Energy Dependent Woods Saxon Potential Research Articles

Fusion dynamics of 9Be + 197Au reaction at near and above barrier energies

The fusion dynamics of reaction has been investigated theoretically by using classical dynamical model and the energy dependent Woods-Saxon potential (EDWSP) model. Calculations of complete fusion (CF) and total fusion (TF) cross-sections within classical dynamical model are done by using code PLATYPUS and such outputs fairly described CF, ICF and TF yields at above barrier area. However, same calculations failed to reproduce CF and TF cross-sections data at near and below barrier area. In contrast, the EDWSP calculations for CF process at above barrier area are turned out to be suppressed when referenced with CF data while data at sub-barrier energies for complete fusion are reasonably addressed by the model calculations. The EDWSP based suppression has been turned out to be smaller than reported values and with an appropriate scale factor (only at above barrier energies), EDWSP outcomes properly explain CF data in complete range of energy. Further, TF data are adequately addressed by the EDWSP based calculations, thereby, reflects the breakup of weakly bound projectile in the force field of the target isotope. Thus, the weakly bound projectile shows break up effects and partially absorbed by the target, which subsequently gives suppression of the CF yields in above barrier area.

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.

Exhaustive Theoretical Investigation of~Phonon Number Alteration, Fusion Cross Sections and Barrier Distributions for \({^{30}\mathrm {Si}}+{^{90,92,94,96}\mathrm {Zr}}\) Reactions via Energy-dependent Woods–Saxon Potential and Coupled Channel Models

Exhaustive Theoretical Investigation of~Phonon Number Alteration, Fusion Cross Sections and Barrier Distributions for \({^{30}\mathrm {Si}}+{^{90,92,94,96}\mathrm {Zr}}\) Reactions via Energy-dependent Woods–Saxon Potential and Coupled Channel Models

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.

Analysis of complete, incomplete and total fusion data of 9Be +169Tm, 187Re, 209Bi reactions

We have analyzed the incomplete fusion (ICF), complete fusion (CF) and total fusion (TF) excitation functions for reactions induced by [Formula: see text] on [Formula: see text], [Formula: see text] and [Formula: see text] targets at near barrier energies using Wong’s formula in conjunction with the energy dependent Woods–Saxon potential. A phenomenological selection function is proposed to separate out the contribution of ICF and CF cross-sections in TF cross-section. The variation of relative contribution of ICF and CF in TF with respect to incident beam energy is very well reproduced through this approach.

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.

Inelastic surface vibrations versus energy-dependent nucleus–nucleus potential in sub-barrier fusion dynamics of 3 6 Li + 62 144 Sm ${~}_{\boldsymbol {3}}^{\boldsymbol {6}} \text {Li}\boldsymbol {+}{~}_{\hspace *{6pt}\boldsymbol {62}}^{\boldsymbol {144}} \text {Sm}$ system

Limitations of the static Woods–Saxon potential and the applicability of the energy-dependent Woods–Saxon potential (EDWSP) model within the framework of one-dimensional Wong formula to explore the sub-barrier fusion data are highlighted. The inelastic surface excitations of the fusing nuclei are found to be dominating in the enhancement of sub-barrier fusion excitation function data and the effects of such dominant vibrational states are exploited through the coupled channel calculations obtained by using the code CCFULL. It is worth mentioning here that the influence of multiphonon vibrational states of the reactants can be simulated by introducing the energy dependence in the nucleus–nucleus potential.

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.

Formation and decay analysis ofCd*4898,104isotopes inCa2040-induced reactions

We have analyzed the fusion dynamics of $_{20}^{40}\mathrm{Ca}+_{28}^{58,64}\mathrm{Ni}$ reactions by using the energy dependent Woods-Saxon potential (EDWSP) model and coupled channel model and subsequently the decay patterns of $_{48}^{98,104}\mathrm{Cd}^{*}$ nuclei are governed via the dynamical cluster-decay model (DCM). The influence of intrinsic degrees of freedom of colliding pairs, such as low lying surface vibrations and neutron transfer channels, are entertained within the context of coupled channel calculations. Interestingly, the energy dependence in the Woods-Saxon potential induces barrier modification effects (barrier height, barrier position, barrier curvature) in a somewhat similar way as that for coupled channel approach, hence adequately explains the observed fusion dynamics of $_{20}^{40}\mathrm{Ca}+_{28}^{58,64}\mathrm{Ni}$ reactions. In addition, the decay analysis of compound nuclei formed in the fusion of $_{20}^{40}\mathrm{Ca}+_{28}^{58,64}\mathrm{Ni}$ reactions is investigated by using DCM. The calculations are done for quadrupole $({\ensuremath{\beta}}_{2})$ deformed fragments having optimum orientations for hot configurations. The experimental data for evaporation residues lying within the wide range of center of mass energy $({E}_{\mathrm{c}.\mathrm{m}.})$ of $64--88$ MeV is nicely addressed using the collective clusterization approach of the DCM. The comparative analysis of decay profiles of $_{48}^{98,104}\mathrm{Cd}^{*}$ is worked out by introducing angular momentum and temperature effects in the fragmentation potential and preformation factor.

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.

Systematic failure of static nucleus–nucleus potential to explore sub-barrier fusion dynamics

This paper addresses the validity of the static Woods–Saxon potential and the energy dependent Woods-Saxon potential (EDWSP) for description of sub-barrier fusion dynamics. The low lying surface vibrations of colliding nuclei and neutron transfer channels are found to be major factors responsible for fusion enhancement at sub-barrier energies. Theoretical calculations based upon the static Woods–Saxon potential obtained using the one-dimensional Wong formula fail to explain the energy dependence of the sub-barrier fusion cross-section of systems. The role of inelastic surface vibrations is properly entertained within the context of coupled channel calculations performed using the CCFULL code. However, the EDWSP model, in conjunction with the one-dimensional Wong formula, accurately explains the sub-barrier fusion enhancement of systems and simulates the influence of nuclear structure degrees of freedom, such as the inelastic surface vibrational states of colliding pairs. In EDWSP model calculations, a wide range of diffuseness parameters, ranging from to which is much larger than a value extracted from the elastic scattering data, is required to bring the observed fusion enhancement.

Effects of intrinsic degrees of freedom in enhancement of sub-barrier fusion excitation function data

This paper is mainly focused on the limitations of energy independent Woods–Saxon potential and the applicability of energy dependent Woods–Saxon potential (EDWSP) model in conjunction with one-dimensional Wong formula for description of the heavy-ion fusion reactions. The effects of neutron transfer channels and inelastic surface vibrations of colliding nuclei in the enhancement of sub-barrier fusion excitation function data, in the various heavy-ion fusion reactions, have been investigated within the framework of energy independent one-dimensional barrier penetration model, the EDWSP model and the coupled channel code CCFULL. In certain projectile-target combinations, the influences of multi-neutrons transfer between reactants are found to be dominating over the coupling to low lying surface vibrational states. Furthermore, the effects of these dominant degrees of freedom can be simulated by introducing the energy dependence in real part of nucleus–nucleus potential.

Neutron transfer versus inelastic surface vibrations in the enhancement of sub-barrier fusion excitation function data and the energy dependent Woods–Saxon potential

This work deeply analyzed the relative importance of the neutron transfer channels and inelastic surface vibrations of colliding nuclei in the sub-barrier fusion enhancement of various heavy ion systems using an energy dependent Woods–Saxon potential (EDWSP) model in conjunction with a one-dimensional Wong formula and the coupled channel formulation using the code CCFULL. The multi-phonon vibrational states of colliding nuclei and the nucleon transfer channels are found to be dominant internal degrees of freedom. The coupling between the relative motion of reactants and these relevant channels produces anomalously large sub-barrier fusion enhancement over the expectations of the one-dimensional barrier penetration model. In some cases, the influence of neutron transfer dominates over the couplings to low lying surface vibrational states of collision partners. Furthermore, the effects of coupling to inelastic surface excitations and the impact of neutron transfer channels with positive ground state Q-values are imitated due to energy dependence in the Woods–Saxon potential. In the EDWSP model calculations, a wide range for the diffuseness parameter, which is much larger than the value extracted from the elastic scattering data, is needed to account for the observed fusion enhancement in the close vicinity of the Coulomb barrier.

Isotopic dependence of fusion enhancement of various heavy ion systems using energy dependent Woods–Saxon potential

In the present work, the fusion of symmetric and asymmetric projectile–target combinations are deeply analyzed within the framework of energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with one dimensional Wong formula and the coupled channel code CCFULL. The neutron transfer channels and the inelastic surface excitations of collision partners are dominating mode of couplings and the coupling of relative motion of colliding nuclei to such relevant internal degrees of freedom produces a significant fusion enhancement at sub-barrier energies. It is quite interesting that the effects of dominant intrinsic degrees of freedom such as multi-phonon vibrational states, neutron transfer channels and proton transfer channels can be simulated by introducing the energy dependence in the nucleus–nucleus potential (EDWSP model). In the EDWSP model calculations, a wide range of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm , which is much larger than a value ( a = 0.65 fm ) extracted from the elastic scattering data, is needed to reproduce sub-barrier fusion data. However, such diffuseness anomaly, which might be an artifact of some dynamical effects, has been resolved by trajectory fluctuation dissipation (TFD) model wherein the resulting nucleus–nucleus potential possesses normal diffuseness parameter.

Role of neutron transfer in the enhancement of sub-barrier fusion excitation functions of various systems using an energy-dependent Woods-Saxon potential

The focus of the present article is to address the effects of the role of a neutron transfer channel in the enhancement of sub-barrier fusion excitation function data of various heavy-ion systems by using an energy-dependent Woods-Saxon potential (EDWSP) model in conjunction with the one-dimensional Wong's formula and the coupled-channel model by using the code ccfull. The effects of coupling to neutron transfer channels are found to have dominance over the coupling to low-lying surface vibrational states, such as the $2{}^{+}$ and $3{}^{\ensuremath{-}}$ vibrational states. Furthermore, the influence of inelastic surface excitations and the effects of six neutron transfer channels with positive ground state $Q$ values are mocked up by the EDWSP model.