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Home , CNO cycle

128 EPJ Web of Conferences , 01005 (2016) DOI: 10.1051/epjconf/201612801005 TESNAT 2016

 γ   α            

Eyyup Tel1, Muhittin Sahan1, Ismail Hakki Sarpun2 , Sureyya Gulistan Okur1

1Osmaniye Korkut Ata University, Faculty of Arts and Science, Department of Physics, Osmaniye, Turkey 2 Afyon Kocatepe University, Faculty of Arts and Sciences, Department of Physics, Afyonkarahisar, Turkey

Abstract. In Knowledge of the -proton (p-p) chain and CNO cycle are required for the evolution of during the early formation of the universe. In this study, we summarized the excitation functions of (p,γ) and (p,α) reactions for 7Be(p,γ)8B, 12C(p,γ)13N, 13C(p,γ)14N, 14N(p,γ)15O and 15N(p,α)15O in p-p chain and CNO cycle using EMPIRE and TALYS computer up to 10 MeV. The calculated data on cross sections in -burning stars were compared with theoretical TENDL-2014 and ENDF/B-VII data from EXFOR. The calculation results show closed agreement between the calculations and the data from literature.

    convert hydrogen to is the dominant source of energy in more massive stars [5]. Animals, plants, soil, air, planets, stars like everything The p-p fusion is the nuclear fusion process which formed by the basic blocks of matter called atoms. After the and other stars which have core the big bang, approximately 13.7 billion years ago, a temperatures less than 15×106 K and a reaction cycle at large part of atoms formed in the early formation of the energy of 25 MeV. The p-p chains occur under lower universe and came unchanged until the present day. temperature than the -- cycle. The Since the universe includes everything from subatomic pp chain in stars like our Sun divides into three main particles to galaxies, from planets to stars, it is needed to branches, called as the ppI, ppII and ppIII chains. These be explored in detailed. are given Eq. 1-3. According to Eq. 1, in the proton- All stars are born from collapsing clouds of gas and proton fusion reaction inside stars like the sun, the first dust the interstellar medium (ISM). During their lives, step in ppI process is the collision of two (p or they deposit energy into the ISM in the form of 1H) to make an atom of heavy hydrogen (2H). The electromagnetic radiation and stellar winds. When they second step containing the weak interaction involves the die, they return some of their matter and energy back collision of a 2H nuclei with a proton to make a nucleus into the ISM. The life time of stars range from a few of 3He, and then is emitted having very high million years for the most massive to trillions of years energy. In the final third step, a normal 4He nucleus are for the least massive [1-3]. created with combining two 3He nuclei and two extra The amount of H and He elements in the universe protons (21H) are released to start the whole process are approximately 73% and 25% of the mass, again. Inside the Sun, about 655×106 tons of H are respectively. After H and He, C, N and O elements are converted into 650×106 tons of 4He every second. In the most abundant elements in the Universe. Energy stars heavier than about 2 solar masses, in which the core production in massive stars is governed by the CNO temperature is more than about 18×106 K, the dominant cycles throughout most of their lifetimes [4]. Hydrogen process in which energy is produced by the fusion of and helium elements having low-mass were produced in hydrogen into helium is a different reaction chain known the hot and dense conditions of the birth of the universe as the carbon-nitrogen cycle. The former case is the last itself. The life of stars is described in terms of of the ppI chain, whereas the latter reaction reactions. leads into either the ppII or the ppIII chain, as given Eq. The Hydrogen burning mechanism is essentially the 2-3. nuclear fusion of four protons into one 4He nucleus. The second process of stable hydrogen burning There are two reaction chains that can convert hydrogen reaction in stars is the CNO cycle, dominates from to helium, namely the proton–proton (or pp chain) chain, 20×106K to 130×106K. This cycle for more massive also called pp reaction, and the CNO cycle. The pp chain than the Sun converts hydrogen to helium according to is more important in stars the mass of the Sun or less and the following sequence of reactions in Eq. 4. The CNO stars of similar mass The CNO cycle by which stars cycle occurs from the following steps. After 12C element captures a proton, 13N is produced and gamma-ray is

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). 128 EPJ Web of Conferences , 01005 (2016) DOI: 10.1051/epjconf/201612801005 TESNAT 2016

emitted. 13N is unstable and decays to the 13C with a Our results from calculations are given Figure 1-5. half-life of about 10 minutes. The 13C captures a Theoretical calculated cross sections of 7Be(p,γ) reaction proton and a gamma-ray is emitted to become 14N in ppIII chain between 0-10 MeV is shown in the Fig. 1. isotope. 14N isotope captures a proton and a gamma-ray This reaction’s cross section data obtained from is emitted to become 15O. 15O isotope undergoes a β+ EMPIRE and ENDF that shows to us increasing values decay to become 15N. Finally, 15N isotope captures a with 0.75-5 MeV energy ranges. However, in spite of proton and then it emits a 4He to close the cycle and increasing these values, reaction cross section value from return to 12C. TALYS was a pick at about 5 MeV energy. At the same ppI chain: time, the data from EMPIRE and TALYS computer code, and also ENDF systems have showed increasing 1H +1H→2H + e+ +ν 1 1 1 e values in the 6.5 MeV with 10 MeV energy range. 2H +1H→ 3He + γ (1) 1 1 2 3He+ 3He→ 4He + 1H 2 2 2 21 ppII chain:

3He+ 4He→ 7Be + γ 2 2 4 7 Be + e− → 7Li +ν (2) 4 3 e 7 Li+ 1H → 4He 3 1 22 ppIII chain:

3He+ 4He→ 7Be + γ 2 2 4 7Be+ 1H → 8B + γ 4 1 5 (3) 8Be→ 8Be + e+ +ν 5 4 e 8Be → 4He 7 γ 4 22 Fig. 1. Theoretical cross sections calculation of Be(p, ) reaction up to 10 MeV. CNO Cycle Reaction cross section of 12C(p,g) accruing in the 12C+ 1H →13N + γ 6 1 7 CNO cycle is given in Fig. 2. As seen from Fig. 2, 13N→13C + e+ +ν ENDF and TALYS theoretical data are in harmony 7 6 e between 2 and 5 MeV. The data from EMPIRE also 13C+ 1H →14N + γ 6 1 7 (4) joins at this harmony between 3 and 5 MeV. Only one 14N+ 1H →15O + γ experimental data of Burtebaev [9] could be found from 7 1 6 EXFOR in literature at approximately 4.27 MeV. This 15O→15N + e+ +ν 6 7 e data is closed agreement with ENDF at around 4 MeV. 15N+ 1H →12C + 4He 7 1 6 2

TALYS computer code system in the from 1 keV to 1 GeV energy range [6] and EMPIRE computer code over from keV up to few hundred MeV energy range [7] have been widely used in order to calculate nuclear reactions. In this study, in order to calculated the excitation functions of (p,γ) and (p,α) cross section for some reactions 15O in pp chain and CNO cycle, we used EMPIRE and TALYS computer up to 10 MeV. Results were compared with theoretical TENDL-2014 and ENDF/B-VII data from EXFOR [8].

2 Results and Discussions Fig. 2. Theoretical cross sections calculation of 12C(p,γ) In this study, in order to calculated the excitation reaction up to 10 MeV. α functions of (p,γ) and (p, ) cross section for some 12 7 12 13 15 Reaction cross section of C(p,γ) in the CNO cycle reactions such as Be(p,γ), C(p,γ), C(p,γ), N(p,a), 13 14N(p,γ) in pp chain and CNO cycle, we used two is given in Fig. 3. When C(p,g) reaction was analyzed, computer code systems called as TALYS-1.6 [6], while it can be seen disharmony between EMPIRE, EMPIRE-3.2.2-Malta [7] up to 10 MeV. Results were TALYS, and ENDF computer data up to 2.5 MeV, there compared with theoretical TENDL-2014 and ENDF/B- is a good harmony over 2.5 MeV. Also, while the line VII data from EXFOR from EXFOR library [8]. from EMPIRE decreases up to 2.5 MeV, the line from

2 128 EPJ Web of Conferences , 01005 (2016) DOI: 10.1051/epjconf/201612801005 TESNAT 2016

TALYS increases. There is no experimental data for    12C(p,g) reaction from literature. The fourth reaction 14 cross section in the CNO cycle is N(p,γ) given in Fig. We know that it is necessary hydrogen burning to be 4. It can be seen from Figure 4, EMPIRE line decreases able to start the nuclear fusion of four protons into one up to about 5 MeV while TALYS and ENDF lines 4He nucleus in stars. In this work, (p,γ) and (p,γ) cross increase. All cross sections data are approximately the section reactions for 7Be, 13C, 15N, and 14N nuclei in pp same values between 5-10 MeV. The fifth and final chain and CNO cycle in stars were calculated in the reaction cross section calculation in the CNO cycle is energy range from 0 to 10 MeV using TALYS 1.6 [7] 15 N(p,α) as given in Fig. 5. For three lines, it can be seen and EMPIRE-3.2.2 [8] computer codes. Since these that there is a good relation from 0 to 10 MeV. All cross reactions in pp chain and CNO cycle occur in low section data have a rising trend up to about 5 MeV but energies, it is difficult to calculate cross sections in these having a stable and constant values after 5 MeV. nuclei. We were able to calculated only five limited elements in in pp chain and CNO cycle. We suggest that we can achieve better results when added resonance effects or resonance parameters in nuclear code calculating programs. This work is supported by the Coordinator ship of Osmaniye Korkut Ata University’s Scientific Research Office (BAP) Contract No. OKÜBAP-2015-PT3-011. The authors would like to thank to Prof.Dr. Arjan Koning for supporting TALYS program code.

  

1. K. M. Ferriere, Rev. Mod. Phys., 73, 1031 (2001) 2. Reynolds R. J., Science, 277, 1446 (1997) Fig. 3. Theoretical cross sections calculation of 13C(p,γ) 3. M.Sahan, et al., Chin. J. . & Astrophys. 5, reaction up to 10 MeV. 211 (2005). 4. N. Przybilla, et al., and Astrophysics 517, A38 (2010). 5. M.C. Santi, Evolution of stars and stellar populations, Wiley (2005). 6. A. Koning, S. Hilaire, S. Goriely, TALYS-1.6-A Nuclear Reaction Program, User Manual, 1st edition NRG, The Netherlands, (2013). 7. M. Herman et al., EMPIRE-3.2 Malta code, User's Manual. http://www.nndc.bnl.gov/empire (2013). 8. Experimental Nuclear Reaction Data (2015), 9. N.Burtebaev, et al., Phys. Rev. C 78, 035802 – Published 11 September (2008)

Fig. 4. Theoretical cross sections calculation of 14N(p,γ) reaction up to 10 MeV.

Fig. 5. Theoretical cross sections calculation of 15N(p,α) reaction up to 10 MeV.

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