The group of authors including E. M. Kozulin, A. A. Bogachev, I. V. Vorobiev, M. G. Itkis, J. M. Itkis, G. N. Knyazheva, D. Kumar, K. V. Novikov, A. N. Pan, I. V. Pchelincev was awarded the First JINR Prize 2020 in the category “Experimental Physics Research” for the paper “Investigation of probabilities of formation and decay of superheavy systems in dependence on the Coulomb factor Z₁Z₂ at energies near the Coulomb barrier”.

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Production of nuclei in the vicinity of the “island of stability” and investigation of their properties is one of the major goals of modern nuclear physics. According to theoretical predictions, the “island of stability” is expected near the neutron shell at N = 184 and proton shells at Z = 114 or Z = 120–126. The proton closed shell number has not yet been established unequivocally since theoretical models give different predictions and strongly depend on the choice of the parameters for nucleon-nucleon interactions in the nucleus. The available experimental data confirm the existence of the “island of stability” but have not yet allowed defining these numbers.

Recently great success has been achieved in the synthesis of new superheavy elements formed in complete fusion of heavy nuclei. At present, both cold (where one of the reaction partners is ²⁰⁸Pb or ²⁰⁹Bi) and hot (using ⁴⁸Ca ions) fusion reactions have been used for their production. The hot fusion reactions of actinide targets with ⁴⁸Ca ions allow producing compound nuclei with relatively low excitation (30–40 MeV) at the interaction energies near the Coulomb barrier. Moreover, the neutron excess of ⁴⁸Ca allows obtaining more neutron-rich nuclei than in the case of the cold fusion reactions. The formation cross sections of new superheavy elements with Z = 112–118 obtained in the reactions with ⁴⁸Ca ions are of the order of a few picobarns [1–4], while in the cold fusion reactions the cross sections drop rapidly with increasing element number, and the cross section for Nh (Z = 113) is about 55 fb [5]. Further progress in synthesis of new superheavy using cold fusion reactions is hindered due to this dramatic decrease of the formation cross sections.

The heaviest element known today is Oganesson (²⁹⁴Og) with Z = 118 produced in the complete fusion reaction ⁴⁸Ca + ²⁴⁹Cf. The production of superheavy elements with Z > 118 and the investigation of their properties is of particular interest in studying the “island of stability”. Unfortunately, these nuclei cannot be synthesized in ⁴⁸Ca-induced reactions since ²⁴⁹Cf is the heaviest target material available for these purposes. A possible alternative pathway is represented by the complete fusion of actinide nuclei with heavier projectiles such as Ti, Cr, Fe, or Ni.

However, an increase of the Coulomb repulsion between the interacting nuclei (Z₁Z₂) results in decrease of compound nucleus formation cross section. The Coulomb factor is one of the key parameters that determine the interaction mechanism of two massive nuclei (compound nucleus formation, quasifission or deep inelastic collisions). Quasifission and deep inelastic collisions are considered binary multinucleon transfer reactions with a full momentum transfer in which the composite system separates after the capture in two main fragments without forming a compound nucleus. Quasifission happens to be the most important mechanism that prevents the formation of superheavy elements in the fusion of heavy nuclei.

To investigate the probability of formation and decay of superheavy systems in the vicinity of the “island of stability” in dependence on the Coulomb factor Z₁Z₂ we conducted a series of experiments to measure the mass, energy and angular distributions of binary fragments formed in the ⁵²Cr + ²³²Th, ^52,54Cr + ²⁴⁸Cm, ⁸⁶Kr + ¹⁹⁸Pt, and ⁶⁸Zn + ²³²Th reactions leading to the formation of the superheavy composite systems with Z = 114 and 120.

A comparative analysis performed in the papers presented for the competition [6–9] with the results obtained earlier for the reactions with ³⁶S, ^40,48Ca, ^48,50Ti, ⁵⁸Fe, and ⁶⁴Ni ions allowed us to evaluate fusion probabilities in the wide range of Coulomb factor Z₁Z₂ from 1472 to 2808. The measurements were carried out at the Flerov Laboratory of Nuclear Reactions, Dubna, and the Physics Department of the Jyväskylä University, Finland, using the double-arm time-of-flight spectrometer CORSET [10].

The investigations [6, 8] showed that in the case of the reactions with ⁴⁸Ti and ^52,54Cr ions the properties of asymmetric quasifission fragments are similar to those obtained in the reactions with ⁴⁸Ca ions with the reaction time of about 5–7×10^-21s (see Fig. 1). However, shorter reaction times of about 3×10^-21 s were observed in the case of Ni and Zn ions, probably, due to the strong Coulomb repulsion between interacting nuclei, which leads to the rather quick decay of the formed dinuclear system.

Fig. 1. The estimated time for asymmetric quasifission processes for the studied reactions in comparison with those obtained for the reactions of ⁴⁸Ca and ⁴⁸Ti ions with actinide nuclei as a function of the mean fissility parameter. The dashed lines guide the eye.

From the comparison of mass and energy distributions and capture cross sections, it was found that the contribution of quasifission fragments formed in long-lived composite systems decreases sharply at the transition from systems with Z₁Z₂ ≈ 2300 (⁵²Cr + ²³²Th, ^52,54Cr + ²⁴⁸Cm) to those with Z₁Z₂ > 2500 (⁸⁶Kr + ¹⁹⁸Pt, ⁶⁸Zn + ²³²Th), and the main reaction channels were shown to be a few-nucleon transfer and deep inelastic collisions.

Mass-total kinetic energy distributions of the binary fragments obtained in the studied reactions are shown in Figures 2 and 3. The fissionlike products within the contour lines are characterized by large mass transfer and energy dissipation and can originate either from compound-nucleus fission or quasifission processes. It should be noted that the fission and quasifission fragments have similar properties that makes difficult to separate them.

Fig. 2. The mass and energy distributions of binary fragments formed in the reactions ^52,54Cr + ²⁴⁸Cm, ⁶⁴Ni + ²³⁸U, and ⁶⁸Zn + ²³²Th leading to the formation of composite systems with Z = 120 at energies near the Coulomb barrier. Top panels: M-TKE matrices of binary reaction products. Bottom panels: mass distributions of fissionlike fragments inside the polygons in M-TKE matrices.

Fig. 3. The mass and energy distributions of binary fragments formed in the reactions ⁴⁸Ca + ²⁴⁴Pu, ⁴⁸Ti + ²³⁸U, ⁵²Cr + ²³²Th, and ⁸⁶Kr + ¹⁹⁸Pt leading to the formation of composite systems with Z = 114. From top to bottom: the M-TKE matrices of binary reaction products, the mass distributions, and the average total kinetic energy as a function of mass of fissionlike fragments inside the contour line on M-TKE matrices.

Moreover, we found that the properties of symmetric fragments change significantly at the transition from ⁴⁸Ca ions to ^48,50Ti (Fig. 3) and ^52,54Cr (Fig. 2) ions. In the case of ⁶⁴Ni- and ⁶⁸Zn-induced reactions (Fig. 2), these changes are drastic. It was shown [6, 8] that at energies above the barrier, the contribution does not change with increasing interaction energy and is about 5–6% for the reactions with ⁵²Cr ions, contrary to the reactions involving actinide nuclei and ⁴⁸Ca ions, where the contribution of symmetric fragments increases monotonically. This may indicate a significant increase in the quasifission process at the transition from ⁴⁸Ca to ⁴⁸Ti and ⁵²Cr ions (Fig. 4). Thus, for the nuclear systems with Z₁Z₂ > 2000, the quasifission is a dominant process even in the formation of symmetric fragments.

Fig. 4. The contribution of symmetric fragments in all fissionlike events formed in the reactions ⁴⁸Ca + ²³⁸U, ⁴⁸Ca + ²⁴⁴Pu, ⁴⁸Ti + ²³⁸U, ⁵²Cr + ²³²Th, and ⁸⁶Kr + ¹⁹⁸Pt in dependence on the interaction energy.

The fusion probabilities for the ^52,54Cr + ²⁴⁸Cm and ⁶⁸Zn + ²³²Th reactions were estimated in Ref. [6] on the basis of the analysis of mass and TKE distributions. The obtained fusion probabilities are in good agreement with the fusion probability dependence on the mean fissility parameter found for the reactions of well-deformed nuclei with ³⁶S, ⁴⁸Ca, ⁴⁸Ti, and ⁶⁴Ni ions. The fusion probability is found to drop by approximately three orders of magnitude at the transition from ⁴⁸Ca + ²³⁸U to the ⁵⁴Cr + ²⁴⁸Cm reaction and by more than a factor of 105 to the ⁶⁸Zn + ²³²Th reaction. Based on the obtained fusion probability for the ⁵⁴Cr + ²⁴⁸Cm reaction, the production cross section of superheavy element with Z = 120 is expected to be about a few femtobarns. In the case of the ⁶⁴Ni + ²³⁸U and ⁶⁸Zn + ²³²Th reactions the production cross sections are one and two orders of magnitude lower, respectively.

Thus, the complete fusion reactions of Ti and Cr ions with actinides can be used to synthesize new superheavy elements with Z > 118. However, the compound nucleus production cross section in these reactions drops down by several orders of magnitude compared to the reactions with ⁴⁸Ca ions. Alternatively, these nuclei can be produced in the multinucleon transfer reactions, such as ²³⁸U + ²³⁸U or ²³⁸U + ²³⁸Cm, that may be makes it possible to obtain more neutron-rich nuclei than in the case of complete fusion reactions.

Fig. 5. Fusion probability for the ⁵⁴Cr + ²⁴⁸Cm and ⁶⁸Zn + ²³²Th reactions in comparison with fusion probabilities in hot fusion (with strongly deformed target nuclei) reactions [11] at energies above the Coulomb barrier as a function of the mean fissility parameter of the reaction. The circles denote the calculated fusion probabilities for cold fusion reactions [12].

To summarize, a wide series of experiments aimed at investigating the probability of formation and decay of superheavy systems in dependence on the Coulomb factor Z₁Z₂ at energies near the Coulomb barrier has been performed.

For the composite systems with Z = 114 and 120 the properties of fusion-fission and quasifission processes have been analyzed. For the systems with the Coulomb factor Z₁Z₂ > 2000 the dominant role of quasifission has been confirmed. For all studied reactions the fusion probabilities have been estimated. The obtained results will be useful in future investigations of the “island of stability” and conducting the experiments to synthesize superheavy elements with Z > 118. The scientific team was awarded the first prize for research and experimental work at the 129th Session of JINR Scientific Council.

Candidate of Science, Eduard M. Kozulin,
the Head of Sector №5 Dynamics
of heavy nuclei interaction,
fission of heavy and superheavy nuclei,
FLNP JINR

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