Investigation of the reaction 64Ni + 238U being an option of synthesizing element 120

Abstract This study is concerned with the search for entrance channels suitable to synthesize elements with Z > 118 . Mass–energy distributions as well as capture cross-sections of fission-like fragments have been measured for the reactions 64Ni + 238U → 302120 and 48Ca + 238U → 286112 at energies near the Coulomb barrier. Compound nucleus fission cross-sections were estimated from the analysis of mass and total kinetic energy distributions. The cross-section drops three orders of magnitude for the formation of the compound nucleus with Z = 120 obtained in the reaction 64Ni + 238U compared to the formation of the compound nucleus with Z = 112 obtained in the reaction 48Ca + 238U at an excitation energy of the compound nucleus of about 45 MeV. From our analysis it turns out that the reaction 64Ni + 238U is not suitable for the synthesis of element Z = 120 .


Introduction
The existence of the island of stability in the region of nuclei with Z = 114 and N = 184 predicted theoretically [1] has induced an extensive experimental investigation in the field of superheavy element (SHE) synthesis. A considerable success was achieved in reactions of actinides with a double magic 48 Ca beam at FLNR [2] where the synthesis of SHEs with atomic number Z up to 118 has been claimed. Experimental data confirm the theoretical prediction of the increase of the half-lives following the increase of the neutron number of the compound nucleus [2]. Unfortunately, the isotopes of SHE formed in these 48 Ca induced reactions can- fusion reactions: 54 Cr + 248 Cm, 58 Fe + 244 Pu or 64 Ni + 238 U. The reaction 54 Cr + 248 Cm is more favorable due to its larger mass asymmetry in the entrance channel [7]. However, some gain in the fusion cross-section for the 64 Ni + 238 U reaction may be caused by the lower excitation energy at the Bass barrier [8] compared to the other two reactions.
The main aim of the present study is to evaluate the reaction 64 Ni + 238 U as a possible candidate for the synthesis of the element with Z = 120. This Letter is concerned with the results of experimental studies of the properties of binary products in reactions of the magic projectiles 48 Ca and 64 Ni with the same target 238 U at energies around the Coulomb barrier. The mass-energy distributions of binary fragments as well as their cross-sections have been measured. The reaction 48 Ca + 238 U has been performed in order to test a data analysis methodology to further apply it to the data of the reaction 64 Ni + 238 U. The method is an attempt to extract estimates of the fusion cross-section from the TKE distribution for fixed fragment mass intervals. Binary reaction products were detected by the two-arm timeof-flight spectrometer CORSET [9]. Each arm of the spectrometer consisted of a compact start detector and a position-sensitive 9 × 7 cm 2 stop detector, both based on microchannel plates. The arms of the spectrometer were positioned at angles +64 • and −64 • to the beam axis for the reactions with 48 Ca and +60 • and −60 • for the reactions with 64 Ni. With this choice of angles, the scission axis is orthogonal to the beam axis for the case of symmetric splitting in both reactions. In other words, the fragments are detected at 90 • in the center of mass frame. The distance between start and stop detectors was 15 cm. Start detectors were placed at a distance of 5 cm from the target. The angular acceptance for both arms was ±12.5 • in-plane and ±10 • out-of-plane.

Experiment
A typical mass resolution of the spectrometer in these conditions is about 2-3 u.
Four silicon detectors, placed above and below the reaction plane, and to the left and right of the beam at the same scattering angle of 16 • were used to monitor the beam intensity and position continuously and also to normalize the yields to cross-sections.
The data processing assumes standard two-body kinematics [9]. Fragment energy losses in the target, the backing and the start detector foils were taken into account. Special attention was paid to the folding angle correlations both in and out of the reaction plane, and only events corresponding to a two-body process with full linear momentum transfer were considered.

Results and discussion
Figs. 1 and 2 display the measured TKE-mass distributions of binary fragments of the reactions 64 Ni + 238 U and 48 Ca + 238 U, respectively. In the TKE-mass matrix the reaction products with masses close to those of the projectile and target are identified as quasi-elastic and deep-inelastic events, and were not considered in the present analysis. Reaction products lying between quasielastic peaks are assumed as totally relaxed events, i.e., as fission (or fission-like) fragments. We  The dispersions of asymmetric QF fragment mass distributions increase as the projectile energies increase. At the lowest excitation energy of the CN of ∼ 18 MeV one can see only asymmetric QF fragments for both reactions. The yield of symmetric fragments increases with increasing excitation energy as well, but the growth is less in the reaction 64 Ni + 238 U.
A guideline for the interpretation of the pattern following from the TKE-mass distributions comes from dynamical models. A realistic description of the mass, energy and angular distributions of the reaction fragments formed in deep inelastic scattering, QF and compound nucleus fission (CNF) processes in low-energy heavy ion collisions was performed in [10] by using Langevin type dynamic equations of motion. It was shown that the multi-dimensional adiabatic potential energy surface (calculated within the two-center shell model) plays the most important role in such processes. Fig. 3 shows the potential energy surface as a function of the mass-asymmetry and elongation for the nuclear system consisting of 120 protons and 182 neutrons (for more details on these calculations see Ref. [7]). This potential energy surface is strongly modulated by shell effects and leads to the appearance of deep valleys corresponding to the formation of well bound magic nuclei. In accordance with these calculations, at least three paths leading to the formation of fission-like fragments can be distinguished: (1) asymmetric QF (QF asym in Fig. 3) caused by the influence of proton shells with Z = 28, 82 and neutron shells with N = 50 and 126; (2) symmetric QF (QF sym in Fig. 3) determined by the shells with Z = 50 and N = 82; (3) CNF (CNF path in Fig. 3) leading to the formation of symmetric fragments. Thus, in the reaction 64 Ni + 238 U the mass-symmetric fragments may be formed by different modes: either as a result of CNF or symmetric QF processes or as a tail of asymmetric QF process. It can be shown that the same pattern holds for the 48 Ca + 238 U reaction.
From Fig. 3 one can see that indeed the contact configuration of the less asymmetric combination 64 Ni + 238 U is located lower in the potential valley with respect to the partners 54 Cr + 248 Cm and 58 Fe + 244 Pu, in particular in the proximity, but slightly after, the bifurcation point between the QF asym and QF sym paths. This means that in the case of 64 Ni + 238 U the nuclear system might be driven more toward the QF asym channel than in the other two reactions. Consequently, a relatively higher contribution from the QF asym path can be reasonably expected.
In Fig. 4a  It is readily seen that both TKE distributions have a complex structure which is not consistent with only CNF. In fact, it is known that in such a case the average TKE of the partner fragments is substantially independent on the excitation energy and shows a typical Gaussian-like shape. By using the theoretical work of Ref. [10] as a guideline, we decompose each TKE distribution as a sum of three Gaussians. We use the systematics [11,12] as a starting point to evaluate mean and variance of the CNF mode. After a 3-Gaussian fitting procedure we can evaluate the cross-sections due to each of the three components. To test this approach, we apply this method to the reaction 48 Ca + 238 U where the capture, QF and CNF crosssections have been measured by other authors [4,5]. Once this method is applied to the TKE distribution of fragments from the reaction 48 Ca + 238 U, the degree of agreement of the estimated cross-sections with known experimental data provide us with the necessary confidence to apply the same method to the reaction 64 Ni + 238 U.
From the Viola systematics we infer that the average TKE is in a first approximation a linear function of the Coulomb parameter Z 2 CN whereas from the systematics in Ref. [11] we can estimate the variance of the TKE distribution. For the 286 112 CN ( Z 2 /A = 43) the variance σ 2 of the TKE distribution of CNF is about 400 MeV 2 [11] and the TKE is 233.7 MeV [12]. From the 3-Gaussian fit we obtain mean TKE values and standard deviation σ as shown in Table 1.
The TKE value of 228 MeV (Table 1) for CNF mode turns out to better agree with the older Viola systematics [13] which predicts a mean TKE of 226 MeV. However, we must consider that in the newer systematics [12] the data from Ref. [4] measured at energies well above the Coulomb barrier were included. In these reactions a considerable amount of QF processes contributes to the fission products. It turns out that the old systematics of Viola [13], without taking into account the experimental data from [4], provides a lower value of TKE better in agreement with our result. The standard deviation σ TKE of the CNF component is around 20 MeV and also agrees well with the predicted value for the CNF process from the systematics [11].  278.0 ± 3.0 8 .9 ± 2.5 2 1 ± 7 * Values were fixed according to [13] and [11].
Given the considerable good agreement with the systematics, we associate the 2-Gaussian component to the CNF process. Since the asymmetric fragments have lower TKE than the symmetric ones, the low energy component of the experimental TKE distribution may be associated with fragments originating from the asymmetric QF process. The high energy part may arise instead from the symmetric mode of the QF process. Furthermore, we note that the mean TKE from the QF sym mode is about 40 MeV higher than the mean TKE for the CNF mode. Considering that both QF sym and CNF modes give rise to symmetric mass fragments, the difference in mean TKE can be taken as an evidence that in the QF process a complete dissipation of the entrance channel energy does not occur. As a consequence, the symmetric fragments with high TKE do not originate from complete fusion because the final fragments retain part of the entrance channel total kinetic energy.
In contrast to the 48 Ca + 238 U reaction, for the reaction 64 Ni + 238 U the TKE distribution has more pronounced low and high energy components (see Fig. 4c), while the component with an average TKE value of 252 MeV, corresponding to the old Viola systematics, is highly reduced. A 3-Gaussian fit, performed according to the method used for 48 Ca + 238 U, provided the means and variances shown in Table 2. Because of the lower statistics, we fixed the mean and variance of the CNF component to the values predicted from the systematics [13] and [11], respectively. Only an upper value for the relative yield of the CNF component can be reasonably given.
To evaluate the integrated cross-section for each component we need to make an assumption about the angular distribution in the center of mass frame. The absolute differential cross-sections for all fission-like events observed in the reactions were measured at an angle θ c.m. = 90 • and at energies from well below to well above the Coulomb barrier. The capture cross-section σ cap for the production of all fission-like events (sum of CNF and QF processes) were estimated assuming that the angular distribution is proportional to 1/ sin θ c.m. . This procedure seems to be the most reasonable and is applied since detailed angular distributions are not available at present. In the estimate of the QF cross-section we took into account a correction due to the overlapping of fission-like events with those corresponding to deep-inelastic and quasi-elastic processes and cut off a part of the asymmetric fission-like fragments in the case of the Ni-induced reactions.
The obtained capture cross-sections as well as the cross-section for the formation of symmetric fragments with masses A CN /2 ± 20 u are presented in Fig. 5 for both reactions. The capture crosssections for the 48 Ca + 238 U and 64 Ni + 238 U agree well with previous measurements [4,5]. Moreover, for the reaction 64 Ni + 238 U at  [4,5]. Open rhombs and circles on the bottom panel are the evaporation residue cross-section from [2,17]. E lab = 390 MeV a total reaction cross-section of 850 mb was derived in [14] which is consistent with the value quoted in Ref. [4]. Subtracting from it the total transfer cross-sections, also measured in [14], amounting to σ tr 670 mb, we obtain a "residual" or capture cross-section of σ res 180 mb. This value compares well with 150 mb quoted in Ref. [4] and this work (σ cap = 122 ± 40 mb at E lab = 382 MeV) and which is denoted as capture reaction (sum of CNF and QF). Additionally, Table 3 gives the relative contributions of the symmetric fragments (with mass A CN /2 ± 20 u) to all fission-like events for the reactions 48 Ca + 238 U and 64 Ni + 238 U at an excitation energy of ∼ 45 MeV of the CN. The relative contribution of the symmetric fragments with TKE corresponding to the older Viola systematics is also presented in Table 3. Earlier the mass-energy distributions of fission-like products for the system 58 Fe + 244 Pu at E lab = 328 MeV which lead to the same superheavy nucleus Z = 120 were measured in Ref. [15]. We have performed a similar analysis also for this system. The TKE distribution, measured under the same conditions, is shown in Fig. 4b and the relative yields are shown in Table 3.
In Fig. 5 the CNF cross-sections estimated in our 48 Ca + 238 U experiment are compared with the ones measured by other authors. This comparison is important to validate the ability of the procedure proposed to extract cross-sections from a 3-Gaussian fit to the TKE distributions. A good agreement with data in the literature would give us more confidence on the results when the same method is applied to the reaction 64 Ni + 238 U.
In the works [4,5], the angular distributions of fission-like fragments from the system 48 Ca + 238 U were measured and these measurements were taken into account to select the CNF (filled stars and pentagons in the left panel of Fig. 5). These data are in very good agreement with the data obtained in this work except for the energy points below the Bass barrier. The reason for this difference might be ascribed to the use of the reverse kinematics method [5] that leads to a worse mass resolution due to the larger velocity of the center of mass. As a result, the separation of fissionlike events from elastic, quasi-elastic and deep inelastic scattering is more difficult to achieve. On the basis of the reasonably good success of the analysis method proposed, we can draw some main conclusion. The capture cross-sections are about a few hundred millibarns for Ca and Ni induced reactions, whereas the formation of symmetric fragments is one order of magnitude less for the reaction 64 Ni + 238 U. Yet, in the case of the Ca + U at the highest energy, approximately 70% of the events have the TKE expected for the CNF process, whereas in the case of the 64 Ni + 238 U only a few percent of symmetric fragments have the TKE compatible with the Viola prediction for the 302 120 CNF. While the 64 Ni + 238 U reaction has lower excitation energy at center of mass energies close to the Bass barrier, the CNF crosssection is suppressed by stronger symmetric and asymmetric QF processes and the expected gain in CN survival probability was not observed.
The CNF cross-section in the 64 Ni + 238 U → 302 120 case drops three orders of magnitude with respect to the 48 Ca + 238 U → 286 112 case. This is unfortunately a limiting factor. Furthermore, the relative contribution of the CNF from 64 Ni + 238 U is much lower than in the case of 58 Fe + 244 Pu → 302 120. Recently the experiments aimed at the synthesis of isotopes of element Z = 120 have been performed using the 244 Pu( 58 Fe, xn) 302−x 120 reaction [16] and 238 U( 64 Ni, xn) 302−x 120 reaction [17]. A cross-section limit of 0.4 pb at E * = 44.7 MeV for the former reaction and 0.09 pb at E * = 36.4 MeV for the latter reaction were obtained. In the case of 48 Ca + 238 U reaction the evaporation residue cross-section for 3n, 4n channels is about a few pb. Thereby in the transition from Ca to Fe and Ni ions, the evaporation residue cross-section drops down at least one and two orders of magnitude, respectively.
Thus, we conclude that the reaction 64 Ni + 238 U is less favorable compared to 58 Fe + 244 Pu for production of the superheavy element with atomic number 120.