Abstract
With the discovery of a large number of superheavy nuclei undergoing decay through α emissions, there has been a revival of interest in α decay in recent years. In the theoretical study of α decay the α-nucleus potential, which is the basic input in the study of α-nucleus systems, is also being studied using advanced theoretical methods. In the light of these, the Wentzel–Kramers–Brillouin (WKB) approximation method often used for the study of α decay is critically examined and its limitations are pointed out. At a given energy, the WKB expression uses barrier penetration formula for the determination of the transmission coefficient. This approach utilizes the α-nucleus potential only at the barrier region and ignores it elsewhere. In the present era, when one has more precise experimental information on decay parameters and better understanding of α-nucleus potential, it is desirable to use a more precise method for the calculation of decay parameters. We describe the analytic S-matrix (SM) method which gives a procedure for the calculation of decay energy and mean life in an integrated way by evaluating the resonance pole of the S-matrix in the complex momentum or energy plane. We make an illustrative comparative study of WKB and S-matrix methods for the determination of decay parameters in a number of superheavy nuclei.
Similar content being viewed by others
References
Z Gamov, Z. Phys. 51, 204 (1928)
G Munzenberg, J. Phys. G: Nucl. Part. Phys. 25, 717 (1999)
S Hoffman and G Munzenberg, Rev. Mod. Phys. 72, 733 (2000)
Yu Ts Oganessian, Nucl. Phys. A 685, 17c (2001)
L I Schiff, Quantum mechanics 3rd ed. (Mc Graw Hill, New York, 1968)
S Flugge, Practical quantum mechanics (Springer, Berlin, 1994) Vol. 1
N Froman and P Froman, JWKB approximation: Contribution to theory (North Holland, Amsterdam, 1965)
S Mahadevan, Analytical S-matrix approach for the study of α decay of super heavy elements, Ph.D. Thesis (Amrita Vishwa Vidyapeetham, 2009) P Prema, S Mahadevan, C S Shastry, A Bhagawat and Y K Gambhir, Int. J. Mod. Phys. E 17, 611 (2008)
R G Newton, Scattering theory of waves and particles (McGraw Hill, New York, 1966)
C J Jochain, Quantum collision theory (North Holland Publishing Company, Amsterdam, 1965)
R J Eden, P V Landshoff, D Lolive and J C Polkinghome, The analytic S matrix (Cambridge University Press, Cambridge, 2002)
S Mukherjee and C S Shastry, Nucl. Phys. B 3, 1 (1967)
Y K Gambhir, P Ring and A Thimet, Ann. Phys. (N.Y.) 198, 132 (1990)
G A Lalazissis, M M Sharma, P Ring and Y K Gambhir, Nucl. Phys. A 608, 202 (1996)
G A Lalazissis, J Konig and P Ring, Phys. Rev. C 55, 549 (1997)
Y K Gambhir, A Bhagawat, M Gupta and Arun K Jain, Phys. Rev. C 68, 044316 (2003)
Y K Gambhir, A Bhagwat and M Gupta, Phys. Rev. C 71, 037301 (2005); Ann. Phys. (N.Y.) 320, 429 (2005)
P Prema, S Mahadevan, C S Shastry and Y K Gambhir, Int. J. Mod. Phys. E 19, 2033 (2010)
S Mahadevan, P Prema and C S Shastry, Phys. Rev. C 74, 57601-1-4 (2006)
D Ni and Z Ren, Phys. Rev. C 80, 014314 (2009); Phys. Rev. C 82, 024311 (2010)
B Sahu, R Paira and B Rath, NPA 908, 40 (2013)
B Sahu, Phys. Rev. C 85, 057601 (2012)
Acknowledgements
The authors thank Prof. Y K Gambhir and Prof. A Bhagawat for providing RMF-based potentials and Dr P Prema for her assistance in the preparation of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
SHASTRY, C.S., MAHADEVAN, S. & ADITYA, K. Unified approach to alpha decay calculations. Pramana - J Phys 82, 867–878 (2014). https://doi.org/10.1007/s12043-014-0740-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-014-0740-7