Analysis of β+ decay of 13N nucleus using a modified one-particle approach

Publication: Canadian Journal of Physics
24 August 2020


It is known that the calculated values of log(ft) and the half-life of beta decay are less than the measured values when a single-particle approach is used to calculate these quantities. In this article, we discuss the importance of taking into account the spectroscopic factor in the calculation of the half-life and log(ft) beta decay of nuclei containing one nucleon in the outermost shell. We also emphasize the dominant role of the asymptotic normalization coefficient, which takes into account the many-particle effect and allows us to obtain the spectroscopic factor necessary to describe the reaction 13N → 13C + β+ + νe. We find the asymptotic normalization coefficients using the experimental data of the elastic scattering phase-shift of the proton and neutron on 12C. Using overlap functions instead of single-particle functions, we obtain a better comparison with the experimental data. The overlap function is represented as the product of the single-particle function and the root of the corresponding spectroscopic factor.


On sait généralement que les valeurs calculées de log(ft) et de la demi-vie de la désintégration bêta sont moindres que les valeurs mesurées lorsque le calcul est fait en utilisant une approche à une particule. Dans cet article, nous discutons l’importance de tenir compte du facteur spectroscopique des noyaux contenant un seul nucléon dans la couche extérieure. Nous soulignons aussi le rôle dominant du coefficient de normalisation asymptotique qui tient compte des effets à plusieurs corps et nous permet d’obtenir le facteur spectroscopique nécessaire pour décrire la réaction 13N → 13C + β+ + νe. Nous trouvons le coefficient de normalisation asymptotique en utilisant les données expérimentales de déphasage dans la diffusion élastique de protons et de neutrons sur 12C. L’usage des fonctions de recouvrement, au lieu des fonctions d’onde à une particule, nous permet d’obtenir une meilleure comparaison avec les données expérimentales. La fonction de recouvrement est représentée comme le produit de la fonction d’onde à une particule avec la racine carrée du facteur spectroscopique. [Traduit par la Rédaction]

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Published In

cover image Canadian Journal of Physics
Canadian Journal of Physics
Volume 99Number 3March 2021
Pages: 176 - 184


Received: 19 March 2020
Accepted: 13 August 2020
Published online: 24 August 2020


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Key Words

  1. CNO cycle
  2. β+ decay
  3. asymptotic normalization coefficient
  4. spectroscopic factor
  5. potential model


  1. cycle CNO
  2. désintégration β+
  3. coefficient de normalisation asymptotique
  4. facteur spectroscopique
  5. modèle de potentiel



Bakhadir F. Irgaziev
GIK Institute of Engineering Sciences & Technology, Topi, Khyber Pakhtunkhwa, 23640, Pakistan.
Jameel-Un Nabi
GIK Institute of Engineering Sciences & Technology, Topi, Khyber Pakhtunkhwa, 23640, Pakistan.
GIK Institute of Engineering Sciences & Technology, Topi, Khyber Pakhtunkhwa, 23640, Pakistan.


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