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.

Theoretical modeling of the above-barrier fusion process for nuclei with [formula omitted] based on the experimental nuclear charge densities

Most of theoretical models of nucleus-nucleus collision are based on the nucleus-nucleus potential. Semi-microscopical double-folding model with the M3Y-Paris NN-forces represents one of the advanced methods for evaluating this potential. Nucleon densities (NDs), being crucial ingredient of this model, must reproduce the experimental nuclear charge densities (NCDs). In theoretical approaches for modeling the fusion process, it is not always so. In the present work, we aim to reach satisfactory description of both the charge nucleon density and the above-barrier fusion cross sections of even-even nuclei with Z=N. We construct an approximation for the ND which is abbreviated as FEV-density (Fermi + Exponential tail with Variable diffuseness). The proton and neutron densities are considered to be identical and having a coordinate-dependent diffuseness. Parameters of the nucleon density are varied to obtain the best fit of the experimental NCD. Then the resulting FEV nucleon densities are used to calculate the nucleus-nucleus potential applying the double-folding model with the density-dependent M3Y-Paris NN-forces. This potential is employed for evaluating the above-barrier fusion cross sections for ten reactions: 32S+12C, 24Mg, 40Ca; 28Si+12C, 16O, 24Mg, 28Si; and 24Mg+12C, 16O, 24Mg where the experimental data are available. The cross sections are calculated using either the barrier penetration model or the trajectory model with surface friction. To find the transmission coefficients for the trajectory model, the Langevin-type equations are solved numerically. For all considered reactions, our trajectory model typically reproduces the above-barrier experimental cross sections within 10–15 % with typical χ2<2. The adjustable parameter of the model, the optimal friction strength KRm, was found to be between 20 and 40 zs·GeV−1 which is in reasonable agreement with two systematics found earlier. We also make predictions for the fusion excitation functions for reactions 32S+16O, 32S+28Si, 24Si+40Ca where we did not manage finding experimental data.

Effect of low lying vibrational and rotational energy levels on the fusion cross-sections

In heavy-ion fusion reactions, the coupling of various degrees of freedom to the relative motion leads to an enhancement in the sub-barrier fusion cross-section compared to the 1-dimensional barrier penetration model. The present work aims to explore the exclusive effect of low-lying vibrational and rotational energy levels in the enhancement of cross-sections for 12C induced reactions at the energy below and around the Coulomb barrier using the CCFULL code. The results show that for the negative and positive values of β4, the rotational energy states up to 2+ and 6+ significantly contributed to the fusion cross-sections which leads to fusion enhancement. These results can be useful for better understanding the dynamics of heavy-ion fusion reactions.

Experimental nuclear charge density and theoretical description of the above-barrier light heavy-ion fusion process* *Supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS.”

Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential. One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3Y-Paris NN-forces. Proton and neutron densities are significant components of this model. The correct nucleon density (ND) must reproduce the experimental nuclear charge density (NCD). However, those who deal with modeling the fusion process typically disregard this circumstance. We aim to achieve a good description of both the nuclear charge density and above-barrier fusion cross sections of even-even light nuclei with . We consider several versions of NDs available in literature and construct our own approximation for the ND of the even-even spherical nuclei 12C, 16O, and 40Ca, abbreviated as FE-density (Fermi+exponential). We carefully compare the NCDs resulting from different versions of NDs with the experimental NCDs. After finding the nucleus-nucleus potential using the double-folding model with the density dependent M3Y-Paris NN-forces and FE densities, we evaluate the above-barrier fusion cross sections for five reactions, 12C+12C, 12C+16O, 16O+16O, 16O+40Ca, and 40Ca+40Ca, for which experimental data are available. The cross sections are calculated using two approaches: a) the barrier penetration model and b) the trajectory model with surface friction (TM). To find the transmission coefficients for the TM, the Langevin equations are employed. For all considered reactions, our TM typically reproduces the above-barrier experimental cross sections within 10−15%. The only adjustable parameter of the model, the optimal friction strength , is found to be approximately 90 for the light reactions 12C+12C, 12C+16O, and 16O+16O and approximately 15 for the heavy reactions 16O+40Ca and 40Ca+40Ca. The latter findings are in reasonable agreement with the systematics found previously. Thus, the FE-recipe allows highly accurate and simultaneous reproduction of both the nuclear charge density and above-barrier fusion cross sections of five reactions involving 12C, 16O, and 40Ca nuclei.

Systematic study of the effect of individual rotational energy levels on the fusion cross-section of 16 O-based reactions of range 480 ≤ Z P Z T ≤ 592

In heavy-ion fusion reactions, the enhancement in the sub-barrier fusion cross-section has been observed as compared to the 1-Dimensional barrier penetration model due to the coupling of many degrees of freedom to the relative motion. This enhancement can be explained theoretically by including nuclear structure effects like deformation and the coupling of relative motion among two colliding nuclei. The present work aims to investigate the effect of individual rotational energy levels on the fusion cross-sections for 16O-based reaction systems, namely, 16O + 182,184,186W, 16O + 176,180Hf, 16O + 174,176Yb, 16O + 166Er, 16O + 148,152,154Sm, 16O + 150Nd at energies below the fusion barrier. Using the CCFULL code, the effect of low-lying rotational energy levels on the fusion cross-section for 16O induced reactions has been investigated at energies below and around the Coulomb barrier. The calculations are performed by assuming the fixed value of diffuseness parameter a 0 = 0.65 fm in the Woods-Saxon nuclear potential and the other two parameters are optimised by fitting the experimental data at the above barrier. Here we have determined the V 0 and r 0 as a function of Z P Z T , where experimental cross-sections are available. From our calculations, it is observed that the hexadecapole deformation (β 4) with different magnitudes has a significant influence on the fusion cross sections. For the case of the +ve value of β 4, beyond 10+, the rotational levels cease to contribute significantly and also there is a significant difference between the contribution of sequential channels. On the other hand, in the case of -ve β 4, up to 6+ levels contribute significantly. Furthermore, we have established an algebraic systematic of fitting, which one can use to determine the parameters V 0, r 0 of Woods-Saxon nuclear potential within the range of Z P Z T lie in between 480 ≤ Z P Z T ≤ 592.

Simple expressions for calculation of proximity interaction of arbitrarily oriented deformed nuclei

Simple expressions for the calculation of proximity interaction of arbitrarily oriented deformed nuclei are obtained in the linear approximation with respect to the deformation parameters of the colliding nuclei. It is shown that these expressions are useful for the analysis and calculation of the nucleus–nucleus potential and the reaction cross-section. The strong dependence of the total potential for the system [Formula: see text] on the orientation of erbium is discussed. The dependence of the barrier height, radius, and curvature on the orientation angle is considered in detail. The experimental data for the fusion cross-section for the systems [Formula: see text] are well described in the framework of the barrier-penetration model when the ground-state quadrupole and hexadecapole deformations of erbium are taken into account.

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.

Nonlocality effect in α decay of heavy and superheavy nuclei

The $\ensuremath{\alpha}$-decay half-life of heavy and superheavy nuclei has been investigated using a potential barrier penetration model that adapts semiclassical WKB calculations to incorporate a coordinate-dependent effective mass for the $\ensuremath{\alpha}$ particle. This effect is a consequence of a dynamic property of nonlocality in the particle-nucleus interaction, as implemented in the barrier tunneling calculations of [N. Teruya, S. B. Duarte, and M. M. N. Rodrigues, Phys. Rev. C 93, 024606 (2016)]. Calculations have been performed for a recent set of experimental data of 255 $\ensuremath{\alpha}$-emitting nuclides, all selected with angular momentum $\ensuremath{\ell}=0$ experimentally assigned. Results show a good agreement when compared to experimental half-life data, obtaining a standard deviation of $\ensuremath{\sigma}=0.306$ and fully satisfying the universal systematics, namely, new universal plot and universal decay law systematics, of $\ensuremath{\alpha}$ decay. Additionally, the present model has been applied to make half-life predictions for 34 possible new $\ensuremath{\alpha}$-decay cases.

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.

Coherent description of elastic scattering and fusion at near-barrier energies for the Be9+Pb208 and Be9+Au197 reactions

Elastic scattering, total reaction, and fusion cross sections of the systems $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ and $^{9}\mathrm{Be}+^{197}\mathrm{Au}$ at near-barrier energies, are coherently analyzed into two theoretical contexts. In a phenomenological approach, a BDM3Y1 interaction is used in an optical model potential analysis of the elastic-scattering data and the energy dependence of the potential is mapped around the Coulomb barrier. In a second approach, the elastic scattering is investigated within a four body framework by using the continuum-discretized coupled-channels method. In both scenarios, total reaction cross sections are determined and compared with phenomenological predictions. Moreover, an effective potential is obtained and in a one barrier penetration model analysis, the fusion excitation function is determined and compared with experimental data, further validating our analysis.

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.

Effect of Shapes Degrees of Freedom on the Fusion Cross-Sections of 16O + 154Sm and 18O + 148Nd

The fusion dynamics of 16O + 154Sm and 18O+148Nd reactions has been investigated to observe the effect of shape degree of freedom on the fusion cross-section using the coupled channel (CC) calculations. The one dimentional barrier penetration model (1-D BPM) is observed to underestimate the experimental data mainly at below barrier energies. The coupled channel calculations, including target projectile excitations with 1 phonon of vibrational state and 2+ rotational state of target, reproduce the experimental fusion cross-section for 16O + 154Sm reaction at below barrier energies, while show some discrepancy for 18O+148Nd reaction. This discrepancy for 18O+148Nd reaction can be addressed with the inclusion of low-lying states with neutron transfer channels and the neck-formation.

Systematic application of the M3Y NN forces for describing the capture process in heavy-ion collisions involving deformed target nuclei

We present results of a systematic study of the capture process through the barrier penetration model. The nucleus-nucleus interaction potential is calculated using the double-folding model (DFM) with the M3Y Paris $\mathit{NN}$ forces. The nucleon densities entering the model are generated from the experimental three-parameter Fermi charge densities. The DFM has been extended to the case of deformed target nuclei. It is shown that the density-dependent M3Y $\mathit{NN}$ forces with the finite range exchange part can be mimicked successfully by the zero-range density-independent forces. The latter option significantly reduces the required computer time. For the nucleon densities and target nuclei deformations, we employ the values from the commonly used data bases. Thus, we do not vary any parameters to reach a better agreement with the data. The resulting cross sections are compared with data for 20 reactions with the product of the charge numbers ${Z}_{P}{Z}_{T}$ ranging from 216 up to 2576. We discuss the opinion met in the literature that the M3Y $\mathit{NN}$ forces provide a poorer description of the capture cross sections in heavy-ion collisions in comparison to the $\mathit{NN}$ forces coming from the relativistic mean-field approach. Our calculations show that the M3Y $\mathit{NN}$ forces give an agreement with the data which is not perfect yet is not worse than the one resulting from the relativistic mean-field approach $\mathit{NN}$ forces.

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.

Influence of halo single-neutron transfer on near barrier ^{15}C + ^{12}C total fusion

A recent comparison of the average fusion cross section, leftlangle sigma _mathrm {F}rightrangle , for energies just above the Coulomb barrier for the ^{12-15}C + ^{12}C systems found that the behaviour as a function of projectile neutron excess could not be satisfactorily explained by static barrier penetration model calculations and suggested that the neutron dynamics plays an important rôle. In this work we demonstrate that the (^{15}C,^{14}C) single neutron transfer has a significant influence on the above barrier ^{15}C + ^{12}C total fusion, although not quite in the way expected since it leads to a reduction in the cross section, contrary to the trend in the measured leftlangle sigma _mathrm {F}rightrangle . However, this result underlines the danger of ignoring the effect of neutron transfer reactions on fusion in systems involving neutron halo nuclei.

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.

Role of the shape deformation in 12C + 12C fusion at sub-Coulomb energies

The fusion cross section of 12C+12C system at the energies of astrophysical interest is calculated in the framework of barrier penetration model taking into account the deformed shape of interacting nuclei. In particular, the quadrupole surface deformation of both projectile and target nuclei has been included during the fusion process. The real and imaginary parts of nucleus-nucleus interactions performed using the Woods-Saxon square and Woods-Saxon functions, respectively have been carefully tested by 12C-12C elastic scattering data analysis before employed to evaluate the astrophysical S factors (the fusion cross sections). The optical model results of elastic angular distributions are consistent with the experimental data. Within the barrier penetration model, the real part of the obtained optical potential gives a good description of the non-resonant astrophysical S factor. It turns out that the taking into account of quadrupole deformation of 12C nuclei increases the astrophysical S factor at energies below Coulomb barrier.

Influence of coupling of excited states and of deuteron transfer on fusion reactions induced by 6,7Li on 64Ni, 152Sm and 209Bi targets

Here, we present a comprehensive analysis of fusion reaction data induced by weakly bound nuclei 6,7Li on medium and heavy mass targets 64Ni, 152Sm and 209Bi at around Coulomb barrier energies within the framework of coupled channel method. Particularly, the influence of coupling of various excited states of the colliding nuclei and the deuteron transfer effects on fusion excitation function have been investigated. It is found that the inclusion of coupling effects leads to an enhancement up to 74% in fusion reaction cross section in close vicinity of Coulomb barrier when compared with one dimensional barrier penetration model predictions. However the inclusion of deuteron transfer effects reduces this enhancement up to 23% in below barrier region while up to 36% in above barrier energy region and reproduces the data reasonably well.