Investigating the effect of entrance channel mass asymmetry on fusion reactions using the Skyrme energy density formalism

M. M. Hosamani; A. Vinayak; N. M. Badiger

doi:10.1007/s41365-020-00802-w

Your Location：

Home >

Browse articles >

Investigating the effect of entrance channel mass asymmetry on fusion reactions using the Skyrme energy density formalism

NUCLEAR PHYSICS AND INTERDISCIPLINARY RESEARCH | Updated：2021-01-26

- Investigating the effect of entrance channel mass asymmetry on fusion reactions using the Skyrme energy density formalism
- Nuclear Science and Techniques Vol. 31, Issue 9, Article number: 89(2020)
- Affiliations：
  
  1.Department of Studies in Physics, Karnatak University, Dharwad 580003, India
- Author bio：
  
  Corresponding author, nbadiger@gmail.com
- Funds：
- DOI：10.1007/s41365-020-00802-w
  CLC：
Scan for full text
M. M. Hosamani, A. Vinayak, N. M. Badiger. Investigating the effect of entrance channel mass asymmetry on fusion reactions using the Skyrme energy density formalism. [J]. Nuclear Science and Techniques 31(9):89(2020)
DOI：

M. M. Hosamani, A. Vinayak, N. M. Badiger. Investigating the effect of entrance channel mass asymmetry on fusion reactions using the Skyrme energy density formalism. [J]. Nuclear Science and Techniques 31(9):89(2020) DOI： 10.1007/s41365-020-00802-w.

摘要

Abstract

In the present investigations, the fusion cross-sections for the formation of ,200,Pb compound nucleus (CN) using ,16,O + ,184,W,30,Si + ,170,Er, and ,40,Ar + ,160,Gd nuclear reactions at energies above the Coulomb barrier were calculated to understand the effect of entrance channel mass asymmetry (,α,) on the fusion reactions; the Skyrme energy density formalism (SEDF) was used for this calculation. The SEDF uses the Hartree–Fock–Bogolyubov (HFB) computational program with Skyrme forces such as SkM*, SLy4, and SLy5 to obtain the nucleus-nucleus potential parameters for the above reactions. Using the SEDF model with SkM*, SLy4, and SLy5 interaction forces, the theoretical fusion cross-sections were determined to be above the barrier energy and compared with the available experimental fusion cross-sections. The results show a close agreement between the theoretical and experimental values for all selected systems at energies well above the barrier. However, near the barrier energies, the theoretical values were observed to be higher than the experimental values.

关键词

Keywords

Skyrme forceEnergy density formalismHartree–Fock–BogolyubovThomas–Fermi modelCoupled-channel calculation

references

W. Kohn, L. J. Sham, Quantum density oscillations in an inhomogeneous electron gas. Phys. Rev. 137, A1697 (1965). https://doi.org/10.1103/PhysRev.137.A1697https://doi.org/10.1103/PhysRev.137.A1697

P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964). https://doi.org/10.1103/PhysRev.136.B864https://doi.org/10.1103/PhysRev.136.B864

R. Kumar, M. K. Sharma, R. K. Gupta, Fusion reaction cross-sections using the Wong model within Skyrme energy density based semiclassical extended Thomas Fermi approach. Nucl. Phys. A 870-871, 42-57 (2011). https://doi.org/10.1016/j.nuclphysa.2011.09.010https://doi.org/10.1016/j.nuclphysa.2011.09.010

R. K. Gupta, Dalip Singh, Raj Kumar et al., Universal functions of nuclear proximity potential for Skyrme nucleus-nucleus interaction in a semiclassical approach. J. Phys. G: Nucl. Part. Phys. 36, 075104 (2009).

K. A. Brueckner, J. R. Buchler, R. C. Clark et al., Phys. Rev. 181, 1534 (1969).

H. Holm, W. Greiner, Influence of nuclear forces on the Coulomb barrier in heavy-ion reactions. Phys. Rev. Lett. 24, 404 (1970). https://doi.org/10.1103/PhysRevLett.24.404https://doi.org/10.1103/PhysRevLett.24.404

A. S. Jensen, C. Y. Wong, Distortion of nuclei in heavy ion reactions. Phys. Lett. B 32, 567-570 (1970). https://doi.org/10.1016/0370-2693(70)90545-9https://doi.org/10.1016/0370-2693(70)90545-9

H. Holm, D. Scharnweber, W. Scheid et al., Coulomb distortion in heavy-ion reactions. Z. Phys. 231, 450 (1970). https://doi.org/10.1007/BF01642535https://doi.org/10.1007/BF01642535

P. W. Riesenfeld, T. D. Thomas, Effect of nuclear deformability on reaction cross sections. Phys. Rev. C 2, 711 (1970). https://doi.org/10.1103/PhysRevC.2.711https://doi.org/10.1103/PhysRevC.2.711

L. Wilets. A. Goldberg, F. H. Lewis, New theoretical approach to nuclear heavy-ion scattering. Phys. Rev. 2, 1576 (1970). https://doi.org/10.1103/PhysRevC.2.1576https://doi.org/10.1103/PhysRevC.2.1576

K. A. Brueckner, J. R. Buchler, M. M. Kelly, New theoretical approach to nuclear heavy-ion scattering. Phys. Rev. 173, 944 (1968). https://doi.org/10.1103/PhysRev.173.944https://doi.org/10.1103/PhysRev.173.944

T. H. R. Skyrme et al., Phil. Mag. 1, 1043 (1956);

T. H. R. Skyrme et al., Phil. Nucl. Phys. A 9, 615 (1959).

C. Ngow, B. Tamain, J. Galin et al, Calculation of interaction barriers using the energy density formalism. Nucl. Phys. A 240, 353 (1975). https://doi.org/10.1016/0375-9474(75)90335-8https://doi.org/10.1016/0375-9474(75)90335-8

D. M. Brink, FL. Stancu, Interaction potential between two 16O nuclei derived from the Skyrme interaction. Nucl. Phys. A 243, 175-188 (1975). https://doi.org/10.1016/0375-9474(75)90027-5https://doi.org/10.1016/0375-9474(75)90027-5

A. Dobrowolski, K. Pomorski, J. Bartel, Mean-field description of fusion barriers with Skyrme`s interaction. Nucl. Phys. A 729, 713 (2003). https://doi.org/10.1016/j.nuclphysa.2003.09.008https://doi.org/10.1016/j.nuclphysa.2003.09.008

L. Kaur, R. Kumari, On the role of deformed Coulomb potential in fusion using energy density formalism. Pramana-Journal of Physics 85, 639 (2015). https://doi.org/10.1007/s12043-014-0898-zhttps://doi.org/10.1007/s12043-014-0898-z

O. N. Ghodsi, F. Torabi, Comparative study of fusion barriers using Skyrme interactions and the energy density functional. Phys. Rev. C 92, 064612 (2015). https://doi.org/10.1103/PhysRevC.92.064612https://doi.org/10.1103/PhysRevC.92.064612

O. N. Ghodsi, F. Torabi, Effect of nuclear matter incompressibility on the 16O + 208Pb system. Phys. Rev. C 93, 064611 (2016). https://doi.org/10.1103/PhysRevC.93.064611https://doi.org/10.1103/PhysRevC.93.064611

R. J. Lombard, The energy density formalism in nuclei. Annals of Physics 77, 380-413 (1973). https://doi.org/10.1016/0003-4916(73)90422-3https://doi.org/10.1016/0003-4916(73)90422-3

M. Brack, C. Guet, H. B. Hakansson, Selfconsistent semiclassical description of average nuclear properties - A link between microscopic and macroscopic models. Phys. Rep. 123, 275 (1985).

J. Bartel, M. Brack, M. Durand, Extended Thomas-Fermi theory at finite temperature. Nucl. Phys. A 445, 263-303 (1985). https://doi.org/10.1016/0375-9474(85)90071-5https://doi.org/10.1016/0375-9474(85)90071-5

D. Singh et al., Proceedings of DAE-BRNS symposium on Nuclear Physics, Vol B46, P-254 (2003).

K. Hagino, N. Rowley, A. T. Kruppa, A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions. Comp. Phys. Comm. 123, 143-152 (1999). https://doi.org/10.1016/S0010-4655(99)00243-Xhttps://doi.org/10.1016/S0010-4655(99)00243-X

A. S. Umar, V. E. Oberacker, Three-dimensional unrestricted time-dependent Hartree-Fock fusion calculations using the full Skyrme interaction. Phys. Rev. C 73, 054607 (2006). https://doi.org/10.1103/PhysRevC.73.054607https://doi.org/10.1103/PhysRevC.73.054607

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

K. T. R. Davies et al., in Treatise on heavy ion science, edited by D. A. Bromley (Plenum, New York, 1985), Vol.03 P.03.

J. P. Svenne, Fourteen years of self-consistent field calculations: What has been learned. Adv. Nucl. Phys. 11, 179 (1979).

R. K. Gupta, D. Singh, W. Greiner, Semiclassical and microscopic calculations of the spin-orbit density part of the Skyrme nucleus-nucleus interaction potential with temperature effects included. Phys. Rev. C 75, 024603 (2007). https://doi.org/10.1103/PhysRevC.75.024603https://doi.org/10.1103/PhysRevC.75.024603

J. Blocki, J. Randrup, W. J. Swiatecki et al., Proximity forces. Ann. Phys. (NY) 105, 427 (1977). https://doi.org/10.1016/0003-4916(77)90249-4https://doi.org/10.1016/0003-4916(77)90249-4

R. K. Puri, R. K. Gupta, Analytical formulation of the ion-ion interaction potential including spin density term in energy density formalism. Int. J. Mod. Phys. E 1, 269 (1992). https://doi.org/10.1142/S0218301392000138https://doi.org/10.1142/S0218301392000138

G. B. Arfken et al, Mathematical Methods for Physicists: A comprehensive guide, 7th edition, Academic Press is an imprint of Elsevier 225 Wyman Street, Waltham, MA 02451, USA.

Ishita Sharma, R. Kumar, M. K. Sharma, Probing the role of Skyrme interactions on the fission dynamics of the 6Li + 238U reaction. Eur. Phys. J. A 53, 140 (2017). https://doi.org/10.1140/epja/i2017-12331-5https://doi.org/10.1140/epja/i2017-12331-5

K. Bennaceur, Coordinate-space solution of the Skyrme-Hartree-Fock-Bogolyubov equations within spherical symmetry. The program HFBRAD (v1.00). Comp. Phys. Comm. 168, 96 (2005). https://doi.org/10.1016/j.cpc.2005.02.002https://doi.org/10.1016/j.cpc.2005.02.002

A. Shamlath, E. Prasad, N. Madhavan et al., Fusion and quasifission studies in reactions forming Rn via evaporation residue measurements. Phys. Rev. C 95, 034610 (2017). https://doi.org/10.1103/PhysRevC.95.034610https://doi.org/10.1103/PhysRevC.95.034610

B. B. Back, R. R. Betts, J. E. Gindler et al., Angular distribution in heavy-ion induced fission. Phys. Rev. C 32, 195 (1985). https://doi.org/10.1103/PhysRevC.32.195https://doi.org/10.1103/PhysRevC.32.195

S. Misicu, H. Esbensen, Signature of shallow potentials in deep sub-barrier fusion reactions. Phys. Rev. C 75, 034606 (2007). https://doi.org/10.1103/PhysRevC.75.034606https://doi.org/10.1103/PhysRevC.75.034606

H. Esbensen, S. Misicu, Hindrance of 16O + 208Pb fusion at extreme sub-barrier energies. Phys. Rev. C 76, 054609 (2007). https://doi.org/10.1103/PhysRevC.76.054609https://doi.org/10.1103/PhysRevC.76.054609

K. Hagino, N. Takigawa, Subbarrier fusion reactions and many-particle quantum tunneling. Progress of Theoretical Physics, 128, 1061-1106 (2012). https://doi.org/10.1143/PTP.128.1061https://doi.org/10.1143/PTP.128.1061

J. Bartel, P. Quentin, Towards a better parameterization of Skyrme-like effective forces: A critical study of the SkM force. Nucl. Phys. A 386, 79 (1982).

E. Chabanat, P. Bonche, P. Haensel et al., A Skyrme parameterization from subnuclear to neutron star densities part II. Nuclei far from stability. Nucl. Phys. A 635, 231 (1998). https://doi.org/10.1016/S0375-9474(98)00180-8https://doi.org/10.1016/S0375-9474(98)00180-8

J. Dobaczewski, J. Dudek, Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis I. The method. Comput. Phys. Comm. 102, 166 (1997).

J. Dobaczewski, J. Dudek, Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis I. The program HFODD. Comput. Phys. Comm. 102, 183 (1997).

P. D. Shidling, N. M. Badiger, S. Nath et al., Fission hindrance studies in 200Pb: Evaporation residue cross section and spin distribution measurements. Phys. Rev. C 74, 064603 (2006). https://doi.org/10.1103/PhysRevC.74.064603https://doi.org/10.1103/PhysRevC.74.064603

G. Mohanto, N. Madhavan, S. Nath et al., Entrance channel effect on ER spin distribution. Nucl. Phys. A 890, 62 (2012). https://doi.org/10.1016/j.nuclphysa.2012.07.004https://doi.org/10.1016/j.nuclphysa.2012.07.004

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Address：Editorial Office of NST, 2019 Jialuo Road, Jiading, Shanghai 201800, China Postal code：201800
Email：nst@sinap.ac.cn
Technical support is provided by Beijing Founder electronics co., LTD 沪ICP备05005479号-1 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰