 4.2 s. Therefore, the
half-life of the nuclei should be well below 4 s in order to
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keep the contribution of random recoil-alpha correlations
small. Comparing the distributions in figs. 5 and 6, one can
notice that, naturally, isotopes of elements with the lowest
observed proton numbers were predominantly populated
by precursor decays because they are at the endpoints of
long α-decay chains. The strongest effect is visible for the
isotopes 214 Po and 215 Po where the contributions from
direct production are merely 3% and 5%, respectively.
Multinucleon transfer reactions in 48 Ca + 248 Cm at the
Coulomb barrier were also investigated in an earlier experiment 30 years ago [3]. Relatively thick targets were used
in that experiment leading to an energy spread within the
target of (248–263) MeV. The energy applied in our experiment, (252–256) MeV, is located in the centre of the
energy window of [3]. For isotope identification two different methods were applied in [3]. In one case the reaction products were collected in a catcher foil and analysed
with radiochemical methods and measurement of α- and
γ-decays. This allowed the identification of long-lived reaction products with half-lives of six hours or more. In
the second case the reaction products were thermalized
in a gas-filled recoil chamber and analysed via their αdecays after extraction. With this method, nuclei with
half-lives down to 10 s were accessible. Our experiment
was rather complementary to the previous one since it also
allowed the detection of short-lived nuclei with half-lives
down to some 10 μs. Cumulative cross-sections were measured in [3] which include both, direct population of the
isotopes and population by precursor decays. Further, the
applied techniques measured the full angular distributions
of the reaction products. Therefore, the data include also
events from more peripheral collisions in contrast to our
experiment where only central collisions with very small
angular momenta contribute to the spectra. Due to the
different experimental conditions, a direct comparison of
the results in [3] with our results is not very useful. Instead, we summarize some of the results from [3] in the
following.
Forty isotopes in the region between Rn and Fm
(Z = 86–100) were observed in [3]; ten of them were also
identified in our experiment. With exception of Rn, the
most neutron-deficient isotopes measured in [3] have 10 to
15 neutrons more compared to the most neutron-deficient
nuclei with the same Z measured in our experiment. This
reflects the access to nuclei with shorter half-lives and
smaller cross-sections in our experiment. The sensitivity
limit reached in [3] was 100 nb. The largest cross-sections
with values of several 100 μb up to 1 mb were measured
for isotopes located close to the valley of β stability. In
principle, the ratio between the cross-sections from our
experiment and from [3] should reflect the angular acceptance of SHIP for the detected transfer products, if the
parameters in both experiments were the same. In the
present case, a main uncertainty factor is the relatively
large beam energy window in [3] spanning a width of 6%.
In one of our previous experiments at SHIP, we observed
that a beam energy change by 5% can already change the
transfer cross-section for a certain isotope by one order of
magnitude [16]. Also the location of the maxima of the
isotopic distributions is influenced by the beam energy.
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The overlap of the isotopic distributions from both experiments concerning position and width is a necessary requirement for the direct comparison of the cross-sections.
For half of the isotopes angular acceptances around 0.1%
are obtained, which is rather close to the 0.3% resulting
from model calculations (see sect. 2.3). But there are also
strong spikes for some isotopes like in the case of 223 Ac
( = 0.01%) and 230 U ( = 14%). Beside the different
conditions underlying both experiments this might also
result from possible errors in the yield determination of
individual isotopes.
Theoretical calculations for primary transfer products
from collisions of 48 Ca + 248 Cm at Ecm = 210 MeV are
so far available from the model based on a stochastic
approach and Langevin-type dynamical equations of motion [6]. The predictive power of the model for the description of damped collisions has been shown in various papers
(see, e.g., [6,17]). The lowest cross-section limit reached in
the calculations was about 100 nb. Therefore, the isotopes
measured in our experiment are nearly all outside the region for which calculated cross-sections exist. Moreover,
calculations for secondary transfer products are not available. Due to this, a direct comparison of experimental and
theoretical isotopic distributions is not possible.
3.2 Energy dissipation and excitation energies
MNT reactions are accompanied by a strong dissipation
of kinetic energy. The dissipated energy is mainly transformed into excitation energy of the primary transfer
products. The amount of energy dissipation is reflected
by the total kinetic energy (TKE) of projectile-like and
target-like transfer products in the exit channel. In our
case TKE, and with this the amount of dissipated energy,
can be determined from the positions of the peak maxima
in the velocity spectra. For this we calculate the kinetic
energy of the target-like transfer product from the velocity
which corresponds to the peak maximum. Then we reconstruct the kinetic energy of the corresponding projectilelike transfer product by considering the reaction as a twobody process and taking into account energy and momentum conservation laws. Energy losses of the nuclei in the
target were taken into account (we calculated them with
the computer code SRIM [18]). We determined TKE only
for nuclei which were directly populated in the reaction
and not by precursor decays. In this case we are sure that
the resulting TKE value is correlated with the observed
nucleus and not with a precursor nucleus. The resulting
TKE values, given in the centre-of-mass frame, are shown
by full squares in fig. 7 for isotopes from polonium to neptunium.
In all cases, we observed a large energy dissipation up
to about 60 MeV with respect to the centre-of-mass beam
energy of 212 MeV which indicates the deep inelastic nature of the transfer process. The TKE values are even
located below the Viola energy which is the TKE of fission fragments from an equilibrated compound nucleus, in
our case of the nucleus 296 Lv∗ (we calculated the Viola energy with the formula in [19]). Since there are no hints for
Eur. Phys. J. A (2016) 52: 278
Fig. 7. Total kinetic energy TKE (full squares) and excitation
energy (open squares) of target-like transfer products measured in multinucleon transfer reactions of 48 Ca + 248 Cm at
5.3 MeV/u. The values are given as a function of the proton
number Z of the target-like transfer product. The error bars
represent the uncertainty given by the velocity acceptance of
SHIP at a given setting (see sect. 2.2). For comparison, also
the expected Viola energies for fragments from the fissioning
compound nucleus 296 116∗ are shown (crosses).
systematic errors in the determination of TKE, one can
consider that the low values point to a strong deformation
of the nuclear system at the scission point. By trend, the
measured TKE values come closer to the Viola energy for
increasing Z of the target-like transfer product, i.e. for a
smaller number of transferred protons. For Np (Z = 93),
it is even 15 MeV above the respective Viola energy. Disregarding the experimental error bars, this might already indicate the movement towards a more quasi-elastic nature
of the transfer process which is expected if the reaction
products approach the Z of the target nucleus. A slight
increase of TKE towards smaller Z by about 50 MeV is
observable within error bars. Since TKE is here given by
the Coulomb barrier between projectile-like and targetlike MNT products, the increase of TKE with decreasing
Z of the target-like nucleus occurs because the system becomes more symmetric which leads to an increase of the
Coulomb barrier.
In the following, we are going to estimate the average
excitation energies of the primary transfer products from
the measured TKE values. The sum of the excitation energies of projectile-like and target-like transfer product,
EP∗ L +ET∗ L , is correlated with TKE by the following equation:
(1)
EP∗ L + ET∗ L = E ∗ ≤ Ecm − T KE.
Here we assume that the positive Q-value of the transfer
reactions leading to below-target nuclei transforms into
kinetic energy of the reaction products and is therefore
already included in the experimental TKE values. The
value of E ∗ according to eq. (1) represents an upper limit
because the dissipated energy can also be transformed
into other degrees of freedom like deformation of the nuclei. In the case of an equilibrated system and not taking
into account possible shell effects one can assume that
Eur. Phys. J. A (2016) 52: 278
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E ∗ is shared between projectile-like and target-like transfer products according to their mass numbers AP L and
AT L [20]:
EP∗ L = E ∗ × AP L /(AP L + AT L ),
ET∗ L = E ∗ × AT L /(AP L + AT L ).
(2)
(3)
The resulting excitation energies ET∗ L for the target-like
transfer products are shown by open squares in fig. 7.
They have values between 30 and 50 MeV. At these excitation energies which are well below 100 MeV, the deexcitation mainly takes place via fission of the primary
transfer products or by evaporation of neutrons. While
fission leads to a loss of the heavy transfer product, neutron evaporation shifts the primary isotopic distributions
towards more neutron-deficient nuclei. The measured isotopic distributions discussed in sect. 3.1 are secondary distributions which result after the deexcitation process. For
nuclei in the observed mass region, about 10 MeV is required to evaporate one neutron. This energy is determined by the neutron separation energy and the kinetic
energy of the neutron in the nucleus. As a result, the primary transfer products evaporate on average three to five
neutrons. This is in good agreement with the theoretical
results given in [6]. According to [6], the excitation energy is increasing with increasing number of transferred
protons. From Np to Po, which corresponds to the region
shown in fig. 7, the calculated excitation energies increase
from 30 MeV to 50 MeV. In the experimental data, the error bars are too large to draw reliable conclusions about
a dependency of the measured excitation energies on the
number of transferred protons.
3.3 Comparison of multinucleon transfer and fusion
reactions
The established method to synthesize neutron-deficient
nuclei in the region around and above uranium is fusionevaporation reactions. Therefore it is interesting to compare them with MNT reactions concerning the capacities
for isotope production. As a starting point, we show in
fig. 8 measured fusion-evaporation cross-sections of various uranium isotopes [21–27] and MNT cross-sections
measured in our experiment and in [3]. Figure 8 can be regarded as a representative example because the behaviour
of the cross-sections is similar for other elements in the
uranium region. The fusion cross-sections for the same
residual nucleus can fluctuate by orders of magnitude depending on the applied projectile-target combination and
beam energy. If cross-sections from more than one experiment were available for the same isotope, we put the
largest known value in fig. 8. Concerning MNT reactions,
it is very likely that the given cross-sections have not the
maximum achievable values, because systematic studies
to find the optimum projectile-target combinations and
measurements of excitation functions for the given MNT
products were not performed so far. Instead of the pure
reaction cross-sections, we show in fig. 8 the product of
cross-section and experimental efficiency, σ, because this
Fig. 8. Product of cross-section and experimental efficiency,
σ, of uranium isotopes measured in fusion-evaporation reactions (crosses) and in multinucleon transfer (MNT) reactions
of 48 Ca + 248 Cm in our experiment (open circles) and in the
experiment in ref. [3] (full circle). For the transfer products
we show cumulative cross-sections. For 219 U we put for better
visibility a small offset on the A value to avoid the overlap of
the data points from fusion and MNT.
is the experimentally relevant parameter which reflects the
event count rate in the detector. In our case, is mainly
determined by the angular acceptance of the applied separators for fusion or transfer products, respectively. Figure 8 indicates already that there is no overall answer if
MNT or fusion reactions are the better option for the synthesis of (new) transuranium isotopes. Rather, the answer
depends on the envisaged region on the nuclear chart:
1) In fig. 8, one can notice that for the more neutronrich nuclei well above A = 220 σ is significantly larger in
fusion-evaporation reactions. This is on one hand caused
by the larger angular acceptances of the separators for
fusion-evaporation residues. Another reason is that these
isotopes can be produced with very asymmetric projectile208
230 ∗
target combinations like 22
10 Ne + 82 Pb → 92 U where the
low entrance channel Coulomb barriers and favourable Qvalues lead to relatively large fusion residue cross-sections.
In this mass region, fusion-evaporation reactions appear
superior to MNT reactions.
2) For very neutron-deficient isotopes the situation
changes and the σ for MNT and fusion products tend
to approximate each other despite the small efficiencies
for MNT products. To reach these nuclei in fusion reactions, more symmetric projectile-target combinations like
40
182
222 ∗
18 Ar + 74 W → 92 U have to be applied. The larger entrance channel Coulomb barriers and less favourable Qvalues lead to relatively low fusion-evaporation residue
cross-sections. In this region, a clear advantage of MNT
reactions comes into play. It results from the broad excitation functions of MNT products and leads to a wide-band
population of many different nuclides with sizeable yields
in the same experiment while fusion-evaporation reactions
are selective on only few specific isotopes. In this region
MNT seems an attractive option and is in competition
with fusion reactions.
Page 8 of 9
3) Finally, we want to mention the case of very heavy
nuclei with Z > 100 where only neutron-deficient isotopes
left of the stability line are known so far. Neutron-rich
nuclei in this area cannot be reached in complete fusion
reactions with stable beams due to the bending of the
stability line toward the neutron axis. Therefore, MNT
reactions are presently the only viable option to enter this
new territory on the chart of nuclides.
4 Conclusions and outlook
Our results show that the existing vacuum separators and
related detection systems are suitable for the study of
multinucleon transfer reactions and even enable the detection of new exotic isotopes. In particular, velocity filters
are very sensitive to the reaction kinematics. They separate fusion products from αxn and transfer channels and
even allow the separation of transfer products with close
lying proton numbers. This leads to a strong background
suppression resulting in one-event cross-section limits on
the subnanobarn scale. Due to their selectivity on reaction
products emitted to zero degree they are selective on nuclei which originate from central collisions with large nuclear overlap and small angular momenta; both are necessary requirements to achieve a large flow of nucleons leading to isotopes far from the original projectile and target
nuclei.
The sensitivity reached in our experiments allows already, in principle, to enter the region of new neutron-rich
isotopes with Z > 100 assuming that the cross-sections
from model calculations are correct. However, the present
bottleneck is the lack of appropriate detection techniques
which allow the identification of nuclei in this region which
are mostly not α emitters and/or have long half-lives.
Therefore, a necessary requirement to access neutron-rich
trans-fermium isotopes is the development of new and efficient detection methods which allow the identification of
single nuclei independent of their decay properties. Activities to reach this goal are ongoing in different laboratories.
One approach is the application of precision mass measurements with a Penning trap [28] or multiple reflection
time-of-flight mass spectrometer [29,30] where a resolving
power of 105 –106 is already sufficient for an isobaric identification of most of the heavy nuclei. Another possible
method is to determine the nuclear charge number of the
reaction products by selective laser ionization while the
mass number of the singly ionized nuclei can be obtained
with a magnetic dipole field.
Beside the development of new detection techniques,
an upgrade or new development of in-flight separators for
multinucleon transfer products is necessary. Our experiments showed that the separation according to velocities is an appropriate tool but the angular acceptances
of present velocity filters are very small with regard to
the broad angular distributions of multinucleon transfer
products. Simulation results [31, 32] showed that, from
technical point of view, the acceptance angle of a velocity filter like SHIP could be increased by a factor of 10
by using large quadrupole triplets with bore radii up to
Eur. Phys. J. A (2016) 52: 278
15 cm at the entrance and exit of the separator. However,
the optimum acceptance angle might be smaller because
an increase of the acceptance means at the same time
an increase of transmitted background events which reach
the focal plane detector (simulations to investigate the
optimum acceptance are still ongoing). The critical background in transfer as well as in fusion reactions is caused
by transfer products with proton numbers close to the target nucleus which are populated with large cross-sections.
In fusion reactions the kinematic properties of the fusionevaporation residues are well separated from the properties of the transfer products which allows an effective suppression of the background events by the separator. For
example, the velocity of fusion-evaporation residues and
target-like transfer products differs by nearly 100% for collision systems like Ca + Cm. In multinucleon transfer reactions, the envisaged reaction products and background
events have necessarily similar kinematics and separation
becomes less effective. Thus, one cannot just increase optionally the acceptance angle of a separator to increase the
efficiency for transfer products because at the same time
the efficiency for background events will equally increase
leading to a decrease in sensitivity for isotope identification.
We would like to thank the crew of the UNILAC accelerator
for the excellent technical support throughout the experiment.
Further, we thank our colleagues from theory, G. Adamian,
N. Antonenko, W. Greiner, J. Maruhn, and V. Zagrebaev for
providing us with model calculations and for many fruitful discussions. The work at LLNL was performed under the auspices
of the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. The
work at Manipal University was performed within the Memorandum of Understanding between Manipal University, GSI
Helmholtzzentrum and Justus-Liebig-Universität Gießen. One
of us, HMD, recieved fundings from the LOEWE program.
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