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, Russian   Periodicity: 4 times per year   Open access peer reviewed journal

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Abstract: A semi-classical approximation is applied to the calculations of single-particle and statistical level densities in excited nuclei. Landau's conception of quasi-particles with the nucleon effective mass m^* < m is used. The approach provides the correct description of the continuum contribution to the level density for realistic finite-depth potentials. It is shown that the continuum states does not affect significantly the thermodynamic calculations for sufficiently small temperatures T ≤ 1 MeV but reduce strongly the results for the excitation energy at high temperatures. By use of standard Woods - Saxon potential and nucleon effective mass m^* = 0.7m the A-dependency of the statistical level density parameter K was evaluated in a good qualitative agreement with experimental data.

1. T. Ericson. The statistical model and nuclear level densities. Adv. Phys. 9(36) (1960) 425. http://dx.doi.org/10.1080/00018736000101239

2. O. Bor, B. Mottel'son. The Structure of the Atomic Nucleus, Vol. 1 (Moskva: Mir, 1971) 456 p. (Rus) Google books

3. A. Gilbert, A. Cameron. A composite nuclear-level density formula with shell corrections. Can. J. Phys. 43(8) (1965) 1446. https://doi.org/10.1139/p65-139

4. J.R. Huizenga, L.G. Moretto. Nuclear Level Densities. Ann. Rev. Nucl. Sci. 22 (1972) 427. https://doi.org/10.1146/annurev.ns.22.120172.002235

5. V.S. Stavinskij. The level density of nuclei. EchAYa. 3(4) (1972) 832. (Rus) Article

6. S.K. Kataria, V.S. Ramamurthy, S.S. Kapoor. Semiempirical nuclear level density formula with shell effects. Phys. Rev. C 18(1) (1978) 549. https://doi.org/10.1103/PhysRevC.18.549

7. A.V. Ignatyuk, I.N. Mikhailov, L.N. Molina et al. The shape of the heated fast-rotating nuclei. Nucl. Phys. A 346(1) (1980) 191. https://doi.org/10.1016/0375-9474(80)90497-2

8. S. Shlomo, V.M. Kolomietz. Hot Nuclei. Rep. Prog. Phys. 68(1) (2005) 1. https://doi.org/10.1088/0034-4885/68/1/R01

9. Ye.A. Bogila, V.M. Kolomietz, A.I. Sanzhur. Nuclear level density with fixed excitation number. Z. Phys. A 341(4) (1992) 373. https://doi.org/10.1007/BF01301380

10. S. Shlomo, Ye.A. Bogila, V.M. Kolomietz, A.I. Sanzhur. Fixed exciton number level density for a finite potential well. Z. Phys. A 353(1) (1995) 27. https://doi.org/10.1007/BF01297723

11. E.M. Lifshits, L.P. Pitaevskij. Physical Kinetics (Moskva: Nauka, 1979) 527 p. (Rus) Google Books

12. A.B. Migdal. The Theory of Finite Fermi Systems and Properties of Atomic Nuclei (Moskva: Nauka, 1965) 572 p. (Rus) Google Books

13. D.A. Kirzhnits. Field Methods in the Theory of Many Particles (Moskva: Atomizdat, 1963) 343 p. (Rus)

14. B. Grammaticos, A. Voros. Semiclassical approximations for nuclear Hamiltonians. I. Spin-independent potentials. Ann. of Phys. 123(2) (1979) 359. https://doi.org/10.1016/0003-4916(79)90343-9

15. P. Ring, P. Schuck. The Nuclear Many-Body Problem (Berlin: Springer-Verlag, 1980) 711 p. Google Books

16. M. Prakash, J. Wambach, Z.Y. Ma. Effective mass in nuclei and the level density parameter. Phys. Lett. B 128(3-4) (1983) 141. https://doi.org/10.1016/0370-2693(83)90377-5

17. S. Shlomo, V.M. Kolomietz, H. Dejbakhsh. Single particle level density in finite depth potential well. Phys. Rev. C 55(4) (1997) 1972. https://doi.org/10.1103/PhysRevC.55.1972

18. N. Levinson. On the uniqueness of the potential in a Schrodinger equation for a given asymptotic phase. Danske Vid. Selsk., Mat-fys. Medd. 25(9) (1949) 129.