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Role of universal function of the nuclear proximity potential: A systematic study on the alpha-decay of heavy/super-heavy nuclei and α-induced reactions

S. Mohammadi, R. Gharaei, S. A. Alavi

TL;DR

This work probes how the universal function in the proximity potential shapes α-decay predictions and α-induced fusion cross sections. By embedding five universal functions (gp 77, Ngo 80, Guo 2013, Zhang 2013, Prox. 2010) into the Prox. 77 framework and applying the one-dimensional WKB method, the authors compute $T_{1/2}$ for $250$ ground-state α decays and compare with data, and they evaluate 10 α-induced fusion reactions with a 1D barrier-penetration approach. The Guo 2013 function (MP-II) delivers the best α-decay agreement for heavy nuclei, reducing the RMS deviation from $\sigma\approx1.17$ to $\sigma\approx0.49$, while the Geiger–Nuttall law is validated under this model; for SHN, MP-IV and MP-I provide the most reliable decay predictions, with MP-III performing poorly. In fusion, MP-IV reproduces light/medium-system cross sections well, whereas MP-II better captures sub-barrier behavior for heavier systems, collectively highlighting the crucial influence of the universal function on proximity-potential predictions and their applicability to heavy and super-heavy nuclear phenomena.

Abstract

The idea of the universal function is fundamental advantage of proximity potential model. We present a systematic study of the role of universal function of the proximity potential model on alpha decay process for 250 ground state to ground state transitions using WKB approximation. In order to realize this goal, five universal functions proposed in the proximity models gp 77, Guo 2013, Ngo 80, Zhang 2013 and Prox. 2010 have been incorporated into the formalism of Prox. 77. The obtained results show that the radial behavior of universal function affects the penetration probability of the α particle. The theoretical α decay half lives are calculated and compared with the corresponding experimental data. It is shown that the Prox. 77 with Guo 2013 universal function provides the best fit to the available data. The role of the different universal functions in the α decay half lives of super heavy nuclei (SHN) with Z from 104 to 118 are also studied. It is shown that the experimental half lives in the super heavy mass region are described well using the Prox. 77 with Zhang 2013 universal function. In this paper, the validity of the original and modified forms of the proximity 77 potential is also examined for complete fusion reactions between α particle and 10 different target nuclei. Our results show that the measured α induced fusion reaction cross sections can be well reproduced using the Prox. 77 with Zhang 2013 universal function for the reactions involving light and medium nuclei. Whereas, the Prox. 77 with Guo 2013 universal function model demonstrates a reliable agreement with the experimental data at sub-barrier energies for heavier systems.

Role of universal function of the nuclear proximity potential: A systematic study on the alpha-decay of heavy/super-heavy nuclei and α-induced reactions

TL;DR

This work probes how the universal function in the proximity potential shapes α-decay predictions and α-induced fusion cross sections. By embedding five universal functions (gp 77, Ngo 80, Guo 2013, Zhang 2013, Prox. 2010) into the Prox. 77 framework and applying the one-dimensional WKB method, the authors compute for ground-state α decays and compare with data, and they evaluate 10 α-induced fusion reactions with a 1D barrier-penetration approach. The Guo 2013 function (MP-II) delivers the best α-decay agreement for heavy nuclei, reducing the RMS deviation from to , while the Geiger–Nuttall law is validated under this model; for SHN, MP-IV and MP-I provide the most reliable decay predictions, with MP-III performing poorly. In fusion, MP-IV reproduces light/medium-system cross sections well, whereas MP-II better captures sub-barrier behavior for heavier systems, collectively highlighting the crucial influence of the universal function on proximity-potential predictions and their applicability to heavy and super-heavy nuclear phenomena.

Abstract

The idea of the universal function is fundamental advantage of proximity potential model. We present a systematic study of the role of universal function of the proximity potential model on alpha decay process for 250 ground state to ground state transitions using WKB approximation. In order to realize this goal, five universal functions proposed in the proximity models gp 77, Guo 2013, Ngo 80, Zhang 2013 and Prox. 2010 have been incorporated into the formalism of Prox. 77. The obtained results show that the radial behavior of universal function affects the penetration probability of the α particle. The theoretical α decay half lives are calculated and compared with the corresponding experimental data. It is shown that the Prox. 77 with Guo 2013 universal function provides the best fit to the available data. The role of the different universal functions in the α decay half lives of super heavy nuclei (SHN) with Z from 104 to 118 are also studied. It is shown that the experimental half lives in the super heavy mass region are described well using the Prox. 77 with Zhang 2013 universal function. In this paper, the validity of the original and modified forms of the proximity 77 potential is also examined for complete fusion reactions between α particle and 10 different target nuclei. Our results show that the measured α induced fusion reaction cross sections can be well reproduced using the Prox. 77 with Zhang 2013 universal function for the reactions involving light and medium nuclei. Whereas, the Prox. 77 with Guo 2013 universal function model demonstrates a reliable agreement with the experimental data at sub-barrier energies for heavier systems.

Paper Structure

This paper contains 14 sections, 17 equations, 8 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. THEORETICAL FRAMEWORK
  3. Potential formalism
  4. The various universal functions
  5. The generalized proximity potential 1977 (gp 77)
  6. Ngo 80
  7. Guo 2013 and Zhang 2013
  8. Prox. 2010
  9. Alpha decay half-life formalism
  10. RESULTS AND DISCUSSION
  11. The Geiger-Nuttall law
  12. Super-heavy nuclei
  13. $\alpha$-induced fusion reactions
  14. Conclusions

Figures (8)

  • Figure 1: (Colored online) The total interaction potentials versus the radial distance $r$ (in fm) using Prox. 77 with different universal functions for alpha-decay from $^{201}$Rn (left panel) and $^{285}$Fl (right panel) parent nuclei, as an example. The variation of the universal functions with separation distance $s$ (in fm) are given in the insert.
  • Figure 2: (Colored online) The behavior of the logarithmic values of the penetration probability using the original and modified forms of the Prox. 77 potential in terms of the neutron number of the daughter nuclei $N_d$. The vertical dotted lines show the magic number $N_d=126.$
  • Figure 3: (Colored online) The behavior of the logarithmic values of the experimental half-life data (gray circle) and the calculated half-lives (colored circle) using Prox. 77 model with different universal functions versus the neutron number of the daughter nuclei $N_d$. The vertical dotted lines show the magic number $N_d=126.$
  • Figure 4: (Colored online) The difference between the predicted alpha half-lives and the experimental data using the original and modified forms of the Prox. 77 potential against the neutron number of daughter nuclei $N_d$.
  • Figure 5: (Colored online) Geiger-Nuttall plot of $\ log _{10} (T_{1/2})$ values versus $\ Q^{-1/2}_{\alpha}$ for the emission of $\alpha$-particle from (a) $^{172-185}$Hg, (b) $^{187-218}$Po, (c) $^{196-219}$At, (d) $^{194-222}$Rn, (e) $^{197-221}$Fr and (f) $^{215-232}$U parent nuclei using the MP-II (solid circles) and Prox. 77 (up-pointing triangles) potential models. $\ T_{1/2}$ is in seconds.
  • ...and 3 more figures