Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 89–92, 200289

Effects of Nuclear Deformation on the Fusion Probability in the Reactions of 76 Ge + 150 Nd
and 82 Se + nat Ce
Katsuhisa Nishio,∗,a Hiroshi Ikezoe,a Shin-ichi Mitsuoka,a Ken-ichirou Satou,a and S. C. JeongbaJapan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japanb
Institute of Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki 305-0801, Japan
Received: December 28, 2001; In Final Form: March 13, 2002
Fusion probabilities for the 76 Ge + 150 Nd and 82 Se + nat Ce reactions were obtained near the Coulomb barrier, andthe effects of nuclear deformation on the fusion process were discussed. The former reaction represents fusion
involving the prolately deformed target 150 Nd, whereas the latter reaction is the fusion with the spherical target
nat
Ce. We obtained the fusion probability by measuring the evaporation residue (ER) cross sections. The system
82
Se + nat Ce showed fusion hindrance in the form of the extra-extra-push energy of 27 ± 5 MeV, whereas the system
76
Ge + 150 Nd does not show any hindrance at the bombarding energy corresponding to the Coulomb barrier for thecollision of 76 Ge on the side of 150 Nd. Our results suggest that the reaction starting from the compact touching point(side collision) results in a higher fusion probability.

1. Introduction
Synthesis of a super-heavy element (SHE), which is madeby heavy ion fusion reactions, is an important and exciting issue for nuclear physics. Because the decay properties of the
SHE give information on the shell effects of nucleus, without
which such a heavy nucleus could not exist due to overwhelming repulsive Coulomb force. It is generally accepted that the
production of evaporation residues comprises of two separate
processes, the fusion between two interacting nuclei (entrance
channel) and the survival against fission in the course of the deexcitation process (exit channel). The former process is successfully described by a coupled channel model1 for projectile-target
combinations with Z 1 Z 2 ≤ 1800. On the other hand, in heavy
systems (Z 1 Z 2 > 1800), the formation of a compound nucleus
is hindered. This is caused by the friction generated between
the interacting two nuclei in the course of fusion process. The
friction force decreases the kinetic energy of the nuclei, whichhinders a complete fusion. To drive the system to the compound
nucleus, an additional bombarding energy is needed above the
Coulomb barrier to compensate for the energy loss by friction,
which is called extra-extra-push energy (EXX ). Investigation in
References 2–5 showed the EXX to increase sharply with Z 1 Z 2above Z 1 Z 2 ∼ 1800.
Fusion hindrance may be related to the contact point of theinteracting two nuclei relative to the fission saddle point of thecompound nucleus, from the consideration that the necessary
condition for forming a compound nucleus is the dynamical trajectory to pass inside the fission saddle point on the potential
energy surface. Simple consideration for the fusion process using two spherical nuclei tells that the distance between masscenters at the contact point expands for heavy systems, which
would result in large fusion hindrance. However, even for systems having Z 1 Z 2 values larger than 1800, the compact configuration may be achieved by using a prolately deformed target
if a projectile collides at the side of the target with θcoll ∼ 90◦ ,where θcoll is the colliding angle of projectile against the symmetry axis of deformed target. We thus expected that the fusion
probability using a deformed target is larger than in the system
involving spherical nuclei. In order to investigate the effectsof nuclear deformation on the fusion process, we have measured the ER cross sections of 76 Ge + 150 Nd (Z 1 Z 2 = 1920)6 and82
Se + nat Ce (Z 1 Z 2 = 1972).7 nat Ce is spherical in shape, whereas
150
Nd is largely deformed with (β2 , β4 ) = (0.358, 0.107).8, 9 Fromthe experimental data, we determined the fusion probability with∗Corresponding author. E-mail: nishio@popsvr.tokai.jaeri.go.jp.
FAX: +81-29-282-5927.

the help of a survival probability determined by a statisticalmodel calculation. The parameters used in this code were determined so as to reproduce the ER cross sections for 28 Si + 198 Pt(Z 1 Z 2 = 1092).6
2. Experiments
Measurements of evaporation residue cross sections following the fusion of 28 Si + 198 Pt, 82 Se + nat Ce, and 76 Ge + 150 Nd weremade by using 28 Si, 82 Se, and 76 Ge beam supplied by the JAERItandem booster accelerator. The targets were made by sputtering the enriched isotopes (Nd2 O3 , 198 Pt-metal) or nat Ce-metal on
a 1.5 or 0.8 µm thick aluminum foil. Typical target thickness
was 400 µg/cm2 . The target was set to a rotating frame in thetarget chamber to prevent heating.
Since the evaporation residues produced in the present reaction are α-decaying nuclei, the evaporation channels could be
identified by observing α-decay energy and lifetime. The experimental details are described elsewhere.6, 10 The evaporation
residues emitted in beam direction were separated in flight fromthe primary beam by the JAERI recoil mass separator (JAERIRMS).11 The separated recoils were implanted into a double
sided position-sensitive strip detector (DPSD). Two large area
timing detectors, one positioned in front of the DPSD and theother 30 cm upstream of the DPSD, were used to obtain thetime-of-flight (TOF) signal of incoming particles. The presence of the TOF signal was used to distinguish ER implantation
events from the subsequent α decays, which generate no TOF
signals. A two-dimensional spectrum of the energy versus TOF
gave a rough estimate of a mass number of the incoming particle, allowing the distinction of ERs from background particles.
Typical energy resolution of the DPSD was ∼70 keV (FWHM).
A silicon surface barrier detector to monitor the beams was positioned at 45◦ direction in the target chamber to determine theabsolute values of the ER cross sections.
3. Results
With help of the known α-decay energy and half-life, theidentification for a specific channel was made by counting the
ER-α1 -α2 or ER-α1 chains, where ER stands for the events produced when the incoming evaporation residue hits the DPSD.
α1 and α2 are the first and the second correlated α-decay event,respectively. The correlated event satisfied the condition that theposition agreement between ER and α event is achieved within(∆X, ∆Y ) = (1.0, 1.0) mm. To obtain the absolute ER cross sections, the efficiency of the ER to be transported to the focal plane
detector through the JAERI-RMS was evaluated by the method

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

90

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002  

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Figure 1. Evaporation residue cross sections for 28 Si + 198 Pt (solid circle). Fission cross sections6 are also shown (open circle), which are compared tothe coupled channel calculation (thin solid curve). Thin dot-dot-dashed curve is the fusion cross section from the one-dimensional barrier penetration
model.

E

10 20 30 40 50 60 70
10-3

(a)

214

ex [MeV]
10 20 30 40 50 60 70
10 20 30 40 50 60 70

(c)

Th

220

216

U+

Th

(e)

218

Pa+

Ac

(g)
214

10-4
216

10 20 30 40 50 60 70

214

220

216

Pa+

Ac

Ac

Th

216

Ac

Cross Section [mb]

10-5

10-6

220
220

U

218

Pa

Pa

10-7
10-3

(b)

219

215

U+

213

Th+

Ac

(d)

221

217

U+

Th

(f)

219

215

Pa+

Ac
215

10-4

215

Th

sum of (a)-(g)

Ac

10-5
221
213

10-6

217
219

10-7

U

Ac

200

220

Th

U

240

219

260

200

220

240

260

200

220

Pa

240

260

200

220

240

260

Ec.m. [MeV]
Figure 2. Evaporation residue cross sections for the reaction 82 Se + nat Ce (solid circle). Open triangle is the upper limit of the cross section. Thicksolid curve is the calculated cross section assuming fusion hindrance in the entrance channel (see text).

described in References 6, 12. We adopted the Shima formula13
to estimate the charge distribution.
Evaporation residue cross sections for 28 Si +198 Pt, 82 Se +nat Ce,
and 76 Ge + 150 Nd are shown in Figure 1, 2, and 3, respectively,
as a function of the c.m. energy (and also excitation energy
Eex ) by solid circles with error bars. Note that Figure 3(a) for76
Ge + 150 Nd contains 1n (225 U) and 2n (224 U) channels. The error includes both statistical contributions and the estimated uncertainty of 50% coming from the ambiguity in transport efficiency of ERs through the JAERI-RMS.
4. Analysis and Discussion
The experimental ER cross section σer,c for the observed
channel c was used to obtain the fusion probability weighted

by the angular momentum l by
Pfus (Ec.m. ) =∑c σer,c (Ec.m. ).
πλ ∑l (2l + 1) ∑c wer,c (Ec.m. + Q, l)
2(1)

The survival probability wer,c against fission for the channel c isa function of the excitation energy Eex = Ec.m. + Q (reaction Q
value) and the angular momentum l. This was calculated by thestatistical model calculation (HIVAP code14 ).
Parameters used in the HIVAP code were determined bymeasuring the ER and the fission cross sections for 28 Si + 198 Pt(Ref. 6). This is the light fusion system with Z 1 Z 2 = 1092 andis expected to have no fusion hindrance. The fusion cross section (Figure 1), which is approximated to the fission cross section for this reaction, was calculated by the coupled channel
calculation (CCDEF code15 ). We took into account the nuclear deformation of 28 Si (β2 = 0.40716 ) and 198 Pt (β2 = −0.060,8

Effects of Nuclear Deformation on the Fusion Probability

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

91

E ex [MeV]
10

-10

20
223

(a)

10-2

225

10-3

Cross section [mb]

10-4
10

40

80 0

60

20

U+219Th+215Ra

40
221

60
217

80 0

20

40

Th

(e)

220

(d) 220U+216Th

(f)

219

(c)

U+

60
216

Pa+

80

Ac

0

20

(g)

40
222

60

80

Pa

U

224

U

-5

10-6
10-1

(b)222U+218Th
214

10-2

+

Ra

Pa+215Ac(h) 221Th

10-3
10-4
10-5
10-6
180 200 220 240

180 200 220 240

180

200

220

240

180

200

220

240

E c.m. [MeV]
Figure 3. Evaporation residue cross sections for the reaction 76 Ge + 150 Nd (solid circle).

β4 = −0.0309 ) as well as the couplings of the octupole (3−)
vibrational states in 28 Si (β3 = 0.398, 6.88 MeV)17 and 198 Pt(β3 = 0.050, 1.68 MeV).17 It is found in Figure 1 that the CCDEF
calculation reproduces the fission cross section quite well down
to the sub-barrier energy region. The corresponding partial wave
distribution was put to the HIVAP code to obtain the ER crosssections. By assuming HIVAP parameters described in References 6,10, the ER cross sections for each channels are obtained
and shown in Figure 1 (thick solid curve). The calculation nicely
reproduced the experimental cross sections, indicating the validity of our parametrization. The fusion probability for 28 Si + 198 Pt
was calculated by eq 1, and the results are shown in Figure 4
as a function of Ec.m. /VB , where VB = 125.5 MeV is the spherical Coulomb barrier for this reaction. Above this barrier Pfus isalmost constant and has the value 1.
The resulting fusion probability for 82 Se + nat Ce is shownin Figure 4 as a function of Ec.m. /VB , where VB is taken as

10

1

10

0

-1

10

-2

Pfus

10

28

Si + 198Pt

1082

Se + natCe-3

76

Ge + 150Nd(

10

upper limit)

-4

0.8

0.9

1.0

1.1

1.2

Ec.m. / VB
Figure 4.
150
Nd.

Fusion probability for 28 Si + 198 Pt, 82 Se + nat Ce, and 76 Ge +215.3 MeV of 82 Se + 140 Ce. Below Ec.m. /VB = 1.15, Pfus for82
Se + nat Ce decreases considerably with lowering the bombarding energy, showing the curve similar to the massive system having fusion hindrance.2, 4, 5 By finding the Ec.m. at which Pfus of82
Se + nat Ce crosses the Pfus = 0.5 level, we obtained the extraextra-push energy EXX = 27 ± 5 MeV for this reaction.
Fusion probability for massive system can be represented
by assuming the fusion barrier distribution to have Gaussianin shape.4, 5 By setting the center of the barrier as VB + EXX(EXX = 25 MeV) and the standard deviation of σB = 10 MeV,
we could describe the Pfus for 82 Se + nat Ce as shown in Figure 4(solid curve). The corresponding partial wave cross section was
calculated and implemented to the HIVAP code as an initial spin
distribution, and the ER cross section was calculated as shownin Figure 2. The calculation reproduces the experimental ER
cross sections.
The fusion probability Pfus for 76 Ge + 150 Nd is shown in Figure 4 by the solid circles with statistical error bars. Pfus values of 76 Ge + 150 Nd are nearly flat with ∼1.0 down to Ec.m. ∼ VB
( = 209 MeV) given by assuming the 150 Nd nucleus to be spherical (spherical Coulomb barrier). This trend is similar to the fusion of 28 Si + 198 Pt which exhibits no fusion hindrance, and theexcitation function shows marked contrast to that of 82 Se + nat Ce.
It is apparent that the reaction 76 Ge + 150 Nd exhibits no fusion
hindrance at and above the spherical Coulomb barrier. We did
not observe any events at Ec.m. < VB and thus the upper limit isshown by the solid reversed-triangle in Figure 4.
Because of the large deformation of 150 Nd, the fusion barrier for 76 Ge + 150 Nd distributes widely. We have calculated thefusion cross section for 76 Ge + 150 Nd by the coupled-channel
model (CCDEF code15 ). The important characteristic in this reaction is that the Coulomb barrier height is nearly constant with210 ∼ 214 MeV in the side collision of 50◦ ∼ 90◦ as a result of
the 150 Nd deformation (β2 = 0.358, β4 = 0.107). The partial wave
cross sections from CCDEF code were inputted to the HIVAP
code to yield ER cross sections. It was found that the calculated
cross sections for the energy range of 185 < Ec.m. < 195 MeV
lie far above the upper limit of the experimental data of the 225 U
channel as indicated by the dashed line in Figure 3(a). This indicates that the system does not fuse if the projectile collides
with the tip of the prolately deformed target of 150 Nd when thebombarding energy is set to the corresponding Coulomb barrier (184 MeV). The experimental data was reproduced only

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J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Nishiowhen the extra-extra-push energy was assumed for the tip collision. The barrier height was effectively enhanced assuming that the shift is linearly scaled with the Coulomb barrier
distance (r) and has the maximum value at the tip collision(θcoll = 0◦ , EXX0 = 13 MeV) and the minimum at the side collision (θcoll = 90◦ , EXX = 0 MeV) as
EXX (r) = EXX0

r − Rside.
Rtip − Rside

Acknowledgment. We would like to thank the crew of the
JAERI tandem accelerator for generating 28 Si, 76 Ge, and 82 Se
beams.

(2)

Note that the Coulomb barrier distance r, determined by the
CCDEF code, is a function of θcoll . Rside and Rtip becomes 11.7
and 14.6 fm, respectively. As seen in Figure 3, the ER cross sections of the 225 U channel decreases by two orders magnitude andis consistent with the experiment. For the bombarding energy ofthe side collision (210 ∼ 214 MeV), the experimental ER crosssections are reproduced in the calculation, supporting that there
is no fusion hindrance at the side collision for 76 Ge + 150 Nd.
The side collision (θ = 90◦ ) for 76 Ge + 150 Nd gives a Coulomb
barrier distance of 11.7 fm, which is smaller than the distancefor 82 Se + 140 Ce (12.3 fm). If we assume that the fission saddle points do not differ very much in the two systems (222 U for82
Se + 140 Ce and 226 U for 76 Ge + 150 Nd), it can be considered thatthe configuration of the side collision of 76 Ge + 150 Nd is close to
the fission saddle point. Thus the loss in kinetic energy in thefusion process is minimized and is smaller than for 82 Se + 140 Ce.
We also want to mention that the tip collision of 76 Ge on 150 Nd
has the Coulomb barrier distance of Rtip = 14.6 fm, which islarger than that of 82 Se + nat Ce. The long distance would results
in a large amount of kinetic energy needed to form the compound nucleus.
5. Conclusions
Evaporation residue cross sections for 76 Ge + 150 Nd and
Se + nat Ce were measured in the vicinity of the Coulomb barrier. We also measured the ER and fission cross sections for28
Si + 198 Pt to determine the parameters used in the statisticalmodel calculation, yielding the survival probability in the exit
channel. The fusion of 82 Se + nat Ce is a reaction characterized by spherical colliding partners with Z 1 Z 2 = 1972. The fusion hindrance was observed in the form of extra-extra-pushenergy 27 ± 5 MeV. For the reaction 76 Ge + 150 Nd, which has
Z 1 Z 2 = 1920 being close to 82 Se + nat Ce, the obtained fusion
probability did not exhibit any fusion hindrance at all for theside collision of 50◦ < θcoll < 90◦ . It therefore can be concluded
that the compact touching configuration promotes fusion evenfor massive system with Z 1 Z 2 > 1800. This idea is supported by
the experimental results that for the tip collision of 76 Ge on 150 Nd
82

the large Coulomb barrier distance caused fusion hindrance andresulted in an extra-extra-push energy for the system to form acompound nucleus.

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