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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R. M. Plekan, V. Yu. Pojda, I. V. Khimich

Uzhgorod National University, Department of Nuclear Physics and Elementary Particles, Uzhgorod, Ukraine

Abstract: A hyperspherical adiabatic approach (HAA) has been suggested to find the energy spectrum of even-even atomic nuclei modelled by a spherically symmetric even-even core plus two valence nucleons in the external shell. The adiabatic three-particle model of nucleus for the case of the spherically symmetric and axially symmetric nucleus has been obtained. The so-called adiabatic three-particle model is based on the assumption on the separability of the motion of valence nucleons into the high-speed motion of nucleons over the angular variables and the adiabatic (slow-speed) motion of nucleons along the hyperradius R. The efficiency of the adiabatic approach is illustrated by the example of the numerical calculations of the energy spectrum of low-lying excited states of the even-even atomic nuclei ⁶He, ¹⁰Be, ¹⁴C, ¹⁶C, ¹⁸O, ¹⁸Ne, ⁴²Ca, and ⁵⁸Ni, which possess two valence nucleons in the shell.

1. Goeppert-Маyer М., Jensen J. H. D. Elementary Theory of Nuclear Shell Structure (New York: Wiley, 1955) 342 p.

2. Barts B. I., Bolotin Yu. L., Inopin E. V., Gonchar V. Yu. Hartree-Fock Method in Nuclear Theory (Kyiv: Naukova dumka, 1982) 208 p. (Rus).

3. Soloviev V. G. Theory of Atomic Nucleus: Nuclear Models (Moscow: Energoizdat, 1981) 296 p. (Rus).

4. Baz' A. I., Grin' Yu. T., Dyomin V. F., Jukov M. V. Some Exhibits of K-Harmonics Method to Calculation of Characteristics of Atomic Nuclei. Fiz. Elem. Chast. Atom. Yadra 3 (1972) 275.

5. Jolos R. V., Lemberg Kh., Mikhailov V. M. The Interacting Boson Model. Physical Grounds and Applications. Fiz. Elem. Chast. Atom. Yadra 16 (1985) 280.

6. Roth R., Neff T., Hergert H., Feldmeier H. Nuclear Structure Based on Correlated Realistic Nucleon-Nucleon Potentials. Nucl. Phys. A 745 (2004) 3. https://doi.org/10.1016/j.nuclphysa.2004.08.024

7. Otsuka T. Monte Carlo Shell Model. Nucl. Phys. A 693 (2001) 383. https://doi.org/10.1016/S0375-9474(00)00605-9

8. Bogolyubov N. N. To a Problem on Condition of Superfluidity in Theory of Nuclear Matter. Reports of Acad. of Sci. USSR 119 (1958) 52.

9. Soloviev V. G. Investigation of the Superfluid State of Atomic Nuclei. Zh. Eksp. Teor. Fiz. 36 (1959) 1869.

10. Belyaev S. T. Effect of Pairing Correlations on Nuclear Properties. Dan. Math. Fys. Medd. 31 (1959) 1.

11. Kapustey M. M., Pojda V. Yu., Khimich I. V. Three-Particle Dynamics of Cluster Nuclei in the Hyperspherical Adiabatic Approach. Ukr. Fiz. Zh. 40 (1995) 1166.

12. Kapustey M. M., Pojda V. Yu., Khimich I. V. The Description of Bound States of Cluster Nuclei in Collective Variables. Reports of Ukr. Nat. Acad. Sci. Ser. Mat. 10 (1995) 71.

13. Kapustey M. M., Pojda V. Yu., Khimich I. V. Three-Particle Model of Stationary States of Atomic Nuclei in the Adiabatic Approach. Ukr. Fiz. Zh. 44 (1999) 1330.

14. Kapustey M. M., Plekan R. M., Pojda V. Yu., Khimich I. V. The Adiabatic Three-Particle Shell Model of Nucleus. Ukr. Fiz. Zh. 46 (2001) 524.

15. Mikhailov V. M., Kraft O. K. Nuclear Physics (Leningrad University, 1988) 328 p. (Rus).

16. Nilsson S. G. Bound States of Individual Nucleons in Deformed Nuclei. Mat. Fys. Medd. Dan. Vid. Selsk. 39 (1955) 1.

17. Nemirovskii P. E., Chepurnov V. A. Neutron States in Deformed Optical Potential. Yad. Fiz. (1966) 998.

18. Gareev A. F., Ivanova S. P., Soloviev V. G., Fedotov S. I. Single-Particle Energies and Wave Functions of the Saxon - Woods Potentials and Nonrotational States of Odd-Mass Nuclei in the Region of 150 < A < 190. Fiz. Elem. Chast. Atom. Yadra 4 (1973) 357.

19. Plekan R. M., Pojda V. Yu., Khimich I. V. Investigation of Correlations of Nucleons of Even-Even Nuclei within the framework of the Adiabatic Three-Particle Model of Nucleus. Ukr. Fiz. Zh. 49 (2004) 743.

20. Evaluated Nuclear Structure Data File (National Nuclear Data Centre, Brookhaven National Laboratory, New York, USA). http://www.nndc.bnl.gov

21. Soloviev V. G. Theory of Complex Nuclei (Moscow: Nauka, 1971) 559 p. (Rus).