Effect of deformations and orientations in 100Sn daughter radioactivity

Based on the preformed cluster model (PCM), we have extended our earlier study to investigate the effects of nuclear deformations and orientations of nuclei in context of ground-state de-excitation of Xe to Gd parents, resulting in a doubly closed shell Sn daughter and the complementary clusters. The comparison is also made with spherical choice of fragments to extract exclusive picture of the dynamics involved. Since PCM is based on collective clusterization picture, the preformation and penetration probabilities are shown to get modified considerably by inclusion of the quadrupole deformations (β2i) alone, which in turn affects the decay half-lives of the clusters. The phenomenon of cluster radioactivity is now well established on experimental as well as theoretical front, besides the familiar α, β and γemissions. The whole family of such decays consisting of light to heavy (14C to 34Si) clusters have been observed from various actinides (221Fr to 242Cm) in trans-lead region. In all these cases, the daughter nucleus is always 208Pb (a doubly closed shell nucleus) or its neighboring nucleus and hence this phenomena has been termed in some literature as “lead radioactivity”. In order to explore the region of possible Sn radioactivity, Gupta and collaborators [1] studied the ground-state decays of neutron-deficient 201 , 0401 (2016) EPJ Web of Conferences DOI: 10.1051/ conf/201611 0401 epj

The phenomenon of cluster radioactivity is now well established on experimental as well as theoretical front, besides the familiar α, β and γemissions. The whole family of such decays consisting of light to heavy ( 14 C to 34 Si) clusters have been observed from various actinides ( 221 Fr to 242 Cm) in trans-lead region. In all these cases, the daughter nucleus is always 208 Pb (a doubly closed shell nucleus) or its neighboring nucleus and hence this phenomena has been termed in some literature as "lead radioactivity". In order to explore the region of possible Sn radioactivity, Gupta and collaborators [1] studied the ground-state decays of neutron-deficient 108−116 Xe, 112−120 Ba, 116−124 Ce, 120−124 Nd, 124−128 Sm, and 128−132 Gd nuclei, and showed a clear preference for A=4n, α-nuclei, like 4 He, 8 Be, 12 C, etc. However, in their later work [2] carried out for neutron-rich isotopes, it was observed that non-α like clusters are preferred for decays into 132 Sndaughter nucleus, though less probable than A=4n, α-nuclei clusters for the case of 100 Sn-daughter radioactivity. Since the shape of a nucleus provides an intuitive understanding of spatial density distribution, therefore, together with shell effects, it is expected that nuclear deformations and orientations should play an important role in the context of Sn radioactivity.
In the present work, we take up this study on the basis of preformed cluster model (PCM) [3] to analyze the influence of quadrupole deformations (β 2i ) alongwith 'optimum' orientations (θ opt i ) [4] on the behavior of possible fragmentation of Xe to Gd parents. The study is confined to only N=Z parent nuclei, referring to 100 Sn as the daughter product. It is relevant to mention here that a majority of parents 108 Xe, 112 Ba, 116 Ce, 120 Nd, 124 Sm, and 128 Gd and their respective emitted clusters 8 Be, 12 C, 16 O, 20 Ne, 24 Mg and 28 Si considered here are deformed and hence the deformation effects seem indispensable, which were not analyzed explicitly in the earlier works [1,2]. Because the PCM treats the fragmentation process in a collective clusterization approach, it is of great interest to see, in what way the deformation and orientation effects of the decay fragments influence the potential energy surfaces (PES) of these neutron-deficient nuclei.
The decay constant λ or the decay half-life T 1/2 in PCM is defined as The clusters are assumed to be preborn in the parent nucleus with preformation probability P 0 , hit the barrier with impinging frequency ν 0 , and penetrate it with penetrability P . The structure information of the decaying nucleus is contained in P 0 via the fragmentation potential, defined as with B i (i=1,2) as binding energies of two fragments and, V C and V P , respectively, as the Coulomb and nuclear proximity potentials for deformed and oriented nuclei. For details, we refer to ref. [3]. Figure 1(a) illustrates the mass fragmentation potential, minimized in charge coordinate, as a function of the cluster mass for the considered parents. The effects of deformations up to quadrupole (β 2i ), in reference to "optimum" orientation of the cold decay process [4], are duly incorporated in the calculations. For a comprehensive analysis, the calculations have been performed at the touching configuration to estimate the possible existence of the most probable cluster emitted with doubly magic daughter 100 Sn. We notice from fig. 1(a) that, even after inclusion of the deformation and orientation effects, potential energy minima occur only at A 2 =4n, which are alpha-like clusters 4 He to 28 Si, although the magnitudes of the fragmentation potential are quite different for different N=Z parents. This observation is in contrast to A 2 =4n, non-alpha like clusters emitted for the case of cluster decays of radioactive nuclei with Pb or its neighboring nuclei as the daughter product.
Since, both deformations and orientations are found [3] to have significant effect on decay half-lives investigated in trans-lead region, we explore the same here in the trans-tin region. Figure 1(b) presents our calculations of preformation probability P 0 for the illustrative decay of 124 Sm, using spherical as well as β 2 -deformed choice of fragments. We find that inclusion of deformation and orientation effects of decay fragments changes the relative preformation probability P 0 , quite significantly. Interestingly, the emergence of 24 Mg cluster in fig. 1(b), corresponding to doubly closed shell 100 Sn daughter, seems more probable for deformed configuration in the fragmentation of 124 Sm. Similarly, the barrier position as well as its height (not shown here) also get modified with inclusion of deformations, thereby affecting the barrier penetrability P accordingly. Figure 2 shows the calculated preformation probabilities, penetrabilities and logarithms of half-life times for clusters referring to minima in fragmen- tation potentials of all the considered N=Z parents. Knowing that, in PCM, T 1/2 exhibits a combined effect of both P 0 and P (ν 0 being almost constant, ∼10 21 s −1 ), we notice in fig. 2 that the clusters referring to doubly magic daughter nucleus 100 Sn have the minimal decay half-lives. This is due to the fact that, both P 0 and P have larger magnitudes for each of the most probable (minimal T 1/2 ) cluster emission. Apparently, the shortest half-life time is obtained for, say, 12 C decay of 112 Ba. In other words, the calculated decay half-lives indicate the possible decay of 8 Be from 108 Xe, 12 C from 112 Ba, 16 O from 116 Ce, etc., giving rise to the doubly magic 100 Sn (Z=N =50) daughter, and hence are predicted to be most probable cases for measurements.
Summarizing, proper understanding of nuclear shapes along with the relative orientations is essential to make concrete and explicit predictions of cluster dynamics in trans-tin region. As an extension of this work, it will be of further interest to analyse the possible role of deformations in 132 Sn radioactivity predicted in the intermediate mass region of the periodic table.