Effects of velocity-dependent and spin-orbit terms of the Skyrme interaction on non-locality parameter of microscopic optical potentials
Từ khóa
DOI:
https://doi.org/10.26459/hueunijns.v135i1B.8422Tóm tắt
We investigate how the velocity-dependent (t1 and t2) and spin-orbit (W0) terms of the Skyrme effective interaction influence the non-locality parameter β of the microscopic optical potential (MOP) for neutron elastic scattering off the doubly closed-shell nuclei 16O, 40Ca, 48Ca, and 208Pb at incident energies below 20 MeV. The MOP is constructed within the particle-vibration coupling framework on top of self-consistent Hartree-Fock plus random-phase approximation calculations by using the SLy5 parametrisation. Three calculation schemes are compared: the full Skyrme interaction, the interaction without t1 and t2, and the interaction without W0 in the residual interaction. The velocity-dependent terms exert a pronounced and mass-dependent influence on β: removing them increases βv by 0.27 fm for 16O but decreases it by 0.50 fm for 208Pb. The spin-orbit term, by contrast, produces much weaker modifications, typically below 0.1 fm. The extracted β values lie in the range 0.70–1.43 fm, with most values exceeding the widely adopted Perey-Buck value of 0.85 fm, suggesting that this empirical parameter underestimates the true microscopic non-locality for most nuclei.Lượt tải
Tài liệu tham khảo
1. Feshbach H. Unified theory of nuclear reactions. Annals of Physics. 1958;5(4):357-390.
2. Dickhoff WH, Charity RJ. Recent developments for the optical model of nuclei. Progress in Particle and Nuclear Physics. 2019;105:252-299.
3. Bonaccorso A. Direct reaction theories for exotic nuclei: An introduction via semi-classical methods. Progress in Particle and Nuclear Physics. 2018;101:1-54.
4. Perey F, Buck B. A non-local potential model for the scattering of neutrons by nuclei. Nuclear Physics. 1962;32:353-380.
5. Titus LJ, Nunes FM, Potel G. Explicit inclusion of nonlocality in (d,p) transfer reactions. Physical Review C. 2016;93(1):014604.
6. Lovell AE, Nunes FM. Systematic uncertainties in direct reaction theories. Journal of Physics G: Nuclear and Particle Physics. 2015;42(3):034014.
7. Deltuva A. Three-body direct nuclear reactions: Nonlocal optical potential. Physical Review C. 2009;79(2):021602(R).
8. Timofeyuk N, Johnson R. Nonlocality in the adiabatic model of A(d,p)B reactions. Physical Review C. 2013;87(6):064610.
9. Timofeyuk N, Johnson R. Nonlocality in deuteron stripping reactions. Physical Review Letters. 2013;110(11):112501.
10. Ross A, Titus LJ, Nunes FM, Mahzoon MH, Dickhoff WH, Charity RJ. Effects of nonlocal potentials on (p, d) transfer reactions. Physical Review C. 2015;92(4):044607.
11. Quaglioni S, Navrátil P. Ab initio many-body calculations of n-3H, n-4He, p-3,4He, and n-10Be scattering. Physical Review Letters. 2008; 101(9):092501.
12. Rotureau J, Danielewicz P, Hagen G, Nunes F, Papenbrock T. Optical potential from first principles. Physical Review C. 2017;95(2):024315.
13. Holt JW, Kaiser N, Miller GA. Microscopic optical potential for exotic isotopes from chiral effective field theory. Physical Review C. 2016;93(6):064603.
14. Whitehead T, Lim Y, Holt JW. Proton elastic scattering on calcium isotopes from chiral nuclear optical potentials. Physical Review C. 2019;100(1):014601.
15. Whitehead T, Lim Y, Holt JW. Global Microscopic Description of Nucleon-Nucleus Scattering with Quantified Uncertainties. Physical Review Letters. 2021;127(18):182502.
16. Bauge E, Delaroche JP, Girod M. Semimicroscopic nucleon-nucleus spherical optical model for nuclei with A ≥ 40 at energies up to 200 MeV. Physical Review C. 1998;58(2):1118-1145.
17. Mahzoon MH, Charity RJ, Dickhoff WH, Dussan H, Waldecker SJ. Forging the link between nuclear reactions and nuclear structure. Physical Review Letters. 2014;112(16):162503.
18. Dickhoff WH, Van Neck D, Waldecker SJ, Charity RJ, Sobotka LG. Nonlocal extension of the dispersive optical model to describe data below the Fermi energy. Physical Review C. 2010;82(5):054306.
19. Mizuyama K, Ogata K. Self-consistent microscopic description of neutron scattering by 16O based on the continuum particle-vibration coupling method. Physical Review C. 2012;86(4):041603(R).
20. Mizuyama K, Ogata K. Low-lying excited states of 24O investigated by a self-consistent microscopic description of proton inelastic scattering. Physical Review C. 2014;89(3):034620.
21. Blanchon G, Dupuis M, Arellano HF, Vinh Mau N. Microscopic positive-energy potential based on the Gogny interaction. Physical Review C. 2015;91(1):014612.
22. Blanchon G, Dupuis M, Arellano HF. Prospective study on microscopic potential with Gogny interaction. The European Physical Journal A. 2015;51:165.
23. Blanchon G, Dupuis M, Bernard RN, Arellano HF. Asymmetry dependence of Gogny-based optical potential. The European Physical Journal A. 2017;53:88.
24. Hao TVN, Loc BM, Phuc NH. Low-energy nucleon-nucleus scattering within the energy density functional approach. Physical Review C. 2015;92(1):014605.
25. Nhan Hao TV, Nhu Le N, Koh M-H, Quang Hung N, Ngoc Duy N, Pham VNT, et al. Microscopic optical potential obtained from energy-density-functional approach for neutron–nucleus elastic scattering. International Journal of Modern Physics E. 2018;27(06):1850052.
26. Hoang Tung N, Quang Tam D, Pham VNT, Lam Truong C, Hao TVN. Effects of velocity-dependent and spin-orbit terms of the Skyrme interaction on neutron elastic scattering observables. Physical Review C. 2020;102(3):034608.
27. Hebborn C, Nunes FM, Potel G, Dickhoff WH, Holt JW, Atkinson MC, et al. Optical potentials for the rare-isotope beam era. Physics G: Nuclear and Particle Physics. 2023;50(6):060501.
28. Mau NV, Bouyssy A. Optical potential for low-energy neutrons: Imaginary potential for neutron-40Ca elastic scattering. Nuclear Physics A. 1976;257(2):189-220.
29. Bernard V, Van Giai N. Microscopic optical potential for 208Pb in the nuclear structure approach. Nuclear Physics A. 1979;327(2):397-418.
30. Arellano HF, Blanchon G. On the separability of microscopic optical model potentials and emerging bell-shape Perey-Buck nonlocality. The European Physical Journal A. 2022;58(7):119.
31. Arellano HF, Blanchon G. Universal separable structure of the optical potential. Physical Review C. 2024;109(6):064609.
32. Vautherin D, Brink DM. Hartree-Fock calculations with Skyrme’s interaction. I. Spherical nuclei. Physical Review C. 1972;5(3):626-47.
33. Chabanat E, Bonche P, Haensel P, Meyer J, Schaeffer R. A Skyrme parametrization from subnuclear to neutron star densities. Part II. Nuclei far from stabilities. Nuclear Physics A. 1998;635(1):231-56.
34. Colò G, Sagawa H, Bortignon PF. Effect of particle-vibration coupling on single-particle states: A consistent study within the Skyrme framework. Physical Review C. 2010;82(6):064307.
35. Cao L-G, Colò G, Sagawa H, Bortignon PF. Properties of single-particle states in a fully self-consistent particle-vibration coupling approach. Physical Review C. 2014;89(4):044314.
36. Colò G, Cao L, Van Giai N, Capelli L. Self-consistent RPA calculations with Skyrme-type interactions: The skyrme_rpa program. Computer Physics Communications. 2013;184(1):142-161.
37. Raynal J. Computer program DWBA98. NEA 1209/05; 1998.
38. National Nuclear Data Center. Experimental data taken from the National Nuclear Data Center. Brookhaven National Laboratory Online Data Service; 2025.