Journal of Nuclear and Radiochemical Sciences, Vol. 7, No.1, pp. R1-R5, 2006

Reviews
Long-Lived Superheavy Nuclei and Giant Quasi-Atoms Produced in Damped Collisions ofTransactinides
Walter Greiner*, a and Valery ZagrebaevbaFrankfurt Institute for Advanced Studies, J.W. Goethe-Universität, 60325 Frankfurt am Main, Germany
Flerov Laboratory of Nuclear Reactions, Joint Institute for Niclear Research, Dubna, Moscow region, 141980,
Russiab

Received: November 22, 2005
Damped collisions of tranactinide nuclei (238U + 238U, 232Th + 250Cf, and 238U + 248Cm) have been studied within therealistic model based on solution of multidimensional transport equations. Large charge and mass transfer was
found in these reactions due to the inverse (anti-symmetrizing) quasi-fission process leading to formation ofsurvived superheavy long-lived neutron-rich nuclei, suitable for subsequent chemical analysis. In many events
lifetime of the composite system consisting of two touching nuclei (giant quasi-atoms) turns out to be rather long;sufficient for spontaneous positron formation from super-strong electric field, a fundamental QED process.

1. Introduction

180*Corresponding author. E-mail: greiner@fias.physik.uni-frankfurt.
de

Z

=

N

160

p

140

proton number

120
100

“co

ld”

“hot”
ion
fus

on dr
rot

Cm

80

ne

Pb

n
issio
ar f
ucle
sn
u
o
ne
nta
spo

n
ip li

fusioneedrip lin

n
utro

60
40
20
0
40

80

120

160

200

240

280

320

neutron number

Figure 1. Nuclear map. Predicted islands of stability are shownaround Z =114, N =184 and Z =164, N =318. Neither in “cold” nor in“hot” fusion reactions with stable nuclei these islands can be reached
due to insufficient neutron number.
Z1

E
+mc

Z2

Z1 +Z 2
U + Cm
40

2

2p
1s

t

-mc 2
eDirac see

e+
delay

positron yield

Damped collisions between very heavy nuclei were studied
extensively about twenty years ago. Among others, there had
been a great deal of interest in the use of heavy-ion transfer
reactions with actinide targets to produce new nuclear species
in the transactinide region.1–5 The cross sections were found to
decrease very rapidly with increasing atomic number of surviving target-like fragments. However, Fm and Md neutron-richisotopes have been produced at the level of 0.1 µb. Note thatsuperheavy (SH) nuclei obtained in “cold” fusion reactions
with Pb or Bi target6 are along the proton drip line and very
neutron-deficient with a short half-life. In fusion of actinides
with 48 Ca more neutron-rich SH nuclei are produced7 withmuch longer half-life. But they are still far from the center ofthe predicted first “island of stability” formed by the neutron
shell around N=184 (see the nuclear map in Figure 1). In the“cold” fusion, the cross sections of SH nuclei formation
decrease very fast with increasing charge of the projectile andbecome less than 1 pb for Z >112. Heaviest transactinide, Cf,
which can be used as a target in the second method, leads to
the SH nucleus with Z =118 being fused with 48Ca. Using thenext nearest elements instead of 48Ca (e.g., 50 Ti, 54 Cr, etc.) in
fusion reactions with actinides is expected less encouraging,
though experiments of such kind are planned to be performed.
In this connection another ways to the production of SH
elements in the region of the “island of stability” should besearched for.
One more effect, which may be expected in the damped
collisions of transactinides, is a formation of giant quasi-atoms
with a nucleus consisting of two closely located heavy nuclei.
If the lifetime of the composite nuclear system with total charge
Z >173 is rather long (~10 –20 s) we may expect a spontaneous
positron emission from superstrong electric field of quasi-atoms
by a static QED process (transition from neutral to charged
QED vacuum) 8,9 (see Figure 2). About twenty years ago asearch for such effect were carried out and narrow line structures in the positron spectra were first reported at GSI.
Unfortunately these results were not confirmed later, neither in
ANL,10 nor in new experiments performed at GSI11,12 (see alsohierarchical references therein). Thus the situation remains
unclear, while the experimental efforts in this field have ended.
We hope that a new analysis, performed within a realistic

30

20

10

E(e+ ), KeV
200

400

600

800

1000

1200

Figure 2. Schematic figure of spontaneous decay of the vacuum
and spectrum of the positrons formed in supercritical electric field(Z 1 + Z 2 > 173), in which 1s-state of the quasi-atom finds itself in the
Dirac’s sea.

dynamical model, may shed additional light on this problem
and also answer the principal question: are there some reaction
features (triggers) testifying to a long reaction delay? If they
are, a new experiment could be planned to detect the positrons
in the specific reaction channels.
Recently a new model has been proposed13 for simultaneousdescription of strongly coupled reaction channels of heavy ion
collisions: deep inelastic (DI) scattering, quasi-fission (QF),
fusion, and regular fission. Reasonable agreement of our first
calculations with experimental data on low-energy DI and QF
reactions induced by heavy ions13 stimulated us to study thereaction dynamics of very heavy transactinide nuclei. The purpose is to find an influence of the shell structure of the driving
potential (in particular, deep valley caused by the double shellclosure Z=82 and N=126) on nucleon rearrangement between© 2006 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 05/18/2006

200

contact point(a)
248 Cm232 Th + 250 Cf

180

900

132 Sn

160

100

150
mass number

(b)

(a)

208 Pb200

250

energy ( MeV )

48 Ca

50

potential energy ( MeV )GreinerJ. Nucl. Radiochem. Sci., Vol. 7, No. 1, 2006

energy ( MeV )potential energy ( MeV )

R2

800

700

(b)
232 Th250 Cf

208 Pb

750

274

106

740
200

220

240
mass number

260

700

1.2
0.4

760

800

280

Figure 3. Potential energy at contact “nose-to-nose” configuration
for two nuclear systems formed in 48Ca + 248Cm (a) and 232Th + 250Cf (b)collisions. Spheroidal deformation is equal 0.2.

primary fragments. In Figure 3 the potential energies areshown depenting on mass rearrangement at contact configuration of the nuclear systems formed in 4 8 Ca + 2 4 8 Cm and232
Th + 250 Cf collisions. In the first case (48 Ca + 248 Cm), discharge of the system into the lead valley (normal or symmetrizing quasi-fission) is the main reaction channel, which decreases
significantly the probability of compound nucleus formation.
In collisions of heavy nuclei (Th + Cf, U + Cm and so on) we
expect that an existence of this valley may noticeably increase
the yield of surviving neutron-rich superheavy nuclei complementary to the projectile-like fragments around 208Pb (“inverse”
or anti-symmetrizing quasi-fission process). Direct time analysis of the collision process allows us to estimate also the lifetime of the composite system consisting of two touching heavy
nuclei with total charge Z >180. Such “long-lived” configurations (if they exist) may lead to spontaneous positron emission
from super-strong electric field of quasi-atoms by a static QED
process.
2. Damped collisions of heavy ions
The distance between the nuclear centers R (corresponding
to the elongation of a mono-nucleus), dynamic spheroidal-typesurface deformations β 1 and β 2 , mutual orientations ofdeformed nuclei ϕ 1 and ϕ 2, and mass asymmetry α = A1 – A2
A1 + A2
are probably the relevant degrees of freedom to describe properly low-energy fusion-fission dynamics of heavy nuclear system. For the re-separation stage in the exit channel neckformation should be included to describe properly mass andenergy distributions of the fission fragments. To avoid increasing the number of degrees of freedom the necking process was
taken into account in a phenomenological way using different
radial form-factors for the friction forces in the entrance andinexit channel (R out
scission >R contact = R1(A1, β 1, ϕ 1) + R 2 (A2, β 2, ϕ 2)).
The corresponding multi-dimensional adiabatic potential
energy surface was calculated here within the semi-empiricaltwo-core approach14 based on the two-center shell model.15
Projections onto the R – α and R – β planes of the threedimensional potential energy are shown in Figure 4 for the
nuclear system formed in collision of 232Th + 250Cf. There is nopotential pocket typical for lighter systems, the potential isrepulsive everywhere.
However, the potential energy is not so much steep in theregion of contact point and two nuclei may keep in contact fora long time increasing their deformations and transfering nucleons to each other (see below).
We studied the whole dynamics of such a nuclear system by

elo 14
ng
a

try
me
ym Pb
0.2

tio 16
n
(f

0

m

-0.2

18

)

ma

-0.4

ss

as

+

10
6

elo 14
ng
a

1.0
0.8

tio 16
n
(f

0.6
0.4
0.2

m 18
)

de

for

m

o
a ti

n

0.0
-0.2

Figure 4. Potential energy surfaces for the nuclear system formed by
232
Th + 250Cf as a function of R and α ( β = 0.22) (a), and R and β (α =0.037) (b). Typical trajectory is shown by the curves with arrows.

numerical solution of the coupled Langevin-type equations of
motion, inertialess motion along the mass-asymmetry coordinate was derived just from the corresponding master equation
for nucleon transfer.13 The inertia parameters µ R and µβ were
calculated within the Werner-Wheeler approach.16 Parametersof the friction forces and nucleon transfer rate were taken from
Reference 13, where they have been estimated from successful
description of experimental regularities of heavy ion deep
inelastic scattering and fusion-fission reactions. Damping of
the shell effects due to the excitation energy has been taken
into account in the level density parameter both on the dynamic
stage of the reaction and in statistical treatment of decay of the
primary fragments.
The cross sections are calculated in a natural way. A large
number of events (trajectories) are tested for a given impact
parameter. Each event in studied reactions ends in the exit
channel with two excited primary fragments. The corresponding
double differential cross-section is calculated as follows
d 2σ α (E, θ ) = ∞bdb ∆ Nα (b, E, θ )1(1)0sin(θ )∆θ ∆ E ·N tot (b)d Ω dE∫

Here ∆N α (b, E, θ ) is the number of events at a given impact
parameter b in which the system enters into the channel α withkinetic energy in the region (E, E + ∆E) and center-of-massoutgoing angle in the region (θ, θ + ∆θ), and Ntot (b) is the total
number of simulated events for a given value of impact
parameter, b.
The expression (1) describes the energy, angular, charge, andmass distributions of the primary fragments formed in thereaction. Subsequent de-excitation of these fragments via
fission or emission of light particles and gamma-rays was taken
into account within the statistical model leading to the final
fragment distributions. The sharing of the excitation energy
between the primary fragments was assumed to be proportional to their masses. Neutron emission during an evolution of
the system was also taken into account. However, it was foundthat the pre-separation neutron evaporation does not influencesignificantly the final distributions.
3. Superheavy nuclei produced in collisions of transactinides
In Figure 5 the available experimental data on the yield ofSH nuclei in collisions of 238U + 238U 2 and 238U + 248 Cm 3 arecompared with our calculations. In these experiments thicktargets have been used, which means that the experimental data
were, in fact, integrated over the energy in the region of about
750–850 MeV.2,3 The estimated excitation functions for theyield of heavy surviving nuclei demonstrate not so sharp as infusion reactions but still rather strong dependence on beamenergy. In spite of that, the agreement of our calculations withexperimental data is quite acceptable (slightly worse for
few-nucleon transfer and better for massive transfer processes).

Long-Lived Superheavy Nuclei and Giant Quasi-Atoms

J. Nucl. Radiochem. Sci., Vol. 7, No. 1, 2006
10 3

10 1

U + 248 Cm

10 1

99
10 -2

100

10 -3

101

10 -4

238

U + 238 U

10 -6

246

248

250

252

252

254

256 252

254

256

256

cross section ( mb/unit )cross section ( mb/unit )

238

10 -1

10 -5

quasi-elastic

(a)

98

10 0

R3

primary

DI transfer

survived

QF

232

survived

10 -1

10 -3

10 -5

Th + 250 Cf

E cm = 800 MeV

10 -7

258

mass number

mass number
10 -9
10 3

Figure 5. Isotopic yield of the elements 98–101 in the reactions
238
U+ 238U (crosses)2 and 238U + 248Cm (circles and squares).3 The curves
show the result of our calculations.

200

220

240

260

280

(b)
primary

cross section ( mb/unit )

10 3

232

Th + 250 Cf, E c.m. = 800 MeV

cross section ( mb/unit )10 1
primary

10 2

survived
10 1

PLF and TLF
fission fragments

10 0

10 -1

survived

10 -3
232
10 -5

Th + 250 Cf

248

Cm + 250 Cf

E cm = 800 MeV

10 -7
80

100

120

140

160

180

200

220

240

260

atomic number

280

mass number

Figure 6. Mass distributions of primary (solid histograms), survived
and sequential fission fragments (hatched areas) in the 232Th + 250Cf
damped collisions at 800 MeV center-of-mass energy.

Using the same parameters of nuclear viscosity and nucleon
transfer rate we calculated the yield of primary and survived
fragments formed in the 232 Th + 250 Cf collision at 800 MeV
center-of-mass energy. Low fission barriers of the colliding
nuclei and of the most of reaction products conjointly withrather high excitation energies of them in the exit channel must
lead to very low yield of survived heavy fragments. Indeed,sequential fission of the projectile-like and target-like fragments dominate in these collisions, see Figure 6. At first sight,
there is no chances to get survived superheavy nuclei in suchthe reactions. However, as mentioned above, the yield of the
primary fragments should be increased due to the QF effect(lead valley) comparing with gradual monotonic decrease typical for damped mass transfer reactions. Secondly, with increasing neutron number the fission barriers increase on average(also there is the closed sub-shell at N =162). Thus we may
expect non-negligible yield (at the level of 1 pb) of survived
superheavy neutron rich nuclei produced in these reactions.
Results of much longer calculations are shown in Figure 7,
where the mass and charge distributions of survived fragments
obtained in the 232 Th + 250Cf collision at 800 MeV are presented.
The pronounced shoulder can be seen in the mass distributionof the primary fragments near the mass number A =208. It is
obviously explained by existence of noticeable valley on thepotential energy surface [see Figure 3 (b) and Figure 4 (a)],which corresponds to formation of doubly magic nucleus 208Pb(α = 0.137). The emerging of the nuclear system into this valley
resembles the well-known quasi-fission process and may becalled “inverse (or anti-symmetrizing) quasi-fission” (the final
mass asymmetry is larger than initial one). For α > 0.137 (onefragment becomes lighter than lead) the potential energy
sharply increases and the mass distribution of the primary fragments falls down rapidly at A < 208 (A > 274). The same is forthe charge distribution at Z < 82 (Z > 106). As a result, in the
charge distribution of survived heavy fragments, see Figure 7(b), there is also a shoulder at Z ~106 and the yield of nuclei

10 -9

80

90

100

110

Figure 7. Mass (a) and charge (b) distributions of primary (solid
histograms) and survived (dashed histograms) fragments in the232
Th + 250Cf collision at 800 MeV center-of-mass energy. Thin solid
histogram in (b) shows the primary fragment distribution in the
hypothetical reaction 248Cm + 250Cf.
100

10 0

primary fragments

101

238

U+

248

102

Cm

103

104

10 -1

(
105

232

Th +

99

98

10 -5

109

97

110

100
98

101
99

10 -6

102
103

100

104

101

10 -7

105
106

102

10 -8
10 -9

Cf )

108

10 -3
10 -4

250

106
107

10 -2

cross section ( mb/unit )

10 -1

103

238

U + 238 U

232

Th + 250 Cf

107
104
105

10 -10106

10 -11

107

10 -12

108
109

250

260

270

280

mass number

Figure 8. Yield of superheavy nuclei in collisions of 238U + 238U
(dashed), 238U + 248Cm (dotted), and 232Th + 250Cf (solid lines) at 800
MeV center-of-mass energy. Solid curves in upper part show isotopic
distribution of primary fragments in the Th + Cf reaction. In the caseof U + Cm the upper curve only is marked by Z-number (Z = 98), theothers are one by one up to Z =107.

with Z >107 was found in this reaction at the level of less than
1 pb. This result differs sharply from those obtained in
Reference 17, where the reactions of such kind have been analyzed within the parameterized diffusion model and the yieldof heavy primary fragments was found diminishing monotonically with increasing charge number. The authors of Reference
17 concluded, however, that the “fluctuations and shell effects
not taken into account may considerably increase the formation
probabilities”. Such is indeed the case.
The estimated isotopic yields of SH nuclei in the 232Th + 250Cf,
238
U + 238U, and 238U + 248Cm collisions at 800 MeV center-ofmass energy are shown in Figure 8. As can be seen, there is a

R4

GreinerJ. Nucl. Radiochem. Sci., Vol. 7, No. 1, 2006
238

U + 248 Cm,
E cm = 800 MeV(a)kinetic energy ( MeV )

750

700

650

600

Figure 9. Reaction time distribution for the 238U + 248Cm collision at
800 MeV center-of-mass energy. Dashed and dotted histograms show
the effect of switching-off dynamic deformations or mass transfer,respectively.

200

210

220

230

240

250

260

280

290

238

U + 248 Cm,
E cm = 800 MeV

(b)
750

kinetic energy ( MeV )real chance for production and chemical study of the long-lived
neutron-rich SH nuclei up to 274
107 Bh produced in the reaction232
Th + 250 Cf. The yield of SH elements in damped reactions
depends strongly on beam energy and on nuclear combination
which should be chosen carefully. In particular, in Figure 7 theestimated yield of the primary fragments obtained in the
hypothetical reaction 248 Cm + 250 Cf (both constituents areradioactive) is shown, demonstrating a possibility for productionof SH neutron-rich nuclei up to the element 112 (complementary
to lead fragments in this reaction).

270

mass number

700

650

600

4. Giant quasi-atoms and spontaneous positron formation

20

40

60

80

100

120

140

160

center-of-mass angle ( degree )The time analysis of the reactions studied shows that in spiteof non-existing attractive potential pocket the system consisting of two very heavy nuclei may hold in contact rather long insome cases. During this time it moves over multidimensional
potential energy surface with almost zero kinetic energy (resultof large nuclear viscosity), a typical trajectory is shown indσ
Figure 4. The total reaction time distribution, dlog(τ ) (τ denotes
the time after the contact of two nuclei), is shown in Figure 9
for the 238U+ 248Cm collision. We found that the dynamic deformations are mainly responsible here for the time delay of thenucleus-nucleus collision. Ignoring the dynamic deformationsin the equations of motion significantly decreases the reaction
time, whereas the nucleon transfer influences the time distribution not so strong. As mentioned above, the lifetime of a giant
composite system more than 10 –20 s is quite enough to expect
for spontaneous e + e– production from the strong electric field
as a fundamental QED process (“decay of the vacuun”).8,9 The
absolute cross section for long events (τ > 10 –20 s) was found to
be maximal just at the beam energy ensuring two nuclei tobe in contact. Note that the same energy is also optimal for
production of the most neutron-rich SH nuclei. Of course,
there are some uncertainties in the used parameters, mostly
in the value of nuclear viscosity. However we found only alinear dependence of the reaction time on the strength of
nuclear viscosity, which means that the obtained reaction
time distribution is rather reliable, see logarithmic scale on
both axes in Figure 9.
Formation of the background positrons in these reactions
forces one to find some additional trigger for the longest events.
Such long events correspond to the most damped collisions
with formation of mostly excited primary fragments decaying
by fission. However there is also a chance for production of the
primary fragments in the region of doubly magic nucleus 208Pb,
which could survive against fission due to nucleon evaporation.
The number of the longest events depends weakly on impact
parameter up to some critical value. On the other hand, in the
angular distribution of all the excited primary fragments

Figure 10. Energy-mass (a) and energy-angular (b) distributions ofprimary fragments in the 238U + 248Cm collision at 800 MeV (Eloss > 15
MeV). Logarithmic landscape of the corresponding double differential
cross sections. Lines are drawn over each half order of magnitude. The
dashed rectangles show the regions of the longest events.

(strongly peaked at the center-of-mass angle slightly larger than90˚) there is the rapidly decreasing tail at small angles. Thus
the detection of the surviving nuclei in the lead region at thecenter-of-mass angles less than 60˚ could be a definite witness
for a long reaction time (see Figure 10).
5. Conclusion
In summary, the production of long-lived neutron-rich SH
nuclei in collisions of transuranium ions seems to be quitepossible due to a large mass and charge rearrangement in the“inverse” (anti-symmetrizing) quasi-fission process caused by
the Z = 82 and N =126 nuclear shells. Radiochemical identification of neutron-rich Db, Sg, and even Bh isotopes, producedin the U + Cm or Th + Cf reactions, could be performed, forexample, to test this conclusion. If the found cross sections
will be higher than 1 pb, then the subsequent experiments withsuch reactions could be planned aimed to the production of SH
nuclei just in the region of the first “island of stability”.
Parallel search for spontaneous positron emission from asupercritical electric field of long-lived giant quasi-atoms
formed in these reactions is also quite promising.
Acknowledgment. The work was supported by the DFGRFBR collaboration project under Grant No. 04-02-04008 andby INTAS, Grant No. 03-51-6417.
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