Excitation Function Data Research Articles

Analysis of elastic scattering angular distributions and fusion excitation functions of reactions induced by 9Be on 27Al, 28Si, 144Sm and 208Pb targets at near barrier energies

The elastic scattering angular distributions and the fusion excitation function data for the reactions induced by the loosely bound projectile 9Be on [Formula: see text]Al, [Formula: see text]Si, [Formula: see text]Sm and [Formula: see text]Pb targets at near and above barrier energies have been analyzed with a motive to investigate the importance of breakup couplings within the framework of continuum discretized coupled channels approach. It is found that at energies much higher than Coulomb barrier, the breakup effects are insignificant for light targets while for heavy targets, the breakup effects play a dominant role at these energies. But at energies comparable to the barrier height, the role of breakup becomes crucial for light mass targets also.

17.9 MeV’lik Enerjide (p,α) Tesir Kesiti Verileri üzerine Sistematik Bir İnceleme

Nuclear cross section data are needed in various applications such as radiation therapy, astrophysics, radioisotope production, fusion and fission. The systematics play a very important role in determining cross sections on neutron- and proton-induced reactions at incoming energies of which there are no experimental values. So, empirical systematics have been extensively used at present in the studies on cross section calculations. In this paper, we proposed empirical cross section formulas considering Q–value dependence on (p,α) reactions at proton energy of 17.9 MeV. The present formulas including Coulomb and odd-even effects are based on the statistical theory. In addition, these formulas are a modification to the Levkovskii’s original asymmetry parameter formulas for neutron induced reactions and the Tel et al.’s empirical formulas for proton reactions. Fitting parameters of formulas were determined by least-squares fitting to experimental excitation function data. It is seen that new empirical formulas give good fits with (p,α) experimental cross section values in the literature at 17.9 MeV.

R -matrix analysis of elastic scattering, phase shifts, and radiative capture reaction cross sections in the α+α system

The unstable nucleus $^8$Be, with its two $\alpha$-cluster configuration, is the doorway to the formation of heavier $\alpha$-cluster nuclei. Most importantly, its the precursor of the production of $^{12}$C through the Hoyle state, a resonance state of three $\alpha$ clusters, in the helium burning phase of a massive star. The nucleus exhibits a ground state band of rotational states established through $\alpha-\alpha$ scattering experiments. A subsequent precision particle-$\gamma$ coincidence measurement of the electromagnetic transition between the 4$^+\rightarrow$ 2$^+$ excited states also corroborated the evidence for a highly deformed dumb-bell shaped structure of $^8$Be. A simultaneous phenomenological R-matrix analysis of the measured capture reaction cross sections along with the elastic excitation function and phase shift data has been performed. The resulting reduced transition strength of 21.96$\pm$3.86 $e^2 fm^4$ compares well with the estimated experimental value of 21.0$\pm$2.3 e$^2$ fm$^4$. The R-matrix yield of the B($E2$) value is closer to the prediction of cluster model but about 19$\%$ less than the {\it ab initio} result.

Quasi-elastic scattering measurements of the 28Si + 142Nd system at back-angle

The barrier distribution of a system can be extracted from excitation function data obtained either through fusion reaction or through quasi-elastic scattering measurement. In the present work, the quasi-elastic excitation function has precisely been measured at back angle for the 28Si + 142Nd system at energies around the Coulomb barrier and the corresponding experimental barrier distribution has been extracted. The experimental data has been interpreted in the frame work of the coupled channel calculations which include couplings to different possible modes of excitations of the interacting target-projectile combination. The possible effect of the nature of projectile excitations on the derived barrier distribution has been presented.

A hybrid model description of 13C(p,γ)14N capture reaction

The radiative capture reaction [Formula: see text] is analyzed using a hybrid model approach where the non-resonant component has been constructed employing the potential model with a folded M3Y potential. The one-level Breit–Wigner formula has been used to estimate the cross-sections of the resonant decays of dominant ([Formula: see text]) state of [Formula: see text]N at 8.06[Formula: see text]MeV. The contribution of the broad resonance at 8.77[Formula: see text]MeV ([Formula: see text]) has been dealt with differently. While Breit–Wigner formula has been used where the excitation function data exist, the [Formula: see text]-matrix prediction for the cross-section of decay to a bound state of [Formula: see text]N from the broad resonance has been used where excitation function data are not available. The single particle spectroscopic factors for ground and six excited states of [Formula: see text]N have been obtained from the fits. The resulting astrophysical [Formula: see text]-factor at zero relative energy is [Formula: see text][Formula: see text]keV b. The value is in good agreement with the previously reported [Formula: see text]-matrix result and also consistent within error bars with the published values.

Measurement of natW(p,xn)177,178,179Re excitation function of natural tungsten by using a 100-MeV proton beam

Measurements of the proton-induced excitation function for the natW(p,xn)177,178,179Re nuclear reaction has been measured in the energy region below 100 MeV by using the 100-MeV proton linear accelerator at the Korea Multi-Purpose Accelerator Complex. The stacked foil activation technique was adopted in the present study. The gamma-rays generated from the proton-irradiated samples were measured by using a gamma-ray spectroscopy system with a HPGe detector. The 27Al(p,3p+n)24Na reaction was used as a monitor reaction for proton flux monitoring. The nuclear reactions of natW(p,xn)177,178,179Re were observed in the present study. The proton-induced excitation functions of natural tungsten were derived from the delayed gamma-ray yield of the produced nucleus. The present results were compared with the previous experimental excitation function data of Yu. E. Titarenko et al. [1].

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

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

Fusion suppression/fusion enhancement around the Coulomb barrier

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

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

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

The effect of breakup of 6Li on elastic scattering and fusion with 28Si at near barrier energies

Elastic scattering angular distributions for 6Li+[Formula: see text]Si system were measured at [Formula: see text] and analyzed along with the existing data from the previous measurements in the energy range of [Formula: see text]. The measured cross-sections and the existing data, forming a set of angular distributions over a range of E/[Formula: see text], were analyzed using the phenomenological optical model potential (OMP). Three different sets of potential parameters were used. The energy dependence of the real and the imaginary potential strengths were, subsequently, extracted at the radius of sensitivity ([Formula: see text]) for the system. Continuum Discretized Coupled Channel (CDCC) calculation was performed to explore the contribution of projectile break-up (BU) on the observed energy dependence of the effective potential for elastic scattering of 6Li from [Formula: see text]Si. The energy variation of the strength of the real potential with continuum coupling was found to agree with the energy dependence of the same extracted from the (OMP) analysis at energies around the barrier. But the behavior of the imaginary strength appeared to be different. The calculated fusion cross-sections, including the effect of BU, clearly overestimated the measured fusion excitation function data in the below and near barrier energies but compared well with the data at higher energies.

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.

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 %.

Influence of Incomplete Fusion Reaction on Complete Fusion Below 10 Mev/ Nucleon Energies

An attempt has been made in the present work to provide an ample opportunity to explore the information about the influence of incomplete fusion (ICf) reaction dynamics on complete fusion in heavy ion induced nuclear reactions. excitation functions for several evaporation residues produced in the interaction of projectile O with target lu have been measured over the wide projectile energy range ≈ 70-100 MeV. the recoil-catcher activation technique followed by the offline γ-ray spectroscopy has been used for the present measurements. In case of precursor decay, we have made use of Cavinato et al. formulation to calculate the independent cross-section of the identified residues. the measured efs are compared with theoretical predictions of statistical model code PACe-2 and any enhancement in the measured cross-section from theoretical prediction may be due to ICf reaction process. An attempt has been made to estimate the ICf contribution of the cross-section from the measured excitation function data and the dependence of ICf cross-section on projectile energy.

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

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

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

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

Interplay of deformation and two neutrons transfer effects in 6 He induced fusion reactions around barrier energies

Abstract We have analyzed the fusion excitation function data of various reactions involving 6 He as projectile in the near barrier energy region using proximity potential and quantum diffusion approach by incorporating the effects arising by assuming two neutrons transfer before fusion. It has been found that the two neutrons transfer enhances the sub-barrier fusion for those systems wherein the change in deformation is negligibly small. But for systems in which there is a substantial change in deformation due to neutrons transfer there may occur either suppression or enhancement depending of nature of change in shape. The inclusion of these effects leads to a reasonable improvement in matching between data and predictions in sub-barrier energy region.

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

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

Relative importance of energy dependent diffuseness parameter and barrier position in the analysis of fusion excitation function data

We have investigated the relative importance of the energy dependence of diffuseness parameter and barrier position in the description of the fusion excitation function data of some heavy ion systems in near barrier energy region. The effects of the energy dependent diffuseness parameter are found to be much more prominent in comparison to those of barrier position.

Analysis of fusion excitation functions of various systems using modified Woods–Saxon potential

Abstract We have analyzed the fusion excitation function data of various heavy ion systems in the near barrier energy region using the coupled channel code CCFULL and a new parameterization scheme for evaluating the depth of the Woods–Saxon nuclear potential. The potential model proposed here explains the fusion excitation function of the various heavy ion systems reasonably well. We have also discussed the role of projectile isotopic effects, target isotopic effects and the mass asymmetry in the entrance channel, by choosing the suitable projectile–target combinations, in the sub-barrier fusion enhancement.

Analysis of fusion excitation function data by using an energy dependent potential model

We have analyzed the fusion excitation function data of various heavy ion systems in the near barrier energy region using Wongʼs formula and an energy dependent potential. The various channel coupling effects for different projectile–target combinations are properly mocked up by the energy dependent potential resulting in a very good agreement between the data and the predictions.