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A systematic calculation of alpha decay half-lives of 347 nuclei is considered in the framework of the Wentzel–Kramers–Brillouin (WKB) approximation using two formulas. A recently proposed barrier penetration formula, with some modified parameters, is used first. Second, a new analytic barrier penetration formula is derived by taking into account the centrifugal potential. A good agreement with experimental data is achieved especially for spherical nuclei. The new formula reproduces experimental alpha decay half-lives with a satisfying accuracy especially for penetration energies much lower than the Coulomb barrier.

Based on the calculations of the shell and the residual pairing correction energies in the framework of Strutinskyʼs approach, we evaluated the proton and neutron magic numbers in the range 72 Z 282 and 96 N 540. New magic numbers and new islands of stability lie in a range defined by Greenʼs formula and the two-neutrons drip lines are presented. Our calculations reproduced known spherical double-magic nuclei and present evidences on new spherical double-magic nuclei in super-and ultraheavy regions.

The interaction potential for a deformed-spherical pair is calculated, and the error in using the truncated multipole expansion is evaluated for different numbers of terms of the expansion considered. It was found for the internal region of the nuclear part that three terms are sufficient, but for the surface and tail region up to five terms are necessary, while for the Coulomb potential three terms were found to be sufficient.In recent years, nuclear reactions involving deformed nuclei have become an important topic of research in nuclear physics ͓1͔. One type of these reactions is the fusion reaction, which is an important intermediate step in the production of superheavy nuclei by heavy ion collisions. The nuclear potential between the interacting nuclei plays an important role in describing the reaction process.A model that is commonly used in deriving a heavy ion ͑HI͒ potential is the double folding model ͓2͔. The basic input into the folding calculation is the nuclear densities of the colliding nuclei. If one or both have deformed density distribution, the use of this model to derive Coulomb or nuclear interaction potentials becomes very difficult, since the six-dimensional integral cannot be simplified to fewer dimensions. In this case, one usually simplifies the folding model by expanding the density distribution of the deformed nuclei using a multipole expansion ͓3͔. This method is useful and reduces the amount of calculation except in some cases, where the nucleon-nucleon ͑NN͒ force is density dependent.In the multipole expansion one may take a finite number of terms ͑usually three terms͒ and neglect the others ͓3͔. Since this method is used frequently in deriving the real part of the HI potential for deformed-deformed and spherical-deformed pairs of nuclei, it is interesting to test its accuracy. In the present paper, we estimate the accuracy of the multipole expansion in deriving the heavy ion potential. We include both quadrupole and hexadecapole deformation parameters, and determine the number of terms in the multipole expansion needed to guarantee a very small percentage error.We limit ourselves here to the interaction potential between deformed target and spherical projectile ͑see Fig. 1͒. The HI potential in this model is divided into a direct part U d , and an exchange part U ex ,They are stated in Refs. ͓2͔ and ͓3͔ as follows:where R is the separation distance between the interacting nuclei, and ␤ is the relative orientation angle of the target nucleus symmetry axis measured with respect to the separation vector R.The deformed density T (r,) has the formwhere R() is the half density radius expressed by the relation R͑ ͒ϭR o ͓1ϩ␦ 2 Y 20 ͑ ͒ϩ␦ 4 Y 40 ͑ ͔͒. ͑5͒ ␦ 2 and ␦ 4 are the quadrupole and hexadecapole deformation parameters. The multipole expansion of the target nuclear density distribution has the form T ͑ r͒ϭ ͚ lm lm ͑ r ͒Y lm ͑ ,͒, ͑6͒FIG. 1. The coordinate system.

The interaction potential for a deformed-spherical pair of nuclei is calculated using the folding model derived from different range nucleon-nucleon (NN) interactions. Five spherical projectiles of different mass numbers scattered on the 238 U deformed target are considered. The error in the heavy ion (HI) potential by using the truncated multipole density expansion is evaluated for each case. We find systematic trends of the percentage error in the HI potential depending on the number of multipoles considered; this percentage decreases if the mass number of the projectile or the range of the NN force increases, and it becomes smaller for small values of the separation distance between two nuclei or when higher deformation parameters vanish. The maximum error in using the truncated density expansion is estimated in the case of two deformed interacting nuclei.

An improved semi-analytic approach to the barrier penetration probability is developed in the frame work of the Wentzel-Kramers-Brillouin (WKB) approximation. It is used to calculate decay half-lives and preformation probabilities for a set of 304 cluster emitters in the range 87 ≤ Z ≤ 96 and a set of 390 α-emitters in the range 52 ≤ Z ≤ 120. For cluster decay, the validity of our approach is tested against Coulomb and proximity potential model (CPPM) by comparing decay half-lives and barrier penetration probabilities. Our results are found to be in a good agreement with CPPM calculations and with the available experimental data. In case of α-decay, our calculations are tested against the experimental data and also a very good agreement is achieved. In both cases, results are also compared with calculations of some other well known universal decay laws that are used in many recent studies. Our approach shows a better agreement with experimental data than most of the other models. Our study is extended to calculate the assault frequency and preformation probability of the cluster inside the parent nucleus. A strong correlation is obtained for all these parameters with each other. Neutron shell closures are found to be more important in the cluster decay process than proton shell closure. It is also noted that the odd–even staggering behavior dominates the decay processes involving the emission of clusters with odd neutron number.

An improved semi-analytic approach for the barrier penetration probability is developed in the framework of the Wentzel–Kramers–Brillouin approximation. It is used to calculate the α-decay half-life, assault frequency and α-preformation probability for many radioactive nuclei in the range Z = 52–99. Calculations are also extended to the super heavy region with Z = 100–120. Results are compared with the experimental data and some other recent studies. This approach achieves a better agreement with the experimental data than many other models. A strong correlation is found between the experimental decay half-life and the calculated penetration probability, assault frequency and preformation probability. Therefore, this approach achieves both reasonable accuracy and good consistency with the expected nuclear physical observations.