Ağır İyon Füzyon Reaksiyonları ve Bariyer Dağılımlarının Çiftlenmiş Kanal Analizi

Öz

Ağır iyon füzyon reaksiyonları, Coulomb bariyeri yakınındaki enerji bölgelerinde, güncel deneysel ve teorik araştırmaların önemli bir odağını oluşturur. Bu enerji aralığındaki çarpışmalar, birbirinden açıkça ayırt edilebilen birden fazla reaksiyon kanalının etkisi altında gerçekleşir. Bariyer yakınındaki rejimde, sistemin dinamik evrimi ağırlıklı olarak elastik saçılma, çeşitli inelastik uyarılma modları ve etkileşen çekirdeklerden birinin veya her ikisinin füzyonu tarafından belirlenir. Füzyon mekanizması, saçılma potansiyelinin Coulomb ve yakınlık potansiyellerinin katkısı şeklinde ifade edilmesiyle karakterize edilir ve süreç tek boyutlu bir bariyer tünelleme modeli çerçevesinde yorumlanır. Bu çalışmada ağır iyon füzyonunu anlamak için bağlanmış-kanallar (coupled-channel, CC) modeli kullanılmıştır. CC hesaplamaları, özellikle bariyer enerjisinin altında füzyon olasılıklarının daha doğru bir şekilde modellenmesine olanak tanır. Bu yaklaşım, füzyon süreci boyunca gerçekleşen etkileşimlerin daha kapsamlı bir şekilde betimlenmesini sağlayarak hem teorik beklentilerin hem de deneysel bulguların daha iyi açıklanmasına yardımcı olur. 30Si + 26Mg, 32S + 58Ni, 46,48,50Ti + 124Sn, 58Ni + 58,64Ni, 64Ni + 64Ni, 64,70Zn + 64,70Zn ağır iyon sistemleri için füzyon tesir kesitleri CC modeli kullanılarak hesaplanmış ve ayrıntılı bir analiz gerçekleştirilmiştir. Hesaplamalarda hem projil hem de hedef çekirdeklere ait en düşük 2⁺ ve 3⁻ uyarılma seviyeleri dâhil edilmiştir. Elde edilen teorik tahminler, deneysel gözlemler ve NRV veri tabanından elde edilen hesaplamalarla karşılaştırılarak değerlendirilmiştir. Genel olarak analizler, uygulanan CC modelinin ağır iyon füzyon dinamiklerini yüksek doğrulukla tanımladığını göstermektedir.

Anahtar Kelimeler

• ağır iyon
• füzyon
• tesir kesiti
• bariyer dağılımı

Coupled-Channel Analysis of Heavy Ion Fusion Reactions and Barrier Distributions

Öz

Heavy-ion fusion reactions in the proximity of the Coulomb barrier constitute a major focus of current experimental and theoretical research. Collisions within this energy domain proceed under the influence of multiple, well-distinguished reaction channels. In the near-barrier regime, the dynamical evolution of the system is predominantly governed by elastic scattering, various inelastic excitation modes, and the fusion of one or both interacting nuclei. The fusion mechanism is characterized by expressing the scattering potential as the contribution of both Coulomb and proximity potentials, and the process is interpreted within the framework of a one-dimensional barrier penetration model. In this study, conducted to understand heavy-ion fusion, the coupled-channel (CC) model was used. CC calculations allow for more accurate modeling of fusion probabilities, particularly below the barrier energy. This approach offers a richer description of the interactions that take place during the fusion process, helping to clarify theoretical expectations as well as experimental findings. Fusion cross sections for 30Si+ 26Mg, 32S+ 58Ni, 46,48,50Ti+ 124Sn,58Ni+ 58,64Ni, 64Ni+64Ni, 64,70Zn+ 64,70Zn heavy-ion systems were calculated using the CC model and a detailed analysis was performed. The calculations incorporated the lowest 2⁺ and 3⁻ excitation levels of both the projectile and target nuclei. The resulting theoretical predictions were subsequently evaluated against experimental observations as well as computations obtained from the NRV database. Overall, the analyses indicate that the applied CC model provides a highly accurate description of heavy-ion fusion dynamics.

Anahtar Kelimeler

• heavy-ion
• fusion
• cross section
• barrier distribution

Kaynakça

1. Beckerman, M., Salomaa, M., Sperduto, A., Molitoris, J.D. (1982). Sub barrier fusion of 58,64Ni with 64Ni and 74Ge. Physical Review C, 25, 837–849. https://doi.org/10.1103/PhysRevC.25.837
2. Cheng, K. X., Xu, C., Ma, C. W., Pu, J., Wang, Y.T. (2022). Pauli blocking potential applied to heavy-ion fusion reactions. Chinese Physics C, 46, 024105. https://doi.org/10.1088/1674-1137/ac4c1d
3. Dasso, C.H. (1987). CCFUS – A simplified coupled-channel code for calculation of fusion cross sections in heavy-ion reactions. Computer Physics Communications, 46(3), 187–191. https://doi.org/10.1016/0010-4655(87)90105-7
4. Del Fabbro, M., Stefanini, A.M., Montagnoli, G., Corradi, L., Fioretto, E., Fornalè, M., Szilner, S. (2023). Influence of the Z = 50 shell closure on heavy-ion sub-barrier fusion. European Physical Journal A, 59, 26. https://doi.org/10.1140/epja/s10050-023-00026-x
5. Deng, W., Cheng, K., Xu, C. (2025). Sub-barrier fusion cross sections: Role of Pauli blocking and isospin asymmetry. Chinese Physics C, 49, 054109. https://doi.org/10.1088/1674-1137/abf123
6. Denisov, V.Y. (2023). Expression for the heavy-ion fusion cross section. Physical Review C, 107, 054618. https://doi.org/10.1103/PhysRevC.107.054618
7. Denisov, V.Y., Jin, Y. (2022). Heavy-ion fusion cross section formula and barrier height distribution. Physical Review C, 105, 064601. https://doi.org/10.1103/PhysRevC.105.064601
8. Diaz-Torres, A., Thompson, I.J. (2002). Coupled-channels calculations in fusion reactions with weakly bound nuclei. Physical Review C, 65(2), 024606. https://doi.org/10.1103/PhysRevC.65.024606

9. Erol, B., Cinan, Z.M., Başkan, T., Yılmaz, A.H. (2021). Investigating medium and heavy mass heavy ion fusion reactions and barrier distributions with coupled channel analyses. Acta Physica Polonica B, 52(9), 1117–1145. https://doi.org/10.5506/aphyspolb.52.1117
10. Fernández Niello, J., Dasso, C.H., Landowne, S. (1989). CCDEF – A simplified coupled channel code for fusion cross sections including static nuclear deformations. Computer Physics Communications, 54(1–2), 409–417. https://doi.org/10.1016/0010-4655(89)90100-8
11. Gharaei, R., Fuji, A., Azadegan, B. (2021). Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon for positive and negative Q-value systems using the proximity-type potential. Chinese Physics C, 45(12), 124101. https://doi.org/10.1088/1674-1137/ac23d3
12. Hagino, K., Rowley, N., Kruppa, A.T. (1999). A program for coupled channel calculations with all order couplings for heavy ion fusion reactions. Computer Physics Communications, 123(2–3), 143–152. https://doi.org/10.1016/S0010-4655(99)00134-2
13. Hagino, K., Takigawa, N. (2012). Subbarrier fusion reactions and many-particle quantum tunneling. Progress in Particle and Nuclear Physics, 66(1), 1–86. https://doi.org/10.1016/j.ppnp.2010.11.002
14. Hill, D.L., Wheeler, J.A. (1953). Nuclear constitution and the interpretation of fission phenomena. Physical Review, 89(5), 1102–1145. https://doi.org/10.1103/PhysRev.89.1102
15. Jiang, C.L., Henning, W.F., Kay, B.P., Watwood, N. (2023). Structures in the heavy-ion fusion excitation function at and above the Coulomb barrier. Physical Review C, 108, L051604. https://doi.org/10.1103/PhysRevC.108.L051604
16. Liang, J.F., Allmond, J.M., Gross, C.J., Mueller, P. E., Shapira, D., Varner, R.L. (2016). Examining the role of transfer coupling in sub barrier fusion of 46,50Ti + 124Sn. Physical Review C, 94(2), 024616. https://doi.org/10.1103/PhysRevC.94.024616
17. Montagnoli, G., Stefanini, A.M. (2023). Recent experimental results in sub- and near-barrier heavy-ion fusion reactions (2nd ed.). European Physical Journal A, 59, 138. https://doi.org/10.1140/epja/s10050-023-01001-0
18. Morsad, A., Kolata, J.J., Tighe, R.J., Kong, X.J., Aguilera, E.F., Vega, J.J. (1990). Subbarrier fusion of 28,30Si with 24,26Mg. Physical Review C, 41(3), 988–994. https://doi.org/10.1103/PhysRevC.41.988
19. Raman, S., Nestor, C.W., Jr., Kahane, S., Bhatt, K.H. (1989). Predictions of B(E2; 01+→ 21+) values for even-even nuclei. Atomic Data and Nuclear Data Tables, 42(1), 1–54. https://doi.org/10.1016/0092-640X(89)90031-4
20. Rawitscher, G.H. (1974). Fusion reactions with a realistic optical potential and the incoming-wave boundary condition. Physical Review C, 9(6), 2210–2217. https://doi.org/10.1103/PhysRevC.9.2210
21. Santhosh, K.P., Jose, V.B. (2014). Heavy-ion fusion cross sections of weakly bound 9Be on 27Al, 64Zn and tightly bound 16O on 64Zn target using Coulomb and proximity potentials. Nuclear Physics A, 922, 191–199.
22. Singh, V., Lahiri, J., Roy Chowdhury, P., Basu, D.N. (2021). Hindrance in heavy-ion fusion for lighter systems of astrophysical interest. arXiv preprint arXiv:2107.09451. https://arxiv.org/abs/2107.09451
23. Spear, R.H. (1989). Reduced electric-octupole transition probabilities, B(E3;01+→ 31−), for even-even nuclides throughout the periodic table. Atomic Data and Nuclear Data Tables, 42(1), 55–104. https://doi.org/10.1016/0092-640X(89)90032-6
24. Stefanini, A.M., Bonamini, D., Tivelli, A., Montagnoli, G., Fortuna, G., Nagashima, Y., Beghini, S., Signorini, C., DeRosa, A., Inglima, G., Sandoli, M., Cardella, G., Rizzo, F. (1987). Strong energy dependence of the optical potential for 32S + 58,64Ni near the Coulomb barrier. Physical Review Letters, 59(12), 2852–2855. https://doi.org/10.1103/PhysRevLett.59.2852
25. Thompson, I.J., Nunes, F.M. (2009). Nuclear reactions for astrophysics: Principles, calculation and applications of low-energy reactions. Cambridge University Press.
26. URL–1, (2020). NRV Web Knowledge Base. Joint Institute for Nuclear Research – Low energy nuclear physics. http://nrv.jinr.ru/nrv/, 02.01.2020.
27. Vijay, N., Grover, N., Sharma, K., Gautam, M.S., Sharma, M.K., Chahal, R.P. (2022). Fusion fission analysis of 12C + 248Cm and 16O + 244Pu nuclear reactions across the Coulomb barrier. Physical Review C, 106, 064609. https://doi.org/10.1103/PhysRevC.106.064609
28. Wong, C.Y. (1973). Interaction barrier in charged-particle nuclear reactions. Physical Review Letters, 31(12), 766–769. https://doi.org/10.1103/PhysRevLett.31.766