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The purpose of the present work is to investigate the alpha (α) emission as competing mode of one proton emission using the preformed cluster decay model (PCM). PCM is based on the quantummechanical tunneling mechanism of penetration of the preformed fragments through a potential barrier, calculated within WKB approximation. To explore the competing aspects of α and one proton radioactivity, we have chosen emitters present immediately above and below the Z = 82 shell closure i.e. 177Tl and 185Bi by taking into account the effects of deformations (β2) and orientations of outgoing nuclei. The minimized values of fragmentation potential and maximized values of preformation probability (P0) for proton and alpha fragment demonstrated the crucial role played by even Z - even N daughter and shell closure effect of Z = 82 daughter, in 177Tl and 185Bi, respectively. The higher values of P0 of the one proton further reveal significance of nuclear structure in the proton radioactivity. From the comparison of proton and α decay, we see that the former is heavily dominating with larger values of P0 in comparison to the later. Theoretically calculated half-lives of one proton and α emission for spherical and deformed considerations have also been compared with available experimental data.

We have investigated the pairing and magicity effect in context of a comparative study of 13,14C induced reactions on 232Th target at energies in the vicinity of Coulomb barrier. The fission distribution and related properties are explored in terms of the summed-up preformation probabilities. The barrierpenetrability is found to be higher for fragments emitted from 246Cm* formed in 14C+232Th reaction than those emitted in the fission of 245Cm*, leading to higher magnitude of cross-section for earlier case. The DCM calculated fusion-fission cross-sections using ΔR=0 fm are normalised to compare with the available experimental data. The calculations are done for spherical shape of fragments and it will be of further interest to explore the fission mass distribution after the inclusion of deformations.

The quantum mechanical fragmentation theory (QMFT)-based dynamical cluster-decay model (DCM) has been applied to predict the fusion cross section ( σ f u s ) for the compound systems (CS) 60Zn⁎, 60Ni⁎ and 60Fe⁎ formed, respectively, via 4He + 56 Ni, 4He + 56 Fe and 4He + 56 Cr, reactions, by fixing the only parameter (neck length Δ R e m p ) of the model, empirically with the available experimental data on σ f u s of 44,48Ti⁎ and 68Ge⁎ formed through 4He induced reactions at different incident energies, i.e., E l a b ∼ 10, 13, 17 MeV. We have investigated the effect of neutron to proton ( N / Z ) ratio in the decay of CS under study, i.e., 60Zn⁎, 60Ni⁎ and 60Fe⁎. The contributions of light-particles cross section ( σ L P s ), intermediate mass fragments cross section ( σ I M F s ) and symmetric mass fragments cross section ( σ S M F s ) are taken together to calculate σ f u s ( = σ L P s + σ I M F s + σ S M F s ). The small contribution of SMFs is seen in σ f u s , the contributions of LPs and IMFs yields being much more prominent, for the decay of all CS under study at different incident energies. We see that the preformation probability ( P 0 ) and penetrability (P) for SMFs decrease with increase in the value of N / Z ratio, and hence the symmetric breakup drops-out-of-favor for higher N / Z values. In other words, the symmetric mass decay is favored in the case of 60Zn⁎ having N = Z , the LPs, IMFs and SMFs yields increasing with increase in incident energy.

The investigation of fusion reactions involving light neutron-rich exotic nuclei is of paramount significance to understand nucleosynthesis in astrophysical scenarios. It is also estimated as a possible heat source to ignite $^{12}\mathrm{C}+^{12}\mathrm{C}$ reaction and production of x-ray superbursts from accreting neutron star. Recently, the fusion of neutron-rich $^{20}\mathrm{O}$ with $^{12}\mathrm{C}$ target has been studied with measurement of fusion cross-section $({\ensuremath{\sigma}}_{\text{fus}})$. Bass model under predicts the ${\ensuremath{\sigma}}_{\text{fus}}$ and time-dependent Hartree-Fock model also fails to explain the experimental data. To explicate the same, the investigation of $^{20}\mathrm{O}+^{12}\mathrm{C}$ reaction at near barrier energies has been made within quantum mechanical fragmentation-based dynamical cluster-decay model (DCM). Within DCM, the fragmentation potential comprises temperature-dependent Coulomb, nuclear and centrifugal potentials, along with temperature-dependent binding energies (T.B.E.) calculated within the macroscopic approach of Davidson mass formula. Recently, we have explored the temperature-dependence of different nuclear properties and nuclear symmetry energy within microscopic relativistic mean-field (RMF) theory [M. Kaur et al., Nucl. Phys. A 1000, 121871 (2020)]. In the present work, we inculcate the microscopic T.B.E. from RMF theory within DCM and investigate the structure of fragmentation potential for $^{32}\mathrm{Si}^{*}$ formed in $^{20}\mathrm{O}+^{12}\mathrm{C}$ reaction, comparatively for macroscopic (mac) and microscopic (mic) T.B.E. obtained from Davidson mass formula and RMF theory, respectively. The structure and magnitude of fragmentation potential are found to change drastically/notably along with a change in energetically favored/minimized fragments for both choices of T.B.E. The $\ensuremath{\alpha}$ particles $(^{4}\mathrm{He}$, $^{5}\mathrm{He})$ are favored at lower angular momenta in fragmentation profile for mic T.B.E. case only, which is in the agreement with predictions of statistical model results. This change in the nuclear structure embodied via fragmentation potential energy carries its imprints in the preformation probability ${P}_{0}$ of different fragments and affects the contribution of individual light-charged particle (LCP) channel in the ${\ensuremath{\sigma}}_{\text{fus}}$. A comparison of the relative cross-section of different LCP channels toward ${\ensuremath{\sigma}}_{\text{fus}}$ is quite different for both cases of T.B.E. The cross-section of $^{2}\mathrm{H}$ and $^{4}\mathrm{He}$ LCP channels is relatively enhanced for mic T.B.E. compared to mac T.B.E. Among different LCP channels, the $^{5}\mathrm{He}$ channel is the major contributor in ${\ensuremath{\sigma}}_{\text{fus}}$, which is in line with the results of the statistical EVAPOR model. The DCM-calculated ${\ensuremath{\sigma}}_{\text{fus}}$ is in agreement with the experimental data.

We investigate the low energy 20O+12C reaction at Ec.m. = 9.29 MeV populating the 32Si* nuclear system within dynamical cluster-decay model (DCM) and bring about the role of temperature (T) dependent binding energies in the reaction dynamics. T-dependent binding energies are one of the crucial ingredients of DCM used to calculate the fragmentation potential and hence the fusion cross-section. The inculcation of T-dependent binding energies from microscopic relativistic mean field (RMF) theory in comparison to that from Davidson formula, leads to considerable change in the fragmentation profile, preformation probability of different fragments. Subsequently, it affects the contribution of individual channel in the fusion cross-section associated with light charged particles (LCP) emission. It is noted that the statistical evapOR model under predicts the LCP cross-section σLCP. On the other hand, DCM calculated σLCP is in nice agreement with experimental data for both cases of T-dependent binding energies although contribution of 3H and 4He channels in σLCP changes significantly for both cases.

The reactions involving fusion-fission of compound nuclei 244,247Cm* formed in low energy heavy ion collisions of 12,15C projectiles with actinide target 232Th have been investigated within dynamical cluster-decay model (DCM). We have probed the effects of transition from a paired to an unpaired valence neutron or halo nature of projectile (15C) on the fusion-fission cross sections (σFF) of decay of compound nuclei (CN) 244,247Cm*, formed in these reactions. The calculations are performed using spherical shape of nuclei at touching configuration at near-barrier energies (Ec.m.= 68-70 MeV) where experimental data is already available. The dynamical behaviour of these reactions is explored via fragmentation potential (V), preformation probability (P0), summed up preformation probability over angular momenta (l) values (ΣP0) and penetrability (P) for fusion-fission fragments (FF) having mass numbers (ACN/2) ±20. It is observed that the overall pattern of fragmentation potential, V(MeV) at different l values remains unaffected, but the potential energy surface (PES) for FF fragments show peculiar behavior with increase in mass of CN. These characteristics of the FF fragments are presented in terms of preformation probability (P0), explicitly. The effect of halo configuration of projectile is evident in the summed-up preformation probabilities (ΣP0) of various FF fragments, which means that the relevant structure information is duly explored. The DCM calculated, normalized values, of σFF are found to be consistent with the experimental data. The observation of enhancement in the magnitude of σFF for neutron-rich matter reveals the modification of nuclear behaviour, as we move towards region close to the drip line.

The investigations of the fragmentation mass distributions have been made in order to emphasize the importance of the shell corrections (δU) in the decay of compound nuclei. The decay of medium and heavy mass compound nuclei 124Ce* and 246Bk* formed in 32S + 92Mo and 11B + 235U reactions, respectively, had been studied within the formalism of Dynamical Cluster Decay model. In the present study, the importance of δU is explored due to the availability of the separate contributions of liquid drop part (VLDM) and δU in the binding energies defined by Strutinsky renormalization procedure. The results shows that in medium mass compound nucleus 124Ce* the effect of δU above vanishing temperature (T=1.5 MeV) are very minute and the change becomes noticeable in the decay of heavy mass 246Bk* at temperature below the vanishing limit. The investigations show that the fragmentation potential and preformation probability contains the nuclear structure information of the nuclear system and its decaying fragments, which depend significantly on the δU values particularly at the temperature values below the vanishing limit.

The purpose of this work is to study the dynamics of competing α and 208Pb daughter cluster radioactive decays using the preformed cluster decay model (PCM), within the collective clusterization approach of Quantum Mechanical Fragmentation Theory (QMFT). The QMFT based fragmentation potential comprises of binding energy (B.E) (which is the sum of liquid drop energy (VLDM), based on semi empirical mass formula of Seeger and shell corrections (δU) given by Myers and Swiatecki), Coulomb potential (VC) and nuclear proximity potential (VP) of the cluster and daughter nuclei in the ground state decay of the radioactive parent nuclei. To explore the competing aspects of α and 208Pb daughter cluster radioactivities, we have chosen 222Ra, 226Th, 228Th, 231Pa, 230U and 232U parent nuclei. The crucial role played by shell closure effects is demonstrated in minimized values of fragmentation potential for cluster accompanied by doubly-magic 208Pb daughter nucleus in comparison to neighboring fragments. The higher values of preformation probabilities, P0 of these clusters further reveal significance of nuclear structure in the cluster radioactivity process. We have calculated the half-lives via fragmentation potential, preformation probability, scattering potential for spherical case, of chosen nuclei, and then compared with the given experimental data. From the comparison of α cluster and 208Pb daughter decays, we see that the former is heavily dominating with larger values of P0 in comparison to the later as evident from the experimentally observed high count rate of α cluster in such decays. However, the penetrability for both types of decays is almost similar. The experimental data and PCM calculated results are in fair comparison for all the chosen cases.

Within the Strutinsky renormalization procedure temperature dependence of binding energies of nuclei has been observed, where the binding energy comprises of the macroscopic and microscopic part i.e. the liquid drop energy VLDM and the shell correction (δU), respectively. It is observed that δU (particularly at energies ≤ 1.5 MeV) along with the VLDM plays a crucial role to give proper understanding of the nuclear reaction dynamics at the given temperatures of the composite nuclei formed in the low energy heavy ion collisions, within the dynamical cluster decay model of Gupta and Collaborators. We observe that effect of temperature on various binding energy terms of the formula is varied at different temperatures (0 - 4 MeV). This variation is guided by the temperature dependence of various energy coefficients obtained by Davidson et. al., which eventually affects the binding energy per nucleon (B.E./A) curve quite significantly. We find that values of B.E./A show consistent increasing trend up to T = 1 MeV, attributing it to the peculiar behavior of the surface energy term, and for higher temperature (say 2 - 4 MeV), it is showing downward trend particularly for nuclei with A ∼ 10-150. While for heavier nuclei, the values of B.E./A start increasing beyond T = 2 MeV, due to the asymmetry energy term.

The study of the heavy-ion reactions at the near- and sub-barrier regimes gives immense information about the nuclear structure and the involved reaction dynamics. It has been observed that a slight difference in the nuclear structure may lead to a significant change in the sub-barrier fusion excitation functions. The studies of different trends of excitation functions below the Coulomb barrier region due to dissimilar structures of the nuclei, which are involved in the reaction, are available in literature. To understand the role of different structures and dynamics involved in such reactions, an investigation of $^{48}\mathrm{Ti}$-induced reactions on $^{58}\mathrm{Fe}$ and $^{58}\mathrm{Ni}$ forming $^{106}\mathrm{Cd}^{*}$ and $^{106}\mathrm{Sn}^{*}$ compound nuclei (CN), respectively, has been made at similar ${E}_{\mathrm{c}.\mathrm{m}.}/{V}_{b}$ values within the framework of the dynamical cluster decay model (DCM). The difference in the structure between the nuclei is quite notable with $^{58}\mathrm{Ni}$ and $^{106}\mathrm{Sn}^{*}$ having a proton shell closure ($Z=28$ and 50, respectively). Within the DCM, the experimental fusion evaporation cross sections are reproduced using deformed configurations effects included up to quadruple deformations (${\ensuremath{\beta}}_{2i}$) for two nuclei having optimum orientations ${\ensuremath{\theta}}^{\mathrm{opt}.}$. The fusion evaporation data at near- and sub-barriers has been explained through the calculated enhanced $\mathrm{\ensuremath{\Sigma}}{P}_{0}$ values of the decaying channels in the case of $^{106}\mathrm{Cd}^{*}$ in comparison to $^{106}\mathrm{Sn}^{*}$. Moreover, it is observed that the quantum tunneling of the fragments is less hindered in the case of $^{106}\mathrm{Cd}^{*}$ as compared to $^{106}\mathrm{Sn}^{*}$ at the lower values of ${E}_{\mathrm{c}.\mathrm{m}.}/{V}_{b}$, i.e., having less barrier modification ($\mathrm{\ensuremath{\Delta}}{V}_{B}$) in the case of the former. The role of magicity has been further explored with the plotted values of the ratio of fusion cross sections (${\ensuremath{\sigma}}_{\mathrm{fus}}$) of CN $^{106}\mathrm{Sn}^{*}$ and $^{112}\mathrm{Xe}^{*}$ (formed in the reaction with both the projectile $^{58}\mathrm{Ni}$ and target $^{54}\mathrm{Fe}$ having proton and neutron magicity, respectively) with respect to $^{106}\mathrm{Cd}^{*}$, which are highly suppressed in the case of the latter in comparison to the former, particularly, below the Coulomb barrier.

From the past few years, increasing experimental evidence has shown that clusters (multiple of $\ensuremath{\alpha}$ particles) of intermediate mass are emitted with quite large cross sections at forward angles in heavy-ion reactions. In the present work a theoretical investigation has been made to explore the role of $\ensuremath{\alpha}$-clustering in $^{13,12}\mathrm{C}+^{12}\mathrm{C}$ reactions populating $^{25,24}\mathrm{Mg}^{*}$ compound nuclei (CN), which results in the enhanced cross sections of intermediate mass fragments (IMFs) within the collective clusterization framework of the dynamical cluster decay model (DCM). With in the formalism the experimental cross sections are reproduced using the spherical as well as deformed configurations effects included up to quadruple deformations (${\ensuremath{\beta}}_{2i}$) for two nuclei having optimum orientations ${\ensuremath{\theta}}^{\mathrm{opt}}$. The ratio of the calculated (fission-like) yields of each isotopic fragment $^{6,7}\mathrm{Li}, ^{7,8,9}\mathrm{Be}$ obtained in the two reactions has been compared with the experimental and statistical model predictions also. The DCM calculated result is in little better comparison to the statistical models due to the inclusion of structure effects in the calculations. In the present calculations, the dynamical yields count for the preformation probability (${P}_{0}$) of the IMFs within the collective clusterization process of DCM, before penetrating the scattering potential barrier. Quite interestingly, the calculated ratio of ${P}_{0}$ of the corresponding IMFs ${P}_{0(\mathrm{IMFs})}^{^{25}\mathrm{Mg}^{*}}/{P}_{0(\mathrm{IMFs})}^{^{24}\mathrm{Mg}^{*}}$ for the CN $^{25,24}\mathrm{Mg}^{*}$ shows the trend of ratio of experimental cross sections, i.e., ${\ensuremath{\sigma}}_{\mathrm{IMFs}}^{^{25}\mathrm{Mg}^{*}}/{\ensuremath{\sigma}}_{\mathrm{IMFs}}^{^{24}\mathrm{Mg}^{*}}$. It is found that $\ensuremath{\alpha}$-cluster structure of complimentary fragments of the IMFs under investigation plays quite a significant role in their decays.

The investigation of Si-induced isotopic chain of reactions 28,30Si+12C populating compound nuclei (CN) 40,42Ca*, respectively, with Z=20 shell closure and neutron number is gradually moving away from N = 20 neutron shell closure, has been performed within clusterisation approach of dynamical cluster-decay model (DCM) using deformed configurations effects included up to quadruple deformations (β2i) for two nuclei having optimum orientations θiopt.. The experimental fusion cross-sections of 30Si+12C is reproduced using DCM and further, the fusion cross-sections are predicted for other isotope of Si beam on 12C at lower energies to investigate the fusion process in terms of hindrance as function of neutron number. It is observed that the quantum tunneling of the fragments is less hindered in case of 40Ca*, as compared to 42Ca*, at the lower values of E c.m. i.e. having less barrier modification ΔVB in the case of former.

The effects of shell closure (proton shell closure Z = 82) in the decay of compound nuclei (CN) having having A ∼ 200 formed through 19F induced reaction at same Elab, is explored. We have investigated the decay of CN 194Hg*, 200Pb*, 203Bi* and 207At* formed in 19F+175Lu, 19F + 181Ta, 19F+184W and 19F+188Os reactions, respectively, at Elab∼85 MeV, using the quantum mechanical fragmentation theory based dynamical cluster decay model (DCM). In DCM, the collective fragmentation potential is calculated within Strutinsky macro-microscopic method and empirical shell corrections are taken from Myres and Swiatecki. The deformations of the interacting nuclei are taken here upto quadruple deformations. The results show interesting interplay between light particles LPs/evaporation residues and fission fragments with special observation that LPs are strongly favored for the 200Pb* and the neighboring CN even at higher l-values.

The quantum mechanical fragmentation theory based dynamical cluster decay model (DCM) has been applied to study the symmetric decay of compound nuclei (CN) 60Zn*, 60Ni* and 60Fe*. The effect of neutron to proton (N/Z) ratio in the decay of CN with A = 60, but formed through different reactions induced by same projectile 4He having same incident energy, have been investigated. Although the contributions of light particles and intermediate mass fragments is more prominent than Symmetric mass fragments (SMFs) in this mass region. But in the present work we have explored the evolution of symmetric decay with changing N/Z for A = 60 CN, under study. We see that the value of preformation probability P0 and penetrability P for SMFs decreases with increase in N/Z ratio, consequently symmetric breakup goes out of favor for higher N/Z values i.e. symmetric decay is highly favored in the case of 60Zn* only having N=Z. Hence, the SMFs cross section σSMFs decreases with increasing N/Z, i.e., highest for N/Z =1. The effect of rising temperature on SMFs cross sections σSMFs have also been studied at three different values. Quite interestingly, the symmetric channel 30P + 30P, 30Si+ 30Si and 30Al+ 30Al, respectively, from CN 60Zn*, 60Ni* and 60Fe*, in the σSMFs, is largest for 60Zn* and smallest for 60Fe*. Moreover, the contributions of symmetric channels increase with increasing temperature of CN, except in the case of Fe*, for which it decreases then increase with rising temperature.

In the present work, the clustering effects on the reaction dynamics of compound systems 24,25 M g ⁎ formed via respective entrance channels C 12 + 12 C and C 13 + 12 C are studied within the collective clusterization approach using the dynamical cluster decay model (DCM). Except experimentally observed 6,7Li and 7,8,9Be fragments we have also studied 5He, 10,11B and 11,12C fragments. We have explored, firstly the effect of pairing coefficient and results shown the minute change in clustering effects due to its inclusion or non-inclusion, as the change in pairing energy coefficient at the given temperature of the reaction is not much significant. We see the enhancement in preformation probability of the fragments having the α-cluster structure in their complementary fragments. Secondly, the role of level density parameter has been investigated for both the spherical and deformed configurations. It is found that by changing level density parameter if there is enhancement in l-summed up preformation probability of a particular fragment then there is decrease in the l-summed up penetrability of the same fragment and vice versa, which accordingly affects the yields of the respective fragments. The DCM calculated cross sections follow the trend of experimental observations. The experimentally observed 6,7Li and 7,8,9Be fragments having complementary fragments 18F and 16,18O i.e. having α-cluster structure contributes more towards the yield as compared to fragments with absence of α-cluster.

A comparative analysis of intermediate mass fragments (IMFs) and light particles (LPs) [equivalently, evaporation residues (ERs)] in the decay of 26,27,28,29 Al ⁎ has been carried out for reactions O 16 + 10 , 11 B and O 18 + 10 , 11 B at the energy range 1 MeV ≤ E / A ≤ 4 MeV , within dynamical cluster decay model (DCM) of collective clusterisation approach. We find that, for IMFs having Z = 3 , 4 , 5 and 6 , the range of mass minima are ∑ i = 5 8 A i , ∑ i = 8 9 A i , ∑ i = 9 13 A i and ∑ i = 11 15 A i , respectively. With increase in the mass of compound nuclei, Z = 6 becomes more prominent as compared to its neighboring fragments which is also observed in the experimental data. The LPs cross sections ( σ L P s ) in the decay of 26–29 Al ⁎ are also estimated. We find that the value of ∑ P 0 of LPs for 26,27 Al ⁎ is less as compared to that for 28,29 Al ⁎ , contrary to the value of ∑ P . Eventually, the cross sections for LPs are having higher contribution in the decay of 28,29 Al ⁎ in agreement with the experimental data. As expected for light mass nuclei, the σ L P s for 26,27 Al ⁎ find better comparison with experimental data for spherical considerations rather than β 2 deformations. We also conform Bohr's hypothesis via the entrance channel independence for compound nucleus 28 Al ⁎ formed through O 18 + 10 B and F 19 + 9 Be channels at an excitation energy E C N ⁎ ∼ 44 MeV , by having a unique choice of neck length parameter Δ R for both the reactions.

A comparative decay analysis of $^{80}\mathrm{Zr}^{*}$, $^{80}\mathrm{Sr}^{*}$, and $^{80}\mathrm{Kr}^{*}$ isobaric nuclear systems formed in $^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$, $^{16}\mathrm{O}+^{64}\mathrm{Zn}$, and $^{32}\mathrm{S}+^{48}\mathrm{Ca}$ reactions, respectively, has been conducted to investigate the $N/Z$ dependence of different decay modes within a dynamical cluster-decay model based on the collective clusterization approach of quantum mechanical fragmentation theory. The comparative contributions of the emission of light particles (LPs), intermediate mass fragments (IMFs), and symmetric mass fragments (SMFs) in the total fusion cross-sections, ${\ensuremath{\sigma}}_{\mathrm{fusion}}$, have been calculated. The results show that LPs have a major contribution to ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ in the decay of all three compound nuclei (CN). The percentage contribution of LPs is larger for CN with higher $N/Z$ ratio. The IMFs and SMFs cross-section are comparatively low in the total ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ but their emissions are in competition in the decay process. The results show that the shape of mass distribution evolves from symmetric to asymmetric with increasing $N/Z$ ratio. The yield around SMFs is greater for the system having the lowest $N/Z$ ratio. This may be attributed to higher ${P}_{0}$ for the symmetric exit channel, particularly at higher $\ensuremath{\ell}$ values. The calculated fusion cross-sections for all three CN are in good agreement with the experimental data.

The mechanism involved in compound nucleus formation through heavy ion induced fusion reactions at near- and sub-barrier energies has been stimulating the interest of both experimentalists and theoreticians. The study of fusion reactions is important not only for the production of superheavy elements but also to unfold the mysteries involved in the evolution of neutron stars and nucleosynthesis of elements in astrophysical scenarios. The detection of gravitational waves originating from the merging of two black holes, and the possibility of observing similar events originating from black-hole--neutron-star mergers, highlighted the necessity of understanding the behavior of neutron-rich nuclear matter. One of the potential methods to understand the character of neutron-rich matter is through the study of fusion of an isotopic chain of reactions. Recently, the first experimental evidence of fusion enhancement at near-barrier energies for neutron-rich nuclei was reported for the light and mid-mass regime. To understand the dynamics involved in such reactions, the investigation of K-induced reactions has been performed using the quantum mechanical fragmentation based dynamical cluster-decay model (DCM). The experimental fusion cross sections of $^{39,47}\mathrm{K}+^{28}\mathrm{Si}$ are reproduced using DCM and, further, the fusion cross sections are predicted for other isotopes of K beam on $^{28}\mathrm{Si}$ to investigate the fusion enhancement as a function of neutron number. It has been observed that fusion enhancement is significant at near-barrier energies for neutron-rich nuclei. The fusion enhancement observed is larger for odd neutron number nuclei as compared to adjacent neutron nuclei. This indicates the influence of unpaired neutrons on fusion cross sections. Also, the fusion cross sections predicted in the present work will act as input for planning more experimental measurements.

The decay of 28S i* and 30S i* compound nuclei (CN) formed at sub-barrier energies, in the reactions induced by stable projectile 16O and exotic projectile 18O, respectively, has been investigated within the quantum mechanical fragmentation theory based dynamical cluster-decay model (DCM). The collective potential energy surface shows that xα-type (x is an integer) clusters are minimized in the decay of 28S i* while in case of 30S i* in addition to xα-type clusters, np-xα (n, p are neutron and proton, respectively) type clusters are also minimized. These minimized fragments have more preformation probability P0, which is an important factor through which nuclear structure effects of decaying CN are probed, within DCM. The results show that light particles (LPs) are contributing mostly in the fusion cross-section, σfusion. In case of 30S i*, the contribution of 1n is highest and more compared to 4He in case of 28S i*, which seems to play an important role in fusion enhancement. The DCM calculated σfusion for both the CN formed with same Ec.m. = 7.0 MeV gives more value for σfusion of 30S i*, in agreement with the experimental data.

Using the preformed cluster model (PCM) of Gupta and collaborators, we have deduced empirically the preformation probability P0emp from experimental data on both the α and exotic-cluster radioactive decays in the trans-lead region having doubly magic 208 Pb or its neighboring nuclei as daughters, using the spherical and (in some cases) deformed relativistic mean field (RMF) densities. For spherical considerations, the P0α(emp) for alpha-decays is almost constant ~ 10-2 - 10-3 for all the parent nuclei studied, and P0c(emp) for cluster-decays of the same parents decrease with increasing size of cluster. The results obtained for spherical P0c(emp) are within two to three orders of magnitude of the well accepted phenomenological formula of Blendowske-Walliser (BW), which led us to propose a new empirical formula. The use of deformed RMF densities, however, tend to bring the results closer to BW formula.

The decay of compound nucleus 202 Pb *, formed in entrance channel reaction 48 Ca +154 Sm at different incident energies, is studied by using the dynamical cluster-decay model (DCM) where all decay products are calculated as emissions of preformed clusters through the interaction barriers. The calculated results show an excellent agreement with experimental data for the fusion-evaporation residue cross-section σ ER together with the fusion-fission cross-section σ FF (taken as a sum of the energetically favored symmetric [Formula: see text] and near symmetric A=65–75 plus complementary fragments), and the competing, non-compound-nucleus quasi-fission cross-section σ QF where the entrance channel is considered not to loose its identity (and hence with preformation factor P0=1). The interesting feature of this study is that the three decay processes (ER, FF and QF) are quite comparable at low energies, ER being the most dominant, whereas at higher energies FF becomes most probable followed by ER and QF. The prediction of two fission windows, the symmetric fission (SF) and the near symmetric fission (nSF) whose contribution is more at lower incident energies, suggests the presence of a fine structure effect in the fusion-fission of 202 Pb *. This result is attributed to the shell effects (magic shells) playing effective role in the fragment preformation yields for 48 Ca +154 Sm reaction at lower excitation energies, giving rise to "shoulders", to an otherwise Gaussian FF mass distribution, responsible for the QF process. As a further verification of this result, absence of "shoulders" (hence, the QF component) in the decay of 192 Pb * due to 48 Ca +144 Sm reaction is also shown to be given by the calculations, in agreement with experiments. The only parameter of the model is the neck-length ΔR which shows that the ER occurs first, having the largest values of ΔR, and the FF and QF processes occur almost simultaneously at lower incident energies but the FF takes over QF at higher incident energies. In other words, the three processes occur in different time scales, QF competing with FF at lower incident energies.

The dynamics of compound nuclei formed in the reactions using loosely bound projectiles are analyzed within the framework of the dynamical cluster-decay model (DCM) of Gupta and Collaborators. We have considered the reactions with neutron-rich and neutron-deficient projectiles, respectively, as $^{7}\mathrm{Li}$, $^{9}\mathrm{Be}$, and $^{7}\mathrm{Be}$, on various targets at three different ${E}_{\mathrm{lab}}$ energies, forming compound nuclei in the mass region $\mathrm{A}\ensuremath{\sim}30--200.$ For these reactions, the contributions of light-particle (LP, $A\ensuremath{\le}4$) cross sections ${\ensuremath{\sigma}}_{\mathrm{LP}}$, energetically favored intermediate-mass-fragment (IMF, $5\ensuremath{\le}{A}_{2}\ensuremath{\le}20$) cross sections ${\ensuremath{\sigma}}_{\mathrm{IMF}}$, as well as the fusion-fission ff cross sections ${\ensuremath{\sigma}}_{\mathrm{ff}}$ constitute the ${\ensuremath{\sigma}}_{\mathrm{fus}}\phantom{\rule{0.16em}{0ex}}(={\ensuremath{\sigma}}_{\mathrm{LP}}+{\ensuremath{\sigma}}_{\mathrm{IMF}}+{\ensuremath{\sigma}}_{\mathrm{ff}})$, i.e., the contributions of the emitted LPs, IMFs, and ff fragments are added for all the angular momenta up to the ${\ensuremath{\ell}}_{\mathrm{max}}$ value for the respective reactions. Interestingly, we find that the empirically fitted neck-length parameter $\mathrm{\ensuremath{\Delta}}{R}^{\mathrm{emp}}$, the only parameter of the DCM, is uniquely fixed to address ${\ensuremath{\sigma}}_{\mathrm{fus}}$ for all the reactions having the same loosely bound projectile at a chosen incident laboratory energy. It may be noted that, in DCM, the dynamical collective mass motion of preformed LPs, IMFs, and ff fragments or clusters, through the modified interaction potential barrier, are treated on parallel footing. The modification of the barrier is due to nonzero $\mathrm{\ensuremath{\Delta}}{R}^{\mathrm{emp}}$, and the values of corresponding modified interaction-barrier heights $\mathrm{\ensuremath{\Delta}}{V}_{B}^{\mathrm{emp}}$ for such reactions are almost of the same order, specifically at the respective ${\ensuremath{\ell}}_{\mathrm{max}}$ value.

The target-like C-yield in the decay of compound systems 32 S ∗ and 31 P ∗ formed in 20 Ne+ 12 C and 19 F+ 12 C reactions at E ∗ CN=60 MeV, is studied for the contribution of fusion-fission (ff) decay cross section σ ff and the deep inelastic (DI) orbiting σorb from the compound nucleus (CN) and non-compound nucleus nCN processes, respectively. The calculations are performed using the collective clusterization of fragments within the dynamical cluster-decay model (DCM) of Gupta and collaborators. Besides studying the compe- tition between ff and DI orbiting phenomenon in the C-yield of these systems, we exclusively investigate the preformation and barrier penetration probabilities P0 and P as a function of angular momentumvalues which subsequently affects the contributions of σ ff and σorb. For calculating the contribution of σ ff in the C-yield, we have added the contributions from all the minimized intermediate mass fragments (IMFs) for Z= 6i n the calculated fragmentation potentials for 32 S ∗ (IMFs 11,12,13 C are minimized) and for 31 P ∗ (IMFs 12,13 C are min- imized), while calculating subsequently, P0 and the P for these IMFs. The distribution of preformed clusters/ fragments as a function of fragment mass visibly explore the nuclear structure effects for the C-yield in decay of these compound systems, wherein, it is shown to be more favoured in the decay of 31 P ∗ in comparison to 32 S ∗ decay. The contribution of σorb to the C-yield is calculated from P at different allowed � -values (uptomax and also P≤1) of the outgoing fragments (same as that in the entrance channel, i.e., P0=1). Though preliminary but useful results indicates the competition between the CN and nCN process in the C-yield for the compound system 32 S ∗ only while the decay of 31 P ∗ is of pure CN origin, as observed in the experimental study. The calculations are in good comparison with the available experimental data.

The entrance-channel effects in the decay of hot and rotating compound nucleus 48 Cr *, formed in symmetric 24 Mg +24 Mg and asymmetric 36 Ar +12 C reactions, are studied as collective clusterization process, for emissions of both the light particles (LPs) as well as the intermediate mass fragments (IMFs), with in the dynamical cluster-decay model (DCM). We find that the little differences observed in the decay of equilibrated compound nucleus 48 Cr *, formed in the two entrance channels with about the same excitation energy, are not in variance with the Bohr's independence hypothesis. In other words, the present study confirms the entrance-channel independence of the decay of compound nucleus 48 Cr * formed due to different target-projectile combinations with similar excitation energies. The collective clusterization process is shown to contain the complete structure of the measured fragment cross sections as well as average total kinetic energies.

Nucleus-nucleus potentials are determined in the framework of the double-folding model for a new microscopic nucleon-nucleon (NN) interaction relativistic mean field-3-Yukawa (R3Y) derived from the popular relativistic mean-field theory Lagrangian, and the results are compared for the use of Michigan-3-Yukawa (M3Y) effective NN interactions. The double-folding potentials so obtained are further taken up in the context of the preformed cluster model (PCM) of Gupta and collaborators and the barrier penetration model to study respectively the ground-state (g.s.) {alpha}-decay and low-energy fusion reactions. In this paper, using PCM, we deduce empirically the {alpha} preformation probability P{sub 0}{sup {alpha}(emp)} from experimental data on a few g.s. {alpha} decays in the trans-lead region. For fusion reactions, two projectile-target systems {sup 12}C+{sup 208}Pb and {sup 16}O+{sup 208}Pb are selected for calculating the barrier energies as well positions, fusion cross sections ({sigma}{sub fus}), and fusion barrier distribution [D(E{sub c.m.})]. The barrier energies and positions change for the R3Y NN interactions in comparison with those of the M3Y NN interactions. We find that in the {alpha}-decay studies the values of P{sub 0}{sup {alpha}(emp)}(R3Y) are similar to those of P{sub 0}{sup {alpha}(emp)}(M3Y). Further, both NN interactions give similar {sigma}{sub fus} values using the Wong formula specifically when more » the R3Y NN interaction calculated {sigma}{sub fus} values are reduced by 1.5 times, and the results are in agreement with the experimental data for both the systems, especially for the higher energies. Results for D(E{sub c.m.}) are also quite similar for both choices of NN interaction. « less

We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability ${{P}_{0}}^{\mathrm{emp}}$ from the experimental data on both the $\ensuremath{\alpha}$- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic $^{208}\mathrm{Pb}$ or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the $\ensuremath{\alpha}$ and heavier clusters in radioactive nuclei. ${{P}_{0}}^{\ensuremath{\alpha}(\mathrm{emp})}$ for $\ensuremath{\alpha}$ decays is almost constant ($~$${10}^{\ensuremath{-}2}$--${10}^{\ensuremath{-}3}$) for all the parent nuclei considered here, and ${{P}_{0}}^{c(\mathrm{emp})}$ for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for ${{P}_{0}}^{c(\mathrm{emp})}$ are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.

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.

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.

The decay of the {sup 246}Bk* nucleus, formed in entrance channel reactions {sup 11}B+{sup 235}U and {sup 14}N+{sup 232}Th at different incident energies, is studied by using the dynamical cluster-decay model (DCM) extended to include the deformations and orientations of nuclei. The main decay mode here is fission. The other (weaker) decay channels are the light particles evaporation (A{

The dynamical cluster-decay model (DCM) of Gupta and collaborators has been applied successfully to the decay of very-light (A ∼ 30), light (A ∼ 40 − 80), medium, heavy and super-heavy mass compound nuclei for their decay to light particles (evaporation residues, ER), fusion-fission (ff), and quasi-fission (qf) depending on the reaction conditions. We intend to extend here the application of DCM to study the extreme case of decay of very-light nuclear systems 20,21,22 Ne ∗ formed in 10,11 B+ 10,11 B reactions, for which experimental data is available for their binary symmetric decay (BSD) cross sections, i.e., σBS D. For the systems under study, the calculations are presented for the σBS D in terms of their preformation and barrier penetration probabilities P0 and P. Interesting results are that in the decay of such lighter systems there is a competing reaction mechanism (specifically, the deep inelastic orbiting of non-compound nucleus (nCN) origin) together with ff .W e have emipirically estimated the contribution of σnCN . Moreover, the important role of nuclear structure characteristics via P0 as well as angular momentumin the reaction dynamics are explored in the study.

The study of the decay of 32S* and 31P* compound systems formed in 20Ne+12C and 19F+12C reactions, respectively, is further extended on the basis of collective clusterization process within the dynamical cluster model (DCM) of Gupta and collaborators, with the effects of deformations and orientations included, at an excitation energy E*CN=60 MeV. In the present study, we have investigated the effects of deformations and orientations on the target, i.e., 12C like yield, denoted C-yield (σC), which contains fusion-fission (FF) decay cross-section, σFF, from compound nucleus process and deep inelastic orbiting (DIO) cross-section, σD1O, from non-compound nucleus process. As observed in one of our earlier study for 32S* system there is a competition between FF and DIO, while, for 31P* there is a contribution of FF cross-section only, in the total C-yield. The comparative analysis of C-Yield for the considerations of spherical and oriented nuclei, shows similar results with the only difference of the values of neck length parameter (ΔR), which are more for the later case. The calculated cross-sections ac show good agreement with experimental data for both the considerations.

A new microscopic nucleon-nucleon (NN) interaction has been derived for the first time from the popular relativistic mean field theory (RMFT) Lagrangian. The NN interaction so obtained remarkably relate to the inbuilt fundamental parameters of RMFT. Furthermore, by folding it with the RMFT-densities of cluster and daughter nuclei to obtain the optical potential, it's application is also examined to study the exotic cluster radioactive decays, and results obtained found comparable with the successfully used M3Y phenomenological effective NN interactions. The presently derived NN-interaction can also be used to calculate a number of other nuclear observables.