Near-barrier Fusion Evaporation and Fission of 28 Si + 174 Yb and 32 S + 170 Er

Fusion evaporation residues and fission fragments have been measured, respectively, at energies around the Coulomb barrier for the 28Si+174Yb and 32S+170Er systems forming the same compound nucleus 202Po. The excitation function of fusion evaporation, fission as well as capture reactions were deduced. Coupled-channels analyses reveal that couplings to the deformations of targets and the two-phonon states of projectiles contribute much to the enhancement of capture cross sections at sub-barrier energies. The mass and total kinetic energy of fission fragments were deduced by the time-difference method assuming full momentum transfer in a two-body kinematics. The mass-energy and mass-angle distributions were obtained and no obvious quasi-fission components were observed in this bombarding energy range. Further, mass distributions of fission fragments were fitted to extract their widths. Results show that the mass widths decrease monotonically with decreasing energy, but might start to increase when Ec.m./VB < 0.95 for both systems.


Introduction
Heavy-ion induced fusion-fission reactions at energies around the Coulomb barrier have attracted much attention [1,2], due to many degrees of freedom involved in the interaction processes.It has been experimentally proved that the coupled interactions of some intrinsic motions and relative motion play a significant role in the process that two nuclei fuse into one, and it is commonly interpreted theoretically as coupled-channels (CC) effects.It is expected that the deformation [3], vibrational state [4] and transfer channel [5][6][7] may be involved in the capture reaction.After two nuclei come into contact with each other, the system evolves along the potential energy surface, the path of which may be complicated.The system may achieve equilibrium of all the degrees of freedom and whereafter the compound nucleus (CN) can survive through evaporating light particles.The system can also go to fission via some equilibrium or non-equilibrium processes, such as complete fusion-fission, pre-equilibrium fission [8], quasi-fission [9] and fast fission [10][11][12].These processes may strongly depend on some factors of the entrance channel, for example, deformations of projectile and target, the mass asymmetry, and so on.Comprehensive research on fusion-fission reactions can cast useful light on the understanding of heavy ion induced reactions.
Previously, we have measured the angular distributions for the fission fragments of the 32 S+ 184 W system [13] and, the mass and energy distributions for the fission fragments of the 34 S+ 186 W system [14].Anisotropy deduced from ⋆ e-mail: cjlin@ciae.ac.cn the measured angular distributions reveals the appearance of non-equilibrium fission.It can be interpreted as quasifission by the dinuclear system model or pre-equilibrium fission [14].In order to further explore on the fission mechanism, study on extensive systems is desired.
In the present work, the 28 Si+ 174 Yb and 32 S+ 170 Er systems were chosen because both systems form the same compound nucleus 202 Po.It is noted that mass-angle correlations and mass ratio distributions of fission fragments have been measured systematically for the systems of 16 O+ 186 Os, 24 Mg+ 178 Hf, 34 S+ 168 Er, and 48 Ti+ 154 Sm [15], also forming the same compound nucleus 202 Po.Therefore, the entrance-channel dependence can be investigated in a systematic manner.Moreover, both fusion evaporation residues (ERs) and fission fragments have been measured for the 34 S+ 168 Er system [16], giving a good reference to the present work.It is worth to point out that both fusion evaporation and fission have observable cross sections at near-barrier energy region due to the higher fission barrier of 202 Po (≈ 15 MeV ) [17].It provides a good case to explore the evolving paths of both fusion and fission along the potential energy surface, to strictly test as well as help to develop relevant theoretical models, and to comprehensively understand the complete fusion-fission dynamics.
In the following Sec.2, details of the experimental procedure for fusion evaporation and fission measurements are present.Experimental results and preliminary discussions are reported in Sec. 3

Experimental procedure
The beams of 32 S and 28 Si, at several energies in the range of 133.0 -181.0MeV and 119.2 -162.1 MeV, respectively, were supplied by the HI-13 tandem accelerator of the China Institute of Atomic Energy, Beijing, China.Highly isotopically-enriched 170 ErO 3 (95 µg/cm 2 ) and 174 Yb (130 µg/cm 2 ) targets sputtered onto carbon backings (20-23 µg/cm 2 ) were used.Four silicon (Si) detectors placed symmetrically at θ lab = ±20 • (right-left and up-down) with respect to the beam direction were used to monitor the Rutherford scattering and to provide a normalization for the fusion evaporation and fission cross sections.Fusion ERs and fission fragments were measured independently with the same beam.

Measurement of fusion ERs
Fusion ERs mainly concentrated within a few degrees of the incident beam direction were separated from the beamlike particles (BLPs) by using an electrostatic deflector setup [18].It consists of two pairs of electrodes followed by two micro-channel plate (MCP) detectors and a 48 × 48 mm 2 quadrant Si detector.Distances of MCP1-MCP2 and MCP2-Si are 41.0 and 22.7 cm, respectively.Time-offlight (ToF) versus E spectra, ToF1-E and ToF2-E, are useful to reduce the spurious backgrounds from the random coincidences between the Si and one of the MCPs, especially for the measurements of low fusion evaporation cross sections at sub-barrier energies and for asymmetric systems studied in this work.The reaction products were limited by a collimator of 2.5 mm in diameter before entering the electric fields, corresponding to an opening angle θ lab = ±0.38 • .Fig. 1 shows a typical ToF1 versus E spectrum for the 32 S+ 170 Er system at an energy near the Coulomb barrier, where BLPs and ERs can be separated clearly.The ERs angular distributions were measured in the range θ lab = −4 • to +8 • with a step of 0.5 • or 1 • for both systems at E lab = 143 MeV and 163 MeV, respectively.Their shapes do not change appreciably with the beam energy, resulting from the dominant neutron and/or proton evaporation from the CN [19], which is consistent with the calculation of the code PACE2 [20].Typical angular distributions of ERs for the 32 S+ 170 Er system as well as their fittings by a single Gaussian function are shown in Fig. 2. For other energies, ERs were measured only at θ lab = 1.5 • .Total fusion evaporation cross sections were obtained by integration of the angular distribution with the same shape.Meanwhile, corrections were made for the transmission efficiency of the electrostatic deflector, which is about 40%.

Measurement of fission fragments
Two fission fragments were detected in coincidence by using two Parallel Plate Avalanche Counters (PPACs).The PPAC1 and PPAC2 have an active area (X ×Y) of 180×100 mm 2 and 250 × 100 mm 2 with X and Y position resolution of about 1 and 2 mm, respectively.The emission angles θ 1 and θ 2 projected on the reaction X − Z plane and the out-of-plane angles φ 1 and φ 2 for the fission fragment 1 and 2 were transformed from the XYZ coordinate, assuming the beam direaction as the Z axis.The detectors were located around the target, centering at θ 1 = 45 • and θ 2 = −105 • with distances of d 1 = 155 mm and d 2 = 125 mm from the target to the centers of entrance windows and covered angles of ∆θ 1 = ±27 • and ∆θ 2 = ±30 • as well as 14.9 • ≤ φ 1 ≤ 75.7 • and 60.0 • ≤ φ 2 ≤ 150.0 • for PPAC1 and PPAC2, respectively.The detectors were operated with isobutane gas at a pressure of about 3 Torr.
The time difference ∆T between the two fission fragments was measured with start and stop signals obtained from PPAC2 and PPAC1, along with the energy losses ∆E 1 and ∆E 2 in both PPACs by passing nuclei.Fig. 3 (a) gives an example of measured coincident events in the ∆E 1 +∆E 2 versus ∆T coordinate plane, for 28 Si+ 174 Yb reactions at the E c.m. /V B = 1.25.A clear separation between fission fragments and scattered particles can be noted.An additional way to distinguish fission fragments from the scattered projectile and recoiled nuclei is to exploit the difference in the reaction kinematics.This is demonstrated in Fig. 3 (b), where events are plotted in the θ 1 + θ 2 versus φ 2 − φ 1 coordinate plane.The calibration for the time difference ∆T was made from the elastic-recoil peak positions appearing in the ∆T spectrum.The timing resolution of a single PPAC pixel was determined to be 0.3 ns.The experimental mass resolution obtained from the elastic scattering peak is about σ exp = 2 − 4 u, depending on the measured angle.
In the present work, the ∆T method was employed to deduce the velocity and mass of fission fragment by applying the momentum conservation as well as the mass conservation in a two-body kinematics.In the laboratory system, we have where m is the mass, v is the velocity and r is the flight distance of outgoing particles before being detected, subscript P, T, CN and 1, 2 represent the projectile, target, CN and fission fragments, respectively.Finally, the velocity and mass of outgoing particles can be expressed as • m CN , (8) and then the total kinetic energy (TKE) can be calculated, 3 Results and discussions

Excitation function
The excitation functions of evaporation were determined by doing the integrals with respect to angular distribution and performing the correction of the transmission efficiency.As for fission, position and time difference of fission fragments detected by PPACs were used to deduce their mass, emission angle and TKE.Integral of the angular distribution leads to the fission cross section, and the fission excitation function was then determined.Adding the excitation functions of ERs and fission together, the excitation function of capture reaction was obtained.
The measured fusion ERs, fission and capture excitation functions are shown in Fig. 4 for 28 Si+ 174 Yb and 32 S+ 170 Er, respectively.The CC code CCFULL [21] was used to reproduce the capture cross sections and the relevant parameters used in the CC calculations are listed in Table 1.It can be seen from the figure that the singlechannel (SC) results (dashed lines) under-predict the subbarrier data.However, experimental capture excitation functions could generally reproduced by the CC calculations with couplings to the vibrational two-phonon 2 + states of projectiles and the rotational 2 + , 4 + , 6 + , 8 + states of targets, except a small deviation at energies around the barrier.

Mass-TKE correlations
The contour diagrams representing the angle integrated fragment mass-TKE correlations for a selected subset of the 28 Si+ 174 Yb and 32 S+ 170 Er systems are shown in Fig. 5.
In both figures, one can distinguish two regions of a scattering region close to the target and projectile masses and a region of fission in the direction of symmetry.The almost independence of the fission TKE on the bombarding energy indicates that the initial excess kinetic energy is completely damped out and transformed into internal excitation in all capture processes.

Mass-angle correlations
The correlations between fragment mass and center-ofmass angle for the 28 Si+ 174 Yb and 32 S+ 170 Er systems are shown as contour diagrams in Fig. 6.Also in these diagrams, the separation between scattering and fission reactions is clearly apparent.Both the two systems show symmetric fission fragment mass distributions at all angles, which is a characteristic feature for the CN fission.

Mass distributions
As mentioned above, no obvious correlations were observed in mass-angle and mass-TKE distributions for the two systems at energies around the barrier.The existing systematic study shows that the width of mass distribution for the quasi-fission is larger than that for the fusion-fission [22].Therefore an increased mass width can be used as an indicator for the presence of quasi-fission.Fig. 7 shows the mass distributions of fission fragments for the 28 Si+ 174 Yb and 32 S+ 170 Er systems at three reaction energies, respectively, where the fission yields are normalized to 200%.The mass spectra can described by a single Gaussian distribution with the center at A CN /2.The standard deviation σ M of the mass distributions was obtained at each reaction energy, as shown in Fig. 8.It is evident from the figure that σ M decreases monotonically with decreasing energy, but seems to increase when E c.m. /V B < 0.95 for both systems.

Conclusions
The evaporation and fission reactions of 32 S+ 170 Er and 28 Si+ 174 Yb were measured at the energy ranges of 0.91≤E c.m. /V B ≤1.23 and 0.93≤E c.m. /V B ≤1.25, respectively.The excitation functions of fusion evaporation, fission well as capture reactions obtained.The coupled-channels calculations, where both the 2 + phonon vibrational-states of projectiles and the 2 + , 4 + , 6 + , 8 + rotational-states of targets are considered, could roughly reproduce the capture excitation functions for the two systems.For fission, the mass-TKE and massangle distributions were deduced and no obvious quasifission components were observed in this bombarding energy range.The mass widths decrease monotonically with decreasing energy, but might start to increase when

Figure 1 .
Figure 1.Two-dimensional plot ToF1-E taken at E lab = 169 MeV and θ lab = 2 • for 32 S+ 170 Er.A group of BLPs and ERs are indicated.

Figure 2 .
Figure 2. Angular distributions of ERs for the 32 S+ 170 Er system at E lab = 143 MeV and 163 MeV.Curves are single Gaussian fits used to obtain the total fusion evaporation cross sections.

Figure 3 .
Figure 3. (a) Events from the 28 Si+ 174 Yb reaction, mapped on the ∆E 1 +∆E 2 versus ∆T axes.Fission events within the polygon and scattering events are clearly separated.(b) Same as in (a) but in the coordinates of θ 1 + θ 2 versus φ 2 − φ 1 .

Figure 4 .
Figure 4. Experimental cross-sections of fusion evaporation (circle), fission (square) and capture (star) for the 28 Si+ 174 Yb (left panel) and 32 S+ 170 Er (right panel) systems, together with the CC (solid curve) and the SC (dashed curve) calculation results.
and conclusions are given in Sec. 4 finally.

Table 1 .
The relevant parameters used in the CCFULL calculations.