Issue 
EPJ Nuclear Sci. Technol.
Volume 4, 2018



Article Number  5  
Number of page(s)  6  
DOI  https://doi.org/10.1051/epjn/2018001  
Published online  09 April 2018 
https://doi.org/10.1051/epjn/2018001
Regular Article
αdecay halflives of some nuclei from ground state to ground state using different nuclear potential
^{1}
Akre Computer Institute Ministry of Education,
Kurdistan, Iraq
^{2}
Becquereal Institute for Radiation Research and Measurements,
Erbil,
Kurdistan, Iraq
^{*} email: akrawy85@gmail.com
Received:
12
July
2017
Received in final form:
19
November
2017
Accepted:
16
January
2018
Published online: 9 April 2018
Theoretical αdecay halflives of some nuclei from ground state to ground state are calculated using different nuclear potential model including Coulomb proximity potential (CPPM), Royer proximity potential and Broglia and Winther 1991. The calculated values comparing with experimental data, it is observed that the CPPM model is in good agreement with the experimental data.
© D.T. Akrawy, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
George Gamow interpreted the theory of alpha decay in terms of the quantum tunneling from the potential well of the nucleus [1]. There are many theoretical schemes that used to define α cluster radioactivity and alphalike models using various ideas such as the groundstate energy, nuclear spin and parity, nuclear deformation and shell effects [2–14]. Frequently used models include the fissionlike [15], generalized liquid drop [16], generalized density dependent cluster [17], unified model for α decay and α capture [18], Coulomb and proximity potential [19] and unified fission [20]. These models, with their own merits and failures, have been in acceptable agreement with the experimental data [21,22]. Spontaneous fission and cluster radioactivity were studied in 1980 by Sandulescu, Poenaru, and Greiner [23] based on the quantum mechanical fragmentation theory. Rose and Jones experimentally observed the radioactive decay of ^{223}Ra by emitting ^{14}C in mid 1980s [24,25]. Recently, the concept of heavyparticle radioactivity is further explored by Poenaru et al. [26]. Hassanabadi et al. considered the alphadecay halflives for the even–even nuclei from ^{178}Po to ^{238}U and derived the decay constant [27]. Also the halflife for the emission of various clusters from even–even isotopes of barium in the ground and excited states were studied using the Coulomb and proximity potential model by Santhosh et al. [28]. Also, there are many efficient and useful empirical formulas to calculate alpha decay halflives which are given in reference [29–32]. In this study we used three different nuclear potential including Coulomb proximity potential (CPPM), Royer proximity potential (RPP) and Broglia and Winther 1991 model (BW91). From those models we calculated alpha decay halflives for 57 nuclei that have Z = 67–91, from ground state to ground state, the root mean square (RMS) deviation was evaluated, and the results are compared with experimental data.
2 Formalism of αdecay
According to one dimensional WKB approximation, the barrier penetration P is given by [33], where a, b are tunneling point of integral which are given as V(a) = V(b) = Q. The interaction potential for two spherical nuclei is given by [34], (2)where the first term represents the Coulomb potential with Z_{1} and Z_{2} are the atomic numbers of parent and daughter nuclei, the second term is nuclear potential and the final term is centrifugal potential which dependent on the angular momentum ℓ_{,} and reduced mass of nuclei µ. The halflife of alpha decay can be calculated as [35] (3)where , is frequency of collision with barrier per second, E is the empirical vibration energy, is given as [36] (4)where Q is the energy released [37], and A_{2} the mass number of αparticle. By substitution value of E and P in equation (3) determines the halflives.
In this section, we present the details of three nuclear potential models used for the calculation of αdecay halflives. When two surfaces approach each other within a distance of 2–3 fm, additional force due to the proximity of the surface is labeled as proximity potential [38]. In this section we discuss each model in details.
2.1 Coulomb and proximity potential model (CPPM)
The proximity potential is considered as [39], (5) where Z_{1} and Z_{2} are the atomic numbers of parent and daughter nuclei, z is the distance between the near surfaces of the fragments, and the nuclear surface tension coefficient is given as, (6)where A, Z and N represent mass, proton and neutron numbers of parent nuclei, respectively, and r is the distance between fragment centers and is given as r = z + C_{1} + C_{2}, and C_{1}, C_{2} are the Susmann central radii of fragments are given as: (7)
ϕ is the universal proximity potential which is given by [40] (8) (9) where ϵ = z/b, is the overlap distance in unit of b where the width of the nuclear surface b ≈ 1 fm.
The semiempirical formula for R_{i} in term of mass number is given as [41], (10)
2.2 Royer proximity potential model (RPPM)
For the α emission where the proximity energy between the two separated α particle and daughter nucleus plays the central role a very accurate formula has been obtained as [42] (11) where A is the mass of the parent nucleus and r the masscenter distance.
2.3 Broglia and Winther 1991 model (BW91)
Broglia and Winther derived a refined version of the BW91 potential by taking Woodsaxon potential with dependent condition of being appropriate with the value of the maximum nuclear force which is predicted by proximity potential model. This model reduced in [38,43] (12) (13) here a = 0.63 fm and (14)
Here the radius R_{i} has the form (15)
The surface energy coefficient γ has the form (16) where A, Z, and N are the total number for (p, d) parent and daughter, respectively, γ_{0} = 0.95 Mev/fm^{2} and k_{s} = 1.8.
3 Results and discussion
The αdecay halflives provided by the above nuclear potential models are presented in Table 1 which included CPPM, Royer proximity potential and BW91. The angular momentum l loaded by αdecay from ground state to ground state transition and obeys by the spinparity selection rule [44] (17) where Δ_{j} = j_{p} − j_{d}, j_{p}, π_{p} and j_{d}, π_{d} are the spin and parity value of parent and daughter, respectively. The relative superiority of the present choice of the potential can be as well seen in the in Table 1 where our results are reported for different potential models. The outcome of our study is presented in Figures 1–3. In Figure 1 to provide best view of the results, we have plotted logarithm αdecay halflives including CPPM, RPP, BW91 and experimental data vs. neutron number of parent nuclei, the figures shows the increasing disposal of logarithm halflive for decreasing neutron number of parent nuclei, also this figure refer the three models are more close to experimental data, which indicates to the agreeable of the results. The ΔT parameter is determined, which is representing the different between experimental halflive to theoretical, and reported in Figure 2; which indicated the ΔT of more isotopes is less than one; it seems that the results are more close to experimental data. We predict that the nuclei with higher neutron number a larger halflife and thence more stable. Figure 3 describes the relation between logarithm αdecay halflives vs. Qvalue, it shown that the logarithm αdecay decreases when Qvalue increases; it is in agreement with a larger Qvalue increases the instability. We calculated the RMS deviation which is defined as [45] (18)for present models which reported in Table 2; which indicate the CPPM model is best model to calculate αdecay halflife comparative with RPP and BW91 models.
Comparative study of αdecay halflives using three nuclear potential models included CPPM, RPPM and BW91.
Fig. 1 Logarithm αdecay halflive for CPPM, RPP, BW91 and experimental data vs. neutron number. 
Fig. 2 Logarithm αdecay halflive for CPPM, RPP, and BW91 vs. neutron number. 
Fig. 3 ΔT vs. neutron number. 
RMS deviation for CPPM, RPP and BW91 nuclear potential model.
4 Conclusion
Three different nuclear potential are used to calculate the αdecay halflives for some nuclei from ground state to ground state including CPPM, RPP and BW91. The angular momentums are taken into account. RMS deviations are calculated, it shows that the best nuclear potential is CPPM. The results are compared with experimental data; this comparison provides a reference how to select nuclear potential to calculate αdecay halflives.
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Cite this article as: Dashty T. Akrawy, αdecay halflives of some nuclei from ground state to ground state using different nuclear potential, EPJ Nuclear Sci. Technol. 4, 5 (2018)
All Tables
Comparative study of αdecay halflives using three nuclear potential models included CPPM, RPPM and BW91.
All Figures
Fig. 1 Logarithm αdecay halflive for CPPM, RPP, BW91 and experimental data vs. neutron number. 

In the text 
Fig. 2 Logarithm αdecay halflive for CPPM, RPP, and BW91 vs. neutron number. 

In the text 
Fig. 3 ΔT vs. neutron number. 

In the text 
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