Neutron Transfer Research Articles

Characteristics of Entry into the Xenon Oscillations Regime in a Reactor with Feedback on the Coolant Temperature

The simplest approximations (one-dimensional reactor, single-group diffusion model of neutron transfer) are used to study the characteristics of xenon oscillations in a reactor with negative feedback on the coolant temperature. It is shown that in this case, in contrast to the situation where the predominant feedback is on the neutron flux density, the emergence into the xenon instability regime will manifest in the form of perturbations of the reactor power and energy release simultaneously. In addition, the deformations of the energy-release field grow with increasing neutron flux and physical dimensions of the reactor.

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

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

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

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

Analysis of the dependence of the few-neutron transfer probability on theQ-value magnitudes

Employing the known experimental fact that the sub-barrier capture (fusion) enhancement in the reactions $^{40}\mathrm{Ca}+^{94,96}\mathrm{Zr}$ and $^{40}\mathrm{Ca}+^{116,124,132}\mathrm{Sn}$ is not proportional to the magnitudes of $Q$ values for the neutron transfer, the similarity of the structure of the target nuclei, and the conservation of the total reaction flux, we analyze the dependence of a few-neutron transfer probability on the magnitudes of $Q$ values. This analysis is checked by the calculations of nucleon transfer probabilities within the time-dependent Hartree-Fock plus BCS approach.

Examination of the different roles of neutron transfer in the sub-barrier fusion reactionsS32+Zr94,96and40Ca+Zr94,96

The sub-barrier capture (fusion) reactions $^{32}\mathrm{S}+^{90,94,96}\mathrm{Zr}$, $^{36}\mathrm{S}+^{90,96}\mathrm{Zr}$, ${}^{40}\mathrm{Ca}+^{90,94,96}\mathrm{Zr}$, and ${}^{48}\mathrm{Ca}+^{90,96}\mathrm{Zr}$ with positive and negative $Q$ values for neutron transfer are studied with the quantum diffusion approach and the universal fusion function representation. For these systems, the $s$-wave capture probabilities are extracted from the experimental excitation functions and are also analyzed. Different effects of the positive ${Q}_{xn}$-value neutron transfer in the fusion enhancement are revealed in the relatively close reactions $^{32}\mathrm{S}+^{94,96}\mathrm{Zr}$ and ${}^{40}\mathrm{Ca}+^{94,96}\mathrm{Zr}$.

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.

Role of neutron transfer processes on the6Li+120Sn and7Li+119Sn fusion reactions

The results concerning the study of 6 Li+ 120 Sn and 7 Li+ 119 Sn systems are presented. These two sistems are characterised by very similar structures of the interacting nuclei and by different Q-value for oneand two- neutron transfer. Our aim is to disentangle the possible effects due to the different n-transfer Q-values, at sub-barriers energies, by comparing the two fusion excitation function. In these experiments the fusion cross section has been measured by using a stack activation technique. No particular differences in the two fusion excitation functions have been observed. The influence of transfer channels on fusion cross-section has been object of investigations in the last years. In particular, the possible dependence of the fusion cross-section on the sign of the neutron transfer Q-value has been much debated in literature. The systematic approach used for the study of the Ca+Zr systems [1] provided relatively clear evidence of the relation between sub-barrier-cross section and the sign of the neutron transfer Q-value, in a model-independent way. According to experimental

Role of neutron rearrangement channels in sub-barrier fusion

Different factors influencing the sub-barrier fusion enhancement owing to neutron rearrangement with positive Q values are studied. It was found that opposite to the previous opinion the presence of positive Q values is necessary but not sufficient to observe enhancement of the sub-barrier fusion. Rigidity of colliding nuclei with respect to collective excitations plays a crucial role for the sub-barrier fusion enhancement due to neutron rearrangement. Neutron binding energy has a strong impact but only in the case of fusion of light nuclei. 1 Motivation Sub-barrier fusion is one of the intensively studied phe- nomena, that is still far from its complete understanding. The sub-barrier fusion enhancement induced by coupling of relative motion to surface deformations or rotation of heavy deformed nuclei is well understood and properly described within the quantum coupled channel approach (see e.g. (1-3)) and within the empirical coupled chan- nel (ECC) model (4). At the same time there are many experimental evidences of additional enhancement of the sub-barrier fusion cross section due to neutron rearrange- ment with positive Q values. The mechanism of sequen- tial fusion was proposed in (5) which described for the first time an additional sub-barrier fusion enhancement owing to neutron rearrangement with positive Q value at approaching stage. The corresponding model (called the ECC model with neutron rearrangement) is used in this work. The mechanism of influence of neutron rearrange- ment on the sub-barrier fusion is connected with the fact that the spreading of the valence neutron's wave func- tion into the volume of the other nucleus takes place be- fore the colliding nuclei overcome the Coulomb barrier (6, 7), and, therefore, neutron rearrangement at approach- ing stage may really influence the sub-barrier fusion dy- namics giving a gain in kinetic energy of colliding nuclei if it occurs with positive Q value. This effect can be easier observed if one compares the sub-barrier fusion cross sec- tions for two close projectile-target combinations for one of which neutron rearrangement with positive Q values is possible whereas for another one all neutron transfers have negative Q values. The pair of reactions 40 Ca+ 96 Zr and 40 Ca+ 90 Zr is classical example of such kind (see Fig. 1 (a)). Coupling of relative motion to the surface vibra- tions explains the observed cross section for the 40 Ca+ 90 Zr reaction, but it is insufficient to describe additional sub-

Time-dependent quantum models of the dynamics of neutron transfer reactions near the barrier

Time-dependent valence neutron wave functions were calculated for nucleus-nucleus collisions 6He + 197Au, 18O + 58Ni, 48Ca + 18O, 40,48Ca + 238U. Probabilities of the neutron transfer and near-barrier population of two-center levels were calculated. The energy dependence of the neutron transfer cross section in the 6He + 197Au reaction has been explained.

One neutron transfer reaction in the9Be+89Y system

One neutron transfer cross sections from the interaction of 9 Be with 89 Y have been measured at energies greater than the fusion barrier. The present measured 1n-transfer cross sections saturate at well above energies in comparison with the available experimental data at lower energies. Results of Coupled Reaction Channels Calculations (CRC) show very good agreement with the present measured cross sections.

Exploring the influence of transfer channels on fusion reactions: the case of40Ca +58,64Ni

Fusion cross sections have been measured in the 40 Ca + 58 Ni and 40 Ca + 64 Ni systems at beam energies ranging from Elab = 104.75 MeV to 153.5 MeV using the Laboratori Nazionali di Legnaro electrostatic deflector. Distributions of barriers have been extracted from the experimental data. Preliminary coupled channel calculations were performed and hints of effects of neutron transfers on the fusion below the barrier in the 40 Ca + 64 Ni are discussed.

Application of the Gauss–Seidel Iteration Process in the Diagonal Element Isolation Method for Thermal Radiation Transfer Problems

The application of the Gauss–Seidel diagonal element isolation method is examined for obtaining an iterative solution of the system of thermal-radiation transfer equations for absorbing, radiating, and scattering media. Calculations of a test problem are preformed for the example of the correction form of the nonlinear variant of the method for the finite-difference WDD scheme in planar geometry. The method can also be used for modeling the transfer of γ-rays and neutrons.

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

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

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 asymmetric fusion reactions at sub-barrier energies

The measured complete fusion (capture) excitation function is presented for the 28Si + 208Pb reaction at deep sub-barrier energies. This excitation function is compared with the one predicted with the quantum diffusion approach.

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.

Fusion ofS32 + Zr94: Further exploration of the effect of the positiveQxnvalue neutron transfer channels

The effect of the positive $Q$-value neutron transfer (PQNT) channels on the subbarrier fusion process is still far from a clear understanding and hence is worth further investigation. To this end, we have measured the fusion excitation function for $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ at energies near and below the Coulomb barrier with rather good accuracy, and deduced the experimental fusion barrier distribution. The reaction system $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ is a good candidate for the evaluation of PQNT effect because it has multineutron transfer channels with positive ground-state ${Q}_{xn}$ values as well as the relatively weak low-lying ${3}^{\ensuremath{-}}$ vibrational state in $^{94}\mathrm{Zr}$. Our results show that the fusion cross sections of $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ are strongly enhanced at the lower-energy region. By means of a cross comparison of the $^{32}\mathrm{S}$,$^{40}\mathrm{Ca}+^{90,94,96}\mathrm{Zr}$ systems, further evidence is given that the positive ${Q}_{xn}$-value neutron transfer channels, rather than the strong low-lying ${3}^{\ensuremath{-}}$ vibrational state, bring about the additional subbarrier fusion enhancement. Relative to the coupled-channels results with couplings to the low-lying inelastic collective excitations, an unexpectedly large enhancement for the subbarrier fusion cross sections is observed in $^{32}\mathrm{S}+^{94}\mathrm{Zr}$ compared to $^{32}\mathrm{S}+^{96}\mathrm{Zr}$. Some existing theoretical models have been discussed, but a good explanation cannot be achieved. Exact coupled-channels theory and more experiments on transfer reactions themselves are strongly desired to comprehensively understand the effect of transfer on fusion.

Fusion of the 6Li+120Sn and 7Li+119Sn and the role of neutron transfer and breakup processes

Excitation functions have been measured for the fusion of the weakly bound nuclei 6Li and 7Li respectively with 120Sn and 119Sn at energies around the Coulomb barrier by using an activation technique. With such a study we aim to investigate the role played by direct processes as neutron transfer and breakup on fusion. At energies above the barrier, the complete fusion cross section are lower than those predicted by fusion models. This suppression is independent of beam energy and is in agreement with the values reported in literature for heavier systems. At energies below the barrier, no significant enhancement due to the positive Q-value for one and two neutron transfer for the 7Li+119Sn system is observed as compared with the 6Li+120Sn.

Nuclear reactions at near-barrier energies with quantum diffusion approach

The role of neutron transfer in the fusion (capture) reactions is discussed.

Systematic analysis of the effect of a positiveQ-value neutron transfer in fusion reactions

The experimental data of fusion cross sections for the different projectile and target nuclei systems are systematically analyzed. In order to explore the positive $Q$-value neutron transfer (PQNT) effect we systematically analyze their fusion functions F($x$) as a function of $x$, which reduces the barrier height, radius, and curvature of fusion systems. From the comparison of F($x$)s among them, it is found that after neutron transfer when the deformation of interacting nuclei increases largely, the enhancement of fusion cross sections can be observed at energies below the Coulomb barrier due to the PQNT effect. However, even if the fusion systems show the PQNT values, the fusion cross sections are almost the same due to the small deformation of interaction nuclei after neutron transfer. Many experiments need to be systematically done for this research.