SavedAdd your journal

Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 30 Sayı: 2

An ANC-Based Indirect Evaluation of the Direct-Capture Rate for Proton Capture on Silicon-26

Silisyum-26 Üzerinde Proton Yakalama İçin Doğrudan Yakalama Hızının ANC Temelli Dolaylı Değerlendirilmesi

Murat Dağ(AHİ EVRAN ÜNİVERSİTESİ)0000-0002-0503-6067
Robert Tribble(Texas A&M University)0009-0002-7694-8255
Pages
435–449
Publication Date
2026-08-25
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The deduced direct-capture rate is nearly a factor of two higher than the earlier estimate, although for T9 > 0.1 the total rate is mainly controlled by resonant capture through the lowest excited state of 27P.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Radiative proton capture on 26Si, leading to the formation of 27P, is relevant to explosive hydrogen-burning nucleosynthesis because it affects the depletion pathway of 26Al.
📊
Key Findings & Data:The short lifetime of 26Si, together with the very small cross sections expected in the stellar energy region, makes a direct determination of this rate experimentally difficult.
💡
Conclusion & Impact:The deduced direct-capture rate is nearly a factor of two higher than the earlier estimate, although for T9 > 0.1 the total rate is mainly controlled by resonant capture through the lowest excited state of 27P.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Silisyum-26 · asimptotik normalizasyon katsayısı · ayna çekirdek sistemi

Abstract

Radiative proton capture on 26Si, leading to the formation of 27P, is relevant to explosive hydrogen-burning nucleosynthesis because it affects the depletion pathway of 26Al. The short lifetime of 26Si, together with the very small cross sections expected in the stellar energy region, makes a direct determination of this rate experimentally difficult. For this reason, the reaction was constrained indirectly through the ANC, using the mirror neutron system associated with 26Mg and 27Mg. Measurements of the ²⁶Mg elastic-scattering channel on ¹³C and the neutron-pickup channel populating ²⁷Mg were carried out with the MDM spectrometer and its focal-plane detector system. The analysis gave a neutron ANC of C²s1/2(27Mg) = 29.19 ± 3.94 fm−1 for the ground state of 27Mg. By applying mirror symmetry, the corresponding proton ANC for 27P was obtained as C²s1/2(27P) = 1126 ± 152 fm−1, with a spectroscopic factor of 0.64 ± 0.09. RADCAP calculations then gave a zero-energy astrophysical S-factor of S(0) = (5.6 ± 0.8) × 10−2 MeV b for the direct-capture component. The deduced direct-capture rate is nearly a factor of two higher than the earlier estimate, although for T9 > 0.1 the total rate is mainly controlled by resonant capture through the lowest excited state of 27P.

Özet

²⁶Si üzerinde gerçekleşen radyatif proton yakalama reaksiyonu sonucunda ²⁷P oluşumu, ²⁶Al’nin tükenme yolunu etkilediği için patlayıcı hidrojen yanması nükleosentezi açısından önemlidir. ²⁶Si’nin kısa ömürlü olması ve yıldızsal enerji bölgesinde beklenen tesir kesitlerinin çok küçük olması, bu reaksiyon hızının doğrudan deneysel olarak belirlenmesini zorlaştırmaktadır. Bu nedenle reaksiyon, ²⁶Mg ve ²⁷Mg ile ilişkili ayna nötron sistemi kullanılarak ANC yöntemiyle dolaylı olarak sınırlandırılmıştır. ¹³C hedefi üzerinde ²⁶Mg elastik saçılma kanalı ve ²⁷Mg’yi besleyen nötron-kapma kanalı ölçümleri, MDM spektrometresi ve onun odak düzlemi dedektör sistemi ile gerçekleştirilmiştir. Analiz sonucunda ²⁷Mg’nin temel durumu için C²s1/2(²⁷Mg) = 29.19 ± 3.94 fm−1 nötron ANC değeri elde edilmiştir. Ayna simetrisi uygulanarak, ²⁷P için karşılık gelen proton ANC değeri C²s1/2(²⁷P) = 1126 ± 152 fm−1 olarak, spektroskopik faktör ise 0.64 ± 0.09 olarak belirlenmiştir. RADCAP hesaplamaları daha sonra doğrudan yakalama bileşeni için sıfır enerjide astrofiziksel S-faktörünü S(0) = (5.6 ± 0.8) × 10−2 MeV b olarak vermiştir. Elde edilen doğrudan yakalama reaksiyon hızı, önceki tahminden yaklaşık iki kat daha yüksektir; ancak T9 > 0.1 için toplam reaksiyon hızı esas olarak ²⁷P’nin en düşük uyarılmış durumu üzerinden gerçekleşen rezonans yakalama tarafından kontrol edilmektedir.

🔖

Cite This Article

Dağ, M., Tribble, R. (2026). An ANC-Based Indirect Evaluation of the Direct-Capture Rate for Proton Capture on Silicon-26. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 30 Sayı: 2, 435–449. https://doi.org/10.19113/sdufenbed.1947786

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (35)

  1. Iliadis, C. 2007. Nuclear Physics of Stars. Wiley-VCH, Weinheim, Germany, 680 p.
  2. Champagne, A. E., Wiescher, M. 1992. Explosive hydrogen burning. Annual Review of Nuclear and Particle Science, 42, 39–76.
  3. Smith, M. S., Rehm, K. E. 2001. Nuclear astrophysics measurements with radioactive beams. Annual Review of Nuclear and Particle Science, 51(1), 91–130.
  4. Tribble, R. E. 2005. Indirect techniques in nuclear astrophysics: The ANC method. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 241(1–4), 204–208.
  5. Tribble, R. E., Bertulani, C. A., La Cognata, M., Mukhamedzhanov, A. M., Spitaleri, C. 2014. Indirect techniques in nuclear astrophysics: a review. Reports on Progress in Physics, 77(10), 106901.
  6. Mukhamedzhanov, A. M., Gagliardi, C. A., Tribble, R. E. 2001. Asymptotic normalization coefficients, spectroscopic factors, and direct radiative capture rates. Physical Review C, 63(2), 024612.
  7. Gagliardi, C. A., Tribble, R. E., Azhari, A., Clark, H. L., Lui, Y.-W., Mukhamedzhanov, A. M., Sattarov, A., Trache, L., Burjan, V., Cejpek, J., Kroha, V., Piskoř, Š., Vincour, J. 1999. Tests of transfer reaction determinations of astrophysical S factors. Physical Review C, 59(2), 1149–1153.
  8. McCleskey, M., Mukhamedzhanov, A. M., Trache, L., Tribble, R. E., Banu, A., Eremenko, V., Goldberg, V. Z., Lui, Y.-W., McCleskey, E., Roeder, B. T., Spiridon, A., Carstoiu, F., Burjan, V., Hons, Z., Thompson, I. J. 2014. Determination of the asymptotic normalization coefficients for 14C+n↔15C, the 14C(n,γ)15C reaction rate, and evaluation of a new method to determine spectroscopic factors. Physical Review C, 89(4), 044605. [9] Al-Abdullah, T., Carstoiu, F., Chen, X., Clark, H. L., Gagliardi, C. A., Lui, Y.-W., Mukhamedzhanov, A. M., Tabacaru, G., Tokimoto, Y., Trache, L., Tribble, R. E., Zhai, Y. 2014. Astrophysical reaction rate for 17F(p,γ)18Ne from the transfer reaction 13C(17O,18O)12C. Physical Review C, 89(2), 025809.
  9. Mahoney, W. A., Ling, J. C., Jacobson, A. S., Lingenfelter, R. E. 1982. Diffuse galactic gamma-ray line emission from nucleosynthetic Fe-60, Al-26, and Na-22—Preliminary limits from HEAO 3. Astrophysical Journal, 262, 742–748.
  10. Diehl, R., Dupraz, C., Bennett, K., Bloemen, H., de Boer, H., Hermsen, W., Lichti, G. G., McConnell, M., Morris, D., Ryan, J., Schoenfelder, V., Steinle, H., Strong, A. W., Swanenburg, B. N., Varendorff, M., Winkler, C. 1994. COMPTEL observations of the 1.809 MeV gamma-ray line from galactic Al-26. The Astrophysical Journal Supplement Series, 92, 429–432.
  11. Diehl, R. 2006. Measuring 26Al and 60Fe in the Galaxy. New Astronomy Reviews, 50, 534–539.
  12. José, J., Coc, A., Hernanz, M. 1999. Nuclear uncertainties in the NeNa–MgAl cycles and production of 22Na and 26Al during nova outbursts. The Astrophysical Journal, 520, 347–360.
  13. Timofeyuk, N. K., Johnson, R. C., Mukhamedzhanov, A. M. 2003. Relation between proton and neutron asymptotic normalization coefficients for light mirror nuclei and its relevance to nuclear astrophysics. Physical Review Letters, 91(23), 232501.
  14. Timofeyuk, N. K., Descouvemont, P. 2005. Asymptotic normalization coefficients for mirror virtual nucleon decays in a microscopic cluster model. Physical Review C, 71(6), 064305.
  15. Herndl, H., Görres, J., Wiescher, M., Brown, B. A., Van Wormer, L. 1995. Proton capture reaction rates in the rp process. Physical Review C, 52(2), 1078–1094.
  16. Guo, B., Li, Z. H., Bai, X. X., Liu, W. P., Shu, N. C., Chen, Y. S. 2006. Determination of the astrophysical 26Si(p,γ)27P reaction rate from the asymptotic normalization coefficients of 27Mg→26Mg+n. Physical Review C, 73(4), 048801.
  17. Togano, Y., Gomi, T., Motobayashi, T., Ando, Y., Aoi, N., Baba, H., Demichi, K., Elekes, Z., Fukuda, N., Fülöp, Z., Futakami, U., Hasegawa, H., Higurashi, Y., Ieki, K., Imai, N., Ishihara, M., Ishikawa, K., Iwasa, N., Kanno, S., Kondo, Y., Kubo, T., Kubono, S., Kunibu, M., Kurita, K., Matsuyama, Y. U., Michimasa, S., Minemura, T., Miura, M., Murakami, H., Nakamura, T., Notani, M., Ota, S., Saito, A., Sakurai, H., Serata, M., Shimoura, S., Sugimoto, T., Takeshita, E., Takeuchi, S., Ue, K., Yamada, K., Yanagisawa, Y., Yoneda, K., Yoshida, A. 2005. Study of 26Si(p,γ)27P reaction using Coulomb dissociation method. Nuclear Physics A, 758, 182–185.
  18. Marganiec, J., Beceiro Novo, S., Typel, S., Langer, C., Wimmer, C., Alvarez-Pol, H., Aumann, T., Boretzky, K., et al. 2016. Coulomb dissociation of 27P at 500 MeV/u. Physical Review C, 93(4), 045811.
  19. D’Agata, G., Kilic, A. I., Burjan, V., Mrázek, J., Glagolev, V., Kroha, V., Guardo, G. L., La Cognata, M., Lamia, L., Palmerini, S., Pizzone, R. G., Rapisarda, G. G., Romano, S., Sergi, M. L., Spartà, R., Spitaleri, C., Siváček, I., Tumino, A. 2021. 26Si(p,γ)27P direct proton capture by means of the asymptotic normalization coefficients method for mirror nuclei. Physical Review C, 103(1), 015806.
  20. Sun, L. J., Xu, X. X., Hou, S. Q., Lin, C. J., José, J., Lee, J., He, J. J., Li, Z. H., Wang, J. S., Yuan, C. X., et al. 2020. Experimentally well-constrained masses of 27P and 27S: Implications for studies of explosive binary systems. Physics Letters B, 802, 135213.
  21. Mondal, A. K., Sharma, S. 2025. Re-evaluation of the 26Si(p,γ)27P astrophysical reaction rate. Nuclear Physics A, 1056, 123031.
  22. Dag, M. 2016. Determination of Astrophysical Direct Capture Reaction Rate for 26Si(p,γ)27P by Extracting the Asymptotic Normalization Coefficients in the Mirror Nuclear System. Ph.D. dissertation, Texas A&M University, College Station, Texas, USA, 112 p. Available at: https://hdl.handle.net/1969.1/159094
  23. Pringle, D. M., Catford, W. N., Winfield, J. S., Lewis, D. G., Jelley, N. A., Allen, K. W. 1986. The Oxford MDM-2 magnetic spectrometer. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 245, 230–247.
  24. Winfield, J. S., Pringle, D. M., Catford, W. N., Lewis, D. G., Jelley, N. A., Allen, K. W. 1986. Focal plane detector for the Oxford MDM-2 spectrometer. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 251, 297–306.
  25. Giomataris, Y., Rebourgeard, Ph., Robert, J. P., Charpak, G. 1996. MICROMEGAS: a high-granularity position-sensitive gaseous detector for high particle-flux environments. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 376, 29–35.
  26. Spiridon, A., Pollacco, E., Roeder, B. T., Saastamoinen, A., Chyzh, R., Dag, M., Tribble, R. E., Trache, L., Pascovici, G., De Oliveira, R. 2016. Upgrade of the TAMU MDM-focal plane detector with MicroMegas technology. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 376, 364–368.
  27. Kowalski, S., Enge, H. A. 1986. RAYTRACE User’s Manual. Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, May 1986.
  28. Tarasov, O. B., Bazin, D. 2016. LISE++: Exotic beam production with fragment separators and their design. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 376, 185–187.
  29. Woods, R. D., Saxon, D. S. 1954. Diffuse surface optical model for nucleon-nuclei scattering. Physical Review, 95(2), 577–578.
  30. Macfarlane, M. H., Pieper, S. C. 1978. PTOLEMY: A Program for Heavy-Ion Direct-Reaction Calculations. Argonne National Laboratory Report ANL-76-11, Rev. 1, Argonne, Illinois, USA.
  31. Jeukenne, J. P., Lejeune, A., Mahaux, C. 1977. Optical-model potential in finite nuclei from Reid’s hard-core interaction. Physical Review C, 16(1), 80–96.
  32. Thompson, I. J. 1988. Coupled reaction channels calculations in nuclear physics. Computer Physics Reports, 7(4), 167–212.
  33. Bertulani, C. A. 2003. RADCAP: A potential model tool for direct capture reactions. Computer Physics Communications, 156(1), 123–141.
  34. Caggiano, J. A., Bazin, D., Benenson, W., Davids, B., Ibbotson, R., Scheit, H., Sherrill, B. M., Steiner, M., Yurkon, J., Zeller, A. F., Blank, B., Chartier, M., Greene, J., Nolen, J. A. Jr., Wuosmaa, A. H., Bhattacharya, M., Garcia, A., Wiescher, M. 2001. Spectroscopy of 23Al and 27P using the (7Li,8He) reaction and the implications for 22Na and 26Al nucleosynthesis in explosive hydrogen burning. Physical Review C, 64(2), 025802.
  35. Audi, G., Wapstra, A. H., Thibault, C. 2003. The AME2003 atomic mass evaluation: (II). Tables, graphs and references. Nuclear Physics A, 729(1), 337–676.