Eur. Phys. J. A (2020) 56:224
https://doi.org/10.1140/epja/s10050-020-00229-2
Regular Article - Experimental Physics
New studies and a short review of heavy neutron-rich transfer
products
H. M. Devaraja1,2,a, S. Heinz1,2, D. Ackermann3, T. Göbel1, F. P. Heßberger2,4, S. Hofmann2, J. Maurer2,
G. Münzenberg2, A. G. Popeko5, A. V. Yeremin5
1 Justus-Liebig-Universität Giessen, II. Physikalisches Institut, 35392 Gießen, Germany
2 GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
3 GANIL, CEA/DRF-CNRS/IN2P3, BP 55027, 14076 Caen Cedex 5, France
4 Helmholtz-Institut Mainz, 55099 Mainz, Germany
5 Joint Institute for Nuclear Research, 141980 Dubna, Russia
Received: 26 May 2020 / Accepted: 17 August 2020 / Published online: 5 September 2020
© The Author(s) 2020
Communicated by Nicolas Alamanos
Abstract We present new results on multi-nucleon transfer very steeply after stripping of every proton along N = 126.
reactions in low-energy collisions of 48Ca+238U measured at Presently, the nucleus 20276 Os is the lightest N = 126 isotone
the velocity filter SHIP of GSI Helmholtz Centre, where we with a production cross-section of 4.4 ± 2.0 pb [2].
observed around 90 different nuclides from Tl to Am (Z = Multi-nucleon transfer (MNT) reactions, which are under
81–95). We followed the idea to use uranium targets for the discussions for the past few decades, established new expec-
synthesis of neutron-rich MNT products, particularly in the tations to reach the still unknown region of neutron-rich N =
region below lead, which was triggered by model calcula- 126 nuclei. This is based on the results of so far performed
tions. The γ ,α and spontaneous fission activities of the popu- experiments [3–24] as well as on predictions based on vari-
lated nuclides have been analyzed for their identification. The ous theoretical models, such as the di-nuclear system (DNS)
cross-sections of the observed isotopes for elements Z =81– model [25–33], model based on Langevin-type dynami-
93 as a function of their mass number have been investi- cal equations [34–39], GRAZING model [40,41], complex
gated. Excitation energy, total kinetic energy and the influ- Wentzel-Kramers-Brillouin (CWKB) model [42], improved
ence of nuclear shell effects on the production cross-sections quantum molecular dynamics model (ImQMD) [43–47],
of the observed transfer products have been studied. Also time-dependent Hartree-Fock (TDHF) theory [48,49], and
we present a compact review and comparative analysis of others (see, e.g., reviews [50–53] and references therein).
various multi-nucleon transfer and fragmentation reactions Model calculations based on the Langevin-type dynam-
which are aimed at the synthesis of neutron-rich nuclides ical equations of motion given in [37] recommend to use
along the N = 126 shell closure in heavy nuclei. deep inelastic MNT reactions in 136Xe+208Pb and estimated
larger cross-sections than that of fragmentation reactions.
Other theoretical results from the DNS model [29] proposed
1 Introduction to apply MNT reactions with neutron-rich lighter beams like
48Ca or 64Ni. Experimental results exist already for both vari-
Exploring the heavy neutron-rich nuclei and their decay ants. An interesting alternative approach of the DNS model
sequences to the valley of β stability is supremely interest- is the suggestion to use uranium targets instead of Pb or Pt
ing for the understanding of the predicted r-process path. to populate nuclei along N = 126. With Pb or Pt targets
Indeed, the evolution of the nuclear shells far from the valley the nucleon flow must proceed in south-east direction of the
of stability and along the neutron shell N = 126 is still an nuclide chart to populate neutron-rich nuclei along N = 126.
open question. The most neutron-rich nuclei in this area were But with uranium or other actinide targets, the same nuclides
so far produced by using 208Pb and 238U fragmentation reac- can be reached with the much more preferred south-west
tions. They reached the cross-section level down to picobarns flow of nucleons, along the stability line. This should shift
[1,2]. In these experiments, cross-sections are decreasing the isotopic distributions toward the neutron-rich side. These
a e-mail: d.haleshappamalligenahalli@gsi.de (corresponding author)
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224 Page 2 of 17 Eur. Phys. J. A (2020) 56 :224
DNS model results motivated our experimental investigation we present an overview of the important aspects of the exper-
of the Ca + U system. iment, which were necessary for this specific measurement.
Already in the 1980s, MNT reactions were applied suc- The experimental investigation of the reaction 48Ca + 238U
cessfully at the GSI on-line mass separator to synthesize was performed at the SHIP separator [70] in three differ-
heavy nuclei. Various reactions with heavy beams like 76Ge ent irradiation periods which took already place in the years
[54,55], 136Xe [56–58], 186W [59,60], 208Pb [61] and 238U 2005–2007. The main focus was on the synthesis of super-
[62] on tantalum and tungsten targets were applied. They heavy nuclei with Z = 112 in fusion-evaporation reactions.
lead to the discovery of 18 isotopes with Z = 25 − 89 on The first part of the investigations was in 2005 from April 6
the neutron-rich side of the nuclide chart. The nuclides were to June 19, the second part was in 2006 from October 4 to 30
identified and investigated by coincident detection of their γ and the third part was in the year 2007 from January 19 to
and X-ray decay activities. February 14. A summary of the beam time along with the key
At the velocity filter SHIP of GSI we performed exten- parameters of the experiments are presented in the Table 1 of
sive studies of MNT reactions over the past years [12–23] the article [70]. The here presented results on MNT reactions
aiming at different areas of heavy and superheavy nuclei were measured in the middle of the fusion experiments. For
on the nuclide chart. In one of our more recent works, this, the SHIP fields were set for 7.7 h to transmit target-like
MNT reactions were successfully applied to synthesize new transfer products moving in forward angles of (0±2) degree.
neutron-deficient uranium and trans-uranium isotopes, and The beam energy of 235.2 MeV delivered from the UNILAC
to populate heavy neutron-rich nuclei up to nobelium in accelerator was continued as it was set for the fusion evap-
48Ca + 248Cm collisions. In other studies, we used 58,64Ni oration study. The beam energy at the center of the target is
beams with 207Pb targets, to investigate below-Pb MNT prod- estimated to be 233.3 MeV, which is close to the Bass inter-
ucts [19] and observed several isotopes of elements down to action barrier of 232.9 MeV [71]. After this, again the fusion
Z = 76. The results are very similar to the ones of other setting was continued for another 199 h. In this case, the
groups who investigated this region with Pb or Pt targets direct passage of target-like transfer products is suppressed
[63–65]. Significant attention is presently drawn to recent by a factor of 1000. This was a very favourable condition to
results presented in [66] who studied the MNT reactions in record the residual long-living α and γ decay activities of
136Xe + 198Pt collisions. They detected the projectile-like the already implanted vast amount of target-like MNT prod-
fragments and deduced from them the isotopic distributions ucts in the silicon detector with half-lives from few hours to
of the complementary target-like fragments. It was revealed several days.
that MNT cross-sections strongly increase with respect to The average intensity of the 48Ca beam was 2.6 × 1012
fragmentation cross-sections toward smaller proton num- particles / s with a total number of 7.16 × 1016 projectiles in
bers. It is an interesting goal for future experiments to con- 7.7 h irradiation time. We used metallic uranium targets with
firm these results by directly detecting the target-like MNT an average thickness of 302µg/cm2 which were deposited
products. on 42µg/cm2 thick carbon backing foils and covered with
In this article we present our experimental results from carbon layers with a thickness of 10µg/cm2 and in some
MNT reactions in 48Ca + 238U, suggested by DNS model cases 20µg/cm2. The lowest accessible life-times of 20µs
calculations to synthesize neutron-rich nuclei below Pb. The were given by the conversion time plus the dead time of the
populated target-like nuclei have been identified using their data acquisition system.
α, γ and spontaneous fission (SF) activities. We investi- SHIP accepts only reaction products which are emitted to
gated isotopic distributions, excitation energy, total kinetic forward angles of (0 ± 2) degrees. MNT reaction products
energy and influence of nuclear shell effects on the produc- produced in deep inelastic collisions around the Coulomb
tion cross-sections of the observed transfer products. The barrier energy have very wide angular distributions. Exper-
results are compared with previously studied MNT reactions imental data for the angular acceptance of SHIP for MNT
in the systems 64Ni+ 207,208Pb [19,63], 136Xe+ 208Pb [64], products are not available. Therefore, we rely on the effi-
136Xe+198Pt [65,66] and with fragmentation reactions using ciencies obtained from calculations in the di-nuclear system
208Pb [1,67] and 238U [2,68] beams, all of them aiming at model [72] for our collision system and beam energy. The
the synthesis of neutron-rich nuclides along the N = 126 respective value is about 0.5% for reactions of 48Ca + 238U.
shell closure. Uncertainties of a factor 5 to 10 might be possible.
2 Experimental details
The SHIP velocity filter and its detection system were
already described in previous articles [22,23,69,70]. Here,
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Eur. Phys. J. A (2020) 56 :224 Page 3 of 17 224
Fig. 1 Measured α spectra of the target-like transfer products from the following the transfer setting. The tails (asterisk) towards higher α ener-
48Ca + 238U reaction. a Spectrum accumulated during the 7.7 h mea- gies are due to the pileup of β− particles emitted from 212Bi and 213Bi
surement of transfer reaction products. b Spectrum accumulated during isotopes with the α energies of the short-living 212Po (T1/2 = 0.3µs)
the 199 h of SHIP settings for fusion-evaporation residues which was and 213Po (T1/2 = 4.2µs) daughter nuclei. For details see text
3 Results of the 48Ca+238U experiment 222Rn (3.82 d). The daughter nuclei of the decay chains have
half-lives from few seconds down to microseconds. The α-
3.1 Isotopic distributions and cross-sections α correlation technique allowed us to attribute these α-lines.
Some of the α-lines of directly populated nuclei and of nuclei
The isotope identification in the present work is mainly asso- which are strongly populated by β-decays of their parents,
ciated with the α, γ and SF decay properties of the populated are also attributed easily. These lines mainly belong to the
nuclei. The literature data for the decay energy, half-lives and isotopes 210−213Po and 211,212,212mBi. Most of the short-
branching ratios were taken from [73]. Within our measure- living rarely populated nuclei (not visible in Fig. 1) with
ment time,α and γ spectra were accumulated for the strongly half-lives up to few hundred milliseconds were identified by
populated nuclides with half-lives up to few hours. Both, the correlating the recoil and subsequentα’s. The γ -spectra mea-
α and γ spectra shown in Figs. 1 and 2 are measured dur- sured during the transfer setting and the following 199 h of
ing the beam-off condition which was given by the pulse fusion-evaporation settings are shown in Fig. 2. The lowest
structure of the UNILAC beam. It consisted of 5 ms long cross-section reached for α emitters was 20 pb/sr. For iso-
beam pulses followed by 15 ms long beam-off periods. In tope identification by γ rays it was 150 nb/sr. These limits
Fig. 1a the α-decay spectrum of the populated candidates are differential cross-sections related to the acceptance angle
during the 7.7 h setting for transfer products is presented. of SHIP. Assuming the SHIP angular efficiency of 0.5%, the
The other Fig. 1b includes the α decays from Fig. 1a and total cross-section limit was 4 nb for α emitters and 30 µb
those decays which occurred up to 199 h after the transfer for isotope identification via γ rays.
setting. It shows therefore mainly the long-lived MNT prod- Figure 3 shows the region of identified nuclides in the
ucts with half-lives up to few days. The α lines in Fig. 1b nuclide chart. The filled boxes without circles are the identi-
belong mainly to the members of the α-decay chains origi- fied nuclides by following the recoil-α and α-α correlations
nating from the parent nuclei 226Ac (T1/2 = 29.37 h), 230U of the implanted nuclides in the silicon detector. The ones
(20.8 d), 225Ac (9.92 d), 223Ra (11.43 d), 224Ra (3.66 d) and indicated by filled circles are the identified nuclei using the
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224 Page 4 of 17 Eur. Phys. J. A (2020) 56 :224
Fig. 2 γ -spectra accumulated during the 7.7 h SHIP settings for transfer products and the following 199 h with settings for fusion-evaporation
residues. Some of the unassigned lines are still uncertain
Fig. 3 The nuclear chart
showing the region of identified
nuclides from the reaction
48Ca + 238U. The filled boxes
without circles represent
isotopes which were identified
using α decay. Isotopes
indicated by filled circles were
identified by their γ decay
properties. The three americium
fission isomers with half-lives
up to 14 ms were identified by
following the
recoil-spontaneous-fission
correlations
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Eur. Phys. J. A (2020) 56 :224 Page 5 of 17 224
sections. It means they contain directly populated nuclei
as well as nuclei populated by precursor decays. In Fig. 5
we present the cross-section versus mass number A for the
directly populated isotopes. Some of the strongly and directly
populated nuclides have some minor contributions from the
decay of other nuclides. In cases where we could not deter-
mine these contributions we indicated the cross-sections as
upper limit values. The cumulative and direct cross-sections
of individual isotopes are listed in Table 1. In the region
below Pb, only isotopes of thallium (Z = 81) could be iden-
tify in our experiment. The measured lowest cross-section
was 70µb for the isotope 208Tl. The detection of nuclei with
smaller Z was prevented by the sensitivity limit of 30µb for
β emitters.
3.2 Excitation energy and total kinetic energy of the MNT
Fig. 4 Production cross-sections as a function of mass number A esti- products
mated from the cumulative yields of the identified target-like transfer
products in the 48Ca + 238U reaction. The upper figure shows isotopic
distributions for even-Z nuclei (a); the lower figure is for odd-Z nuclei The total kinetic energy (TKE) of the MNT products we cal-
(b). Error bars represent statistical errors. The lines are used to guide culated from the velocity of the detected target-like nucleus
the eye and by assuming a binary reaction process like described
in our earlier publication [22]. Figure 6 shows the calcu-
lated values of TKE (open squares) as a function of Z of
the target-like MNT products of elements Po, Rn, Fr and
Ra. For comparison we show in Fig. 6 also the expected
Viola energies which we calculated according to [74]. The
Viola energy is the total kinetic energy of two fission frag-
ments which are emitted from a compound system in ther-
mal equilibrium. The increase of TKE towards smaller Z of
the target-like MNT product is dominated by the increas-
ing charge symmetry of projectile-like and target-like frag-
ment which increases the Coulomb repulsion between them.
We observe that the experimental TKE values are about 25
MeV lower than the Viola energy which confirms the deep
inelastic nature of the underlying process. In this case, the
system has “forgotten” the entrance channel kinematics and
the TKE of the exit channel fragments is determined by the
Fig. 5 Production cross-sections as a function of mass number A of
the directly populated target-like transfer products in the 48Ca + 238U Coulomb repulsion between of projectile-like and target-like
reaction. The arrows indicate upper limit cross-sections for nuclei with MNT product. The observation that the experimental TKE
small contributions from parent decays which could not be resolved values are even below the Viola energy indicates a strong
from the direct production cross-section. The upper figure shows iso- deformation of the MNT products at their scission point. We
topic distributions for even-Z nuclei (a); the lower figure is for odd-Z
nuclei (b). Error bars represent statistical errors. The lines are used to made this observation also in other systems [18,22].
guide the eye The sum of excitation energies of the projectile-like and
target-like MNT product, E∗ ∗PL + ET L , is determined by the
TKE and the centre-of-mass energy ECM according to the
γ -decay properties. Three short-living isotopes of americium following equation:
fission isomers with half-lives up to 14 ms were identified by
analysing the recoil-SF correlations. The experimental cross- E∗ + E∗ ∗PL T L = E ≤ ECM − T K E (1)
sections of target-like MNT products of individual elements
as a function of mass number of the identified isotopes are The dissipated energy is also contributing to other degrees
shown in Fig. 4. The estimated errors represent the statis- of freedom like deformation of the nuclei hence the value
tical uncertainties. The even and odd elements are shown of E∗ in eq. (1) represents the upper limit. Neglecting shell
separately. The given cross-sections are cumulative cross- effects in systems approaching equilibrium, like indicated
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224 Page 6 of 17 Eur. Phys. J. A (2020) 56 :224
Table 1 Cross-sections of directly populated MNT products (σDC ) and Table 1 continued
cumulative cross-sections (σCC ) of the observed MNT products from
collisions of 48Ca + 238U. The cross-sections are differential cross- El. Z N A σDC (nb/sr) σCC (nb/sr)
sections related to the SHIP acceptance angle of (0 ± 2) degrees. Error
Th 90 133 223 0.09 ± 0.04 0.09 ± 0.04
bars represent statistical errors
134 224 0.56 ± 0.12 0.56 ± 0.12
El. Z N A σDC (nb/sr) σCC (nb/sr) 136 226 – 311 ± 2
Tl 81 126 207 – 1747 ± 7 141 231 ≤ 18716 18716 ± 241
127 208 348 ± 12 851 ± 4 143 233 5285 ± 374 5285 ± 374
128 209 45 ± 0.9 221 ± 7 Pa 91 141 232 6097 ± 75 6097 ± 75
129 210 0.04 ± 0.03 146 ± 6 143 234 14145 ± 112 14145 ± 112
Pb 82 129 211 – 1421 ± 9 145 236 ≤ 2999 2999 ± 62
130 212 – 1702 ± 6 146 237 ≤ 1970 1970 ± 71
131 213 – 139 ± 4 147 238 ≤ 227 227 ± 15
132 214 – 118 ± 2 U 92 138 230 15 ± 1 15 ± 1
Bi 83 128 211 – 1752 ± 8 145 237 16572 ± 127 18542 ± 142
129 212 – 1702 ± 6 147 239 ≤ 6737 6737 ± 54
130 213 – 2031 ± 8 Np 93 145 238 4810 ± 133 4810 ± 133
131 214 – 118 ± 2 146 239 2701 ± 38 9438 ± 133
Po 84 129 213 – 2350 ± 9 147 240 ≤ 4240 4240 ± 115
130 214 15.7 ± 0.6 1814 ± 6 148 241 ≤ 6166 6166 ± 186
131 215 42.7 ± 0.9 1421 ± 9 149 242 223 ± 15 223 ± 15
132 216 107 ± 3 1702 ± 6
133 217 – 139 ± 4
134 218 – 118 ± 2
At 85 128 213 – 54 ± 1.2
130 215 14.8 ± 0.6 331 ± 2
132 217 525.6 ± 3.5 1892 ± 8
Rn 86 127 213 33 ± 0.9 33 ± 0.9
131 217 153 ± 3 458 ± 5
132 218 231 ± 2 1745 ± 6
133 219 307 ± 3 1378 ± 9
134 220 148 ± 2 1702 ± 6
135 221 ≤ 139 139 ± 4
136 222 ≤ 118 118 ± 2
Fr 87 127 214 5 ± 0.3 5 ± 0.3
132 219 294 ± 3 326 ± 3
134 221 335 ± 2 1366 ± 7
Ra 88 127 215 0.8 ± 0.1 0.8 ± 0.1 Fig. 6 Total kinetic energy TKE (squares) and excitation energy E∗T L
132 220 85.4 ± 2.3 85.4 ± 2.3 (triangles) of target-like transfer products as a function of the proton
± ± number Z of the transfer product. The measurement is from
48Ca+238U
133 221 305 4 305 4 collisions at 233.3 MeV beam energy. The error bars are related to the
134 222 944 ± 4 1513 ± 6 uncertainty given by the SHIP velocity acceptance at a given setting.
135 223 ≤ 1071 1071 ± 9 For comparison, also the expected Viola energies [74] for fragments
286
136 224 ≤ 1554 1554 ± 6 from the fissioning compound nucleus Cn are given (asterisks)
Ac 89 127 216 0.36 ± 0.09 0.36 ± 0.09
132 221 18.0 ± 1.4 18.0 ± 1.4
± ± by our small observed TKE values, E
∗ would be distributed
134 223 31.3 0.87 31.3 0.87
≤ ± between projectile-like and target-like MNT products lin-136 225 796 796 7 early to their mass numbers APL and AT L . This results from
137 226 570 ± 4 570 ± 4 the linear increase of the level densities with mass number
139 228 ≤ 5235 5235 ± 136 in the liquid drop model. However, the results of the Ca + U
140 229 ≤ 2192 2192 ± 117 data indicate that shell effects cannot be neglected. There-
fore, we used another method to derive E∗ ∗PL and ET L , which
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Eur. Phys. J. A (2020) 56 :224 Page 7 of 17 224
we described already in a previous publication [18]. In this
approach we compared the measured isotopic distributions
of secondary MNT products (after de-excitation) in Fig. 5
with the expected isotopic distributions of the primary trans-
fer products (before the de-excitation). For this we assume
that the yields of primary transfer products are strongly influ-
enced by the effective reaction Q-value (Qe f f ) [75], which
depends on the reaction Q-value and the differences between
Coulomb barrier in entrance (Vc.i ) and exit (Vc. f ) channel,
and is expressed by the following equation:
Qef f = Q + Vc.i − Vc. f (2)
= 1.44Z1Z2 1.44Z3Z4Qef f Q + −
1 2[A1/3 + A1/3] 1 2[A1/3 + A1/3
(3)
. 1 2 . 3 4 ]
where A1 (Z1) and A2 (Z2) are the mass (atomic) numbers of
projectile and target in the entrance channel and A3 (Z3) and
A4 (Z4) are the mass (atomic) numbers of projectile-like and
target-like primary transferred products in the exit channel
respectively. With
Q = (M1 + M2 − M3 − M4)c2 (4)
where M1 (M2) is the ground state mass of the projectile (tar-
get) and M3 (M4) is the ground state mass of the projectile-
like (target-like) primary MNT products respectively.
Figure 7 represents the distributions of Q and Qe f f as
a function of mass number of the primary transfer products.
The Q-values according to equ. 4 are continuously increasing
Fig. 7 Reaction Q value (upper fig.) and effective Q value (lower fig.) toward smaller proton number of the target-like MNT prod-
as a function of mass number of the primary MNT products are presented ucts which results from their increasing binding energy or
decreasing mass, respectively. The effect becomes most pro-
Table 2 Column 1: Isotopes in the maxima of the expected primary nounced if we approach the Pb valley. The increase of Qe f f
isotopic distributions of target-like transfer products. column 2: Iso- values toward the Pb valley, is much smoother because the
topes in the maxima of the measured secondary isotopic distributions of
+ exit channel Coulomb barrier becomes larger with increasingtarget-like transfer products from collisions of 48Ca 238U (see Fig. 5). mass (charge) symmetry of the system. For a given proton
column 3: Difference of the neutron numbers ΔN between the primary
and secondary transfer products from columns 1 and 2, which indicates number those isotopes are preferably populated for which
the shift between primary and secondary isotopic distributions. column the reaction Qe f f -value has a maximum. The isotopes where
4: Excitation energies of the target-like transfer products deduced from the Qe f f -values have a maximum are expected as the most
ΔN probable primary products. The difference ΔN between the
Primary Secondary ΔN E∗ neutron number where the Qe f f -value distribution has a max-
MNT product MNT product [MeV] imum and the neutron number where the measured distribu-
238Np 237Np 1 10 tion has a maximum reflects the average number of evapo-
236U 237U – 0 rated neutrons from the primary products. From the value of
234Pa 234Pa 0 0 ΔN we estimated the excitation energy of the nuclei. The
232Th 231Th 1 10 neutron separation energies for nuclei in this mass region are
230 228 7 to 8 MeV [73] and the kinetic energy of a neutron in theAc Ac 2 20
226 223 nucleus is 1.7 MeV (energy at the maximum of the Boltz-Ra Ra 3 30
223 220 mann distribution). Therefore one can assume that about 10Fr Fr 3 30
MeV are required for the evaporation of one neutron and the
220Rn 219Rn 1 10 excitation energy is given by E∗ = ΔN × 10 MeV. This
method gives a direct information about the excitation ener-
gies of the primary target-like MNT products.
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224 Page 8 of 17 Eur. Phys. J. A (2020) 56 :224
The given theoretical cross-sections correspond to the max-
ima of the isotopic distributions shown in [29]. Our data did
not reveal isotopes of elements below Z = 81. Therefore we
cannot directly compare them with the DNS model cross-
sections from [29], but one can see that the experimental
values join the model calculations within less than one order
of magnitude in the transition region around Z = 80. It can
be noticed in the figure that the experimental cross-sections
for elements 81 to 87 are nearly constant. We presume that
this is mainly caused by the Pb shell effects at Z = 82,
N = 126 which create a deep valley in the potential energy
surface. The nucleon flow follows the valley which leads to a
preferred creation of Pb-like transfer products. Shell effects
which influence the nucleon flow in deep inelastic reactions
Fig. 8 Maximum cross-sections of multi-nucleon transfer products as were also revealed in earlier experimental and theoretical
a function of their proton number Z. The given cross-sections corre- works (see e.g. [34,76,77]). Another effect which might con-
spond to the maxima of the respective isotopic distributions. filled cir-
48 + 238 tribute to the enhanced cross-sections in the Pb region is thecles: experimental cross-sections from collisions of Ca U (this
work), open circles: DNS model calculations for 48Ca+238U [29], filled high survivability of these nuclei against fission. This leads to
squares: experimental cross-sections from collisions of 64Ni + 208Pb smaller losses of Pb-like primary transfer products compared
[63] to actinide nuclei which have lower fission barriers.
In the region below Pb, the so far most comprehensive
∗ experimental data from MNT reactions with Pb targets areThe resulting values of E are shown in Table 2 and in from [63] where collisions of 64Ni+208Pb were investigated.
Fig. 6 (open triangles). A pronounced structure is revealed
∗ ≈ The maximum cross-sections for each isotopic distributionwhere E adopts maximum values of 30 MeV for iso-
= − from this work are also shown in Fig. 8. Due to the lack oftopes of Fr, Ra and Ac (Z 87 89). Elements close experimental data from Ca + U in this region we can com-
to the target nucleus U have smaller excitation energies of pare the Ni + Pb data only with model calculations. Since Pb
< 10 MeV. These nuclei are usually not produced in deep is 10 protons closer to this region than U, it is not surprising
inelastic processes where all kinetic energy dissipates, there- that about 50 times larger maximum cross-sections for MNT
fore less energy is available for excitation. A drop of excita- products with Z < 82 are reached with Pb targets. The max-
tion energies to values < 10 MeV is also observed for ele- imum cross-sections in Ni + Pb and Ca + U reactions drop
ments below Fr. These nuclei are already located in the “Pb- moderately and with similar slope toward smaller Z of the
valley” and it is very likely that the double shell closure at
= MNT products. Roughly one can extract that in both casesZ 82, N = 126 is the reason for their low excitation the maximum cross-section decreases by a factor of 10 per
energies. In these cases, the projectile-like complementary eight protons which are moved from target to projectile.
nucleus must overtake the higher excitation energy. Figure 8 reveals still another interesting structure. There
is a peak in the experimental cross-sections around Z = 70
3.3 Comparison of the Ca + U data with model calculations and also the DNS model calculations reveal a peak around
and with experimental data from other collision systems Z = 68. It cannot be caused by shell closure effects because
neither the target-like nor the complementary projectile-like
In this section we are going to compare measured and nucleus have closed shells at the respective Z and N. How-
calculated isotopic distributions of MNT products from dif- ever, it could be an effect of strong deformation of the transfer
ferent collision systems. The collision systems for which products at Z = (68 − 70) for target-like and Z = (44 − 42)
experimental data are available are listed in Table 3. Model for projectile-like nuclei. The smaller Coulomb interaction
calculations are available for reactions of 48Ca + 238U [29] of strongly deformed nuclei with respect to the neighbouring
and 136Xe + 208Pb [37,39]. The aim of this study is to get elements reduces the potential energy of the DNS and creates
information if Pb or actinide targets are more profitable to a valley to which the system is preferably driven [72].
reach neutron-rich MNT products. First, we show in Fig. 8 In Fig. 9 we show the Z versus N values of MNT products
the maximum cross-sections which are reached in collisions which are in the maxima of the isotopic distributions for reac-
of Ca + U and Ni + Pb for isotopes of a certain element. The tions of 48Ca + 238U, 64Ni + 208Pb [63] and 136Xe + 208Pb
denoted experimental cross-sections for Ca + U correspond [64]. Also, we included experimental data from 238U+ 238U
to the maxima of the isotopic distributions in Fig. 5 and collisions from one of our previous experiments [78]. Since
belong to isotopes which are close to the stability valley. no or only few experimental data below Pb are available
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Eur. Phys. J. A (2020) 56 :224 Page 9 of 17 224
Table 3 The MNT reactions
Reactions Energy [MeV/u] E /Bint Observed TL elementsfrom which experimental data
are available in the region below 64Ni + 208Pb [63] 5.5 1.08 Z = 64 − 88
Pb (column 1), the respective
64 207
beam energies are given in Ni + Pb [19] 5.0 1.01 Z = 76 − 89
column 2. The beam energy 136Xe + 208Pb [64] 5.5 1.04 Z = 70 − 88
with respect to the interaction 136Xe + 198Pt [66] 7.98 1.54 Z = 50 − 80
barrier is given in column 3. The
136 198
range of elements in which Xe + Pt [65] 5.6 1.08 Z = 72 − 83
MNT products were observed is 48Ca + 238U (this work) 4.86 1.00 Z = 81 − 95
given in column 4 48Ca + 248Cm [22,23] 5.63 1.05 Z = 82 − 102
The above shown results reveal that Pb targets lead to
about 50 times larger maximum cross-sections than U tar-
gets, but the isotope distributions from U targets are the most
neutron-rich ones. They are tightly followed by the distri-
butions from Xe + Pb, which have on average only two neu-
trons less. With Ni beams on Pb the distributions are much
more neutron-deficient with a difference of 10 neutrons with
respect to Ca + U reactions.
In Fig. 10 we compare exemplary the isotope distribu-
tions for MNT products of Pt (Z = 78), Re (Z = 75)
and Yb (Z = 70) measured in reactions of Ni + Pb [63] and
compare them with model calculations for Ca + U [29] and
with experimental (if available) [64] and theoretical data for
Xe + Pb [39]. It can be noticed that in Ni + Pb collisions quite
high cross-sections were measured also for isotopes quite far
Fig. 9 Each data point denotes the location of an isotope distribution of below Pb and that the maximum cross-sections decrease only
(secondary) MNT products with element number Z on the neutron axis slightly with proton number. However, the populated isotopes
N. The given N is the neutron number where the respective distribution are more neutron-deficient compared to the other two reac-
has its maximum cross-section. Filled symbols represent experimental
data from 48Ca + 238U (this work), 64Ni + 208Pb [63], 136Xe + 208Pb tions and it is indicated that for isotopes along the N = 126
[64] and 238U+ 238U [78]. Open symbols represent model calculations shell the cross-sections reach already the sub-picobarn scale,
for 48Ca + 238U [29] and 136Xe + 208Pb [39]. Data points on the same which makes them experimentally not accessible. It is also
curve belong to the same collision system. For example: the measured
= 136 + indicated that the (theoretical) cross-sections for Ca + U over-distribution of Pt isotopes (Z 78) from MNT reactions of Xe
208Pb has the cross-section maximum at 196Pt , i.e. N = 118 take the ones of Ni + Pb toward the neutron-rich side. For Xe
beams on Pb, the theoretical distributions and the experimen-
tal one which is available for Pt indicate wide and neutron-
rich distributions with higher cross-sections than Ca + U. But
for Ca + U and Xe + Pb, we show for these systems theoret-
it is also revealed that toward smaller proton numbers the
ical values. The representation in Fig. 9 reflects how far the
cross-sections in Ca + U collisions come closer to the ones
isotopic distributions of the individual reaction systems are
from Xe + Pb.
shifted toward the neutron-rich side. One can see that the
isotope distributions from Ca + U reach the largest neutron
numbers, tightly followed by Xe + Pb. One can also see that
the slope of all curves becomes flatter when they approach the 4 Fragmentation versus transfer reactions
Pb-valley. We interpret this as influence of the Pb shells on the
potential energy surface which leads to the effect that isotope 4.1 Neutron-rich isotopes with 82 ≤ Z ≤ 92
distributions of elements close to Pb centre around N = 126.
In fact, it is the same reason which induces the small exci- Projectile fragmentation at relativistic energies together with
tation energies and constant maximum cross-sections of Pb- effective separation and detection of the exotic fragments is
like fragments revealed by Figs. 6 and 8. Noteworthy is, that so far a powerful method to populate wide regions of the
a slight flattening is even revealed for U + U collisions which nuclide chart up to uranium. At the GSI fragment separator
indicates that shell effects are still acting to a certain extent (FRS) neutron-rich nuclides below uranium were success-
also in such heavy systems [78]. fully made in reactions of 1 GeV/u 238U (Z = 92, N = 146)
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224 Page 10 of 17 Eur. Phys. J. A (2020) 56 :224
Fig. 11 The production cross-sections of uranium, protactinium, tho-
rium and actinium transfer products from the 48Ca + 238U reaction
(open circles) and 48Ca + 248Cm (solid circles) [22] are compared
with the cross-sections from the spallation–evaporation reaction of 238U
(1 GeV/u)+1H (solid squares) [68]. The available fragmentation yields
for protactinium and thorium (open squares) from 1 A GeV 238U on a
beryllium target [79] are also shown
In addition, in the same irradiations neutron-rich nuclides of
238Pa, 237Th and 236Ac have also been observed as a result of
Fig. 10 Isotopic distributions of MNT products of elements Pt (Z = (n, p) nuclear charge-exchange reactions [81]. The process
78), Re (Z = 75) and Yb (Z = 70). Filled squares: experimental data is rather complicated for the production of these isotopes,
from 64Ni + 208Pb collisions [63], filled red circles: experimental data
136 +208 because in each case after removal of protons one neutronfrom Xe Pb collisions [64], open red circles: model calculations
for 136Xe+208Pb [39], open black circles: model calculations for 48Ca+ was picked up via relativistic nucleon-nucleon collisions.
238U [29] Production cross-sections of 10 nb (≈ 1 particle/day) is the
current limit for the isotope production at the present GSI
FRS facility.
on beryllium targets [79] and in spallation-evaporation reac- Our experiments on transfer reactions revealed that the
tions of 1 GeV/u 238U on proton target [68]. In the follow- region between Pb and U is also populated quite strongly in
ing we compare the capacity of fragmentation and transfer MNT reactions with actinide targets. In Fig. 11, the isotopic
reactions for the production of neutron-rich isotopes below distributions of MNT products from Ca + U and Ca + Cm [22]
uranium. collisions are compared with fragmentation results for iso-
In fragmentation reactions of 238U beams, neutron-rich topes of elements U, Pa, Th and Ac [68,79]. For the iso-
isotopes of elements down to francium (Z = 87) were topic distributions of Th and Ac, the cross-section maxima
observed having neutron numbers close to the neutron num- reached in MNT reactions are comparable to the ones from
ber of the primary beam [80]. Cross-sections are dropping fragmentation reactions and toward the neutron-rich side it is
dramatically for every proton removal along N = 146 and indicated that MNT cross-sections become larger than frag-
reached a value of ∼ 1 nb for 233Fr [80]. The process is mentation cross-sections. In the case of U and Pa, fragmen-
described as cold fragmentation because of the low fragment tation cross-sections are about 10 times larger than MNT
excitation energy, resulting in no evaporation of neutrons. cross-sections. The data points from MNT as well as frag-
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Eur. Phys. J. A (2020) 56 :224 Page 11 of 17 224
Fig. 12 Section of the nuclide chart showing the transfer products with 65 ≤ Z ≤ 82 which were so far observed in experiments of 136Xe+ 198Pt,
208Pb [64,65] and 64Ni + 207,208Pb [19,63]
Fig. 13 The measured isotopic distributions of transfer products of elements with 65 ≤ Z ≤ 83 in collisions of 64Ni + 208Pb [63], 136Xe + 208Pb
[64], 136Xe+198Pt [65] are compared with fragmentation reactions of 238U (1 GeV/u)+Be [2], 238U (1 GeV/u)+1H [68] and 208Pb (1 GeV/u)+9Be
[67]
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224 Page 12 of 17 Eur. Phys. J. A (2020) 56 :224
mentation reactions end on the neutron-rich side shortly after Table 4 Typical values for beam intensities Nb and target thicknesses
the maxima are reached. The cross-sections are still huge in dt (respectively, number of target nuclei Nt ) in multi-nucleon transfer
this region with values between 100 b and 1 mb, and it is reactions and in fragmentation reactions. For fragmentation reactionsµ
we give Nb values for Pb or U beams. For relatively light beams like Ca
obvious that they are not the reason for the cut-off. Actually, or Ni intensities of 1013 can be provided. The product Nb×Nt , which
the reason is the lack of additional neutrons in the projectile determines the yields, is also given. The present sensitivities of MNT
nucleus in fragmentation reactions and the lack of suitable and fragmentation reactions in the region below Pb are denoted by the
detection techniques in the case of MNT reactions (see Sect. cross-section limits σmin in the last row
5). MNT reactions Fragmentation
Nb [particles / s] 1010–1013 1010
4.2 Neutron-rich isotopes with Z < 82
dt [mg / cm2] 1–50 1000–10000
N [1 / cm2] 1018–5 × 1019 1023–1024
It is expected that the maxima observed in the solar abun- t −1 −2 32 34
dance distributions at mass number around A = 195 are Nb × Nt [s cm ] ≤ 5 × 10 ≤ 10
populated from the remnants of the r-process last waiting σmin > 1µb > 1 pb
point nuclei along the N = 126 neutron shell. These nuclei
are likely to be produced at extreme stellar conditions of very
high temperature and neutron densities. Still there is no con- rable in many cases to fragmentation cross-sections, and in
clusive evidence from the experiments due to the scarcity some cases even larger cross-sections are measured in MNT
of measured data along N = 126 for elements Z ≤ 80. reactions.
Presently, 202Os is the lightest known N = 126 isotone. It An interesting observation is reported in [66] from MNT
was populated in two separate experiments in projectile frag- reactions of 136Xe + 198Pt measured at GANIL at the beam
mentation of 208Pb [1] and 238U [2] beams at 1 GeV/u at the energy of 7.98 MeV/u. A strong increase of MNT cross-
GSI FRS facility. The measured production cross-section for sections compared to fragmentation for isotopes toward the
202Os is 4.4 picobarn [2] and is nearly the limit cross-section neutron-rich side was observed. However, in this experi-
of the present FRS facility. ment the heavy target-like MNT product was not detected
In the following we give an impression how the cross- directly. Only the projectile-like fragments were measured
sections and yields in MNT reactions compare to fragmen- at the VAMOS spectrometer around the grazing angle (33◦).
tation results. We base our discussion on the results of so The cross-sections for the (target-like) isotopes W, Re, Os,
far performed experiments [3–23] and on theoretical predic- Ir and Pt have been deduced from the measured isotopi-
tions [24–31]. Between 2003 and 2019 transfer reactions in cally identified projectile-like products [66] by assuming
the collision systems 64Ni+207,208Pb [19,63], 136Xe+208Pb binary kinematics and including particle evaporation from
[64], 136Xe+ 198Pt [65,66] have been experimentally inves- both fragments. The detected γ -rays confirmed the produc-
tigated. The identified nuclei for the region of 65 ≤ Z ≤ 82 tion of corresponding target-like products. The detection of
are shown in the nuclide chart in Fig. 12. The isotopic identi- unknown nuclei by γ -decays requires knowledge about the
fication of the heavy target-like transfer products was per- decay scheme. The most neutron-rich isotopes were expected
formed in these experiments [19,63–65] via the γ -decay to be produced in reactions associated with small kinetic
spectroscopy. Only in [66] projectile-like transfer products energy loss. With decreasing proton number of neutron-rich
were identified using the large acceptance magnetic spec- below-Pb nuclei they observed a strong increase of the MNT
trometer VAMOS++. The distribution of the complementary cross-sections compared to fragmentation cross-sections. For
target-like fragments was then deduced from the measured N = 126 isotones, the cross-section for Z = 77 is already
cross-sections of projectile-like nuclei. The chart reveals that five orders of magnitude larger in MNT reactions. In the data
the most neutron-rich isotopes of the shown elements were of directly identified target-like nuclei, this trend is slightly
so far produced in fragmentation reactions. indicated, but available information from neutron-rich nuclei
Isotopic distributions of MNT products have been estab- is not sufficient to confirm it. However, model calculations
lished for the different reactions (see Fig. 13). For the nearly for Xe + Pb collisions [39] also reveal this trend.
identical collision systems 64Ni+208Pb measured in [63] and The experimental conditions in MNT and fragmentation
64Ni+207Pb measured in [19], the cross-sections are in agree- reactions are quite different concerning the applicable target
ment within an order of magnitude for most of the nuclei. thicknesses and beam intensities. This affects the resulting
The MNT cross-section data for elements Z =(65–83) isotope yields which depend on the product of beam intensity
are compared in Fig. 13 with fragmentation cross-sections and number of target atoms. Typical parameters are given in
for reactions of 1 GeV/u 238U beams on Be targets [2], Table 4. In Fig. 14 we show an example for yields which
238U (1 GeV/u) + p [68] and with 208Pb (1 GeV/u) + Be could be expected for Pt (Z = 78) isotopes in MNT and in
reactions [67]. The MNT cross-section values are compa- fragmentation reactions for the parameters denoted in the fig-
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Eur. Phys. J. A (2020) 56 :224 Page 13 of 17 224
sections with respect to fragmentation cross-sections is indi-
cated for very neutron-rich MNT products below Z = 77
by the results of [66] and also by model calculations (see
Fig. 15).
One has to note that the above given yields are expected
at the target and do not yet include the efficiencies of the
experimental setups. In projectile fragmentation reactions the
efficiencies are large. For the reaction U + Be at 1 GeV/u an
efficiency of (40–60)% is given in [2]. In MNT reactions
the efficiencies are much less. At SHIP, the bottleneck is
the angular acceptance which was ≈ 0.5% for Ni + Pb and
Ca + U reactions. For the thick-target experiments efficien-
cies are not given in refs. [63–65], but it is realistic that they
are smaller than 10%. The small efficiencies are connected
with the isotope identification via the γ decay in MNT exper-
Fig. 14 An example for the yields which can be expected for Pt iments.
(Z = 78) isotopes in fragmentation reactions of 208Pb (1 GeV/u) + Be
and in transfer reactions of 64Ni + 208Pb and 136Xe + 208Pb. All
underlying cross-sections were taken from experimental data [2,63,64]
(see Fig. 13). The realistic values for beam intensities and target 5 Experimental challenges
thicknesses were taken as follows. For fragmentation: Nb(Pb) =
1010 / s, dt (Be) = 5 g/cm2; MNT: Nb(Ni) = 1012 / s, dt (Pb) =
50 mg/cm2, N Xe = 1010 s d Pb = 50mg/cm2 Many efforts are presently put in the development of sep-b( ) / , t ( )
aration and detection techniques for heavy MNT products,
which must be sensitive enough to allow the detection of
nuclei with picobarn cross-sections. The wide angular and
energy distributions of low-energy MNT products make sep-
aration from background events difficult. Our method to use
in-flight separation by velocities allowed us to reach total
cross-section limits of 0.5 nb for α emitters which was so
far the smallest limit cross-section in MNT experiments. But
the angular efficiency on the scale of one percent leads to
large losses of events. The approach by another group, to use
chemical separation techniques allows the 4π collection of
MNT products and lead to a sensitivity of 20 nb for α emit-
ters. However, the minimum time for one detection cycle is
1 min which is too long for the separation of neutron-rich
nuclei below Pb which reach half-lives on the millisecond
scale.
Fig. 15 Cross-sections of N = 126 isotones with the given Z from Still more problematic is the direct identification of very
transfer and fragmentation reactions. We made this figure according to heavy MNT products with masses around A ∼ 200 and
[66] and added the graphs for U + Be fragmentation reactions [2] and beyond. Due to the pulse height deficit of the heavy and
calculated cross-sections for transfer reactions in Xe + Pb [39]
low energetic MNT products, the A and Z identification can-
not be performed with the universal E-ΔE-TOF technique.
ure caption. The trend is clearly visible. The MNT yields with Therefore, these nuclei are so far identified by their radioac-
Ni beams are large because Ni can be delivered with higher tive decays. These are very sensitive for α emitters where
intensities as heavier beams like Xe, Pb or U. But the isotope principally one decay chain is sufficient to pin down the iso-
distributions are quite neutron-deficient. The yield curve for tope. But for β emitters, γ decay spectroscopy must be used
Xe + Pb MNT reactions is more neutron-rich, but the smaller where the small peak-to-background ratio restricts the sensi-
intensities of the Xe beams lead to smaller yields. The highest tivity to cross-sections larger than 1µb. Also, the method is
yields can be expected from fragmentation reactions of Pb only applicable if excited states in the daughter nucleus are
beams caused by the much thicker targets. The curves indi- populated with sufficient branching and if the γ transitions
cate that the cross-sections in MNT reactions should be sig- in the daughter nucleus are already well known.
nificantly larger than fragmentation cross-sections to make To overcome the bottleneck of isotope identification, two
them profitable. And indeed, this increase of MNT cross- alternative approaches are presently investigated, one of them
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224 Page 14 of 17 Eur. Phys. J. A (2020) 56 :224
high-intensity RF gas catcher and transported then into the
low energy beamline for mass separation using a medium
resolution electromagnetic separator (Δm/m  1/1500).
Then, bunching in an RFQ buncher, followed by mass mea-
surements with the MR-TOF (Δm/m  1/100, 000) and
spectroscopic investigations will be performed.
Investigations are also undertaken to increase the A and
Z resolution of the large acceptance magnetic spectrometers
such as VAMOS++ at GANIL [87] and PRISMA at Leg-
naro [51]. Also, MNT reactions using inverse kinematics are
investigated there. The recent investigations at PRISMA were
successful in the identification of reaction products up to the
A ∼ 130 mass region [88–90].
Another possible method of isotope identification is the
selective laser ionization of the MNT products. A dedicated
facility named KEK Isotope Separation System (KISS) is
developed at the Radioactive Ion Beam Factory at RIKEN
specifically for the investigation of neutron-rich MNT prod-
ucts below Pb [91]. The MNT products are stopped in an
argon gas-filled ion catcher. The ion catcher is doughnut-
shaped to prevent the primary beam from entering the cell.
Laser resonance ionization inside the ion catcher is used for Z
selection. After extraction from the gas cell, the laser ionized
reaction products are passing a mass separator. The selected
ions are then guided to a detection system to perform spec-
troscopy studies. The method is applicable for ions with a
lifetime of 1 s or more. This is mainly determined by the
Fig. 16 Calculated β-decay half-lives for neutron-rich isotopes of ele- extraction times from the gas catcher which are about 0.5
ments from Z = 65 to 88. The calculated values were taken from [84] s. The overall efficiency of the present KISS setup is on the
scale of 0.1%.
is the application of high-precision mass measurements with 6 Summary and conclusions
a multi-reflection time-of-flight mass spectrometer (MR-
TOF-MS) [82,83] which is presently tested at the Fragment The possibility to synthesize neutron-rich nuclei below Pb in
Separator Facility FRS at GSI. It allows the direct and very multi-nucleon transfer reactions was so far studied by differ-
precise measurement of the nuclide mass with resolutions in ent groups in experiments of 64Ni+207,208Pb, 136Xe+208Pb
the range 10−5 to 10−6 which is mostly sensitive enough to and 136Xe+ 196Pt. We made a systematic comparison of the
resolve also the isobars. The lower half-live limit is about 10 published data to find out, which reaction systems lead to
ms, given by the stopping and extraction time of the nuclei the largest cross-sections for neutron-rich isotopes. Also, we
from the ion catcher which is used to slow down the ions presented our new MNT reaction results from collisions of
before injection into the MR-TOF-MS. The estimated β- 48Ca + 238U at the SHIP velocity filter where we identified
decay half-lives in [84] are greater than 10 ms for the below- nuclides in the region from Tl to Np (Z = 81 to 93). In the
Pb N = 126 isotones down to Z = 65 (see Fig. 16) which could below-Pb region, sufficient experimental MNT data are only
be accessible with this method. According to simulations, the available for Ni + Pb. Therefore, we completed the missing
MR-TOF-MS method is presently limited to cross-sections experimental information for 48Ca+238U and 136Xe+208Pb
of minimum 100µb [85]. In order to avoid space charge collisions by available model calculations. Our analysis leads
effects in the ion catcher, the maximum beam intensity is to the following conclusions.
limited. Estimates for uranium beams arrived at maximum
intensities of 107 ions/s. • Experimental and theoretical data from MNT reactions
Also at Argonne National Laboratory, USA, a new facil- indicate that Xe beams on Pb target lead to the largest
ity using an MR-TOF for mass measurements is under con- cross-sections of neutron-rich below-Pb isotopes. Also
struction [86]. The transfer products will be stopped in a model calculations for Ca + U reveal similarly neutron-
123
Eur. Phys. J. A (2020) 56 :224 Page 15 of 17 224
rich isotope distributions but with smaller cross-sections, tion of MNT products and provide higher yields because
especially toward the neutron-rich side. More experi- of the much larger target thicknesses. Therefore they
mental data are needed to confirm this trend. If con- seem better suitable for experiments in the region of β
firmed, Ca + U collisions might nevertheless compete emitters. Beside, reactions with relatively symmetric col-
with Xe + Pb, because Ca beams are available with higher lision systems like Xe + Pb are not suitable for veloc-
intensities than the heavier Xe beams, resulting in accord- ity filters because the separation of primary beam from
ingly larger yields. target-like reaction products fails more and more with
• In the below-Pb region, fragmentation reactions compete increasing symmetry of the collision system.
with MNT reactions. For neutron-rich fragments down
to Z ≈ 75, fragmentation of Pb beams results in the Acknowledgements We gratefully acknowledge the support of this
largest cross-sections while for isotopes with Z < 75, project and of one of us (HMD) by grants of the Deutsche Forschungs-
gemeinschaft (DFG) Ref. No. DE 2946/1-1 and HE 5469/3-1.
the largest cross-sections are measured in fragmentation
of U beams. Experimental and theoretical data indicate, Funding Open Access funding provided by Projekt DEAL.
however, that MNT cross-sections from Xe + Pb,Pt col-
lisions become many orders higher than fragmentation Data Availability Statement This manuscript has no associated dataor the data will not be deposited. [Authors’ comment: Any data that
cross-sections for decreasing Z of the transfer products support the findings of this study are included within the article.]
and toward increasing neutron-number.
• For a given cross-section, the yields in fragmentation Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adaptation,
reactions are normally larger than in MNT reactions
∼ distribution and reproduction in any medium or format, as long as youbecause of the 1000 times larger target thicknesses and give appropriate credit to the original author(s) and the source, pro-
larger efficiencies of the separation and detection setups. vide a link to the Creative Commons licence, and indicate if changes
This should be individually considered for experiments were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indi-
where both reaction types principally allow to produce cated otherwise in a credit line to the material. If material is not
an isotope. included in the article’s Creative Commons licence and your intended
• The applicability of fragmentation reactions naturally use is not permitted by statutory regulation or exceeds the permit-
ends at reaction products with neutron numbers exceed- ted use, you will need to obtain permission directly from the copy-
right holder. To view a copy of this licence, visit http://creativecomm
ing the neutron number of the beam particle. In this ons.org/licenses/by/4.0/.
case, MNT reactions are the only alternative to produce
nuclei with higher number of neutrons. One such region
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