J. Nucl. Phys. Mat. Sci. Rad. A. Vol. 8, No. 1 (2020), pp.55–63 Journal of Nuclear Physics, Material Sciences, Radiation and Applications Journal homepage: https://jnp.chitkara.edu.in/ Cluster Radioactivity in Super-Heavy Nuclei 299-306122 H.C. Manjunatha1 , S. Alfred Cecil Raj2 , A.M. Nagaraja1,2 and N. Sowmya1,3 1Department of Physics, Government College for Women, Kolar-563101, Karnataka, India 2Department of Physics, St. Joseph’s College, Tiruchirapalli-620002, Tamilnadu, India 3Deptartment of Physics, BMS Institute of Technology and Management, Bengaluru-560064, Karnataka, India [email protected] 1,[email protected] 1,[email protected] [email protected] (Corresponding Author) ARTICLE INFORMATION ABSTRACT Received: August 28, 2020 Cluster radioactivity is an intermediate process between alpha decay and spontaneous fission. It is Revised: October 07, 2020 also an exotic decay mode in super-heavy nuclei. When super-heavy nuclei undergo cluster decay, the Accepted: October 09, 2020 daughter nuclei is having near or equal to doubly magic nuclei. We have investigated cluster decay of Published Online: November 09, 2020 isotopes of He, Li, Be, Ne, N, Mg, Si, P, S, Cl, Ar and Ca in the super-heavy nuclei region 299-306122. We have also compared the logarithmic half-lives of cluster decay with that of other models such as Univ [1], NRDX [2], UDL [3] and Horoi [4]. From this study it is concluded that an alpha decay is the Keywords: dominant decay mode in the superheavy nuclei 299-306122. Super-heavy Nuclei, Cluster Radioactivity DOI: 10.15415/jnp.2020.81007 1. Introduction Cluster emission, and decay from super-heavy elements leads to cluster radioactivity. Poenaru et al., [5-6] studied Super-heavy elements are not natural elements. These super- branching ratios and half-lives in the super-heavy region. heavy elements have to be synthesized and their synthesis plays Ismail and Seif [7] studied half-lives of cluster 14C, 20O, 20Ne a very dynamic role in the extension of the periodic table. and 24Ne in heavy and super-heavy nuclei region. Zang et al., Poenaru et al., [1] plotted single line universal curve both for [8] evaluated half-lives of heavy and super-heavy nuclei using alpha and cluster radioactivity by plotting the sum of decimal WKB approximation. Zhang and Wang [9] studied cluster logarithm of the half-life and cluster preformation probability and alpha decay in the isotopes of super-heavy nuclei 294118, against the decimal logarithmic penetration probability. They 296120 and 298122. Wang et al., [10] studied preformation considered fission theory for large mass asymmetry based on probability using generalised liquid drop model. Zagrebaev the quantum mechanical tunnelling process. Ni et al., [2] et al., [11] studied ternary fission in doubly magic nuclei of proposed NRDX formula by considering quantum tunnelling tin. Ismail et al., [12] studied alpha decay half-lives in the through the potential barrier. The half-lives were evaluated super-heavy nuclei. Shanmugam et al., [13] studied alpha by using the preformation probability, which varies from decay chains in the super-heavy region Z=114-116 and one decay mode to another but does not significantly change 118. Previous workers [14-15] studied alpha decay half-lives for a given radioactivity. Qi et al., [3] presented universal of super-heavy region using generalized liquid-drop model decay formula by considering microscopic mechanism of (GLDM) and density-dependent cluster model. the charged-particle emission. The half-lives were evaluated Agbemava et al., [16] theoretically studied the by using Q-values of the outgoing particles as well as the properties such as charge radii and neutron skins of the masses and charges of the nuclei involved in the decay. Horoi hyperheavy nuclei using density functional theory. Cui et al., [4] proposed independent model and analysed the et al., [17] studied alpha decay half-lives with in the frame of accumulated data by pointing important variables in case of the effective liquid drop model (ELDM). Previous workers alpha and cluster decay of the even-even heavy nuclei. ©Author(s) 2020. This article is published with open access at https://jnp.chitkara.edu.in. ISSN No.: 2321-8649(Print) ISSN No.: 2321-9289(Online); Registration No. : CHAENG/2013/51628 H.C. Manjunatha et al., J. Nucl. Phys. Mat. Sci. Rad. A. Vol. 8, No. 1 (2020) p.56 [18-20] estimated the alpha decay half-lives in the super-heavy V(R) =+V (R)V(R) (1) region using generalised density dependent model. The alpha N C decay half-lives of spherical and deformed nuclei for the study The interaction with atom is given by of nuclear structure of super-heavy elements was reported by earlier workers [21-22]. Matheson et al., [23] reported 1 ()RR> C dependence of Q value on cluster emissions. Warda et al., R 2 [24] predicted a sharp fission fragment mass distribution with = 2 VC ()rZ12Ze 208 1 R (2) the heavy fragment close to Pb. Karim and Ahmed [25] 3- ()RR< C investigated alpha decay half-lives in the super-heavy nuclei 2R CC R Z=120. Routray et al., [26] evaluated half-lives using WKB integral method in the very heavy nuclei region. Earlier workers [27-44] studied different decay modes where Z1 and Z2 are the atomic number of emitted cluster/ such as spontaneous fission, ternary fission, cluster decay alpha particle and daughter nuclei. RC1=×1.24 (R + R2 ) and alpha decay in the heavy and super-heavy region and where R1 and R2 are the radii of the emitted alpha/cluster also predicted suitable projectile-target combinations to and daughter nuclei respectively. The proximity potential synthesize these super-heavy nuclei. Karpeshin [45] has is based on proximity force theorem [52]. The nuclear shown that the choice of a specific shape of the proximity proximity potential is given by potential affects not only the shape of the barrier, but can also change the total kinetic energy of fragments by tens of z VZP ()= 4πγRΦ (3) MeV. From the available literature it is witnessed that the b cluster decay plays a very important role in identifying the existence of the super-heavy nuclei. where z is the distance between the near surfaces of the = Extensive theoretical and experimental search for fragments, and b is the nuclear surface thickness (b 0.99). Φ cluster emission from various heavy and super-heavy nuclei where is the universal proximity potential which ranging from 14C to 80Ge [46-49] have been studied. The depends on the minimum separation distance present study focus on the cluster decay such as 4He, 22Ne, and is independent of geometry and shape of the 26Mg, 28,30Si, 34S, 40Ca and 46Ca which are magic nuclei or nuclei. The surface tension co-efficient is given by 2 γ =-1..25284 12345 ()NZ- A 2 near the magic nuclei whose half-lives are maximum. The MeV/fm . The hypothetical super-heavy nuclei such as Z=120, 122 124 mean curvature is given by RC=+12CC12C where C1 and 126 are most predictable super-heavy nuclei in the and C2 are the sussmann’s central radius of cluster/alpha island of stability. From the literature [50] it is observed nuclei and daughter nuclei respectively. The Sussmann that the super-heavy nuclei 299-306122 survives fission. In central radii C1 and C2 are related to sharp radii Ri and it is order to check whether, the isotopes of Z=122 also survives 2 expressed as CRii=-()b Ri . The sharp radii R is written the cluster decay such as Li, Be, Ne, N, Mg, Si, P, S, Cl, i as RA=-12..8013//76 + 08. A-13. The proximity function Ar and Ca, we made an attempt to study different cluster ii i decay in the super-heavy nuclei region of 299-306122 by using specially defined for cluster/alpha decay is as follows; proximity potential 2013. The overlap between the two p Φ(s ) = 1 nuclei increases, the proximity potential model becomes 0 sp02+ (4) more complex due to the nuclear potential interacting 1e+ xp p within the shorter distance of the nuclear surfaces. Hence in 3 the present work we have used the DFM with the density- The constants p1=-7.65, p2=1.02 and p3=0.89. The dependent nucleon-nucleon interaction and studied nuclear S0 is evaluated from the equation sR01=-RR- 2 b potential with the universal function (Prox13) [51]. where R, R1 and R2 are the radii of parent, daughter and The present paper is organised as follows. The Sec II emitted cluster. The half-lives of the cluster decay can consists of theory for the present model and semi-empirical also be evaluated by using Hill-Wheeler formalism, since formulae the coulomb intercation is not included in the formalism [53] we have evaluated the cluster decay half-lives using 2. a. Theory WKB integral; R3 The total interacting potential is the sum of the coulomb 2 PV=-exp( 2µ T ()rQ- )dr (5) potential and proximity potential and it is studied using the ∫ R2 following equation; ISSN No.: 2321-8649(Print) ISSN No.: 2321-9289(Online); Registration No. : CHAENG/2013/51628 H.C. Manjunatha et al., J. Nucl. Phys. Mat. Sci. Rad. A. Vol. 8, No. 1 (2020) p.57 where µ is the reduced mass of the fission fragments. R and a where A =+AA ()AA R are the initial and finishing turning points, and it can cd cd b where a, b, and c are fitting coefficients and corresponding be evaluated as V (R ) = Q = V (R ). The half-life of the T a T b values are 0.3949, -0.3693 and -23.7615 respectively.