Preformed Cluster Model Research Articles

Preformation of clusters in heavy nuclei and cluster radioactivity

Within the preformed cluster model approach, the values of the preformation factors have been deduced from the experimental cluster decay half-lives assuming that the decay constant of the heavy-ion emission is the product of the assault frequency, the preformation factor and the penetrability. The law according to which the preformation factors follow a simple dependence on the mass of the cluster was confirmed. Then predictions for some of the most possible cluster decays are provided.

Cluster radioactivity with effects of deformations and orientations of nuclei included

Based on the preformed cluster model (PCM) of Gupta and collaborators, we have extended our recent study on ground-state cluster decays to parent nuclei resulting in daughters other than spherical {sup 208}Pb, i.e., to deformed daughters, and the very new cases of {sup 14}C and {sup 15}N decays of {sup 223}Ac, and {sup 34}Si decay of {sup 238}U, taking nuclei as spherical, quadrupole deformed ({beta}{sub 2}) alone, and with higher multipole deformations up to hexadecapole ({beta}{sub 2}, {beta}{sub 3}, {beta}{sub 4}) together with the 'optimum' orientations of cold decay process. Except for {sup 14}C decays of {sup 221}Fr, {sup 221-224,226}Ra, and {sup 225}Ac where higher multipole deformations up to {beta}{sub 4} are found essential, the quadrupole deformation {beta}{sub 2} alone is found good enough to fit the experimental data. Because the PCM treats the cluster-decay process as the tunneling of a preformed cluster, the deformations and orientations of nuclei modify both the preformation probability P{sub 0} and tunneling probability P, and hence the decay half-life, considerably.

Decay studies of 288−287115 alpha-decay chains

The α-decay chains of 288−287115 are studied along with the possible cluster decay modes by using the preformed cluster model (PCM). The calculated α-decay half-lives are compared with experimental data and other model calculations. The calculated Q-values, penetration probabilities and preformation probabilities factors for α-decay suggest that 283170113, 287172115 and 272165107 parent nuclei are more stable against the α-decay. These alpha-decay chains are further explored for the possibilities of cluster decay. Decay half-lives of different clusters from different nuclei of the decay chains point to the extra stability near or at the deformed shells Z = 108, N = 162 and Z = 100, N = 152. The decay half-lives for 14C and 48Ca clusters are lower than the current experimental limit (≈1028s).

Pb208-daughter cluster radioactivity and the deformations and orientations of nuclei

The role of deformations and orientations of nuclei is studied for the first time in cluster decays of various radioactive nuclei, particularly those decaying to doubly closed shell, spherical $^{208}\mathrm{Pb}$ daughter nucleus. Also, the significance of using the correct $Q$-value of the decay process is pointed out. The model used is the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta et al., Proc. Int. Conf. on Nuclear Reactions Mechanisms, Varenna, 1988, p. 416; Phys. Rev. C 39, 1992 (1989); 55, 218 (1997); Heavy Elements and Related New Phenomena, edited by W. Greiner and R. K. Gupta, World Sc. 1999, Vol. II, p. 731]. In this model, cluster emission is treated as a tunneling of the confining interaction barrier by a cluster considered already preformed with a relative probability ${P}_{0}$. Since both the scattering potential and potential energy surface due to the fragmentation process in the ground state of the parent nucleus change significantly with the inclusion of deformation and orientation effects, both the penetrability $P$ and preformation probability ${P}_{0}$ of clusters change accordingly. The calculated decay half-lives for all the cluster decays investigated here are generally in good agreement with measured values for the calculation performed with quadrupole deformations ${\ensuremath{\beta}}_{2}$ alone and ``optimum'' orientations of cold elongated configurations. In some cases, particularly for $^{14}\mathrm{C}$ decay of Ra nuclei, the inclusion of multipole deformations up to hexadecapole ${\ensuremath{\beta}}_{4}$ is found to be essential for a comparison with data. However, the available ${\ensuremath{\beta}}_{4}$-values, particularly for nuclei in the mass region $16\ensuremath{\leqslant}A\ensuremath{\leqslant}26$, need be used with caution.

Three-cluster model for theα-accompanied fission of californium nuclei

A three-cluster model is proposed to explain the particle-accompanied binary fission of radioactive nuclei. The model is developed as an extension of the preformed cluster model of Gupta and collaborators. The advantage of this model is that, for a fixed third fragment, we can calculate the fragmentation potential minimized in charge coordinate. For our study we chose the various neutron-deficient to neutron-rich californium nuclei, whose analysis reveals that the closed-shell effect of any one of the fragments in ternary fragmentation presents itself as the most favorable configuration to be observed. As one goes from a neutron-deficient to a neutron-rich californium isotope, the role of the neutron closed shell associated with any one of the preferred fragments changes to that of the proton closed shell, and for very neutron rich isotopes of californium the presence of a double closed shell nucleus enhances the decay probability. The quadrupole deformation of the light fragment $({A}_{2})$ associated with the preferred configuration in the symmetric mass region also has a transition from positive to negative deformation as one goes from neutron-deficient to neutron-rich californium isotopes. The calculated relative yields of different fragmentation channels are compared with the available experimental yields for $^{252}\mathrm{Cf}$.

Shell closure effects studied via cluster decay in heavy nuclei

The effects of a shell closure in nuclei via cluster decay have been investigated. In this context, we used the preformed cluster model (PCM) of Gupta and collaborators based on quantum-mechanical fragmentation theory. The key point in the cluster radioactivity is that it involves the interplay of close shell effects of parent and daughter nuclei. Small half-life for a parent indicates the shell stabilized daughter and long half-life indicates the stability of the parent against the decay. In the cluster decay of trans-lead nuclei observed so far, the end product is doubly magic lead for its neighboring nuclei. We have extended the idea of cluster radioactivity. We have investigated the decay of different nuclei where zirconium is taken as a daughter nucleus, which is a very well-known deformed shell closure nucleus. The branching ratios of cluster decay and α-decay have also been studied for various nuclei, leading to magic or almost doubly magic daughter nuclei. The calculated cluster decay half-lives are in well agreement with the observed data. For the first time a possibility of cluster decay of 218U nucleus is predicted.

Proton andα-radioactivity of spherical proton emitters

The half-lives of different spherical proton emitters are calculated. The preformed cluster model modified into a unified fission model of Gupta and collaborators with the effects of Coulomb repulsion, nuclear attraction due to proximity potential, and rotational energy due to angular momentum is used for the calculations. This includes the study of observed ground and isomeric state proton emitters of 26 proton-rich nuclei. The results are compared with experimental results and other theoretical calculations. The calculated results are in fair agreement with experimental values. It is evident from some experiments that $\ensuremath{\alpha}$ decay is a competing mode of branching for proton decay. Hence, the half-lives of $\ensuremath{\alpha}$ decay from these proton emitters are also presented for $s$ waves.

Cluster emission in superdeformed Sr isotopes in the ground state and formed in heavy-ion reaction

Cluster decay of superdeformed76, 78, 80Sr isotopes in their ground state are studied taking the Coulomb and proximity potential as the interacting barrier for the post-scission region. The predictedT 1/2 values are found to be in close agreement with those values reported by the preformed cluster model (PCM). Our calculation shows that these nuclei are stable against both light and heavy cluster emissions. We studied the decay of these nuclei produced as an excited compound system in heavy-ion reaction. It is found that inclusion of excitation energy increases the decay rate (decreasesT 1/2 value) considerably and these nuclei become unstable against decay. These findings support earlier observation of Guptaet al based on PCM.

Cluster radioactivity in xenon isotopes

Half-life time and branching ratio for cluster decay from various xenon isotopes are studied taking Coulomb and proximity potentials as interacting barrier. Inclusion of proximity potential reduces the height of potential barrier, which closely agrees with the experiments. It is found that4He,8Be,12C and16O emissions are well within the present upper limit for measurements (T 1/2 1030 s). Our predicted half-life time values lie close to those values reported by Gupta and collaborators based on preformed cluster model (PCM) and also with those values reported by Poenaruet al based on ASAFM. The calculated half-life time shows that8Be from108Xe and110Xe are most favourable for emission (T 1/2 ≈ 108 s). LowestT 1/2 value for8Be emission from108Xe stress the role of doubly magic100Sn daughter in cluster decay process. The logarithm of half-life time calculated for4He emission from110Xe is −0.39 s which is in good agreement with experimental value which is −0.40 s. Geiger-Nuttall plots for all clusters are studied and are found to be linear. Nuclear structure effect and shell effect are evident from the observed variation in slope and intercept of Geiger—Nuttall plots. It is found that neutron excess in the parent will slow down the cluster decay process.

Structure effects in the region of superheavy elements via the α-decay chain of 293118

The α-decay chain of 293118, first proposed in the Berkeley cold fusion experiment 208Pb(86Kr, 1n) and now retracted, is calculated by using the preformed cluster model (PCM) of one of the authors (RKG). Also, the possible branchings of α-decays to heavier cluster decays of all the parents in this chain are calculated for the first time. The calculated Q-values, penetrabilities and preformation factors for α-decays suggest that the 285114 nucleus with Z = 114, N = 171 is a magic nucleus, either due to the magicity of Z = 114, or N = 172 or both. The N = 172 is proposed to be a magic number in certain relativistic mean-field calculations, but with Z = 120. The calculated cluster decays point to new interesting possibilities of 14C decay of the 281112 parent, giving rise to a (reasonably) deformed Z = 106, N = 161, 267106 daughter (N = 162 being now established as the deformed magic shell) or to a doubly magic 48Ca cluster emitted from any of the parent nucleus in the α-decay chain. Apparently, these are exciting new directions for future experiments.

Exotic decay in cerium isotopes

Half life for the emission of exotic clusters like 8Be, 12C, 16O, 20Ne, 24Mg and 28Si are computed taking Coulomb and proximity potentials as interacting barrier and many of these are found well within the present upper limit of measurement. These results lie very close to those values reported by Shanmugam et al using their cubic plus Yukawa plus exponential model (CYEM). It is found that 12C and 16O emissions from 116Ce and 16O from 118Ce are most favorable for measurement (T 1/2<1010 s). Lowest half life time for 16O emission from 116Ce stress the role of doubly magic 100Sn daughter in exotic decay. Geiger-Nuttall plots were studied for different clusters and are found to be linear. Inclusion of proximity potential will not produce much deviation to linear nature of Geiger-Nuttall plots. It is observed that neutron excess in the parent nuclei slow down the exotic decay process. These findings support the earlier observations of Gupta and collaborators using their preformed cluster model (PCM).

Cold fission versus exotic cluster decay in 234,236,238Unuclei

Cold fission and cluster decay processes are studied for 234,236,238Unuclei in the super-asymmetric mass region of exotic clusterradioactivity.The idea is to see whether the clusters already observed as cluster decays (herefor234,236U parents) could also be observed via the cold fissionprocess.Our calculations are made on the well acceptedquantum mechanical fragmentation theory and the saddle-pointfissionmodel and the preformed-cluster model that are also based onthistheory.

34Sidecay of the242Cmnucleus

The emission of the ${}^{34}\mathrm{Si}$ cluster, with respect to the $\ensuremath{\alpha}$ particle, in the spontanous decay of the ${}^{242}\mathrm{Cm}$ nucleus is studied within a preformed cluster model developed by one of us (R.K.G.) and collaborators. The preformation factors are predicted to be very small, $\ensuremath{\sim}{10}^{\ensuremath{-}9}$ and $\ensuremath{\sim}{10}^{\ensuremath{-}24},$ respectively, for the $\ensuremath{\alpha}$ particle and ${}^{34}\mathrm{Si}$ cluster. With no parameter of the model fitted to experimental data, the half-life times for both the $\ensuremath{\alpha}$ particle and ${}^{34}\mathrm{Si}$ decays of ${}^{242}\mathrm{Cm}$ are predicted within only one to two orders of magnitude of the experimental values.

Heavy-ion emission in spontaneous decays of249,252Cfnuclei

Theoretical possibilities for exotic cluster emissions from ${}^{249}\mathrm{Cf}$ and ${}^{252}\mathrm{Cf}$ parents are explored on the basis of the very much used preformed cluster model of one of us (R.K.G.) and collaborators. The calculated \ensuremath{\alpha}-decay half-life time for ${}^{252}\mathrm{Cf}$ match the experiments exactly and the same for ${}^{249}\mathrm{Cf}$ within an order of 3. The most probable heavy cluster decay for both the parents is predicted to be ${}^{46}\mathrm{Ar}$ or ${}^{48}\mathrm{Ca},$ with the predicted decay half-life times far more than the presently available experimental upper limiting values. In other words, the predicted heavy-ion emission probabilities for both the parents are so small that there seem to be very little chance for their exotic cluster decays to be observed in the very near future.

Search for heavy-ion emission in249Cfdecay

Using phosphate glass detectors PKS-50, we have searched for possible emission of heavy clusters in the decay of ${}^{249}\mathrm{Cf}$ with the aim of confirming the result obtained from a recent $\ensuremath{\gamma}$ ray spectrometry experiment. After a 20-day exposure to a 7.4 MBq activity ${}^{249}\mathrm{Cf}$ source of $37.5 {\mathrm{cm}}^{2}$ PKS-50 glasses covered with polymide foils to stop fission fragments, no ions with $17&lt;~Z&lt;~21$ were detected. We could deduce an upper limit of the branching ratio (90% C.L.) $b&lt;~1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ and a partial half-life ${T}_{1/2}&gt;~7.4\ifmmode\times\else\texttimes\fi{}{10}^{21} \mathrm{s}.$ According to calculations performed on the basis of the preformed cluster model there seems to be very little chance that such an exotic decay might be detected, at least in the next few years.

Fission and cluster decay of the76Srnucleus in the ground state and formed in heavy-ion reactions

Calculations for fission and cluster decay of ${}^{76}\mathrm{Sr}$ are presented for this nucleus to be in its ground state or formed as an excited compound system in heavy-ion reactions. The predicted mass distribution, for the dynamical collective mass transfer process assumed for fission of ${}^{76}\mathrm{Sr},$ is clearly asymmetric, favoring \ensuremath{\alpha} nuclei. Cluster decay is studied within a preformed cluster model, both for ground-state to ground-state decays and from excited compound system to the ground state(s) or excited states(s) of the fragments.

Neck formation and deformation effects in a preformed cluster model of exotic cluster decays

Using the nuclear proximity approach and the two center nuclear shape parametrization, the interaction potential between two deformed and pole-to-pole oriented nuclei forming a necked configuration in the overlap region is calculated and its role is studied for the cluster decay half-lives. The barrier is found to move to a larger relative separation, with its proximity minimum lying in the neighborhood of the Q value of decay and its height and width reduced considerably. For cluster decay calculations in the preformed cluster model of Malik and Gupta, due to deformations and orientations of nuclei, the (empirical) preformation factor is found to get reduced considerably and agrees nicely with other model calculations known to be successful for their predictions of cluster decay half-lives. Comparison with the earlier case of nuclei treated as spheres suggests that the effects of both deformations and neck formation get compensated by choosing the position of cluster preformation and the inner classical turning point for penetrability calculations at the touching configuration of spherical nuclei.

Cluster emissions with daughter from neutron-rich nuclei

Cluster emissions from neutron-rich , and nuclei are studied within the preformed cluster model of Malik and Gupta. Q-value estimates of the decays selected on the basis of shell effects in binding energies and their relative preformation probabilities show that these nuclei are stable (Q<0) against and decays and all the metastable (Q>0) decays are of non-alpha-like heavy clusters. The most probable decays (minimum half-life times) are the ones with a doubly magic nucleus as the daughter nucleus, arising due to the WKB penetrability. Compared to the presently measurable alpha-like cluster decays of the corresponding neutron-deficient parents into a daughter nucleus, these decays are suppressed by many orders of magnitude.

Measurable decay modes of barium isotopes via exotic cluster emissions.

Cluster decays of $^{112\mathrm{\ensuremath{-}}120}\mathrm{Ba}$ nuclei are calculated within a preformed cluster model. The \ensuremath{\alpha}-nuclei $^{4}\mathrm{He}$, $^{8}\mathrm{Be}$, $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{20}\mathrm{Ne}$ are predicted as the possible decay modes, lying within the limits of present experimental methods. Other than the \ensuremath{\alpha} particle, $^{12}\mathrm{C}$ decay of $^{112}\mathrm{Ba}$ is shown to be the most probable one with half-life time ${\mathit{T}}_{1/2}$\ensuremath{\sim}${10}^{4}$ s, stressing the role of doubly magic $_{50}^{100}\mathrm{Sn}$ daughter nucleus in cluster radioactivity. The use of different Q values for ${\mathit{T}}_{1/2}$ estimates and presence of nuclear structure effects in Geiger-Nuttall plots are also discussed.

SUPER-ASYMMETRIC COLD FISSION AND EXOTIC CLUSTER-DECAY

Cold fission of radioactive nuclei is studied in the super-asymmetric mass region of exotic cluster radioactivity, using the quantum-mechanical fragmentation theory (QMFT) based saddle-point fission (SPF) model for calculating the decay half-life times. The calculations show that cold fission also prefers light fragments like 24–26Ne, 28,30Mg, 32,34,36Si, 37P 38S, 46Ar and 48,50Ca, some of which are observed in exotic cluster radioactivity. The predictions of the SPF model calculations are compared with the available exotic cluster-decay experimental data and the calculations based on the preformed-cluster model (PCM). The SPF model calculations show large disagreements with both the PCM and cluster-decay experimental data. For clusters of mass A2&lt;46, the predicted half-lives for the SPF model are much smaller than for the PCM, which apparently means predicting the cold fission as a more probable process than the cluster-decay. The cold fission predicts some new decay modes which are far more probable (smaller log10 T1/2-values) as cold fission fragments than as cluster-decay products. For heavier clusters (A2≥46), the two models (SPF and PCM) make nearly identical predictions, which means predicting an overlap of two processes (cold fission and cluster-decay) for A2&gt;46. Also, cold fission is found to be more probable than hot fission and a new fission mode (known as bimodel fission) is identified in the neighbourhood of the doubly magic [Formula: see text] fragment. Our calculations are made for 234U, 238Pu, 241Am and 252Cf.