Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

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A. G. Magner<sup>1

1</sup>Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine

Abstract: We derived the semiclassical trace formulas for the level density as sums over periodic-orbit families and isolated orbits within the improved stationary phase method. Averaged level-density shell corrections and shell-structure energies are continuous through all symmetry-breaking (bifurcation) points with the correct asymptotics of the standard stationary phase approach accounting for continuous symmetries. We found enhancement of the nuclear shell structure near bifurcations in the superdeformed region. Our semiclassical results for the averaged level densities with the gross-shell and more thin-shell structures and the energy shell corrections for critical deformations are in good agreement with the quantum calculations for several single-particle Hamiltonians, in particular for the potentials with a sharp spheroidal shape. Enhancement of the shell structure owing to bifurcations of the shortest 3-dimensional orbits from equatorial orbits is responsible for the second well of fission barrier in a superdeformation region.

Keywords: nuclear shell structure, fission barriers, nuclear deformations, energy shell corrections, semiclassical periodic orbit theory, quantum and classical chaos.

1. Strutinsky V. M. Shell effects in nuclear masses and deformation energies. Nucl. Phys. A 95 (1967) 420. https://doi.org/10.1016/0375-9474(67)90510-6

2. Strutinsky V. M. "Shells" in deformed nuclei. Nucl. Phys. A 122 (1968) 1. https://doi.org/10.1016/0375-9474(68)90699-4

3. M. Brack, J. Damgård, A. S. Jensen, H. C. Pauli, V. M. Strutinsky, V. Wong. Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process. Rev. Mod. Phys. 44 (1972) 320. https://doi.org/10.1103/RevModPhys.44.320

4. Brack M. Vilen Mitrofanovich Strutinsky's impact on nuclear and many-particle physics. The 3rd Int. Conf. "Current Problems in Nuclear Physics and Atomic Energies": Book of Abstracts, Kyiv, 7 - 11 June, 2010. Proc. of this conference. In print (Kyiv, 2010) p. 73.

5. Gutzwiller M. C. Periodic Orbits and Classical Quantization Conditions. J. Math. Phys. 12 (1971) 343; https://doi.org/10.1063/1.1665596

Chaos in Classical and Quantum Mechanics (New York: Springer, 1990) 432 p.

6. Strutinsky V. M. Semiclassical theory of the nuclear shell structure. Nucleonica 20 (1975) 679.

7. Strutinsky V. M., Magner A. G. Quasiclassical theory of the nuclear shell structure. Sov. Phys. Part. & Nucl. 7 (1977) 138.

8. Strutinsky V. M., Magner A. G., Ofengenden S. R., Døssing T. Semiclassical interpretation of the gross-shell structure in deformed nuclei. Z. Phys. A 283 (1977) 269. https://doi.org/10.1007/BF01407208

9. Strutinsky V. M. Why are atomic nuclei deformed. Bul. Acad. Sci. USSR, Sect. Phys. 47 (1983) 2007.

10. Strutinsky V. M. Shell structure in fission. Proc. of the Int. Workshop IAEA-SM-241/C12 "Physics and Chemistry of fission 1979" (1980) Vol. 1, p. 475.

11. Strutinsky V. M. Shell structure in deformed nuclei and nuclear fission. Pramana 33 (1989) 21. https://doi.org/10.1007/BF02845908

12. Brack M., Bhaduri R. K. Semiclassical Physics. Frontiers in Physics. Vol. 96 (Addison-Wesley, Reading, 1997) 458 p.

13. Arita K. Periodic orbit bifurcations and nuclear deformations. The 3rd Int. Conf. "Current Problems in Nuclear Physics and Atomic Energies": Book of Abstracts, Kyiv, 7 - 11 June, 2010 (Kyiv, 2010) p. 71.

14. A. G. Magner, S. N. Fedotkin, K. Arita, K. Matsuyanagi, M. Brack. Periodic-orbit bifurcations and superdeformed shell structure. Phys. Rev. E 63 (2001) 065201. https://doi.org/10.1103/PhysRevE.63.065201

15. Magner A. G., Fedotkin S. N., Arita K., Matsuyanagi K. Symmetry Breaking and Bifurcations in the Periodic Orbit Theory. II: Spheroidal Cavity. Prog. Theor. Phys. 108 (2002) 853. https://doi.org/10.1143/PTP.108.853

16. Magner A. G., Arita K., Fedotkin S. N. Semiclassical Approach for Bifurcations in a Smooth Finite-Depth Potential. Prog. Theor. Phys. 115 (2006) 523. https://doi.org/10.1143/PTP.115.523

17. Magner A. G., Sitdikov A. S., Khamzin A. A., Bartel J. Semiclassical shell structure in rotating Fermi systems. Phys. Rev. C 81 (2010) 064302. https://doi.org/10.1103/PhysRevC.81.064302

18. Gzhebinsky A. M., Magner A. G., Fedotkin S. N. Low-lying excitations as a semiclassical response. Phys. Rev. C 76 (2007) 064315. https://doi.org/10.1103/PhysRevC.76.064315