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Systematic investigation on the superheavy nucleus formation in the reactions of $^{48}$Ca, $^{50}$Ti, $^{51}$V and $^{54}$Cr on actinide nuclei

Zi-Han Wang, Peng-Hui Chen, Ya-Ling Zhang, Ming-Hui Huang, Zhao-Qing Feng

TL;DR

This work develops and applies a dinuclear system (DNS) model that incorporates cluster transfer and dynamical quadrupole deformations to study fusion-evaporation production of superheavy nuclei in reactions of $^{48}$Ca, $^{50}$Ti, $^{51}$V, and $^{54}$Cr with actinide targets. By coupling a barrier-distribution capture framework, a DNS master equation for fusion probability, and a Weisskopf-based survival treatment with detailed fission barriers and level densities, the authors quantify how five mass models—FRDM2012, KTUY05, LDM1966, SkyHFB, WS4—affect excitation functions and the formation of SHN up to Z=120. They demonstrate strong mass-model dependence, with FRDM2012 typically predicting larger cross sections and SkyHFB smaller fusion barriers, and they identify 2n–4n channels as favorable for producing SHN Z=119–120, providing guidance for future experiments with $^{50}$Ti, $^{51}$V, and $^{54}$Cr projectiles. The study highlights the critical role of mass-model inputs in PES and survival probabilities and verifies that DNS with cluster transfer can reproduce available experimental data across a broad range of systems, aiding the optimization of beam energies and evaporation channels in SHN campaigns.

Abstract

The synthesis of superheavy elements strongly relies on the competition of the quasifission and fusion fission dynamics in the fusion-evaporation reactions. The systematics on the formation of superheavy nuclei in the $^{48}$Ca, $^{50}$Ti, $^{51}$V and $^{54}$Cr induced fusion reactions on actinide nuclei $^{232}$Th, $^{231}$Pa, $^{238}$U, $^{237}$Np, $^{242,244}$Pu, $^{243}$Am, $^{245,248}$Cm, $^{249}$Bk, $^{249}$Cf has been thoroughly investigated with the dinuclear system model by including the cluster transfer and coupling to the dynamical evolution of the quadrupole deformation parameters. The uncertainties of the fusion-evaporation excitation functions with the mass models of FRDM2012, KTUY05, LDM1966, SkyHFB, WS4 are investigated and compared with the available experimental data from Dubna, GSI, Berkeley and RIKEN. The production cross sections, optimal evaporation channels and beam energies in the synthesis of superheavy elements Z = 119 and 120 were predicted and compared for the different mass models in the reactions of $^{50}\mathrm{Ti} + ^{249}\mathrm{Bk}$, $^{51}\mathrm{V} + ^{248}\mathrm{Cm}$, $^{54}\mathrm{Cr} + ^{243}\mathrm{Am}$, $^{50}\mathrm{Ti} + ^{249}\mathrm{Cf}$, $^{51}\mathrm{V} + ^{249}\mathrm{Bk}$, $^{54}\mathrm{Cr} + ^{248}\mathrm{Cm}$, respectively.

Systematic investigation on the superheavy nucleus formation in the reactions of $^{48}$Ca, $^{50}$Ti, $^{51}$V and $^{54}$Cr on actinide nuclei

TL;DR

This work develops and applies a dinuclear system (DNS) model that incorporates cluster transfer and dynamical quadrupole deformations to study fusion-evaporation production of superheavy nuclei in reactions of Ca, Ti, V, and Cr with actinide targets. By coupling a barrier-distribution capture framework, a DNS master equation for fusion probability, and a Weisskopf-based survival treatment with detailed fission barriers and level densities, the authors quantify how five mass models—FRDM2012, KTUY05, LDM1966, SkyHFB, WS4—affect excitation functions and the formation of SHN up to Z=120. They demonstrate strong mass-model dependence, with FRDM2012 typically predicting larger cross sections and SkyHFB smaller fusion barriers, and they identify 2n–4n channels as favorable for producing SHN Z=119–120, providing guidance for future experiments with Ti, V, and Cr projectiles. The study highlights the critical role of mass-model inputs in PES and survival probabilities and verifies that DNS with cluster transfer can reproduce available experimental data across a broad range of systems, aiding the optimization of beam energies and evaporation channels in SHN campaigns.

Abstract

The synthesis of superheavy elements strongly relies on the competition of the quasifission and fusion fission dynamics in the fusion-evaporation reactions. The systematics on the formation of superheavy nuclei in the Ca, Ti, V and Cr induced fusion reactions on actinide nuclei Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf has been thoroughly investigated with the dinuclear system model by including the cluster transfer and coupling to the dynamical evolution of the quadrupole deformation parameters. The uncertainties of the fusion-evaporation excitation functions with the mass models of FRDM2012, KTUY05, LDM1966, SkyHFB, WS4 are investigated and compared with the available experimental data from Dubna, GSI, Berkeley and RIKEN. The production cross sections, optimal evaporation channels and beam energies in the synthesis of superheavy elements Z = 119 and 120 were predicted and compared for the different mass models in the reactions of , , , , , , respectively.

Paper Structure

This paper contains 8 sections, 34 equations, 10 figures, 2 tables.

Table of Contents

  1. I. Introduction
  2. II. Model Description
  3. A. Capture probability
  4. B. Fusion probability
  5. C. Survival probability
  6. III. Results and discussion
  7. IV. Conclusions
  8. Acknowledgements

Figures (10)

  • Figure 1: Driving potential of the reaction of $^{48}\mathrm{Ca} + ^{248}\mathrm{Cm}$ with different mass tables. The black arrow indicates the position of the incident point. The five-pointed stars represent the B.G. points of different mass tables, and the red line for FRDM2012, blue line for KTUY05, magenta line for LDM1966, yellow line for SkyHFB and dark cyan line for WS4, respectively.
  • Figure 2: (a) The capture cross section, (b) fusion probability and (c) survival probability as a function of the excitation energy of compound nucleus in the reaction of $^{48}\mathrm{Ca} + ^{248}\mathrm{Cm}$ with different mass models.
  • Figure 3: The fusion-evaporation excitation functions in the reaction of $^{48}\mathrm{Ca} + ^{248}\mathrm{Cm}$ with different mass models. The experimental data of Dubna were taken from Ref. Yu2000Yu2001Yu2002Yu2004Yu2004(2), GSI data from Ref. Ho2012 and RIKEN data from Ref. Ka2017. The arrow indicates the maximum cross-section estimated experimentally. The dotted lines in panel (f) represent the excitation functions provided by the FRDM2012 model, while the shaded areas are the excitation function ranges given by the other four mass tables.
  • Figure 4: The excitation functions of the reaction systems of $^{48}\mathrm{Ca} + ^{232}\mathrm{Th}$Yu2023Yu2024, $^{48}\mathrm{Ca} + ^{231}\mathrm{Pa}$, $^{48}\mathrm{Ca} + ^{238}\mathrm{U}$Yu1999Yu2004Ho2007Ka2017(2)Yu2022, $^{48}\mathrm{Ca} + ^{237}\mathrm{Np}$Yu2007, $^{48}\mathrm{Ca} + ^{242}\mathrm{Pu}$Yu2004St2009El2010Yu2022, $^{48}\mathrm{Ca} + ^{244}\mathrm{Pu}$Yu2004Yu1999(2)Yu2000(2)Yu2000(3)Yu2004(3)Yu2004(2)Du2010Ga2011 with different mass models. Symbols with arrows show upper cross-section limits. The shaded areas are the excitation function ranges given by the five mass tables. However, for $^{48}\mathrm{Ca} + ^{237}\mathrm{Np}$, since mass tables FRDM2012 and LDM1966 do not provide the excitation function information of 5n channels owing to the very low cross section.
  • Figure 5: The excitation functions of the reaction systems of $^{48}\mathrm{Ca} + ^{243}\mathrm{Am}$Yu2004(4)Yu2005Yu2012Yu2013Fo2016Yu2022(2)Yu2022(3), $^{48}\mathrm{Ca} + ^{245}\mathrm{Cm}$Yu2004(3)Yu2006, $^{48}\mathrm{Ca} + ^{249}\mathrm{Bk}$Yu2010Yu2011Yu2011(2)Yu2012(2)Yu2013(2)Kh2014Yu2014Kh2019, $^{48}\mathrm{Ca} + ^{249}\mathrm{Cf}$Yu2006Yu2012(2) with different mass models. The arrow indicates the maximum cross section estimated experimentally. The shaded areas are the excitation function ranges given by these five mass tables.
  • ...and 5 more figures