{"title":"The Aspects of \\(^{12}\\textrm{C}(p, \\gamma )^{13}\\textrm{N}\\) Reaction in Astrophysical Regime","authors":"Soumya Saha","doi":"10.1007/s13538-025-01745-6","DOIUrl":null,"url":null,"abstract":"<div><p>The carbon-nitrogen-oxygen (CNO) cycle is fundamental to the process of hydrogen burning in stars, serving as a pivotal mechanism. At its core, the primary reaction involves the radiative capture of a proton by <span>\\( ^{12}\\textrm{C} \\)</span>, which crucially influences the isotopic ratio of <span>\\( ^{12}\\textrm{C} \\)</span> to <span>\\( ^{13}\\textrm{C} \\)</span> observed in celestial bodies, including our Solar System. To address this, we applied the astrophysical <span>\\(R\\)</span>-matrix approach to extrapolate low-energy cross sections and S-factors, thereby improving the precision of nuclear reaction rates. At a proton energy of around 25 keV (C.M. system), the extrapolated value of the astrophysical S-factor is determined to be <span>\\( 1.34 \\pm 0.10 \\, \\mathrm {keV \\, barn} \\)</span>. Our investigation sheds light on its implications for nuclear reaction rates, suggesting that at low temperatures in hydrogen-burning sites, the conversion of <span>\\( ^{12}\\textrm{C} \\)</span> to <span>\\( ^{13}\\textrm{C} \\)</span> via proton capture is relatively slow, thereby influencing the abundance ratios in the cosmic environment. This slow conversion affects stellar nucleosynthesis and isotopic evolution, particularly in low-mass stars <span>\\((M \\le 2 \\, M_\\odot )\\)</span> where hydrogen burning proceeds at relatively low temperatures. Unlike previous analyses with large uncertainties at low energies, our approach refines the S-factor determination by incorporating improved ANC (Asymptotic Normalization Constant) values, reducing extrapolation uncertainties.</p></div>","PeriodicalId":499,"journal":{"name":"Brazilian Journal of Physics","volume":"55 3","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s13538-025-01745-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The carbon-nitrogen-oxygen (CNO) cycle is fundamental to the process of hydrogen burning in stars, serving as a pivotal mechanism. At its core, the primary reaction involves the radiative capture of a proton by \( ^{12}\textrm{C} \), which crucially influences the isotopic ratio of \( ^{12}\textrm{C} \) to \( ^{13}\textrm{C} \) observed in celestial bodies, including our Solar System. To address this, we applied the astrophysical \(R\)-matrix approach to extrapolate low-energy cross sections and S-factors, thereby improving the precision of nuclear reaction rates. At a proton energy of around 25 keV (C.M. system), the extrapolated value of the astrophysical S-factor is determined to be \( 1.34 \pm 0.10 \, \mathrm {keV \, barn} \). Our investigation sheds light on its implications for nuclear reaction rates, suggesting that at low temperatures in hydrogen-burning sites, the conversion of \( ^{12}\textrm{C} \) to \( ^{13}\textrm{C} \) via proton capture is relatively slow, thereby influencing the abundance ratios in the cosmic environment. This slow conversion affects stellar nucleosynthesis and isotopic evolution, particularly in low-mass stars \((M \le 2 \, M_\odot )\) where hydrogen burning proceeds at relatively low temperatures. Unlike previous analyses with large uncertainties at low energies, our approach refines the S-factor determination by incorporating improved ANC (Asymptotic Normalization Constant) values, reducing extrapolation uncertainties.
期刊介绍:
The Brazilian Journal of Physics is a peer-reviewed international journal published by the Brazilian Physical Society (SBF). The journal publishes new and original research results from all areas of physics, obtained in Brazil and from anywhere else in the world. Contents include theoretical, practical and experimental papers as well as high-quality review papers. Submissions should follow the generally accepted structure for journal articles with basic elements: title, abstract, introduction, results, conclusions, and references.