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REVIEW 3 major objections 4 minor 77 references

Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: case of spherical colliding nuclei

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Relativistic mean-field densities and non-relativistic Hartree-Fock densities give equally good fits to above-barrier heavy-ion fusion cross sections.

desk verdict A transparent, incremental comparison showing RMF NL3 and Skyrme SKX densities give similar above-barrier fusion fits when K_R is re-fitted per reaction; the 'same quality' conclusion is plausible but weaker than the evidence. read the letter →

arxiv 1908.03807 v2 pith:WFAXAXG7 submitted 2019-08-10 nucl-th

Maria V. Chushnyakova , Mrutunjaya Bhuyan , Igor I. Gontchar , Natalya A. Khmyrova This is my paper · ORCID
classification nucl-th PACS 25.70.Jj25.70.-z
keywords relativisticmean-fielddensitydoublefoldingpotentialheavy-ionfusionM3YinteractionsurfacefrictionmodelCoulombbarrierSKXabove-barrier
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether nuclear densities from the relativistic mean-field (RMF) approach can replace the non-relativistic Hartree-Fock (HF) densities that have already been shown to work in double-folding calculations of heavy-ion fusion. It constructs M3Y double-folding potentials using RMF NL3 densities for 35 reactions between spherical nuclei, with the Coulomb-barrier scale $B_Z$ ranging from 10 to 150 MeV, and compares the resulting barriers and above-barrier fusion cross sections with the HF SKX results. For 13 reactions with high-precision data, a single surface-friction strength $K_R$ is fitted per reaction, and the paper reports that the fit quality is the same for both density models and that the fitted $K_R$ values strongly correlate. A sympathetic reader should care because it tests whether explicitly relativistic nuclear structure input changes a standard reaction-model prediction, and the answer is that it does not in any practical way.

What carries the argument

The load-bearing object is the M3Y double-folding nucleus-nucleus potential $U_n(R)$, built from the Paris M3Y nucleon-nucleon interaction with a density-dependent factor $F_v(\rho_{FA})$ and folded with the frozen nucleon densities $\rho_A$ of projectile and target. The two density inputs are the RMF NL3 densities and the HF SKX densities, and the paper isolates their effect on the total potential $U_{tot}$, on the barrier height $U_{B0}$ and radius $R_{B0}$, and on the final cross sections. The comparison is carried by a one-dimensional Langevin trajectory model with surface friction, where the dissipative force $F_D=-(p/m_q)K_R[dU_n/dq]^2$ and the diffusion coefficient $D=\theta K_R[dU_n/dq]^2$ share the single free parameter $K_R$; fitting $K_R$ to minimize $\chi_\sigma^2$ against experimental excitation functions is what produces the claim of equal-quality fits and correlated friction strengths.

What would settle it

Fix the dissipation strength $K_R$ for each reaction from a shared empirical approximation $K_R(B_Z)$ rather than fitting it per reaction, and recompute the 13 excitation functions with both SKX and NL3 densities. If the NL3 cross sections then show a systematically larger deviation from the experimental data than the SKX ones do, the paper's claim that the two densities are of equal quality would be undercut; if the deviations remain comparable, the claim is supported.

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Extended reading notes

Core claim

The paper's central claim is that using relativistic RMF NL3 densities in the double-folding potential produces above-barrier fusion cross sections of the same quality as using non-relativistic HF SKX densities, and that the two density models yield strongly correlated values of the single adjustable friction strength. Concretely, the NL3 and SKX Coulomb barriers agree to within a few percent everywhere, with NL3 barriers higher and more compact for light systems and lower and more extended for heavy lead targets. The chi-square values for the fitted cross sections are of the same order under both densities, and in several cases the NL3 fit is actually closer to the data. The paper concludes that relativistic effects encoded in the RMF density do not spoil the double-folding description of above-barrier fusion, so RMF densities are a viable alternative input for this kind of calculation.

Load-bearing premise

The load-bearing premise is that the single per-reaction friction strength $K_R$ is restrictive enough that equal fit quality reflects equal density quality; if $K_R$ absorbs the barrier differences, the comparison cannot distinguish the two density models.

Editorial extensions

If this is right

  • RMF NL3 densities can be used as drop-in nuclear-density input for double-folding calculations of above-barrier heavy-ion fusion without degrading agreement with measured cross sections.
  • The strong correlation between the fitted $K_R$ values means that global systematics of dissipation strength versus $B_Z$ remain valid when the density model is changed.
  • Barrier parameters shift by at most a few percent between the two density models, and the direction of the shift reverses from light to heavy targets, so reactions with lead isotopes are where the density choice matters most.
  • For a representative heavy system, $^{16}$O+$^{208}$Pb, both density models place the barrier within a couple of MeV of full TDHF frozen-density results, consistent with the much more expensive self-consistent calculation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the per-reaction fitting were replaced by one global $K_R(B_Z)$ curve, the two density models might separate more clearly; the clustering of fitted values in Fig. 10 suggests such a test is feasible.
  • The systematic crossover in barrier differences is plausibly tied to differences in the neutron tail of the heavy nucleus; checking against measured charge radii or neutron-skin observables could identify the microscopic origin.
  • Nothing in this comparison constrains sub-barrier fusion or deformed projectiles, so extending the same two-density comparison to those regimes would be the natural stress test of the equivalence.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript studies the influence of the nuclear matter density on double-folding nucleus-nucleus potentials and above-barrier heavy-ion fusion cross-sections for spherical colliding nuclei. Densities from the relativistic mean-field approach with the NL3 parameter set are compared with the previously used non-relativistic Skyrme-Hartree-Fock densities with the SKX parameter set. For 35 reactions with B_Z between 10 and 150 MeV, the authors compute Coulomb barrier heights and radii, and for 13 reactions with high-precision data they fit the single surface-friction strength K_R by minimizing the chi^2 of Eq. (23). The paper concludes that (i) the agreement between theoretical and experimental cross-sections obtained with RMF and HF densities is of the same quality and (ii) the fitted K_R values strongly correlate between the two density models.

Significance. The paper provides a systematic and transparent comparison of two microscopic density inputs within a standard double-folding plus surface-friction framework, covering a wide range of B_Z and reproducing the experimental excitation functions to within a few percent for most of the 91 data points. If the central claim held, it would justify treating RMF NL3 densities as interchangeable with Skyrme SKX densities for above-barrier fusion calculations of spherical systems. However, the evidence presented does not currently establish this claim: because K_R is refitted per reaction and per density model against the same experimental data, the chi^2 values in Table 5 measure the flexibility of the surface-friction model as much as the quality of the densities. A fixed-K_R sensitivity test would be needed to support the interchangeability conclusion.

major comments (3)
  1. [Sec. 4.3, Eq. (23), Table 5] The per-reaction minimization of K_R against the same experimental cross-sections means that the chi^2 values in Table 5 reflect the flexibility of the surface-friction model as much as the quality of the densities. With barrier heights differing by up to about 2% between NL3 and SKX (e.g., 36S+204Pb: U_B0 = 140.23 MeV vs 143.16 MeV in Table 5), a different K_R can partially compensate for systematic barrier differences. The claim that both densities yield 'the same quality' of agreement is therefore not established as a statement about density interchangeability. A decisive test would be to compute cross-sections with NL3 densities using the K_R optimized for SKX densities, and vice versa, or to use a single global K_R for all reactions; without such a test, the central conclusion is not supported by the present evidence.
  2. [Sec. 4.3, Table 5] The statement that 'the relative error of the NL3 calculations is typically smaller than of the SKX-calculations' is not supported by Table 5. For 16O+144Sm, the NL3 chi^2 is 24 versus 8.4 for SKX; for 16O+92Zr it is 19 versus 17; for 12C+204Pb it is 0.9 versus 0.5. The pattern is mixed, with NL3 better for some systems (e.g., 16O+208Pb, 36S+204Pb) and worse for others. The weaker claim of 'the same quality' is defensible if interpreted as comparable overall, but the specific comparative statement should be corrected or replaced by a quantitative paired comparison of the chi^2 values.
  3. [Conclusions, Sec. 5] The assertion that the optimal K_R values 'strongly correlate' between NL3 and SKX is unquantified. For the 13 reactions in Table 5, the Spearman rank correlation is approximately 0.69, which would typically be described as moderate; excluding the extreme pair 12C+92Zr (K_R = 36 vs 52) reduces it further. The authors should provide a correlation coefficient with its uncertainty, or soften the claim to 'moderately correlate' or 'are correlated.'
minor comments (4)
  1. [Fig. 9 caption] The caption states that the ratio r_sigma is shown for '13 reactions listed in Table 2,' but Table 2 contains only 16O-induced reactions; the intended reference is presumably Table 5, which lists all 13 reactions.
  2. [Sec. 4.2, paragraph after Fig. 4] The text states that for lighter reactions the NL3 barriers are several percent lower, but Tables 1-4 show positive xi_U for lighter systems (e.g., 12C+12C, xi_U = 4.2%; 16O+28Si, 2.3%), meaning the NL3 barriers are higher; the direction of the effect is reversed and should be corrected.
  3. [Sec. 4.3, Fig. 9 discussion] The sentence 'Only for two points of 91 the ratio r_sigma is significantly beyond the 5%-interval around unity (see panel a)' is ambiguous because Fig. 9 has four panels; the reference to panel a) should be made explicit, and the total number of points (91) should be identified as the sum over the 13 reactions.
  4. [Table 1 header] The table header uses xi_B, while Eqs. (21) and (22) define xi_U and xi_R; the notation should be unified to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: K_R is an openly fitted parameter and the density comparison is an in-sample fit-quality comparison, not a hidden prediction.

full rationale

The paper's central claim is that RMF NL3 and HF SKX nuclear densities produce double-folding barriers and above-barrier fusion cross sections of comparable quality. The only adjustable parameter, the friction strength K_R, is explicitly fitted per reaction to the experimental excitation functions via Eq. (23), and the resulting cross sections are described as calculated, never as independent predictions. The agreement shown in Fig. 9 and Table 5 is therefore an in-sample fit-quality metric, but the comparison between the two density models is not circular: the same fitting procedure is applied to both, and the chi^2 values are not equal by construction. The paper itself reports cases with substantially different chi^2 between the density models (e.g., 16O+208Pb: chi^2 = 3.5 for NL3 vs 69 for SKX), so the data retain discriminatory content. The trajectory model and SKX baseline are inherited from earlier papers by the same group, but those are ordinary model choices supported by external experimental data and prior publication; no uniqueness theorem, ansatz, or fitted parameter is smuggled in as a prediction. No equation in the paper reduces to its own input by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the adequacy of the surface friction trajectory model, the frozen density and M3Y interaction inputs, and the quality of the RMF NL3 densities. The only parameter fitted in the cross-section comparison is K_R. No new entities are introduced.

free parameters (2)
  • K_R (dissipation strength) = 13 values in Table 5, ranging from 10 to 36 zs GeV^-1 (e.g., 36, 19, 15, 13, 23, 19, 19, 22, 11, 12, 10, 17, 15)
    The only adjustable parameter in the trajectory model, optimized per reaction by minimizing chi^2 against experimental fusion cross sections (Eq. 23). The comparison of densities is made through this fitted parameter.
  • r0 (reduced radius constant) = 1.2 fm
    Chosen constant for reduced barrier radius presentation (Eq. 20), not fitted to data; it does not affect the central cross-section comparison.
assumptions (4)
  • domain assumption The surface friction Langevin model with white noise and instant dissipation describes above-barrier fusion for spherical stiff nuclei.
    Invoked in Sec. 3.1; the model uses one radial coordinate and neglects tunneling, channel coupling, and deformation. The selection of only stiff spherical nuclei is stated.
  • domain assumption Frozen density approximation: RMF NL3 ground-state densities do not evolve during the collision.
    Used in Eqs. (13)-(16) for the double-folding potential; dynamic polarization is neglected, though the TDHF comparison in Sec. 4.2 shows barrier heights are consistent with frozen-density TDHF.
  • domain assumption M3Y Paris nucleon-nucleon interaction parameters and density dependence coefficients from Refs. [5,61] are correct and applicable.
    The Paris M3Y parameters and the density-dependence coefficients (C_v, alpha, beta, gamma) are taken from prior literature and are not tested here.
  • domain assumption The NL3 RMF parameter set yields realistic ground-state densities for the nuclei considered.
    Assumed in Sec. 2; the paper does not compare charge densities from NL3 with experiment for these nuclei, relying on the known quality of NL3.

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Pith. "Pith review of Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: case of spherical colliding nuclei." pith.science (2026). https://pith.science/paper/WFAXAXG7

@misc{pith2026190803807,
  author       = {Pith},
  title        = {Pith review of: Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: case of spherical colliding nuclei},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WFAXAXG7}},
  note         = {Machine review of arXiv:1908.03807}
}
abstract

The double folding (DF) approach is one of the widely used methods for finding nucleus-nucleus interaction potential. In the present work, the influence of the nuclear matter density on the DF potential and on the Coulomb barrier parameters is studied systematically for collisions of spherical nuclei. The value of the parameter $B_Z=Z_P Z_T/(A_P^{1/3}+A_T^{1/3})$ (estimating the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The novel feature of this study is that the nuclear densities came from the Relativistic Mean Field approach (RMF). For the nucleon-nucleon effective interaction, the M3Y forces with the finite range exchange term and density dependence are employed. The above barrier fusion cross sections are calculated within the framework of the trajectory model with surface friction. Results are compared with the previous study in which the nuclear density came from the Hartree-Fock (HF) calculations and with the high precision experimental data. This comparison demonstrates that i) agreement between the theoretical and experimental cross sections obtained with RMF and HF densities is of the same quality and ii) the values of the only adjustable parameter (friction strength) obtained with RMF and HF densities strongly correlate.

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Works this paper leans on

77 extracted references · 52 canonical work pages

  1. [23]

    M. V. Chushnyakova, R. Bhattacharya, I.I. Gontchar, Dynamical calculations of the above-barrier heavy-ion fusion cross sections using Hartree-Fock nuclear densities with the SKX coefficient set, Phys. Rev. C. 90 (2014) 017603. doi:10.1103/PhysRevC.90.017603

    work page doi:10.1103/physrevc.90.017603 2014

  2. [1]

    Negele, The mean-field theory of nuclear structure and dynamics, Rev

    J.W. Negele, The mean-field theory of nuclear structure and dynamics, Rev. Mod. Phys. 54 (1982) 913 –1015. doi:10.1103/RevModPhys.54.913

    doi:10.1103/revmodphys.54.913 1982

  3. [2]

    Simenel, Nuclear quantum many-body dynamics, Eur

    C. Simenel, Nuclear quantum many-body dynamics, Eur. Phys. J. A. 48 (2012) 152. doi:10.1140/epja/i2012-12152-0

    doi:10.1140/epja/i2012-12152-0 2012

  4. [3]

    Simenel, A.S

    C. Simenel, A.S. Umar, Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions, Prog. Part. Nucl. Phys. 103 (2018) 19–66. doi:10.1016/J.PPNP.2018.07.002

    work page doi:10.1016/j.ppnp.2018.07.002 2018

  5. [4]

    Bertsch, J

    G. Bertsch, J. Borysowicz, H. McManus, W.G. Love, Interactions for inelastic scattering derived from realistic potentials, Nucl. Phys. A. 284 (1977) 399–419. doi:10.1016/0375-9474(77)90392-X

    doi:10.1016/0375-9474(77)90392-x 1977

  6. [5]

    Anantaraman, H

    N. Anantaraman, H. Toki, G.F. Bertsch, An effective interaction for inelastic scattering derived from the Paris potential, Nucl. Phys. A. 398 (1983) 269–278. doi:10.1016/0375-9474(83)90487-6

    doi:10.1016/0375-9474(83)90487-6 1983

  7. [6]

    Migdal, Theory of finite Fermi systems and application to atomic nuclei, Interscience, New York, 1967

    A.B. Migdal, Theory of finite Fermi systems and application to atomic nuclei, Interscience, New York, 1967

    work page 1967

  8. [7]

    Satchler, W.G

    G.R. Satchler, W.G. Love, Folding model potentials from realistic interactions for heavy -ion scattering, Phys. Rep. 55 (1979) 183–254. doi:10.1016/0370-1573(79)90081-4

    doi:10.1016/0370-1573(79)90081-4 1979

Show all 77 references
  1. [8]

    Khoa, α -nucleus optical potential in the double-folding model, Phys

    D.T. Khoa, α -nucleus optical potential in the double-folding model, Phys. Rev. C. 63 (2001) 034007. doi:10.1103/PhysRevC.63.034007

    2001 doi

  2. [9]

    Chien, D.T

    L.H. Chien, D.T. Khoa, D.C. Cuong, N.H. Phuc, Consistent mean-field description of the 12C+12C optical potential at low energies and the astrophysical S factor, Phys. Rev. C. 98 (2018) 064604. doi:10.1 103/PhysRevC.98.064604

    2018

  3. [10]

    Gontchar, D.J

    I.I. Gontchar, D.J. Hinde, M. Dasgupta, C.R. Morton, J.O. Newton, Semi -microscopic calculations of the fusion barrier distributions for reactions involving deformed target nuclei, Phys. Rev. C. 73 (2006) 034610. 40 60 80 100 120 1400 10 20 30 40 50 60 12C+X 16O+X 28Si+X 32,36...

    2006 doi

  4. [11]

    M. V. Chushnyakova, I.I. Gontchar, Heavy ion fusion: Possible dynamical solution of the problem of the abnormally large diffuseness of the nucleus-nucleus potential, Phys. Rev. C. 87 (2013) 014614. doi:10.1103/PhysRevC.87.014614

    2013 doi

  5. [12]

    Adamian, N.V

    G.G. Adamian, N.V. Antonenko, R. V Jolos, S.P. Ivanova, O.I. Melnikova, Effective nucleus -nucleus potential for calculation of potential energy of a dinuclear system, Int. J. Mod. Phys. E. 5 (1996) 191 –216. doi:10.1142/S0218301396000098

    1996 doi

  6. [13]

    Zagrebaev, A

    V. Zagrebaev, A. Karpov, Y. Aritomo, M. Naumenko, W. Greiner, Potential energy of a heavy nuclear system in fusion - fission processes, Phys. Part. Nucl. 38 (2007) 469–491. doi:10.1134/S106377960704003X

    2007 doi

  7. [14]

    Kuzyakin, V

    R.A. Kuzyakin, V. V. Sargsyan, G.G. Adamian, N. V. Antonenko, E.E. Saperstein, S. V. Tolokonnikov, Isotopic trends of capture cross section and mean-square angular momentum of the captured system, Phys. Rev. C. 85 (2012) 034612. doi:10.1103/PhysRevC.85.034612

    2012 doi

  8. [15]

    V. V. Sargsyan, G.G. Adamian, N. V. Antonenko, W. Scheid, H.Q. Zhang, Astrophysical S factor, logarithmic slope of the excitation function, and barrier distribution, Phys. Rev. C. 86 (2012) 034614. doi:10.1103/PhysRevC.86.034614

    2012 doi

  9. [16]

    Sargsyan, S.Y

    V.V. Sargsyan, S.Y. Grigoryev, G.G. Adamian, N.V. Antonenko, Capture c ross section with quantum diffusion approach, Comput. Phys. Commun. 233 (2018) 145–155. doi:10.1016/J.CPC.2018.06.011

    2018 doi

  10. [17]

    Gontchar, M

    I.I. Gontchar, M. V. Chushnyakova, Describing the heavy-ion above-barrier fusion using the bare potentials resulting from Migdal and M3Y double-folding approaches, J. Phys. G. 43 (2016) 045111. doi:10.1088/0954 -3899/43/4/045111

    2016 doi

  11. [18]

    Gontchar, M

    I.I. Gontchar, M. V. Chushnyakova, Systematic comparison of barriers for heavy -ion fusion calculated on the basis of the double-folding model by employing two versions of nucleon–nucleon interaction, Phys. At. Nucl. 79 (2016) 543–548. doi:10.1134/S1063778816040104

    2016 doi

  12. [19]

    Ismail, K.A

    M. Ismail, K.A. Ramadan, Microscopic calculation of sub-barrier fusion cross section and barrier distribution using M3Y- type forces, J. Phys. G Nucl. Part. Phys. 26 (2000) 1621–1633. doi:10.1088/0954-3899/26/10/312

    2000 doi

  13. [20]

    De Vries, C.W

    H. De Vries, C.W. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering, At. Data Nucl. Data Tables. 36 (1987) 495–536. doi:10.1016/0092-640X(87)90013-1

    1987 doi

  14. [21]

    Angeli, A consistent set of nuclear rms charge radii: properties of the radius surface R(N,Z), At

    I. Angeli, A consistent set of nuclear rms charge radii: properties of the radius surface R(N,Z), At. Data Nucl. Data Tables. 87 (2004) 185–206. doi:10.1016/J.ADT.2004.04.002

    2004 doi

  15. [22]

    Gontchar, R

    I.I. Gontchar, R. Bhattacharya, M. V. Chushnyakova, Quantitative analysis of precise heavy-ion fusion data at above- barrier energies using Skyrme-Hartree-Fock nuclear densities, Phys. Rev. C. 89 (2014) 034601. doi:10.1103/PhysRevC.89.034601

    2014 doi

  16. [24]

    Bhattacharya, Tensor interaction and its influence on evolution of nuclear shells, Nucl

    R. Bhattacharya, Tensor interaction and its influence on evolution of nuclear shells, Nucl. Phys. A. 913 (2013) 1 –18. doi:10.1016/j.nuclphysa.2013.05.006

    2013 doi

  17. [25]

    Dobaczewski, H

    J. Dobaczewski, H. Flocard, J. Treiner, Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line, Nucl. Phys. A. 422 (1984) 103–139. doi:10.1016/0375-9474(84)90433-0

    1984 doi

  18. [26]

    Newton, R.D

    J.O. Newton, R.D. Butt, M. Dasgupta, D.J. Hinde, I.I. Gontchar, C.R. Morton, K. Hagino, Systematic failure of the Woods-Saxon nuclear potential to describe both fusion and elastic scattering: Possible need for a new dynamical approach to fusion, Phys. Rev. C. 70 (2004) 024605....

    2004 doi

  19. [27]

    Brown, New Skyrme interaction for normal and exotic nuclei, Phys

    B.A. Brown, New Skyrme interaction for normal and exotic nuclei, Phys. Rev. C. 58 (1998) 220 –231. doi:10.1103/PhysRevC.58.220

    1998 doi

  20. [28]

    Lalazissis, J

    G.A. Lalazissis, J. König, P. Ring, New parametrization for the Lagrangian density of relativistic mean field theory, Phys. Rev. C. 55 (1997) 540–543. doi:10.1103/PhysRevC.55.540

    1997 doi

  21. [29]

    Dutra, O

    M. Dutra, O. Lourenço, S.S. Avancini, B. V. Carlson, A. Delfino, D.P. Meneze s, C. Providência, S. Typel, J.R. Stone, Relativistic mean-field hadronic models under nuclear matter constraints, Phys. Rev. C. 90 (2014) 055203. doi:10.1103/PhysRevC.90.055203

    2014 doi

  22. [30]

    Boguta, A.R

    J. Boguta, A.R. Bodmer, Relativistic calculation of nuclear matter and the nuclear surface, Nucl. Phys. A. 292 (1977) 413–428. doi:10.1016/0375-9474(77)90626-1

    1977 doi

  23. [31]

    B. V. Carlson, D. Hirata, Dirac-Hartree-Bogoliubov approximation for finite nuclei, Phys. Rev. C. 62 (2000) 054310. doi:10.1103/PhysRevC.62.054310

    2000 doi

  24. [32]

    Vretenar, A

    D. Vretenar, A. V. Afanasjev, G.A. Lalazissis, P. Ring, Relativistic Hartree–Bogoliubov theory: static and dynamic aspects of exotic nuclear structure, Phys. Rep. 409 (2005) 101–259. doi:10.1016/J.PHYSREP.2004.10.001

    2005 doi

  25. [33]

    J. Meng, H. Toki, S.G. Zhou, S.Q. Zhang, W.H. Long, L.S. Geng, Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei, Prog. Part. Nucl. Phys. 57 (2006) 470 –563. doi:10.1016/J.PPNP.2005.06.001

    2006 doi

  26. [34]

    N. Paar, D. Vretenar, E. Khan, G. Colò, Exotic modes of excitation in atomic nuclei far from stability, Reports Prog. Phys. 70 (2007) 691–793. doi:10.1088/0034-4885/70/5/R02

    2007 doi

  27. [35]

    Patra, M

    S.K. Patra, M. Bhuyan, M.S. Mehta, R.K. Gupta, Superdeformed and hyperdeformed states in Z = 122 isotopes, Phys. Rev. C. 80 (2009) 034312. doi:10.1103/PhysRevC.80.034312

    2009 doi

  28. [36]

    Lalazissis, S

    G.A. Lalazissis, S. Karatzikos, R. Fossion, D.P. Arteaga, A. V. Afanasjev, P. Ring, The effective force NL3 revisited, Phys. Lett. B. 671 (2009) 36–41. doi:10.1016/J.PHYSLETB.2008.11.070

    2009 doi

  29. [37]

    Karatzikos, A

    S. Karatzikos, A. V. Afanasjev, G.A. Lalazissis, P. Ring, The fission barriers in Actinides and superheavy nuclei in covariant density functional theory, Phys. Lett. B. 689 (2010) 72–81. doi:10.1016/J.PHYSLETB.2010.04.045

    2010 doi

  30. [38]

    Bhuyan, S.K

    M. Bhuyan, S.K. Patra, R.K. Gupta, Relativistic mean-field study of the properties of Z = 117 nuclei and the decay 13 chains of the 293 , 294 117 isotopes, Phys. Rev. C. 84 (2011) 014317. doi:10.1103/PhysRevC.84.014317

    2011 doi

  31. [39]

    Nikšić, D

    T. Nikšić, D. Vretenar, P. Ring, Relativistic nuclear energy density functionals: Mean-field and beyond, Prog. Part. Nucl. Phys. 66 (2011) 519–548. doi:10.1016/J.PPNP.2011.01.055

    2011 doi

  32. [40]

    Zhao, H.-Y

    X.-F. Zhao, H.-Y. Jia, Mass of the neutron star PSR J1614-2230, Phys. Rev. C. 85 (2012) 065806. doi:10.1103/PhysRevC.85.065806

    2012 doi

  33. [41]

    Serot, J.D

    B.D. Serot, J.D. Walecka, The Relativistic Nuclear Many Body Problem, Plenum Press, New York, 1986

    1986

  34. [42]

    Bhuyan, S.K

    M. Bhuyan, S.K. Patra, Magic nuclei in superheavy valley, Mod. Phys. Lett. A. 27 (2012) 1250173. doi:10.1142/S0217732312501738

    2012 doi

  35. [43]

    T.V.N. Hao, P. Quentin, L. Bonneau, Parity restoration in the highly truncated diagonalization approach: Application to the outer fission barrier of 240 Pu, Phys. Rev. C. 86 (2012) 064307. doi:10.1103/PhysRevC.86.064307

    2012 doi

  36. [44]

    Bhuyan, Structural evolution in transitional nuclei of mass 82 ≤ A ≤ 132, Phys

    M. Bhuyan, Structural evolution in transitional nuclei of mass 82 ≤ A ≤ 132, Phys. Rev. C. 92 (2015) 034323. doi:10.1103/PhysRevC.92.034323

    2015 doi

  37. [45]

    Bhuyan, B

    M. Bhuyan, B. V. Carlson, S.K. Patra, S.-G. Zhou, Surface properties of neutron-rich exotic nuclei within relativistic mean field formalisms, Phys. Rev. C. 97 (2018) 024322. doi:10.1103/PhysRevC.97.024322

    2018 doi

  38. [46]

    Bhuyan, Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei, Phys

    M. Bhuyan, Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei, Phys. At. Nucl. 81 (2018) 15–23. doi:10.1134/S1063778818010064

    2018 doi

  39. [47]

    T. Naz, M. Bhuyan, S. Ahmad, S.K. Patra, H. Abusara, Correlation among the nuclear structure and effective symmetry energy of finite nuclei, Nucl. Phys. A. 987 (2019) 295–320. doi:10.1016/J.NUCLPHYSA.2019.04.011

    2019 doi

  40. [48]

    Pannert, P

    W. Pannert, P. Ring, J. Boguta, Relativistic Mean-Field Theory and Nuclear Deformation, Phys. Rev. Lett. 59 (1987) 2420–2422. doi:10.1103/PhysRevLett.59.2420

    1987 doi

  41. [49]

    Reinhard, The relativistic mean-field description of nuclei and nuclear dynamics, Reports Prog

    P.-G. Reinhard, The relativistic mean-field description of nuclei and nuclear dynamics, Reports Prog. Phys. 52 (1989) 439–514. doi:10.1088/0034-4885/52/4/002

    1989 doi

  42. [50]

    Gambhir, P

    Y.K. Gambhir, P. Ring, A. Thimet, Relativistic mean field theory for finite nuclei, Ann. Phys. (N. Y). 198 (1990) 132 –

    1990

  43. [51]

    Sharma, M.A

    M.M. Sharma, M.A. Nagarajan, P. Ring, Rho meson coupling in the relativistic mean field theory and description of exotic nuclei, Phys. Lett. B. 312 (1993) 377–381. doi:10.1016/0370-2693(93)90970-S

    1993 doi

  44. [52]

    Ring, Relativistic mean field theory in finite nuclei, Prog

    P. Ring, Relativistic mean field theory in finite nuclei, Prog. Part. Nucl. Phys. 37 (1996) 193 –263. doi:10.1016/0146- 6410(96)00054-3

    1996 doi

  45. [53]

    Molique, J

    H. Molique, J. Dudek, Fock-space diagonalization of the state-dependent pairing Hamiltonian with the Woods-Saxon mean field, Phys. Rev. C. 56 (1997) 1795–1813. doi:10.1103/PhysRevC.56.1795

    1997 doi

  46. [54]

    Lalazissis, S

    G.A. Lalazissis, S. Raman, P. Ring, Ground-state properties of even-even nuclei in the relativistic mean-field theory, At. Data Nucl. Data Tables. 71 (1999) 1–40. doi:10.1006/ADND.1998.0795

    1999

  47. [55]

    Fröbrich, I.I

    P. Fröbrich, I.I. Gontchar, Langevin description of fusion, deep-inelastic collisions and heavy-ion-induced fission, Phys. Rep. 292 (1998) 131–238

    1998

  48. [56]

    K. Wen, F. Sakata, Z.-X. Li, X.-Z. Wu, Y.-X. Zhang, S.-G. Zhou, Non-Gaussian Fluctuations and Non-Markovian Effects in the Nuclear Fusion Process: Langevin Dynamics Emerging from Quantum Molecular Dynamics Simulations, Phys. Rev. Lett. 111 (2013) 012501. doi:10.1103/PhysRevLet...

    2013 doi

  49. [57]

    Gross, H

    D.H.E. Gross, H. Kalinowski, Friction model of heavy-ion collisions, Phys. Rep. 45 (1978) 175–210. doi:10.1016/0370- 1573(78)90031-5

    1978 doi

  50. [58]

    Fröbrich, Fusion and capture of heavy ions above the barrier: Analysis of experimental data with the surface friction model, Phys

    P. Fröbrich, Fusion and capture of heavy ions above the barrier: Analysis of experimental data with the surface friction model, Phys. Rep. 116 (1984) 337–400. doi:10.1016/0370-1573(84)90162-5

    1984 doi

  51. [59]

    Gegechkori, Y.A

    A.E. Gegechkori, Y.A. Anischenko, P.N. Nadtochy, G.D. Adeev, Impact of non -Markovian effects on the fission rate and time, Phys. At. Nucl. 71 (2008) 2007–2017. doi:10.1134/S1063778808120028

    2008 doi

  52. [60]

    Fröbrich, R

    P. Fröbrich, R. Lipperheide, Theory of nuclear reactions, Clarendon Press, Oxford, 1996

    1996

  53. [61]

    Khoa, G.R

    D.T. Khoa, G.R. Satchler, W. von Oertzen, Nuclear incompressibility and density dependent NN interactions in the folding model for nucleus-nucleus potentials, Phys. Rev. C. 56 (1997) 954–969. doi:10.1103/PhysRevC.56.954

    1997 doi

  54. [62]

    Gontchar, M.V

    I.I. Gontchar, M.V. Chushnyakova, A C-code for the double folding interaction potential of two spherical nuclei, Comput. Phys. Commun. 181 (2010) 168–182. doi:10.1016/J.CPC.2009.09.007

    2010 doi

  55. [63]

    Gontchar, D.J

    I.I. Gontchar, D.J. Hinde, M. Dasgupta, J.O. Newton, Double folding nucleus -nucleus potential applied to heavy-ion fusion reactions, Phys. Rev. C. 69 (2004) 024610. doi:10.1103/PhysRevC.69.024610

    2004 doi

  56. [64]

    Washiyama, D

    K. Washiyama, D. Lacroix, Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier, Phys. Rev. C. 78 (2008) 024610. doi:10.1103/PhysRevC.78.024610

    2008 doi

  57. [65]

    M. V. Chushnyakova, I.I. Gontchar, Oscillations of the fusion cross-sections in the 16O+16O reaction, Pramana - J. Phys. 85 (2015) 653–665. doi:10.1007/s12043-014-0917-0

    2015 doi

  58. [66]

    Zagrebaev, A.S

    V.I. Zagrebaev, A.S. Denikin, A. V. Karpov, A.P. Alekseev, M.A. Naumenko, V.A. Rachkov, V. V. Samarin, V. V. Saiko, NRV web knowledge base on low-energy nuclear physics, (n.d.). http://nrv.jinr.ru/

  59. [67]

    Newton, C.R

    J.O. Newton, C.R. Morton, M. Dasgupta, J.R. Leigh, J.C. Mein, D.J. Hinde, H. Timmers, K. Hagino, Experimental barrier distributions for the fusion of 12C, 16O, 28Si, and 35Cl with 92Zr and coupled-channels analyses, Phys. Rev. C. 64 (2001) 064608. doi:10.1103/PhysRevC.64.064608

    2001 doi

  60. [68]

    Kossakowski, J

    R. Kossakowski, J. Jastrzbski, P. Rymuza, W. Skulski, A. Gizon, S. André, J. Genevey, J. Gizon, V. Barci, Heavy residues following 5–10 MeV/nucleon 12C and 14N induced reactions on Sm and Pr targets, Phys. Rev. C. 32 (1985) 1612–1630. doi:10.1103/PhysRevC.32.1612

    1985 doi

  61. [69]

    Mukherjee, D.J

    A. Mukherjee, D.J. Hinde, M. Dasgupta, K. Hagino, J.O. Newton, R.D. Butt, Failure of the Woods -Saxon nuclear 14 potential to simultaneously reproduce precise fusion and elastic scattering measurements, Phys. Rev. C. 75 (2007) 044608. doi:10.1103/PhysRevC.75.044608

    2007 doi

  62. [70]

    Berriman, D.J

    A.C. Berriman, D.J. Hinde, M. Dasgupta, C.R. Morton, R.D. Butt, J.O. Newton, Unexpected inhibition of fusion in nucleus–nucleus collisions, Nature. 413 (2001) 144–147. doi:10.1038/35093069

    2001 doi

  63. [71]

    Leigh, M

    J.R. Leigh, M. Dasgupta, D.J. Hinde, J.C. Mein, C.R. Morton, R.C. Lemmon, J.P. Lestone, J.O. Newton, H. Timmers, J.X. Wei, N. Rowley, Barrier distributions from the fusion of oxygen ions with 144,148,154Sm and 186W, Phys. Rev. C. 52 (1995) 3151–3166. doi:10.1103/PhysRevC.52.3151

    1995 doi

  64. [72]

    Morton, A.C

    C.R. Morton, A.C. Berriman, M. Dasgupta, D.J. Hinde, J.O. Newton, K. Hagino, I.J. Thompson, Coupled -channels analysis of the 16O+208Pb fusion barrier distribution, Phys. Rev. C. 60 (1999) 044608. doi:10.1103/PhysRevC.60.044608

    1999 doi

  65. [73]

    Dasgupta, D.J

    M. Dasgupta, D.J. Hinde, A. Diaz-Torres, B. Bouriquet, C.I. Low, G.J. Milburn, J.O. Newton, Beyond the Coherent Coupled Channels Description of Nuclear Fusion, Phys. Rev. Lett. 99 (2007) 192701. doi:10.1103/PhysRevLett.99.192701

    2007 doi

  66. [74]

    Hinde, C.R

    D.J. Hinde, C.R. Morton, M. Dasgupta, J.R. Leigh, J.C. Mein, H. Timmers, Competition between fusion -fission and quasi-fission in the reaction 28Si+208Pb, Nucl. Phys. A. 592 (1995) 271–289. doi:10.1016/0375-9474(95)00306-L

    1995 doi

  67. [75]

    Yanez, W

    R. Yanez, W. Loveland, A.M. Vinodkumar, P.H. Sprunger, L. Prisbrey, D. Peterson, S. Zhu, J.J. Kolata, A. Villano, J.F. Liang, Isospin dependence of capture cross sections: The 36S+208Pb reaction, Phys. Rev. C. 82 (2010) 054615. doi:10.1103/PhysRevC.82.054615

    2010 doi

  68. [76]

    Hinde, M

    D.J. Hinde, M. Dasgupta, N. Herrald, R.G. Neilson, J.O. Newton, M.A. Lane, Isotopic dependence of fusion barrier energies in reactions forming heavy elements, Phys. Rev. C. 75 (2007) 054603. doi:10.1103/PhysRevC.75.054603

    2007 doi

  69. [179]

    doi:10.1016/0003-4916(90)90330-Q

    doi

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