One-dimensional Barrier Penetration Model Research Articles

Evaporation residue cross-section measurements for 30Si+142Ce system

Evaporation residue (ER) cross-sections were measured for 30Si+142Ce reaction at laboratory energies in the range of 105 - 132 MeV using the HYbrid Recoil mass Analyzer (HYRA) at IUAC, New Delhi. The transmission efficiency of the HYRA was estimated using the calibration reaction 28Si+142Ce. Sub-barrier fusion enhancement was observed when compared with the one-dimensional barrier penetration model predictions for the present system. To explore the phenomena responsible for sub-barrier fusion enhancement, coupled-channels calculations were performed using the CCFULL code. The effect of couplings and the role of positive Q-value neutron transfer (PQNT) channels on sub-barrier fusion cross-sections were investigated. Coupled-channels calculations were able to reproduce the data by including the coupling in both projectile and target nucleus along with two neutron-transfer channels having positive Q-value. The measured ER cross-sections were compared with the nearby systems to explore the role of deformation of the colliding nuclei.

Examining the correlation between multi-neutron transfer and inelastic excitations in sub-barrier fusion enhancement

Background: Heavy-ion fusion cross-sections at sub barrier energies are found to be enhanced by orders of magnitude as compared to the predictions of one-dimensional barrier penetration model (1-D BPM). The coupling of various internal degrees of freedom has been employed to decrypt the mechanism responsible for the observed sub-barrier fusion enhancement. However, the unambiguous role of multi-neutron transfer channels in the sub-barrier domain is still elusive.Purpose: We aim to explore and disentangle the effects of multi-neutron transfer channels from the inelastic excitations in the vicinity of the Coulomb barrier.Method: The fusion excitation functions for $^{28}\mathrm{Si} + ^{116,120,124}\mathrm{Sn}$ systems were measured from $\ensuremath{\approx}14%\phantom{\rule{0.222222em}{0ex}}$ below to $\ensuremath{\approx}15%\phantom{\rule{0.222222em}{0ex}}$ above the Coulomb barrier by detecting the evaporation residues (ERs) at the focal plane of the Recoil Mass Separator (RMS), Heavy Ion Reaction Analyzer (HIRA) at the Inter-University Accelerator Centre (IUAC), New Delhi.Results: The extracted fusion cross sections for the investigated systems at sub-barrier energies are significantly enhanced as compared to the predictions of 1-D BPM calculations. To probe the underlying mechanism responsible for the observed sub-barrier fusion enhancement, the coupled-channels (CC) formalism was employed. Coupled reaction channels (CRC) calculations by incorporating the one-neutron transfer channel to elucidate the significance of the transfer channel on the fusion dynamics were performed. Further, the semiempirical coupled channels (ECC) approach was explored to decipher the possible cause of the observed fusion excitation function trend. A systematic analysis of the neighboring systems available in the literature was also performed.Conclusions: CC calculations were able to reproduce the measured fusion excitation functions for $^{28}\mathrm{Si} + ^{116,120}\mathrm{Sn}$ systems to a reasonable extent. However, observed sub-barrier fusion enhancement in $^{28}\mathrm{Si}+^{124}\mathrm{Sn}$ system could not be explained using CC calculations. The influence of multi-neutron transfer channels was highlighted in the coupled-channels calculations. The interplay of collective excitations and neutron transfer was observed.

Fusion and back-angle quasielastic measurements in Si30+Gd156 near the Coulomb barrier

Background: Advancement in accelerator facilities has opened the door to dig deep to understand the interplay between nuclear reactions and structures. Although the influence of inelastic excitations on nuclear scattering and sub-barrier fusion is somewhat established, a clear understanding of nucleon transfer with a positive-$Q$ value is yet to achieve.Purpose: The objective of this paper is to examine the role of the $2n$-transfer channel with a positive $Q$ value on sub-barrier fusion and back-angle quasielastic (QE) scattering in the $^{30}\mathrm{Si}+^{156}\mathrm{Gd}$ reaction. Furthermore, extraction of barrier distributions (BDs) from fusion and QE scattering to infer their shapes is also a prime goal.Method: The excitation functions (EFs) of fusion and back-angle QE scattering have been measured over a wide range of incident beam energy around the Coulomb barrier using a recoil mass spectrometer. Furthermore, BDs have been extracted using the measured fusion and back-scattered QE data. The underlying findings have been analyzed within the framework of coupled-channel (CC) formalism using ccfull and ecc programs.Results: Fusion enhancement has been observed compared to those predicted from the one-dimensional barrier penetration model at sub-barrier energies. Fusion enhancement and QE EFs are explained by CC predictions considering the collective excitations among the colliding nuclei. The inclusion of $2n$ transfer and collective excitations in ccfull improves the fit to the experimental fusion data in a short span of energy window around the Coulomb barrier, whereas no significant effect has been observed at the sub-barrier region. However, no such effect of $2n$-pickup transfer has been observed from ecc model calculations. Thus, no firm conclusion can be made on the role of $2n$-pickup transfer with a positive $Q$ value in present measurements.Conclusion: Fusion EFs have been successfully explained by the CC calculations using ccfull and ecc model codes. No significant effect of the $2n$-pickup channel with a positive $Q$ value was observed on sub-barrier fusion enhancement. However, QE EFs are reproduced by considering the collective excitations and $2n$-transfer channel couplings. Fusion and QE BDs are similar in shape within the experimental uncertainty. One-dimensional barrier parameters extracted from the measured data agree with the different theoretical models. Also, the present system obeys the systematic based on deformation values after transfer at the exit.

Investigation of isotopic dependence on the O + Ni fusion cross section near barrier energies

Fusion excitation functions have been measured for $^{16}\mathrm{O}+^{61}\mathrm{Ni}$ and $^{18}\mathrm{O}+^{61,62}\mathrm{Ni}$ systems around the Coulomb barrier ($\ensuremath{\approx}0.7{V}_{B}$--$1.3{V}_{B}$) using the recoil mass spectrometer, heavy ion reaction analyzer. The ground state $Q$ value for two neutron stripping is positive for both systems with $^{18}\mathrm{O}$ as the projectile. Strong enhancement of the experimental fusion cross sections were observed below the barrier for all the systems compared to that of the predictions of the one-dimensional barrier penetration model. To understand such enhancement, a coupled-channels formalism has been used. A comparative study of these systems indicated that the coupling of two neutron transfer channels with the collective excitations could play the role behind the sub-barrier fusion enhancement for $^{18}\mathrm{O}$ induced reactions. However, the sub-barrier enhancement for $^{16}\mathrm{O} + ^{61}\mathrm{Ni}$ is found to be due to the coupling of quadrupole vibrations of both the interacting nuclei. Also after comparing these systems with other systems of different Ni isotopes, we have found that the signature of the role of coupling to neutron transfer channels due to ground state positive $Q$ value for neutron transfer is ambiguous.

Fusion studies in O16+Nd142,150 reactions at energies near the Coulomb barrier

Background: Enhancement in fusion cross sections over one-dimensional barrier penetration model (1D-BPM) predictions has been observed at sub-barrier energies owing to the coupling of various internal degrees of freedom to the relative motion. On the other hand, hindrance in fusion is noticed at energies well above the barrier in a few cases.Purpose: The purpose is to probe the dynamics of heavy ion fusion at energies below and well above the Coulomb barrier.Methods: Fusion excitation functions for the $^{16}\mathrm{O}+^{142,150}\mathrm{Nd}$ reactions are measured using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Measurements have been performed in the range $12%$ below to $50%$ above the Coulomb barrier for both systems. The measured fusion cross sections are compared with coupled channels calculations using ccfull code. The cross sections are also compared with reactions using $^{16}\mathrm{O}$ beams with other isotopes of Nd to explore the systematic behavior of fusion.Results: Compared with 1D-BPM predictions, fusion enhancement is observed in both $^{16}\mathrm{O}+^{142}\mathrm{Nd}$ and $^{16}\mathrm{O}+^{150}\mathrm{Nd}$ reactions at below-barrier energies, with the latter reaction showing a higher enhancement. Coupled channels calculations incorporating the collective excitations of the target nuclei reproduce the fusion cross sections in both reactions. The collective excitations of the projectile nucleus do not seem to contribute to the observed fusion enhancement. Calculations using Aky\"uz-Winther potential parameters fail to reproduce the fusion cross sections at energies well above the barrier.Conclusions: Fusion enhancement is observed in both reactions studied. Degree of enhancement of sub-barrier fusion cross section is larger for the reaction using $^{150}\mathrm{Nd}$ target. Fusion hindrance is observed in both reactions at very high energies. The hindrance seems to increase with increasing beam energy. Larger value of diffuseness parameter compared with the value consistent with elastic-scattering measurements is required to reproduce the fusion excitation function at energies well above the barrier. This could be a strong indication of dynamical effects in fusion at very high energies.

Evaporation residue cross section in the Cl37+Zn68 fusion reaction near the Coulomb barrier

Background: The measured subbarrier fusion cross sections in heavy-ion reactions are found to be significantly large as compared with those expected from the one-dimensional barrier penetration model (1d-BPM). Although attempts have been made to comprehend the enhancement in terms of different intrinsic degrees of freedom of the colliding nuclei, a clear understanding of the same is yet to come.Purpose: The objectives of this study is to understand the interplay of the channel coupling effect on fusion excitation function and explore the decay dynamics of the excited compound nucleus in the sub-and-near barrier region.Method: Fusion excitation function has been measured at energies from 7% below to 38% above the Bass barrier using a recoil mass spectrometer. Furthermore, cross sections of the different evaporation residues, such as 98, 99, 100, and 101 u, have been extracted.Results: The observed enhancement in the subbarrier fusion cross sections over the 1d-BPM predictions has been explained by considering the low-lying inelastic excitations among the interacting partners using ccfull code and by the barrier modification using the dynamical cluster-decay model (DCM). The cross sections of individual residual mass fractions (98, 99, 100, and 101 u) have been compared with the Hauser-Feshbach model.Conclusion: Coupled-channel calculations and DCM have successfully explained the total fusion cross sections data. The measured total fusion cross section ${\ensuremath{\sigma}}_{\mathrm{fus}}$ was found to be approximately equal to the sum of various residual mass fractions ($\mathrm{\ensuremath{\Sigma}}{\ensuremath{\sigma}}_{\mathrm{ER}}$) at energies above the Bass barrier. One-dimensional barrier height and radius parameters extracted from the measured data are in good agreement with the Bass model and DCM parameters.

Role of neutron transfer in the sub-barrier fusion cross section in O18 + Sn116

Background: In heavy-ion-induced fusion reactions, cross sections in the sub-barrier region are enhanced compared to predictions of the one-dimensional barrier penetration model. This enhancement is often understood by invoking deformation and coupling of the relative motion with low-lying inelastic states of the reaction partners. However, effects of nucleon transfer on fusion below the barrier, especially for the systems having positive $Q$ value neutron transfer (PQNT) channels, are yet to be disentangled completely.Purpose: We intend to study the role of the PQNT effect on the sub-barrier fusion of the $^{18}\mathrm{O} + ^{116}\mathrm{Sn}$ system having positive $Q$ value for the two-neutron stripping channel. Also we reflect on the interplay of couplings involved in the system around the Coulomb barrier.Method: The fusion excitation function was measured at energies from $11%$ below to $46%$ above the Coulomb barrier for $^{18}\mathrm{O} + ^{116}\mathrm{Sn}$ using a recoil mass spectrometer, viz., the Heavy-Ion Reaction Analyser (HIRA). Fusion barrier distributions were extracted from the data. Results from the experiment were analyzed within the framework of the coupled-channels model.Results: Fusion cross sections at energies below the Coulomb barrier showed strong enhancement compared to predictions of the one-dimensional barrier penetration model. The fusion process is influenced by couplings to the collective excitations with coupling to single- and two-phonon vibrational states of the target and the projectile respectively. Inclusion of the two-neutron transfer channel in the calculation along with these couplings could reproduce the data satisfactorily.Conclusions: The significant role of PQNT in enhancing the sub-barrier fusion cross section for the chosen system is not observed. It simply reduced the sub-barrier fusion cross section. Therefore, a consistent link between PQNT and sub-barrier fusion enhancement could not be established vividly while comparing the fusion excitation function from this work with the same from other $^{16,18}\mathrm{O}$-induced reactions. This clearly points to the need for more experimental as well as theoretical investigation in this field.

Sub-barrier fusion in the Cl37+Te130 system

Background: In heavy-ion induced reactions, the sub-barrier fusion cross sections are found to be higher as compared to the predictions of the one-dimensional barrier penetration model. Attempts have been made to explain sub-barrier fusion enhancement by including the static deformations, the couplings to inelastic excitations, and non-fusion channels.Purpose: To investigate factors which influence the sub-barrier fusion in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system and to understand the interplay of couplings, the fusion excitation function was measured at energies from $10%$ below to $15%$ above the Bass barrier.Method: The fusion excitation function was measured by employing a recoil mass spectrometer, the Heavy-Ion Reaction Analyser (HIRA), at the Inter-University Accelerator Centre, New Delhi. To study the behavior of the fusion excitation function and the effect of couplings at sub-barrier energies, the excitation function was analyzed in the framework of the coupled-channels code ccfull.Results: In the present work, the fusion cross section was measured down to 1 $\ensuremath{\mu}\mathrm{b}$ at the lowest measured energy, i.e., $10%$ below the barrier. It was found that the inclusion of couplings of low-lying excited states along with the modified barrier between interacting nuclei satisfactorily reproduces the fusion excitation function of the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system. For better insight into the sub-barrier fusion, the fusion barrier distribution, the logarithmic derivative L(E) factor, and the astrophysical S factor were extracted from the analysis of the experimentally measured fusion excitation function.Conclusions: The analysis of the fusion excitation function in terms of the astrophysical S factor and the L(E) factor suggests the absence of fusion hindrance in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system down to a 1 $\ensuremath{\mu}\mathrm{b}$ cross section achieved at the lowest measured energy. The excitation function of the present system is compared with the existing measurements in which $^{37}\mathrm{Cl}$ has been used as a projectile to understand the interplay of entrance-channel parameters in sub-barrier fusion enhancement.

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.

Coupled-Channel Analyses on 〖Ti〗^(46,48,50)+〖Sn〗^124 Heav-ion Fusion Reactions

Heavy-ion fusion near the Coulomb barrier attract experimental and theoretical interest. The collisons are typically characterized by the presence of many open reaction channels. In the energies around the Coulomb barrier, the processes are elastic scattering, inelastic excitations and fusion operations of one or two nuclei. The fusion process is defined as the effect of one-dimensional barrier penetration model, taking scattering potential as the sum of Coulomb and proximity potential. We have performed heay-ion fusion reactions with coupled-channels (CC) calculations. CC formalism is carried out under barrier energy in heavy- ion fusion reactions. In this work fusion cross sections have been calculated and analyzed in detail for the three systems in the framework of CC approach (using the codes CCFULL[16], CCFUS [17] and CCDEF [18]) . Calculated results are compared with experimental data, including excitation of the projectile and target to the lowestand states and with the datas computed from ‘nrv’. CCDEF, CCFULL and ‘nrv’ explains the fusion reactions of heavy-ions very well. There is a good agreement between the calculated results with the experimental and nrv results [19].

Quantitative analysis of the fusion cross sections using different microscopic nucleus-nucleus interactions

The fusion cross sections for reactions involving medium and heavy nucleus-nucleus systems are investigated near and above the Coulomb barrier using the one-dimensional barrier penetration model. The microscopic nuclear interaction potential is computed by four methods, namely: the double-folding model based on a realistic density-dependent M3Y NN interaction with a finite-range exchange part, the Skyrme energy density functional in the semiclassical extended Thomas-Fermi approximation, the generalized Proximity potential, and the Akyuz-Winther interaction. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the calculations of the DFM give quite satisfactory agreement with the experimental data, being much better than the other methods. New parameterized forms for the fusion barrier heights and positions are presented. Furthermore, the effects of deformation and orientation degrees of freedom on the distribution of the Coulomb barrier characteristics as well as the fusion cross sections are studied for the reactions 16O + 70Ge and 28Si + 100Mo. The calculated values of the total fusion cross sections are compared with coupled channel calculations using the code CCFULL and compared with the experimental data. Our results reveal that the inclusion of deformations and orientation degrees of freedom improves the comparison with the experimental data.

Fusion and elastic scattering of 6Li + 58Ni at low energies

Sub-barrier fusion cross sections (σfus ) for the 6 Li + 58 Ni system, obtained from the respective evaporation protons, are examined in the present work. With respect to expectations of a simple one-dimensional barrier penetration model, a large enhancement of the data is observed. Good consistency with equivalent data reported previously for similar systems is found. A comparison with total reaction cross sections (σR ), deduced from elastic scattering measurements reported previously, indicates that σfus is close to σR within the measured energy range. To estimate the contribution of complete fusion (CF), an optical model analysis of the elastic scattering data is performed where CF is identified with the absorption in a short range volume potential. A surface polarization potential is added to the bare nuclear potential to simulate the effect of peripheral reactions. The results obtained indicate that other mechanisms different from CF may be dominant, especially in the lower energy region.

Estimating total fusion cross sections by using a coupled-channel method

We calculate the total fusion cross sections for the 6He + 209Bi, 6Li + 209Bi,9Be + 208Pb, 10Be + 209Bi, and 11Li + 208Pb systems by using a coupled-channel (CC) method and compare the results with the experimental data. In the CC approach for the total fusion cross sections, we exploit a globally determined Wood-Saxon potential with Akyuz-Winther parameters and couplings of the ground state to the low-lying excited states in the projectile and the target nuclei. The total fusion cross sections obtained with the CC are compared with those obtained without the CC couplings. The latter approach is tantamount to a one-dimensional barrier penetration model. Finally, our approach is applied to understand new data for the 11Li+208Pb system. Possible ambiguities inherent in those approaches are discussed in detail for further applications to the fusion system of halo and/or neutron-rich nuclei.

Deformation effects on sub-barrier fusion cross sections inO16+Yb174,176

Background: Couplings with various reaction channels are known to enhance sub-barrier fusion cross sections by several orders in magnitude. However, a few open questions still remain. For example, the influence of higher order static deformations on sub-barrier fusion cross sections is yet to be comprehensively understood.Purpose: We study the role of hexadecapole nuclear deformation effect on sub-barrier fusion cross sections. Also, this work aims to extract hexadecapole deformation $({\ensuremath{\beta}}_{4})$ in nuclei in the lanthanide region.Method: The evaporation residue (ER) excitation functions for $^{16}\mathrm{O}+^{\phantom{\rule{0.16em}{0ex}}174,176}\mathrm{Yb}$ were measured at laboratory beam energies $({E}_{\mathrm{lab}})$ in the range of 64.6--103.6 MeV. Measurements were carried out by employing the recoil mass spectrometer Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Fusion barrier distributions (BDs) were extracted from data. Results from the experiment were subjected to coupled-channels analysis, in which ${\ensuremath{\beta}}_{4}$ was varied as a free parameter.Results: Experimental fusion cross sections at energies below the barrier expectedly showed strong enhancement compared to the predictions from the one-dimensional barrier penetration model. Data were satisfactorily reproduced after inclusion of negative ${\ensuremath{\beta}}_{4}$ for both the targets in the coupled-channels calculation.Conclusions: The significant role of hexadecapole deformation was observed in the sub-barrier fusion of $^{16}\mathrm{O}+^{\phantom{\rule{0.16em}{0ex}}174,176}\mathrm{Yb}$. The proposed value of ${\ensuremath{\beta}}_{4}$ reproduced the measured fusion excitation function reasonably well. The BDs from these data were also extracted but no definitive conclusions could be drawn from them.

Probing the fusion ofLi7withNi64at near-barrier energies

Background: The stable isotopes of Li, $^{6}\text{Li}$ and $^{7}\text{Li}$, have two-body cluster structures of $\ensuremath{\alpha}+d$ and $\ensuremath{\alpha}+t$ with $\ensuremath{\alpha}$-separation energies or breakup thresholds at 1.47 and 2.47 MeV, respectively. The weak binding of these projectiles introduces several new reaction channels not usually observed in the case of strongly bound projectiles. The impact of these breakup or breakup-like reaction channels on fusion, the dominant reaction process at near-barrier energies, with different target masses is of current interest.Purpose: Our purpose is to explore the fusion, at above and below the Coulmb barrier, of $^{7}\text{Li}$ with $^{64}\text{Ni}$ target in order to understand the effect of breakup or breakup-like processes with medium-mass target in comparison with $^{6}\text{Li}$, which has a lower breakup threshold.Measurement: The total fusion (TF) excitation of the weakly bound projectile $^{7}\text{Li}$ with the medium-mass target $^{64}\text{Ni}$ has been measured at the near-barrier energies (0.8 to $2 {V}_{B}$). The measurement was performed using the online characteristic $\ensuremath{\gamma}$-ray detection method. The complete fusion (CF) excitation function for the system was obtained using the $xn$-evaporation channels with the help of statistical model predictions.Results: At the above barrier energies CF cross sections exhibit an average suppression of about 6.5% compared to the one-dimensional barrier penetration model (1DBPM) predictions, while the model describes the measured TF cross section well. But below the barrier, both TF and CF show enhancements compared to 1DBPM predictions. Unlike $^{6}\text{Li}$, enhancement of CF for $^{7}\text{Li}$ could not be explained by inelastic coupling alone.Conclusion: Whereas the ${\ensuremath{\sigma}}_{\mathrm{TF}}$ cross sections are almost the same for both the systems in the above barrier region, the suppression of ${\ensuremath{\sigma}}_{\mathrm{CF}}$ at above the barrier is less for the $^{7}\text{Li}+^{64}\text{Ni}$ system than for the $^{6}\text{Li}+^{64}\text{Ni}$ system. Also direct cluster transfer has been identified as the probable source for producing large enhancement in TF cross sections.

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.

Effects of intrinsic degrees of freedom in enhancement of sub-barrier fusion excitation function data and energy-dependent one-dimensional barrier penetration model

We have analyzed the role of barrier modification effects (barrier height, barrier position, barrier curvature) introduced due to the energy-dependent Woods–Saxon potential model (EDWSP model) and the coupled channel model on the sub-barrier fusion dynamics of $$ {}_{16}^{32,36} {\text{S}} + {}_{40}^{90,96} {\text{Zr}} $$ reactions. The influence of inelastic surface excitations of colliding pairs and multi-neutron transfer channels is found to be a dominant mode of couplings. The coupling of relative motion of colliding nuclei to these dominant intrinsic degrees of freedom leads to a substantially large fusion enhancement at below-barrier energies over the expectations of one-dimensional barrier penetration model. The coupled channel calculations based upon static Woods–Saxon potential must include the internal nuclear structure degrees of freedom of colliding nuclei for complete description of experimental data. On the other hand, theoretical calculations based upon the EDWSP model along with Wong formula provide a complete description of sub-barrier fusion enhancement of various heavy-ion fusion reactions. In EDWSP model calculations, significantly larger values of diffuseness parameter ranging from a = 0.98 fm to a = 0.85 fm are required to address the observed sub-barrier fusion enhancement of $$ {}_{16}^{32,36} {\text{S}} + {}_{40}^{90,96} {\text{Zr}} $$ reactions. Furthermore, within the context of EDWSP model, it is possible to achieve an agreement with the experimental fusion cross-sectional data within 10 %. For four heavy-ion fusion reactions, only at 4 fusion data points out of 90 fusion data points deviates exceeding 5 %, while 86 fusion data points lie within 5 % and hence the EDWSP model is able to account the above-barrier portion of the fusion cross-sectional data within 5 % with a probability greater than 90 %.

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.

Reliability of the double-folding potential for fusion cross sections of light systems

We study the fusion reaction of light systems with one-dimensional barrier penetration model using the $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ double-folding cluster (DFC) potential. We especially analyze the fusion cross sections of the $^{12}\mathrm{C}+^{12}\mathrm{C},^{16}\mathrm{O},^{24}\mathrm{Mg},^{28}\mathrm{Si},^{16}\mathrm{O}+^{16}\mathrm{O},^{24}\mathrm{Mg}+^{24}\mathrm{Mg},^{28}\mathrm{Si}$, and $^{28}\mathrm{Si}+^{28}\mathrm{Si}$ reactions. The results are compared with the one obtained with M3Y double folding (DFM) and the Aky\"uz-Winther (A-W) potentials. It is found that the calculations with DFM and DFC potentials can reproduce the experimental data much better than the calculations using the A-W potential. We also carried out an analysis on the astrophysical aspect of the $^{12}\mathrm{C}+^{12}\mathrm{C},^{16}\mathrm{O}$, and $^{16}\mathrm{O}+^{16}\mathrm{O}$ reactions. The calculations using DFC and DFM potentials could fit the $S$-factor data reasonably well. However, the calculated reaction rates are lower than the compilation of Caughlan and Fowler at low temperatures. In the important range of temperatures in stellar evolution, the DFC potential reproduces very satisfactory fitting to the experimental cross section and the $S$-factor data and gives a consistent prediction of astrophysical reaction rates. This finding indicates that the DFC potential could be used as an alternative potential to study the fusion reactions in the astrophysical interest.