Gama-kararsız Bölgede Kratzer Potansiyeli İçeren Bohr Hamiltoniyeninin Analitik Çözümü

Abstract

Bu çalışmada, gama-kararsız bölge için Kratzer potensiyeli içeren Kollektif Bohr Hamiltoniyeni’nin analitik çözümleri, ilk defa Nikiforov-Uvarov metodu kullanılarak yapılmıştır. Enerji özdeğer denklemi kapalı formda elde edilmiş ve 102-116Pd izotoplarının deneysel enerji değerlerini tahmin etmek için uygulanmıştır. Deney ve teori arasında iyi bir uyum olduğu görülmüştür.

Keywords

• Kollektif model
• Gama-kararsız bölge
• Çift-çift çekirdekler
• Kratzer potansiyeli

Analytical Solution of the Bohr Hamiltonian with the Kratzer Potential in Gamma-unstable Region

Abstract

In this study, the analytical solution of the Collective Bohr Hamiltonian with the Kratzer potential for the gamma-unstable region has been done for the first time by using the Nikiforov-Uvarov method. The energy eigenvalue equation was obtained in a closed form and applied to predict the experimental energy data of 102-116Pd isotopes. It was seen a good agreement between theory and experiment.

Keywords

• Collective model
• Gamma-unstable region
• Even-even nuclei
• Kratzer potential

References

1. ‏Bohr, A. (1952). The Coupling of Nuclear Surface Oscillations to the Motion of Individual Nucleons. Dan. Mat. Fys. Medd. 26(14).
2. Bonatsos, D., McCutchan, E. A., Minkov, N., Casten, R. F., Yotov, P., Lenis, D. and Yigitoglu, I. (2007). Exactly separable version of the Bohr Hamiltonian with the Davidson potential. Physical Review C, 76(6), 064312.‏
3. Boztosun, I., Bonatsos, D., and Inci, I. (2008). Analytical solutions of the Bohr Hamiltonian with the Morse potential. Physical Review C, 77(4), 044302.‏
4. Casten, R. F. (2006). Shape phase transitions and critical-point phenomena in atomic nuclei. Nature Physics, 2(12), 811-820.‏
5. Firestone, R. B. (1996). Table of Isotopes CD ROM Edition. Version 1.0 Virginia S. Shirley.
6. Fortunato, L., and Vitturi, A. (2003). Analytically solvable potentials for γ-unstable nuclei. Journal of Physics G: Nuclear and Particle Physics, 29(7), 1341.‏
7. Iachello, F. (2000). Dynamic symmetries at the critical point. Physical Review Letters, 85(17), 3580.‏
8. Iachello, F. (2001). Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition. Physical Review Letters, 87(5), 052502.‏

9. Kratzer, A. (1920). Die ultraroten rotationsspektren der halogenwasserstoffe. Zeitschrift für Physik, 3, 289-307.
10. Nikiforov, A. V. and Uvarov, V. B. (1988). Special Functions of Mathematical Physics, Birkhauser, Bassel.‏
11. Wilets, L., and Jean, M. (1956). Surface oscillations in even-even nuclei. Physical Review, 102(3), 788.‏