Sub-barrier Fusion Enhancement Research Articles

Role of multi-neutron transfer channels on fusion enhancement

Fusion reactions 40Ar + 116Sn, 40Ar + 122Sn and 40Ca + 124Sn have been examined by employing coupled channel (CC) approach using code-CCFULL. Here we aim to investigate the influence of multi-neutron transfer channels in addition to coupling of collective excitations on sub-barrier fusion enhancement. Incorporation of inelastic excitations alone reproduced the experimental results for 40Ar + 116Sn system while for 40Ar + 122Sn contribution of 2n transfer channel is required to explain the experimental data. However, CC calculations with 2n transfer could not explain the enhancement at sub-barrier energies for 40Ca + 124Sn system. Therefore, the empirical coupled channel (ECC) calculations have been carried out to include the effect of multi-neutron transfer channels and it is found that the incorporation of sequential 4n transfer channel reproduced the experimental results in entire energy region. Nevertheless, it is observed that multi-neutron transfer coupling significantly contributed in raising the sub-barrier fusion cross sections particularly for the reactions where colliding partners are spherical. Importantly, it is also found that transfer of even number of neutrons play dominating role in sub-barrier fusion enhancement.

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.

Influence of neutron transfer channels on fusion dynamics near the Coulomb barrier for 28Si + 116,120,124Sn systems

The phenomenon of enhanced fusion cross-section as compared to the theoretical predictions of 1-D BPM has been extensively studied over the past few decades. However, the unambiguous role of neutron transfer channels on the sub-barrier fusion enhancement is still elusive in most cases. Fusion cross-section measurements ≈ 15% below and above the Coulomb barrier were performed to elucidate the mechanisms responsible for the experimentally observed sub-barrier fusion enhancement. Coupled-channels calculations using CCFULL were used to decipher the reaction dynamics. CC calculations explained the fusion excitation function for 28Si + 116,120Sn systems after the inclusion of inelastic excitations along with a pair transfer. However, the observed behavior for the 28Si + 124Sn system could not be explained. The fusion barrier distribution has been extracted from the experimental data to unveil the various channels coupled in the concerned rection. A single uncoupled barrier was transformed into a distribution of barriers depicting the presence of different channels coupled in the reaction. The results indicate a significant effect from multi-neutron transfer channels on the fusion dynamics.

Fusion-fission analysis of C12+Cm248 and O16+Pu244 nuclear reactions across the Coulomb barrier

By using the symmetric-asymmetric Gaussian barrier distribution (SAGBD) model, Wong formula, and coupled channel approach, heavy ion fusion dynamics is investigated for $^{12}\mathrm{C}+^{248}\mathrm{Cm}$ and $^{16}\mathrm{O}+^{244}\mathrm{Pu}$ reactions at energies lying below and near the Coulomb barrier. Coupling of various channels linked with the structure of participants to the relative motion of the collision partners is done by considering a Gaussian type of weight function in the SAGBD model and cross sections are found to be enhanced relative to the calculations obtained by the simple barrier penetration model. In the SAGBD model, the channel coupling effects are calculated in terms of channel coupling parameter ($\ensuremath{\lambda}$) and percentage reduction in the height of apparent fusion barrier with respect to the Coulomb barrier (${V}_{\mathrm{CBRED}}$). The channel coupling parameter estimates the cumulative influence of dominant intrinsic channels, which are responsible for the sub-barrier fusion enhancement. The SAGBD calculations appropriately explain the dynamics of $^{12}\mathrm{C}+^{248}\mathrm{Cm}$ and $^{16}\mathrm{O}+^{244}\mathrm{Pu}$ reactions at energies lying around the Coulomb barrier. The coupled channel analysis of the present reactions is done by using the code ccfull and the coupled channel calculations unambiguously identify the dominant influences of the rotational states up to ${10}^{+}$ spin states of the ground state rotational band of target isotopes in both reactions. In addition, the couplings to higher order deformation, such as ${\ensuremath{\beta}}_{4}$ for target and low lying quantum states of the projectile, are necessarily required to reproduce the experimental data of $^{12}\mathrm{C}+^{248}\mathrm{Cm}$ and $^{16}\mathrm{O}+^{244}\mathrm{Pu}$ reactions. Apart from the fusion analysis, the dynamical cluster-decay model (DCM) is applied to understand the fission dynamics of the $^{260}\mathrm{No}^{*}$ nucleus formed via the above-mentioned reactions. The decay study is carried out at the center-of-mass energies spread, ${E}_{\mathrm{c}.\mathrm{m}.}$ ($\ensuremath{\approx}79$ to 109 MeV) by including the quadrupole deformations (${\ensuremath{\beta}}_{2}$) and optimum orientations (${\ensuremath{\theta}}_{i}^{\mathrm{opt}}$) of the decaying fragments. According to the experimental observation, the noncompound nucleus (nCN) fission component competes with the compound nucleus (CN) fission processes. Consequently, the possibility of nCN contribution is also explored in the decay of the $^{260}\mathrm{No}^{*}$ compound nucleus. With an aim to have a comprehensive analysis of CN and nCN fission mechanisms, the role of the center-of-mass energy (${E}_{\mathrm{c}.\mathrm{m}.}$) and angular momentum ($\ensuremath{\ell}$) is explored in terms of various parameters of DCM such as fragmentation potential, preformation probability, barrier modification, etc.

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 cross sections and barrier distributions for O16+Ge70,72,73,74,76 and O18+Ge74 reactions at energies near and below the Coulomb barrier

In this paper, we have investigated the sensitivity of fusion cross section and the barrier distribution data with respect to the choice of the potential parameters. To ascertain this, the fusion dynamics of $^{16}\mathrm{O}+^{70,72,73,74,76}\mathrm{Ge}$ and $^{18}\mathrm{O}+^{74}\mathrm{Ge}$ reactions at near and sub-barrier energies have been examined. In the present study, we have used the one-dimensional Wong formula, symmetric-asymmetric Gaussian barrier distribution (SAGBD) model, and coupled channel approach. For theoretical estimations, the Woods-Saxon form of nuclear potential has been adopted, and it has been found that both the fusion cross section and barrier distribution are quite sensitive to the choice of potential parameters in the entire range of incident energies. Calculations based on the Wong formula are significantly smaller than the sub-barrier fusion data, which has clearly suggested that the couplings to the nuclear structure's degrees of freedom of the colliding nuclei are needed to reproduce the experimental data. On the other hand, in the SAGBD model calculations the multidimensional character of nucleus-nucleus potential has been incorporated and it has reasonably recovered both the fusion cross-section data and the barrier distribution data of $^{16}\mathrm{O}+^{70,72,73,74,76}\mathrm{Ge}$ and $^{18}\mathrm{O}+^{74}\mathrm{Ge}$ reactions. In the SAGBD model, channel coupling parameter $\ensuremath{\lambda}$ has been determined from barrier distribution and hence $\ensuremath{\lambda}$ is related to the various channel coupling effects which have arisen because of the nuclear structure of the participating nuclei. The increase in $\ensuremath{\lambda}$ with an increase in target isotopic mass has clearly indicated that there are shape transition effects in Ge isotopes, which change their shape from spherical symmetry to prolate deformed shape as one moves from $^{70}\mathrm{Ge}$ to $^{76}\mathrm{Ge}$. Similarly, the percentage reduction of effective fusion barrier ${V}_{\mathit{CBRED}}$ with respect to uncoupled Coulomb barrier has also shown an increasing trend with the increase in target isotopic mass. In order to confirm the shape transition effects, the coupled channel calculations have been performed by using the code CCFULL. The present coupled channel analysis has clearly pointed out the importance of nuclear structure degrees of freedom of participating nuclei in the sub-barrier region. Similar results have also been evident from SAGBD analysis. Hence the model predictions incorporate the contributions from vibrational excitations and/or static deformation in the fusion of $^{16}\mathrm{O}+^{70,72,73,74,76}\mathrm{Ge}$ reactions. For the $^{18}\mathrm{O}+^{74}\mathrm{Ge}$ reaction, the vibrational excitations along with the neutron transfer channel have led to larger sub-barrier fusion enhancement and their influences have been automatically included in the SAGBD calculations. Furthermore, $^{16}\mathrm{O}+^{76}\mathrm{Ge}$ and $^{18}\mathrm{O}+^{74}\mathrm{Ge}$ reactions have formed the same compound nucleus $^{92}\mathrm{Zr}$ via different entrance channels. Their comparative study has indicated that the effect of the neutron transfer channel has dominated over the entrance channel mass asymmetry effects. In addition, the minimum value of ${\ensuremath{\chi}}^{2}$ that has been obtained for the SAGBD calculations is consistent with that of the coupled channel calculations.

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.

Searching the reason for sub-barrier fusion enhancement through multineutron transfer channels

Background: The influence of inelastic excitations on sub-barrier fusion enhancement is well established; however, the transfer channel effect can be surprising. Recently, it has been shown that the $2n$ transfer channel is mainly responsible for sub-barrier fusion enhancement despite having a positive-$Q$ value for many-neutron transfer channels. Moreover, some systems do not show enhancement even if they possess positive-$Q$-value transfer channels. It has also been reported that enhancement can be found in those systems for which deformation of nuclei increases after neutron transfer.Purpose: The aim of this work is to examine the role of multineutron transfer channels on sub-barrier fusion enhancement.Method: Fusion cross sections were measured with a recoil mass separator for the $^{40}\mathrm{Ca}+^{70}\mathrm{Zn}$ system and analyzed theoretically within the framework of coupled-channels calculations.Results: Positive $Q$-value neutron transfer channels seem to be essential for the sub-barrier region, since inelastic excitation coupling was unable to reproduce the trend of experimental fusion cross sections. However, up to $2n$ pick-up channel was found to be sufficient for describing the sub-barrier cross sections.Conclusions: Sub-barrier fusion in the $^{40}\mathrm{Ca}+^{70}\mathrm{Zn}$ system is hardly affected by transfer of more than two neutrons. The fusion enhancement due to the transfer channel can be observed in systems for which the deformation of colliding nuclei increases after transfer, though the amount of enhancement does not seem to be proportional to the deformation change.

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.

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.

Relationship between and effect of inelastic excitations and transfer channels on sub-barrier fusion enhancement

Background: It is a well established fact that nuclear deformation and vibration influence fusion dynamics around the Coulomb barrier. This effect was observed for several systems with the inclusion of inelastic excitations in coupled-channels calculations. Sub-barrier fusion cross sections were also observed to be affected by neutron transfer in systems carrying positive $Q$ value for transfer channels. However, recent experimental analysis with a few systems showed that inelastic excitations are enough to explain the sub-barrier fusion behavior, and no effect was noticed due to positive $Q$-value transfer channels.Purpose: The motivation behind present investigation is to explore the effects of colliding nuclei structure and the transfer channel on enhancement of sub-barrier fusion cross sections.Method: An experiment was performed with Heavy Ion Reaction Analyzer (HIRA) at New Delhi to measure the fusion cross sections for $^{28}\mathrm{Si}+^{92,96}\mathrm{Zr}$ systems. These cross sections were later compared with quantum mechanical coupled-channels calculations. In order to explore the effects of nuclear deformation on fusion cross sections, the present data were compared with those of other researchers on fusion who have used various projectiles of different structural properties on a $^{96}\mathrm{Zr}$ target.Results: Experimental fusion cross sections have been extracted around the Coulomb barrier. In the coupled-channels framework, inclusion of inelastic excitations of both projectile $(^{28}\mathrm{Si})$ and targets $(^{92,96}\mathrm{Zr})$ could reproduce the experimental cross sections around the Coulomb barrier, but they deviated substantially in the sub-barrier region. This indicates that positive $Q$-value neutron transfer channels may need to be included in the calculations to reproduce the experimental cross sections at sub-barrier energies.Conclusions: The nuclear structure of interacting nuclei has a strong influence on sub-barrier fusion enhancement. The effect of multineutron transfer channels was observed to be significant for fusion, especially for those systems where interacting nuclei are less deformed or spherical.

Self-consistent analysis of sub-barrier fusion enhancement effect in Ca + Ca and Ni + Ni**Supported by the National Key Basic Research Development Program of China (2013CB834404) and the National Natural Science Foundation of China (11475263, 11375268, U1432246 and U1432127)

The fusion dynamic mechanism of heavy ions at energies near the Coulomb barrier is complicated and still not very clear up to now. Accordingly, a self-consistent method based on the CCFULL calculations has been developed and applied for an ongoing study of the effect of the positive Q-value neutron transfer (PQNT) channels in this work. The typical experimental fusion data of Ca + Ca and Ni + Ni is analyzed within the unified calculation scheme. The PQNT effect in near-barrier fusion is further confirmed based on the self-consistent analysis and extracted quantitatively.

Examining the role of transfer coupling in sub-barrier fusion ofTi46,50+Sn124

In this study, the presence of neutron transfer channels with positive Q values can enhance sub-barrier fusion cross sections. Recent measurements of the fusion excitation functions for 58Ni+132,124Sn found that the fusion enhancement due to the influence of neutron transfer is smaller than that in 40Ca +132,124Sn although the Q values for multineutron transfer are comparable. The purpose of this study is to investigate the differences observed between the fusion of Sn + Ni and Sn + Ca. Methods: Fusion excitation functions for 46,50Ti +124Sn have been measured at energies near the Coulomb barrier. As a result, a comparison of the barrier distributions for 46Ti+124Sn and 40Ca+124Sn shows that the 40Ca+124Sn system has a barrier strength resulting from the coupling to the very collective octupole state in 40Ca at an energy significantly lower than the uncoupled barrier. In conclusion, the large sub-barrier fusion enhancement in 40Ca induced reactions is attributed to both couplings to neutron transfer and inelastic excitation, with the octupole vibration of 40Ca playing a major role.

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%.

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.

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.

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 %.