Energy-dependent Woods-Saxon Potential Model Research Articles

Analysis of formation and decay of Ba*122,128 formed via Ni58,64+Ni64 reactions near the Coulomb barrier

The fusion mechanics of $^{58}\mathrm{Ni}+^{64}\mathrm{Ni}$ and $^{64}\mathrm{Ni} +^{64}\mathrm{Ni}$ reactions is analyzed by using the energy dependent Woods-Saxon potential (EDWSP) model and the subsequent decay dynamics of $^{122}\mathrm{Ba}^{*}$ and $^{128}\mathrm{Ba}^{*}$ isotopes formed in these fusion channels is examined via the dynamical cluster-decay model (DCM). In the EDWSP model, the energy dependent nature of the Woods-Saxon potential causes modifications in the profile of the fusion barrier between fusing nuclei. Such barrier modifications lead to the lowering of the effective fusion barrier of the colliding nuclei. Hence, EDWSP outcomes satisfactorily describe the energy dependence of fusion cross sections of the chosen reactions in near- and sub-barrier energy regions. Following this, the fragmentation of compound nuclei $^{122}\mathrm{Ba}^{*}$ and $^{128}\mathrm{Ba}^{*}$ formed using the above-mentioned reactions is investigated by using the collective clusterization approach of DCM. The calculations are done for quadrupole $({\ensuremath{\beta}}_{2})$ choice of fragmentation with hot configurations having optimized orientations. The evaporation residues' cross-section data lying within beam energy $({E}_{\mathrm{beam}})$ = 171--220 MeV are nicely addressed. The comparative analysis of decaying $^{122}\mathrm{Ba}^{*}$ and $^{128}\mathrm{Ba}^{*}$ nuclei is worked out in terms of fragmentation potential and preformation probability, along with the investigation of barrier characteristics.

Influence of neutron transfer channels and collective excitations in the fusion of Si28 with Zr90,92,94,96 targets

This work theoretically explores the role of neutron transfer channels and/or collective inelastic surface excitations in the fusion of $^{28}\mathrm{Si}$ with $^{90,92,94,96}\mathrm{Zr}$ targets by using the coupled channel theory and the energy dependent Woods-Saxon potential (EDWSP) model. The series of $^{90,92,94,96}\mathrm{Zr}$ targets is quite interesting due to the fact that the possibilities of neutron transfer channels with positive ground state $Q$ values increase with the increase of isotopic mass. For $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ reaction, the influences of inelastic surface excitations turned out to be important and coupling of such channels to their relative motion reproduced the experimental data. In the case of $^{28}\mathrm{Si}+^{92}\mathrm{Zr}$ reaction, in addition to consideration of low lying states such as ${2}^{+}$ and ${3}^{\ensuremath{-}}$ vibrational states of colliding nuclei, the coupling to two neutron pickup channels is necessarily required to address the sub-barrier fusion anomalies. For $^{28}\mathrm{Si}+^{94,96}\mathrm{Zr}$ reactions, the inclusions of multiphonon states of type ${2}^{+}$ and ${3}^{\ensuremath{-}}$ of colliding nuclei were not able to reproduce the fusion enhancement particularly at below barrier energies. In this case, neutron transfer channels with positive ground state $Q$ value play a crucial role in the enhancement of fusion cross-section data at sub-barrier energies and therefore must be included in the coupled channel description. In distinction, in the EDWSP model, the energy dependence in the nucleus-nucleus potential causes barrier modification effects and subsequently induces a barrier lowering phenomenon. In this way, the EDWSP based outcomes reasonably address the sub-barrier fusion anomalies of $^{28}\mathrm{Si}+^{90,92,94,96}\mathrm{Zr}$ reactions and thus impacts of dominant intrinsic channels are intrinsically included due to the dynamical nature of the energy dependent interaction potential. For studied systems, the EDWSP outcomes are able to achieve an agreement with the portion of above barrier fusion data within 10% with a probability greater than 90%. Within this model, 33 fusion data points out of 38 fusion data points lie within 5%. Only five fusion data points lie within 10% and thereby the EDWSP model adequately addresses the fusion anomalies of the chosen reactions. The smaller values of ${\ensuremath{\chi}}^{2}$ analysis for the EDWSP calculations, which range from 2.82 to 3.14, indicate that the model predictions appropriately describe the observed fusion dynamics of the studied reactions.

Projectile breakup effects in the fusion dynamics of 6,7Li +144,152Sm reactions around Coulomb barrier

This work emphasized the role of the projectile breakup channel by studying the complete fusion (CF) and incomplete fusion (ICF) dynamics of [Formula: see text] reactions. The theoretical calculations for the chosen reactions have been done by opting for the coupled channel approach and the energy dependent Woods–Saxon potential (EDWSP) model. The below barrier fusion enhancements of the studied reactions are reasonably addressed by the outcomes of the adopted models, which in turn can be attributed to the couplings of nuclear structure degrees of freedom of the collision partners to their relative motion. In contrast, at above barrier energies, the CF cross-section data of the chosen reactions are found to be suppressed significantly when compared with the predictions made by using the present models. Interestingly, the fusion suppression factors of the given reactions can be minimized considerably with respect to the reported value when it is analyzed within the framework of the EDWSP model. For instance, in case of [Formula: see text] ([Formula: see text] reaction, the magnitude of fusion suppression factor is minimized up to 7% (13%) relative to the reported value whereas for [Formula: see text] ([Formula: see text] reaction, the fusion suppression factor is found to be less by 7% (8%) with reference to the reported value. Such suppression effects can be correlated with the low breakup threshold of alpha breakup channel associated with the loosely bound projectile. The projectiles being weakly bound systems split into two charged fragments and either of the breakup components is absorbed by the target resulting in the reduction of incoming flux going into fusion channel. The flux lost from the CF channel appears in the form of ICF yields. For [Formula: see text], total fusion (TF) cross-sections that are sum of CF and ICF cross-sections are also analyzed in conjunction with the EDWSP model and thus reasonably explained by the model calculations. In order to identify the ICF contribution, the ratio of ICF/TF cross-section data of [Formula: see text] reaction has been examined and thus properly addressed by using the EDWSP model. The presence of ICF component in TF cross-section clearly pointed out the breakup of projectile due to its loosely bound nature prior to the Coulomb barrier. Although ICF data of other systems are not available in the literature, a similar behavior is expected for ICF and TF data for [Formula: see text] and [Formula: see text] reactions.

Investigation of contribution of complete and incomplete fusion in the total fusion process of 6Li+90,96Zr reactions in vicinity of the Coulomb barrier

The impacts of breakup channel on fusion of L6i with Z90,96r-nuclei are investigated within the context of the coupled channel model and the energy dependent Woods-Saxon potential (EDWSP) model. For studied reactions, the complete fusion (CF) cross-sections data at above barrier energies are found to be suppressed with respect to the calculated results. In case of L6i+90Zr (L6i+96Zr) reaction, the CF data at above barrier energies is found to be less by 34% (25%) with reference to the estimations of the coupled channel approach. However, EDWSP model calculations predict fusion suppression up to 20% (10%) for L6i+90Zr (L6i+96Zr) reaction. The extracted suppression factor for L6i+90Zr(L6i+96Zr) reaction is smaller by 14% (15%) than the reported value. Such effects can be accredited to the low threshold of α-breakup channel associated with the weakly bound system and hence may be responsible for incomplete fusion (ICF) products. Therefore, the total fusion (TF) cross-sections that are the sum of complete fusion (CF) and incomplete fusion (ICF) yields, are not expected to reduce in the above barrier regions when compared with no-breakup case. In this regard, the TF cross-sections data are analyzed within the view of the EDWSP model and so obtained calculations have close agreement with the TF cross-sections data. The EDWSP based results appreciably explained CF, ICF and TF cross-sections data over a wide range of energies around the Coulomb barrier. Although, the cluster-transfer or stripping process from the ground state of weakly bound nucleus L6i may significantly contribute to ICF yields, therefore, the presence of ICF product is an indication of the partial absorption of projectile by target, henceforth, reduces the CF cross-section data in above barrier regimes.

Interplay of neutron transfer and collective degrees of freedom in the fusion dynamics of 16O +76Ge and 18O +74Ge reactions

This work examined the fusion dynamics of [Formula: see text] and [Formula: see text] reactions within the framework of the static Woods–Saxon potential model, the energy dependent Woods–Saxon potential (EDWSP) model and coupled channel formulation. The effects of inelastic surface excitations, static deformation of colliding pairs and /or neutron transfer channels on fusion process are investigated through the coupled channel method. The calculations based upon static Woods–Saxon potential in conjunction with one-dimensional Wong formula strongly under predict the fusion data of [Formula: see text] and [Formula: see text] reactions at sub-barrier energies. However, such discrepancies are removed if one uses couplings to nuclear structure degrees of freedom of reacting nuclei. The coupled channel calculations obtained by considering the vibrational nature of the colliding nuclei fairly reproduce the fusion data of [Formula: see text] reactions. For this reaction, the neutron transfer channels, which are expected to influence strongly the fusion yields at below barrier energies, in reality contribute very weakly to fusion process. While in case of [Formula: see text] reaction, the consideration of vibrational couplings as well as the rotational couplings for target provides a reasonable explanation to the fusion cross-section data at near and above barrier energies. In distinction, the energy dependence in the nucleus–nucleus potential causes barrier modulation effects and subsequently modifies the barrier profile of the interaction barrier in such a way that the effective fusion barrier between the colliding pair reduces. This ultimately brings larger fusion cross-sections over the outcomes of one-dimensional barrier penetration model and the EDWSP model based calculations appreciably explained the fusion dynamics of chosen reaction at energy spanning around the Coulomb barrier. Both models (EDWSP and coupled channel model) lead to barrier lowering effects and modeled quantum tunneling in different way, henceforth, adequately explore the fusion dynamics of the studied reactions in near and above barrier energy regions.

Fusion dynamics of 30Si +238U reaction using variety of interaction potentials

The fusion dynamics of [Formula: see text] reaction has been studied using different theoretical approaches like energy-dependent Woods–Saxon potential (EDWSP) model, coupled channel formulation and Wong approach. At sub-barrier energies, the anomalously large enhancement of the fusion cross-section signifies the importance of barrier modification effects for the adequate addressal of experimental data. The EDWSP model, wherein barrier modification effects are introduced via the energy-dependent diffuseness parameter, is used to examine the sub-barrier fusion anomalies. In the framework of coupled channel model, the impacts of collective excitations and/or static deformations of colliding partners are incorporated in the fusion dynamics. In Wong formula, the role of different Skyrme forces such as SIII, KDE0v1, SkT1, SSk, GSkI is analyzed to address the observed fusion enhancement around the Coulomb barrier. Among these, GSkI and SSk forces seem more appropriate for the addressal of fusion dynamics at sub-barrier energies while SIII, SkT1 and KDE0v1 forces give relatively better results at the above barrier region. The SSk (GSkI) force at higher energies overestimate the experimental data and hence treated with the [Formula: see text]-summed Wong approach. The effect of deformations and optimum orientations is duly incorporated in the calculation and hence gives better description to the observed data. In addition, the fusion cross-sections are predicted over extreme energies using EDWSP and [Formula: see text]-summed Wong approach. It is worth mentioning here that the different theoretical approaches (EDWSP, coupled channel and Wong) induce similar kinds of barrier lowering effects, henceforth, they reasonably describe the sub-barrier fusion data of [Formula: see text] reaction.

Dynamics of complete and incomplete fusion of 6,7Li, 15N and 16O with a 209Bi target

The dynamics of complete and incomplete fusion of 6,7Li, 15N and 16O with a common target (209Bi) around the Coulomb barrier are analyzed within the context of the coupled channel formulation and the energy dependent Woods-Saxon potential (EDWSP) model. The calculated results are compared with experimental fusion cross-sections and it has been shown that complete fusion (CF) data of weakly bound projectile with a heavy target (209Bi) gets suppressed at above barrier energies. In the case of the 6Li + 209Bi (7Li + 209Bi) reaction, the CF data at above barrier energies is reduced by 34% (26%) with reference to the expectations of the coupled channel approach. However, the theoretical estimations due to the EDWSP model can minimize the suppression factor by 9% with respect to the reported value and consequently the portion of above barrier CF cross-section data of 6Li + 209Bi (7Li + 209Bi) reaction is suppressed by 25% (17%) when compared with the present model calculations. This fusion inhibition can be correlated with the low breakup threshold of projectile which in turn breaks up into two fragments in the entrance channel prior to fusion barrier. The total fusion (TF) data, which is sum of complete fusion (CF) data and incomplete fusion (ICF) data, is not suppressed when compared with the predictions of the theoretical approaches and thus breakup channel has very little influence on the total fusion cross-sections. Although the breakup fragments appeared in both reactions, the enhanced suppression effects observed for the lighter projectile can be correlated with its low binding energy associated with the $\alpha$ -breakup channel. Further the outcomes of the EDWSP model reasonably explained the ICF contribution appeared in the fusion of 6,7Li + 209Bi reactions. In contrast to this, the observed fusion dynamics of 15N + 209Bi and 16O + 209Bi reactions, wherein the collective excitations such as two phonon, three phonon vibrational states contribute to produce below barrier fusion enhancement, has been adequately explored by the adopted models, and henceforth ensures the stability of well bound nuclei against breakup effects.

Fusion dynamics of stable and weakly bound colliding systems

This work systematically analyzed the fusion dynamics of the projectile-target combinations involving stable and loosely bound systems within the view of the energy-dependent Woods–Saxon potential model (EDWSP model) and the coupled channel approach. The different projectiles are bombarded onto series of Sm-isotopes, which possess the dominance of the different kinds of the nuclear structure degrees of freedom and with the increase of the neutron richness, the Sm-isotopes gradually shift from spherical shape to a statically deformed shape. In the fusion of [Formula: see text] reaction, the impacts of vibrational degrees of freedom of the colliding nuclei are dominant while in the case of [Formula: see text] systems, the rotational states of the deformed target isotopes have a strong impression on the below-barrier fusion data. The heavier target isotopes ([Formula: see text] also exhibit the higher order deformation such as [Formula: see text], [Formula: see text]-deformation parameter in its ground state and couplings to such channels must be incorporated in theoretical calculations in order to achieve close agreement with the sub-barrier fusion data. However, in the case of the loosely bound systems, the projectile breakup channel significantly affects the fusion excitation functions in the domain of the Coulomb barrier. To ensure the role of the projectile breakup channel, the fusion of the different loosely bound projectiles ([Formula: see text] and [Formula: see text] with Sm-isotopes are investigated, wherein the above-barrier fusion data of these reactions are suppressed with reference to the coupled channel calculations. This hindrance is the result of the projectile breakup effects that occur as a consequence of the breakup of the projectile before reaching the fusion barrier due to its low binding energy. However, in the EDWSP model calculations the magnitude of the hindrance of the above-barrier fusion data of [Formula: see text] and [Formula: see text] reactions is reduced by a factor varying from 7% to 13% with respect to a value reported in the literature. In contrast to this, the sub-barrier fusion enhancement of [Formula: see text] and [Formula: see text] reactions is the result of the dominance of the nuclear structure degrees of freedom of the colliding systems.

Role of Barrier Modification and Nuclear Structure Effects in Sub-Barrier Fusion Dynamics of Various Heavy Ion Fusion Reactions

The role of barrier modifications and the relevant nuclear structure effects in the fusion of the $$ {}_8{}^{16}O+{}_{62}{}^{144,148,150,152,154}Sm $$ and $$ {}_3{}^{6,7}Li+{}_{62}{}^{152}Sm $$ systems is analyzed within the context of the energy-dependent Woods-Saxon potential model (EDWSP model) and the coupled channel model. For the $$ {}_8{}^{16}O+{}_{62}{}^{144,148,150,152,154}Sm $$ reactions, where the colliding pairs are stable against breakup, the collective excitations and/or static deformations are sufficient to account for the observed fusion enhancement. In contrast, the model calculations overpredict the complete fusion data at above - barrier energies for the $$ {}_3{}^{6,7}Li+{}_{62}{}^{152}Sm $$ systems, where the importance of projectile breakup effects has been pointed out. Due to the low threshold of the alpha-breakup channel, the weakly bound projectiles $$ \left({}_3{}^{6,7}Li\right) $$ break up into charged fragments before reaching the fusion barrier and consequently the complete fusion cross section is suppressed by 28% (25%) in the $$ {}_3{}^6Li+{}_{62}{}^{152}Sm\;\left({}_3{}^7Li+{}_{62}{}^{152}Sm\right) $$ reaction with respect to predictions of coupled channel calculations. However, the EDWSP model based calculations can minimize the suppression factor by as much as of 13% (8%) in the $$ {}_3{}^6Li+{}_{62}{}^{152}Sm\;\left({}_3{}^7Li+{}_{62}{}^{152}Sm\right) $$ reaction with reference to the predictions made by the coupled channel calculations. Therefore, the complete fusion data of the $$ {}_3{}^6Li+{}_{62}{}^{152}Sm\;\left({}_3{}^7Li+{}_{62}{}^{152}Sm\right) $$ reaction at above - barrier energies is reduced by 15% (17%) with respect to the expectations of the EDWSP model. The extracted suppression factors for the studied reactions are due to the modifications of the barrier profile as a consequence of the energy - dependence in nucleus-nucleus potential, and thus greater barrier modifications occur for more weakly bound system, which in turn, confirms the breakup of projectile in the incoming channel.

Complete and incomplete fusion dynamics of 6,7Li + 159Tb reactions near the Coulomb barrier

The complete fusion (CF) and incomplete fusion (ICF) cross-sections are estimated for 6, 7Li + 159Tb reactions using the energy-dependent Woods-Saxon potential model (EDWSP model) and dynamical cluster-decay model (DCM). The CF data of the 6Li + 159Tb(7Li + 159Tb) reaction at above barrier energies is suppressed with reference to expectations of the EDWSP model by 25% (20%) which is smaller than the reported data by ∼ 9% (6%). This suppression is correlated with the projectile breakup effect. The projectiles 6,7Li are loosely bound systems, which may break up into charged fragments prior to reaching the fusion barrier and subsequently one of the fragment is captured by the target leading to the suppression of fusion data at above barrier energies. The sum of CF and ICF, which is termed as total fusion cross-section (TF), removes the discrepancies between theoretical predictions and the above barrier complete fusion data and hence is adequately explained via the EDWSP model over a wide range of energy spread across the Coulomb barrier. In addition to fusion, the decay mechanism of 6Li + 159Tb reaction is studied within the framework of the dynamical cluster-decay model (DCM). The breakup of the projectile (6Li) in the entrance channel indicates the presence of ICF, which is investigated further using the collective clusterization approach of DCM. The present theoretical analysis suggests that a larger barrier modification is needed to address the fusion data of chosen reactions in the below barrier energy region.

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.

Fusion suppression/fusion enhancement around the Coulomb barrier

This work explored the fusion dynamics of 36Li+2759Co, 49Be+50124Sn, 49Be+82208Pb, 2040Ca+50124Sn and 612C+82208Pb reactions by using energy dependent Woods–Saxon potential model (EDWSP model) and coupled channel model. The roles of projectile breakup channel on fusion process are directly reflected from fusion mechanism of 36Li+2759Co, 49Be+50124Sn and 49Be+82208Pb reactions. Whereas, the impacts of collective excitations and/or nucleon transfer channels on fusion process are evident from analysis of 2040Ca+50124Sn and 612C+82208Pb reactions. The total fusion data (sum of complete and incomplete fusion data) of 36Li+2759Co reaction is reasonably recovered by the EDWSP model calculations which in turn indicate that total fusion excitation function data is not suppressed with reference to theoretical predictions. In contrast, for 49Be+50124Sn (49Be+82208Pb) reaction, the above barrier fusion data is suppressed with respect to the expectations of coupled channel approach and single barrier penetration model by 28% (32%). However, the EDWSP model based calculations reduce the magnitude of suppression factor by 8% (12%) for 49Be+50124Sn (49Be+82208Pb) reaction and consequently the fusion data at above barrier energies is inhibited for both reactions by 20% with reference to the EDWSP model calculations. This fusion suppression can be correlated with loosely bound nature of the projectile. On the other hand, the above barrier fusion data of 2040Ca+50124Sn and 612C+82208Pb reactions is not inhibited with respect to the predictions of coupled channel approach and EDWSP method, henceforth, confirms stability of projectiles against breakup effects.

Role of projectile breakup effects and intrinsic degrees of freedom on fusion dynamics**Supported by Dr. D. S. Kothari Post-Doctoral Fellowship Scheme sponsored by University Grants Commission (UGC), New Delhi, India

This article analyzes the fusion dynamics of loosely bound and stable projectiles with Zr-target isotopes within the context of the coupled channel approach and the energy-dependent Woods-Saxon potential model (EDWSP model). In the case of the 28Si + 90Zr reaction, the coupling to the inelastic surface excitations results in an adequate description of the observed fusion dynamics while in case of the 28Si + 94Zr reaction, the coupling to collective surface vibrational states as well as the neutron (multi-neutron) transfer channel is necessary in the coupled channel calculations to reproduce the below-barrier fusion data. However, the EDWSP model calculation provides an accurate explanation of the fusion data of 28Si + 90,94Zr reactions in the domain of the Coulomb barrier. In the fusion of the 6Li + 90Zr reaction, the inclusion of the nuclear structure degrees of freedom recovers the observed sub-barrier fusion enhancement but results in suppression of the above barrier fusion data by 34% with respect to the coupled channel calculations. Using EDWSP model calculations, this suppression factor is reduced by 14% and consequently, the above-barrier fusion data of 6Li + 90Zr reaction is suppressed by 20% with reference to the EDWSP model calculations. Such fusion suppression at above-barrier energies can be correlated with the breakup of the projectile (6Li) before reaching the fusion barrier, as a consequence of low binding energy.

Absence of isotopic dependence of sub-barrier fusion enhancement in the formation of Sn-isotopes via different entrance channels

The roles of the intrinsic degrees of freedom of the colliding pairs, the entrance channel mass asymmetry effects and variation of the N/Z ratio in the formation of the Sn-isotopes via different channels are analyzed within the view of coupled channel approach and the energy dependent Woods-Saxon potential model (EDWSP model). In the fusion of T2248i + N2858,60,64i, T2246i + N2864i, T2250i + N2860i, and F919 + N4193b reactions, which result in the formation of different Sn-isotopes, the effects of inelastic surface excitations and multi-nucleon transfer channels are found to be dominant while the entrance channel mass asymmetry and variation of the N/Z ratio with neutron richness show a weak influence on the sub-barrier fusion dynamics. With the increase of the N/Z ratio, the strong isotopic sub-barrier fusion enhancement is expected for neutron rich target isotope. But such effects are found to be absent in the fusion dynamics of these reactions and consequently display a weak isotopic fusion enhancement at below barrier energies. Both coupled channel approach and the EDWSP model reasonably describe the observed fusion dynamics of chosen reactions. In addition, the EDWSP model based calculations are capable of providing an agreement with the experimental fusion cross-section data within 10%. For six heavy ion fusion reactions, only at 7 fusion data points out of 54 fusion data points does the deviation exceed 5% while 47 fusion data points lie within 5%. Therefore, within the view of the EDWSP model, it is possible to recover the above barrier portion of the fusion cross-section data within 5% with a probability greater than 87%.

Role of Barrier Modification and Inelastic Surface Excitations in Sub-Barrier Fusion of 16 32 S + 40 94 Zr Reaction

The fusion dynamics of 16 S+40 Zr reaction at near and sub-barrier energies is investigated within the context of different theoretical approaches. The various theoretical models like one-dimensional Wong formula, l-summed ex- tended Wong formula, the energy-dependent Woods-Saxon potential model (EDWSP model), and coupled channel for- mulation have been used to address the impacts of nuclear structure degrees of freedom of the colliding pairs. The roles of different Skyrme forces along with Wong formalism are also tested in the analysis of the sub-barrier fusion dynamics of the 16 S+40 Zr reaction. The influence of the low-lying sur- face vibrational states of the collision partners is investigated within the framework of coupled channel calculations per- formed by the code CCFULL. In the present work, it has been observed that the EDWSP model introduces barrier modifica- tion effects somewhat similar to those of the coupled channel approach, as well as those of using different Skyrme forces and hence it reasonably addresses the observed fusion data of 16 S+40 Zr reaction in the close vicinity of the Coulomb barrier.

Role of Projectile Degrees of Freedom in Sub-Barrier Fusion Dynamics

This work theoretically investigates the role of the projectile degrees of freedom on the fusion dynamics of various heavy-ion fusion reactions. The impact of the projectile breakup channel is studied for the fusion mechanism of the 4 9 Be + 39 89 Y, 6 12 C + 39 89 Y, and 16 32,34 S + 39 89 Y reactions within the view of the coupled channel approach and the energy-dependent Woods-Saxon potential model (EDWSP model). The above-barrier fusion cross-section data of the 4 9 Be + 39 89 Y reaction is suppressed by about 20 % with respect to the theoretical predictions of the coupled channel approach and the single barrier penetration model while this suppression factor is reduced to 10 % within the context of the EDWSP model calculations. Such fusion hindrance at above-barrier energies can be understood in terms of the projectile breakup effects that arise due to its low breakup threshold. However, the observed fusion enhancement of the 6 12 C + 39 89 Y and 16 32,34 S + 39 89 Y reactions, wherein the colliding pairs are stable against breakup, is adequately explained by the EDWSP model and the coupled channel approach in the whole range of energy around the Coulomb barrier. This reveals that the energy dependence in the nucleus-nucleus potential governs barrier modification effects (barrier height, barrier position, barrier curvature) in closely similar way as reflected from the coupled channel formulation.

Entrance Channel Mass Asymmetry Effects in Sub-Barrier Fusion Dynamics by Using Energy Dependent Woods–Saxon Potential**Supported by Dr. D.S. Kothari Post-Doctoral Fellowship Scheme sponsored by University Grants Commission (UGC), New Delhi, India

The present article highlights the inconsistency of static Woods–Saxon potential and the applicability of energy dependent Woods–Saxon potential to explore the fusion dynamics of , and reactions leading to formation of different Sn-isotopes via different entrance channels. Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods–Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations. However, the predictions of one-dimensional Wong formula based upon energy dependent Woods–Saxon potential model (EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy. Therefore, the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.

Analysis of fusion dynamics of colliding systems involving stable, loosely bound and halo nuclei

This article analyzed the fusion dynamics of stable nuclei, loosely bound nuclei and halo nuclei within the view of coupled channel approach and the energy dependent Woods–Saxon potential model (EDWSP model). The different projectiles ( and are bombarded onto common spherical target isotope ( wherein target isotope exhibits inelastic surface excitations as dominant mode of coupling. The fusion dynamics of reactions, wherein there is no signature of fusion suppression at above barrier energies, are adequately explained by both theoretical approaches in domain of Coulomb barrier. In case of reactions, the couplings of inelastic surface excitations of colliding systems remove the discrepancies between below barrier fusion data and expectations of one-dimensional barrier penetration model. However, at above barrier energies, the fusion excitation function data are suppressed in comparison to the theoretical predictions of both approaches. Interestingly, this suppression of above barrier fusion data is minimized by the present model calculation by a factor of 7% with respect to a value reported in literature. Within the view of the EDWSP model calculations, the above barrier fusion data of reaction are hindered by a factor of 25% and by a factor of 17% for reaction which is smaller than a value as pointed out in literature. The observed sub-barrier fusion dynamics of and reactions are reasonably described by the coupled channel model and the EDWSP model. Furthermore, the applicability of the EDWSP model has been tested for exploration of the fusion of reaction and hence due to barrier modification effects, the EDWSP model successfully explains the observed fusion enhancement of reaction. The present calculations clearly indicate that different theoretical approaches (coupled channel formulation and EDWSP model) induce similar kinds of barrier modification effects in the heavy ion fusion reactions.

Static and energy dependent nucleus–nucleus potential for description of near and sub-barrier fusion data

This article analyzes the validity of static Woods–Saxon potential and the energy-dependent Woods–Saxon potential (EDWSP) to explore the specific features of fusion dynamics of [Formula: see text] and [Formula: see text] systems. The intrinsic degrees of freedom, such as inelastic surface excitations, play a crucial role in the enhancement of sub-barrier fusion excitation functions over the expectations of the one-dimensional barrier penetration model. Role of dominant intrinsic degrees of freedom of collision partners are entertained within the context of coupled channel calculations. Furthermore, the one-dimensional Wong formula using static Woods–Saxon potential fails miserably to describe the fusion enhancement of [Formula: see text] and [Formula: see text] systems. However, the Wong formula along with the EDWSP model accurately explains the observed fusion enhancement of [Formula: see text] reactions. In the fusion of [Formula: see text] reaction, the above-barrier fusion data are suppressed by a factor of 0.66 with reference to the EDWSP model calculations while the below-barrier fusion data are adequately addressed by the EDWSP model and the coupled channel calculations. Therefore, the coupled channel calculations and the EDWSP model calculations reasonably describe the observed fusion mechanism of [Formula: see text] and [Formula: see text] reactions. This suggests that the energy dependence in the Woods–Saxon potential model introduces similar kinds of barrier modification effects (barrier height, barrier position, and barrier curvature) as reflected from the coupled channel calculations. In the EDWSP model calculations, significantly larger values of diffuseness ranging from a = 0.86 to 0.94 fm, which is much larger than a value extracted from the elastic scattering analysis, are needed to address the sub-barrier fusion data.

Static versus energy-dependent nucleus-nucleus potential for description of sub-barrier fusion dynamics of reactions**Supported by Dr. D. S. Kothari Post-Doctoral Fellowship Scheme sponsored by University Grants Commission (UGC), New Delhi, India

The static and energy-dependent nucleus-nucleus potentials are simultaneously used along with the Wong formula for exploration of fusion dynamics of reactions. The role of internal structure degrees of freedom of colliding pairs, such as inelastic surface vibrations, are examined within the context of coupled channel calculations performed using the code CCFULL. Theoretical calculations based on the static Woods-Saxon potential along with the one-dimensional Wong formula fail to address the fusion data of reactions. Such discrepancies can be removed if one uses couplings to internal structure degrees of freedom of colliding nuclei. However, the energy-dependent Woods-Saxon potential model (EDWSP model) accurately describes the sub-barrier fusion enhancement of reactions. Therefore, in sub-barrier fusion dynamics, energy dependence in the nucleus-nucleus potential governs barrier modification effects in a closely similar way to that of the coupled channel approach.