Experimental study of high-energy ﬁssion and quasi-ﬁssion with fusion-induced ﬁssion reactions at VAMOS++

. Over the past decade, inverse kinematics has been increasingly employed in experimental studies of ﬁssion. This approach has yielded a wealth of new observables that can be obtained in single measurements, enabling their analysis and correlations. One ongoing application of this technique involves a series of experiments performed at GANIL using the variable-mode, large-acceptance VAMOS ++ spectrometer. A recent experiment focused on examining the survival of nuclear structure e ﬀ ects at high excitation energy in both ﬁs-sion and quasi-ﬁssion. The results of the study involved a full isotopic identiﬁcation of fragments, as well as an analysis of the elemental yields their relation to ﬁssion dynamics. The results indicate that ﬁssion and quasi-ﬁssion involve di ﬀ erent mechanisms, which could be exploited to distinguish between the two phenomena


Introduction
Although both fission and quasi-fission lead to similar final products, there are notable distinctions between these processes.Firstly, fission comes from an equilibrated compound nucleus, while quasi-fission does not.Additionally, quasi-fission is significantly faster than fission [1].Researchers aim to identify observables that can differentiate between the two phenomena, and the complete identification of fragments offers new opportunities.
A prior experiment [2] demonstrated that in fusioninduced fission of 250 Cf, structural effects may persist in both the neutron-to-proton ratio of fragments and the total kinetic energy, even at high excitation energies of approximately 40 MeV.
In 2017, the E753 experiment was performed at GANIL using the VAMOS++ spectrometer to study the fission and quasi-fission processes also at high excitation energy, and analyse the survival of nuclear structure effects in both processes.The study of fusion-fission reactions is critical for advancing our knowledge of nuclear physics and has important practical applications such as nuclear energy production and nuclear waste management.In this paper, preliminary results of 265 Db high-energy fission from 238 U + 27 Al reaction are presented and discussed.The isotopic-fission yields Y(Z, A), the elemental yields Y(Z), the neutron excess and the velocity in center of mass are presented.

Experimental setup
VAMOS++ is a variable mode spectrometer [3,4] composed of a large magnetic dipole and two quadrupoles, and a set of detectors at the focal plane that measure the energy, energy loss, angles and positions before and after the magnets, and time of flight of those particles that reach the end of the focal plane.The magnetic rigidity is reconstructed using the positions and the angles at focal plane, while the emission vector is measured with those at the target position, before the spectrometer.Regarding the fission fragments, the measured observables are: atomic number (Z), mass number (A), and velocity vector.For the fissioning system, Z, A, and its excitation energy (E * ) are obtained [5].
In this experiment, a 238 U beam at 5.9A MeV impinged on four different light targets (0.5 mg/cm 2 of 9 Be, 0.1 mg/cm 2 of nat B, 0.5 mg/cm 2 of 24 Mg, and 0.2 mg/cm 2 of 27 Al) to generate different fissioning systems (FS) through transfer and fusion reactions.In the case of transfer or inelastic reactions, the target-like recoil is measured with a silicon telescope placed around the target.Fusion reactions are assumed when no recoil is detected [9].Once a FS is formed, it splits into two fission fragments (FF) and one of them may be detected in VAMOS++.
Using inverse kinematics in fission experiments offers several advantages.One of the key benefits is the higher velocity of the FF in the laboratory frame, which facilitates their traversal of multiple detector layers.This, in turn, provides access to a broader range of observables that cannot be achieved through direct kinematics.Additionally, inverse kinematics allows for better control over the reaction products, leading to more accurate measurements and increased understanding of the fission process.Finally, the use of inverse kinematics can also reduce the effects of background noise, which can improve the overall quality of the experimental results.

Results with the aluminium target
The compound nucleus produced in the reaction with the Al target is 265 Db with E * = 61.2MeV.The properties of this compound and its subsequent fission products provide valuable insights into the fundamental physics of nuclear fusion and fission reactions.

Fission yields
Isotopic-fission yields are derived using the procedure presented in Refs.[10,11].In this procedure, the fission events are counted and weighted by various factors, including the spectrometer acceptance, the angular and intrinsic efficiencies, and the relative normalisation between settings.The procedure also includes the subtraction of contamination from transfer-fission events.The resulting isotopic-fission yields provide information about the distribution of fission products and can be used to study the underlying process.  in Fig. 2 and are compared to the predictions of the semiempirical code GEF [12] as well as a previous measurement of a similar reaction [13].In addition, an approximation of the quasi-fission distribution is shown in a solid red line, which is obtained from the difference between the yield and its complementary using the symmetry of the elemental fission yields.This approximation assumes that the yield for a given element Y(Z) is equal to the yield of its complementary element at Z comp = Z FS − Z, where Z FS is the nuclear charge of the compound nucleus.The results reveal a non-symmetric distribution, which is produced by to the restricted coverage of the centre-ofmass (c.m.) angle of the experiment.This limited coverage is illustrated in Fig. 3, where the blue solid lines indicate the angle restriction, and the dashed blue lines shows the limits of mass identification (before neutron evaporation).As mentioned earlier, there is a strong correlation between the fragment mass and the c.m. angle.In this case, the experimental coverage only includes the heavyfragment mass of quasi-fission, represented by the solid red line circle in Fig. 3, while the corresponding light fragments would be in the complementary c.m. angle, indicated by the dashed red line circle, which is not covered in this experiment.
The Y(Z) distribution is in agreement with the previous measurement [13], once the same restrictions are applied.The comparison with the GEF model [12] shows an agreement on the light-fragment part of the distribution.This is because the fission component of the reaction is not affected by the restriction in angular coverage.

Neutron excess
The fissioning system is excited before the saddle point and will emit neutrons.Since the information on these neutrons cannot be accessed directly in this experiment, an estimation with the GEF code is used, resulting in a FS average mass of A FS ∼262.4.Assuming a negligible proton emission, the pre-evaporation masses of the fragments A * i can be evaluated with this estimated mass A FS .The nuclear structure effects would appear in the pre-evaporation step (at scission).The information about the fissioning system at the scission point can be obtained from the neutron excess after evaporation and the fragment velocities in c.m.The neutron excess Since the fissioning system is highly excited, it can emit neutrons before reaching the saddle point, leading to a decrease in the effective excitation energy before the start of the fission process.The calculations with GEF show a smaller N /Z than what is measured; although the evolution as a function of Z is very similar.GEF predicts a large number of emitted neutrons before scission, including 2.4 pre-saddle neutrons, which could explain the excess.However, there is no way to access information on these neutrons due to current experimental limitations.Further studies on neutron evaporation are necessary to explain this behaviour.

Isotopic velocities
As both the laboratory frame (V lab , θ lab ) and the fissioning system frame are measured, the c.m. velocity of the fission fragments V FF c.m. can be determined on an event-byevent basis, enabling access to fission dynamics.Figure 5 displays V FF c.m. as a function of the fragment A with each panel corresponding to one Z.Although the experimental data agree well with GEF for Z > 40, there is a deviation observed for the light fragments.The figure exhibits a slight overestimation in GEF prediction, with the largest deviations occurring in more neutron-rich isotopes.

Conclusions
The preliminary results presented were obtained with the VAMOS++ setup, which allows for the measurement of a variety of observables, including complete isotopic and elemental yield distributions of the 265 Db fissioning system.The data analysis reveals a contribution from the quasi-fission process in the elemental fission yields, which is identified with the heaviest contribution of the quasifission.This process can contribute to the observed fragment mass distributions, and it is important to account for it when studying heavy-ion reactions.Furthermore, the neutron excess and isotopic velocity in the centre-of-mass frame of the fission fragments are also reported.

Figure 1
displays the isotopic yields of 265 Db as a function of the fragment mass, with each color representing a different atomic number (Z) between Z = 30 and Z = 66.In this and the rest of the figures of this document, the error bars represent the statistical uncertainties; systematic uncertainties range from 2% in the heavier fragments up to 10% in the lighter ones.The resolution in the identification of atomic number is ∆Z/Z ∼ 1/80, while the resolution in mass identification is ∆A/A ∼ 1/200.The elemental yields Y(Z) can be calculated by summing the contributions of each mass A: Y(Z) = A Y(Z, A).The resulting elemental yields are displayed

Figure 1 .
Figure 1.Isotopic fission yields Y(Z, A) of fusion-induced fission of 265 Db at E * = 61.2MeV.Each colour line corresponds to one element.Zr 40 , Te 52 , and Nd 60 are shown for reference.

Figure 2 .
Figure 2. Elemental yield distribution Y(Z) of fragments from 265 Db fusion-fission reactions (black points and solid black line) compared with the GEF prediction (solid green line) and previous measurement from [13] (dashed blue line).The minimum quasi-fission contribution is shown with solid red line.

Figure 3 .
Figure 3. Experimental measurement [13] of fragment masses before evaporation versus c.m. angle for the reaction 238 U + 27 Al with the VAMOS++ limits in angle and mass (blue solid and dashed lines, respectively).Red circles show approximately the quasi-fission contribution to the reaction.The solid red line corresponds to the contribution accessible with VAMOS++.

Figure 4 .
Figure 4. Post-evaporation average neutron-excess N /Z of 265 Db fission fragments as a function of fragment Z (black symbols) and corresponding GEF predictions (solid red line).

Figure 5 .
Figure 5.Each panel shows the centre of mass velocity as a function of A for the different elements produced in fusion-fission of 265 Db (black points).The GEF prediction is shown with red lines.