Systematic of alpha decay half-lives: role of quantization condition

Publication: Canadian Journal of Physics
6 January 2021


Using the semiclassical WKB method and considering the WKB quantization condition, the alpha decay half-lives of 420 alpha emitters were calculated with eight forms of the proximity and Woods–Saxon type potentials. The effect of quantization condition on the nuclear potential, effective potential, assault frequency, tunneling probability, alpha decay half-life, and root mean square deviation between theory and the experiment were investigated. Significant differences between calculated half-lives with and without inclusion of the quantization condition were observed specially for proximity potentials. By including the quantization, the Woods–Saxon potential was found as the best potential for even–even, even–odd, odd–even, odd–odd, and all alpha emitters. The quantization condition normalized the nuclear potentials. Therefore, by considering this condition, the thirteen forms of the prox77 potential with different sets of the surface energy and surface asymmetry constants gave the same results. This result was justified with two sets of parameters.


Utilisant la méthode semi-classique WKB et considérant la condition de quantification de WKB, les demi-vies de désintégration de 420 émetteurs alpha sont calculées avec huit variations des potentiels de proximité et de Woods-Saxon. Nous examinons l’effet de la condition de quantification sur le potentiel nucléaire, le potentiel effectif, la fréquence des assauts sur la barrière, la probabilité d’effet tunnel, la demi-vie de désintégration alpha et la déviation moyenne quadratique (rms) entre la théorie et l’expérience. Nous observons des différences significatives entre les valeurs de demi-vie calculées avec et sans la condition de quantification, spécialement pour le potentiel de proximité. En incluant la quantification, nous trouvons que le potentiel de Woods-Saxon est le meilleur potentiel pour les noyaux pair-pair, impair-pair, pair-impair, impair-impair et tous les émetteurs alpha. La condition de quantification normalise les potentiels nucléaires. Tenant compte de cette condition, les treize formes du potentiel prox77 avec différents ensembles de constantes d’énergie et d’asymétrie de surface donnent les mêmes résultats. Cette conclusion est vérifiée avec deux ensembles de paramètres. [Traduit par la Rédaction]

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Published In

cover image Canadian Journal of Physics
Canadian Journal of Physics
Volume 99Number 1January 2021
Pages: 24 - 32


Received: 22 October 2019
Accepted: 3 April 2020
Published online: 6 January 2021


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Key Words

  1. nuclear potential
  2. alpha decay
  3. WKB
  4. quantization condition


  1. potentiel nucléaire
  2. désintégration alpha
  3. WKB
  4. condition de quantification
  5. demi-vie



M. Hosseini-Tabatabaei
Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran.
Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran.
V. Dehghani
Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran.


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