Effects of nuclear orientation on fusion and fission in the reaction using 238 U target nucleus

Fission fragment mass distributions in the reaction of 30Si+ 238U were measured around the Coulomb barrier. At the above-barrier energies, the mass distribution s h wed a Gaussian shape. At the subbarrier energies, triple-humped distribution was observed, which cons ists of symmetric fission and asymmetric fission peaked at AL/AH ≈ 90/178. The asymmetric fission should be attributed to quasifission from the re sults of the measured evaporation residue (ER) cross-sections for 30Si+ 238U. The cross-section for 263Sg at the abovebarrier energy agree with the statistical model calculation which assumes th at the measured fission cross-section originates from fusion-fission, whereas the one for 264Sg measured at the sub-barrier energy is smaller than the calculation, which suggests the presence of quasifission.


Introduction
In the production of superheavy nuclei (SHN) based on the actinide target nuclei and 48 Ca beams [1] the cross-sections do not drop at increasing atomic number, but maintain values of a few picobarn even for the production of the heaviest elements.This makes large difference from cold fusion reactions using lead or bismuth targets [2,3], where the cross-sections decrease exponentially with atomic number.The relatively large cross-sections for actinide based reactions are explained by a high survival probability of the compound nuclei in competition with fission due to large fission barriers of nuclei in the vicinity of the N = 184 shell closure [1].Another possible reason could be higher fusion probability.Since nuclei of the actinides are prolately deformed, there exists a configuration where the projectiles hit the equatorial region of the deformed target nuclei.In this case a compact configuration is achieved and the system may have a larger fusion probability than in the reactions using spherical target nuclei of lead or bismuth.
In the reactions with the light projectile 16 O with 238 U target, it is concluded that the system results in fusion even at deep sub-barrier energies from the measured evaporation residue (ER) cross-sections [4].Fusion occurs from every colliding angle, independently of the nuclear orientation.In the reaction using heavier projectile, 30 Si + 238 U, the measured ER cross-section for 264 Sg at above-barrier energy agrees with a statistical calculation based on the assumption that system captured inside the Coulomb barrier all results in fusion [5].On the contrary, the crosssection for 264 Sg at the sub-barrier energy are lower than a Josef Buchmann-Professor Laureatus the calculation, which suggests the presence of fusion hindrance in polar collisions.In this case two different process should be involved in fissions.One is the fission from the fully equilibrated compound nucleus produced in complete fusion.The other is quasifission that system disintegrate without forming a compound nucleus.
The fission fragment mass distributions for the reaction 36 S + 238 U have been measured [6].In this reaction, we found strong variation of the mass distribution with bombarding energies.At the above-barrier the spectra showed nearly symmetric distribution.In the sub-barrier region, the distribution showed mass asymmetry with the maximum yields at around A H /A L ≈ 200/74.We interpreted that the symmetric fission originates from compound-nucleus fission and the asymmetric fission results from quasifission.
We report the measurement of fission fragment mass distributions for 30 Si + 238 U from above-to sub-barrier energies.We expect the asymmetric fission to appear in the sub-barrier region from the measured ER cross-section at the sub-barrier energy.

Experiment
The fission experiments were carried out at the JAEA tandem accelerator by using the 30 Si beams.The experimental setup is almost the same as in [6].Beam energies are changed from 191 to 146 MeV to measure the energy dependence of the fragment mass distributions and fission cross-sections.Typical beam intensities were about 0.5−1.0particle-nA.The 238 U target was prepared by electrodeposition of natural UO 2 on a Ni backing of 90 µg/cm 2 thick-EPJ Web of Conferences ness with a diameter of 5 mm.The thickness of the 238 U contents was about 80 µg/cm 2 .
Two fission fragments (FFs) were detected in coincidence by using position-sensitive multi-wire proportional counters (MWPCs).The MWPCs have an active area of 200 mm×120 mm in horizontal and vertical direction, respectively.The detectors were located on both sides of the target each at a distance of 211 mm and at angles of The time difference ∆t between the signals from two MWPCs were recorded.The signals from both MWPCs contain the information on the energy deposition ∆E 1 and ∆E 2 of particles passing through the detectors.The fragment incident position on MWPCs were recorded to give the direction of fragment emission.The folding angle between two fission fragments was used to separate the full momentum transfer (FMT) fissions from fission events following nucleon transfer, which occurs when fissile targets like 238 U are used.
For normalization of the beam current, a silicon surface barrier detector with the solid angle 1.96 msr was mounted at 27.5 • relative to the beam direction.

Experimental results and discussions
The cross-sections for the FMT fissions (σ fiss ) for 30 Si + 238 U are shown in the upper part of Fig . 1 as a function of the center-of-mass energy E c.m. .The cross-sections are almost equal to those of the projectiles being captured inside the Coulomb barrier (σ cap ).The cross-section was determined by drawing the angular distribution in the center-of-mass 85 • ≤ θ c.m. ≤125 • , which were fitted to a function in [13] to yield the cross-section.Since the angular range covered in our experiment was limited, so that the σ fiss values contain an error arising from the uncertainties in dσ fiss /dΩ(θ c.m. ) at forward and backward angles.We estimated 28 % uncertainty in σ fiss in addition to the statistical uncertainty.
The experimental data are compared to the coupledchannels calculations using the code CCDEGEN [7].The dashed curve is the result without considering any collective properties of target and projectile (one-dimensional barrier penetration model).The dash-dotted curve is the results taking into account the prolate deformation of 238 U with β 2 = 0.275 and β 4 = 0.05 [8,4].We have also additionally taken into account the couplings to the 2 + state at 2.235 MeV (β 2 =0.316 [9]) in 30 Si and to the 3 − state at 0.73 MeV in 238 U ( β 3 =0.086[10]), and the results is shown by the solid curve.The experimental data agree with the calculation when the deformation of 238 U was taken into account.
Figure .2shows the fission fragment mass distributions for 30 Si + 238 U.The fragment masses were determined by using the conservation law for momentum and mass with the assumption that mass of the composite system is equal to the sum of those for the projectile and target masses.The distributions are symmetric with Gaussian shape in the energy range from E c.m. = 144.0MeV to 159.0 MeV, where width of the distribution decreases gradually when beam energy decreases.
At the sub-barrier energies of E c.m. =134.0 and 129.0 MeV, the distributions have asymmetric component at around A L /A H ≈ 90/178.The distribution at 129.0 MeV has triplehumped structure because of the enhanced asymmetric fission.Such a structure of asymmetric fission was not observed in the fragment mass distributions for lighter projectile reaction 16 O + 238 U [11], although the standard deviation for the mass distributions increase in the sub-barrier energies.The reaction 26 Mg + 248 Cm also do not show significant asymmetric fission peaks [12].The data indicates that the projectile 30  The mass distributions for 30 Si + 238 U at sub-barrier energies apparently include different origin in fission which should be attribute to quasifission in order to explain consistently the measured ER cross-sections shown in the lower part of Fig. 1 [5].The cross-section for 263 Sg (5n) obtained at the above-barrier energy of E c.m. =144.0MeV agree with the statistical model calculation (solid curve), which means that fusion is the main process after the system is captured inside the Coulomb barrier and the fragments should originate from the excited compound nucleus.The fragment mass distribution at this energy shows the Gaussian shape typical for the compound nucleus fission.On the other hand, cross-section for 264 Sg (4n) measured at the sub-barrier energy E c.m. =133.0MeV is about a few factors of magnitude smaller than the calculation, indicating that quasifission should be involved in the reaction.
The appearance of quasifission in the sub-barrier energies represents the effects of nuclear orientation on fusion and/or quasifission.At the sub-barrier energy, projectile collides on the polar sides of the target nucleus 238 U.The reaction from this configuration has large charge-center distance between the projectile and target nucleus, which results in larger quasifission probability than the reaction starting from the equatorial collisions.
The mass asymmetry of the quasifission for 36 S + 238 U was A L /A H ≈ 74/200.The difference could have information for the system approached to the fully amalgamated compound system even when quasifission take place.Such a model calculation is going based on the fluctuation-dissipation model [14].

Fig. 1 .
Fig. 1.Fission (upper part) and evaporation residue cross-sections (lower part) of the reaction 30 Si + 238 U → 268 Sg * as function of the center-of-mass energy E c.m. and excitation energy E * .The fission cross-section is obtained in this experiment.The ER cross-section data were from [5].Curves are the model calculations (see text).

Fig. 2 .
Fig. 2. Mass distributions for the full-momentum transfer fissions of the reaction 30 Si + 238 U.The spectra are obtained by normalizing the total yields to be 200 %.Reaction energies E c.m. and excitation energies E * of the compound nucleus are given.