Neutron Transfer Research Articles

Effect of nuclear-reaction mechanisms on the population of excited nuclear states and isomeric ratios

Experimental data on the cross sections for channels of fusion and transfer reactions induced by beams of radioactive halo nuclei and clustered and stable loosely bound nuclei were analyzed, and the results of this analysis were summarized. The interplay of the excitation of single-particle states in reaction-product nuclei and direct reaction channels was established for transfer reactions. Respective experiments were performed in stable (6Li) and radioactive (6Не) beams of the DRIBs accelerator complex at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, and in deuteron and 3Не beams of the U-120M cyclotron at the Nuclear Physics Institute, Academy Sciences of Czech Republic (Řež and Prague, Czech Republic). Data on subbarrier and near-barrier fusion reactions involving clustered and loosely bound light nuclei (6Li and 3He) can be described quite reliably within simple evaporation models with allowance for different reaction Q-values and couple channels. In reactions involving halo nuclei, their structure manifests itself most strongly in the region of energies below the Coulomb barrier. Neutron transfer occurs with a high probability in the interactions of all loosely bound nuclei with light and heavy stable nuclei at positive Q-values. The cross sections for such reactions and the respective isomeric ratios differ drastically for nucleon stripping and nucleon pickup mechanisms. This is due to the difference in the population probabilities for excited single-particle states.

The Giant Pairing Vibration in Carbon isotopes

The 13C(18O,16O)15C and 12C(18O,16O)14C reactions at 84 MeV incident energy were explored up to high excitation energy of the residual nucleus thanks to the use of the MAGNEX spectrometer to detect the ejectiles. In the region above the two-neutron separation energy, a resonance has been observed in both nuclei, attributed to the Giant Pairing Vibration (GPV). The neutron decay of the 15C resonances, including the GPV, populated via the two- neutron transfer reaction has been studied using an innovative technique, which couples MAGNEX with the EDEN neutron detector array. The data show that the 15C GPV mainly decays via two-neutron emission.

Near-barrier neutron transfer in reactions 3,6He + 45Sc and 3,6He + 197Au

Experimental cross sections for formation of 196,198Au isotopes in reactions 3,6He + 197Au and cross sections for formation of 44,46Sc isotopes in reactions 3,6He + 45Sc have been analyzed. To calculate neutron transfer probabilities and cross sections the time- dependent Schrödinger equation for external neutrons of 3He, 6He, 45Sc and 197Au nuclei has been solved numerically. It is shown that the contribution of fusion and subsequent evaporation is significant in the case of reactions 3,6He + 45Sc, whereas in the case of reactions 3,6He + 197Au, it is negligible. Fusion-evaporation was taken into account using NRV evaporation code. Results of calculations demonstrate overall satisfactory agreement with experimental data.

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.

Revised analysis ofCa40+Zr96fusion reactions

Fusion data for $^{40}$Ca+$^{96}$Zr are analyzed by coupled-channels calculations that are based on a standard Woods-Saxon potential and include couplings to multiphonon excitations and transfer channels. The couplings to multiphonon excitations are the same as used in a previous work. The transfer couplings are calibrated to reproduce the measured neutron transfer data. This type of calculation gives a poor fit to the fusion data. However, by multiplying the transfer couplings with a $\sqrt{2}$ one obtains an excellent fit. The scaling of the transfer strengths is supposed to simulate the combined effect of neutron and proton transfer, and the calculated one- and two-nucleon transfer cross sections are indeed in reasonable agreement with the measured cross sections.

Microscopic study ofCa40+Ni58,64fusion reactions

Background: Heavy-ion fusion reactions at energies near the Coulomb barrier are influenced by couplings between the relative motion and nuclear intrinsic degrees of freedom of the colliding nuclei. The time-dependent Hartree-Fock (TDHF) theory, incorporating the couplings at the mean-field level, as well as the coupled-channels (CC) method are standard approaches to describe low energy nuclear reactions. Purpose: To investigate the effect of couplings to inelastic and transfer channels on the fusion cross sections for the reactions $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni. Methods: Fusion cross sections around and below the Coulomb barrier have been obtained from coupled-channels (CC) calculations, using the bare nucleus-nucleus potential calculated with the frozen Hartree-Fock method and coupling parameters taken from known nuclear structure data. The fusion thresholds and neutron transfer probabilities have been calculated with the TDHF method. Results: For $^{40}$Ca+$^{58}$Ni, the TDHF fusion threshold is in agreement with the most probable barrier obtained in the CC calculations including the couplings to the low-lying octupole $3_1^{-}$ state for $^{40}$Ca and to the low-lying quadrupole $2_1^{+}$ state for $^{58}$Ni. This indicates that the octupole and quadrupole states are the dominant excitations while neutron transfer is shown to be weak. For $^{40}$Ca+$^{64}$Ni, the TDHF barrier is lower than predicted by the CC calculations including the same inelastic couplings as those for $^{40}$Ca+$^{58}$Ni. TDHF calculations show large neutron transfer probabilities in $^{40}$Ca+$^{64}$Ni which could result in a lowering of the fusion threshold. Conclusions: Inelastic channels play an important role in $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni reactions. The role of neutron transfer channels has been highlighted in $^{40}$Ca+$^{64}$Ni.

Near-barrier neutron transfer in reactions with 3He nucleus

Experimental cross sections for the formation of 196,198Au isotopes in the 3He + 197Au reaction and 44,46Sc isotopes in the 3He + 45Sc reaction are analyzed. To calculate transfer probabilities and cross sections, the time-dependent Schrodinger equation is numerically solved for the external neutrons of the 3He, 45Sc, and 197Au nuclei. It is shown that the contribution from the fusion channel with subsequent evaporation is important for the 3He + 45Sc reaction and negligibly small for the 3He + 197Au reaction. Fusion–evaporation is taken into account using the NRV and PACE codes. Calculation results demonstrate overall satisfactory agreement with experimental data.

A self-consistent method to analyze the effects of the positive Q-value neutron transfers on fusion

Abstract Considering the present limitation of the need for external parameters to describe the nucleus–nucleus potential and the couplings in the coupled-channels calculations, this work introduces an improved method without adjustable parameter to overcome the limitation and then sort out the positive Q-value neutron transfers (PQNT) effects based on the CCFULL calculations. The corresponding analysis for Ca + Ca , S , Ca + Sn , and S , Ca + Zr provides a reliable proof and a quantitative evaluation for the residual enhancement (RE) related to PQNT. In addition, the RE for S 32 , Ca 40 + Zr 94 shows an unexpected larger enhancement than S 32 , Ca 40 + Zr 96 despite the similar multi-neutron transfer Q-values. This method should rather strictly test the fusion models and be helpful for excavating the underlying physics.

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

The dynamic coupling effects on fusion cross sections for reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr are studied with the universal fusion function formalism and an empirical coupled channel (ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in $^{32}$S + $^{94}$Zr ($^{40}$Ca + $^{94}$Zr) is almost the same as that in $^{32}$S + $^{96}$Zr ($^{40}$Ca + $^{96}$Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with $^{94}$Zr as target should be similar as that in the reactions with $^{96}$Zr as target. This implies that the quadrupole deformation parameters $\beta_2$ of $^{94}$Zr and $^{96}$Zr should be similar to each other. However, $\beta_2$'s predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on $^{48}$Ca + $^{94}$Zr or $^{36}$S + $^{94}$Zr are suggested to solve the puzzling issue concerning $\beta_2$ for $^{94}$Zr.

Barrier distribution from28Si+154Sm quasielastic scattering: Coupling effects in the fusion process

Barrier distribution for the 28 Si+ 154 Sm system has been extracted from large angle quasielastic scattering measurement to investigate the role of various channel couplings on fusion dynamics. The coupled channel calculations, including the collective excitation of the target and projectile, are observed to reproduce the experimental BD rather well. It seems that the role of neutron transfer, relative to collective excitation, is in fact weak in the 28 Si+ 154 Sm system even though it has positive Q-value for neutron transfer channels.

Calculations of Compound Nucleus Spin-Parity Distributions Populated via the (p,t) Reaction in Support of Surrogate Neutron Capture Measurements

The surrogate reaction method may be used to determine the cross section for neutron induced reactions not accessible through standard experimental techniques. This is achieved by creating the same compound nucleus as would be expected in the desired reaction, but through a different incident channel, generally a direct transfer reaction. So far, the surrogate technique has been applied with reasonable success to determine the fission cross section for a number of actinides, but has been less successful when applied to other reactions, e.g. neutron capture, due to a ‘spin-parity mismatch’. This mismatch, between the spin and parity distributions of the excited levels of the compound nucleus populated in the desired and surrogate channels, leads to differing decay probabilities and hence reduces the validity of using the surrogate method to infer the cross section in the desired channel. A greater theoretical understanding of the expected distribution of levels excited in both the desired and surrogate channels is therefore required in order to attempt to address this mismatch and allow the method to be utilised with greater confidence. Two neutron transfer reactions, e.g. (p,t), which allow the technique to be utilised for isotopes further removed from the line of stability, are the subject of this study. Results are presented for the calculated distribution of compound nucleus states populated in 90Zr, via the 90Zr(p,t)90Zr reaction, and are compared against measured data at an incident proton energy of 28.56 MeV.

Studies for the effect of the positiveQ-value neutron transfers on sub-barrier heavy-ion fusion

This contribution reports the recent experimental studies for the coupling effect of the positive Q-value neutron transfer (PQNT) channels on near-barrier fusion with heavy-ions, measured by an electrostatic deflector setup. This effect is expected to be important in some situations. In this presentation, the experimental studies for the nearbarrier fusion of 32 S +90,94,96 Zr,16 O +76 Ge,18 O +74 Ge, and16,18 O +58 Ni are reported. Also a method, based on the CCFULL calculations with suitable inelastic couplings, to sort out the PQNT effect is presented.

Sub-barrier fusion and transfers in the40Ca +58,64Ni systems

Fusion cross sections have been measured in the 40 Ca + 58 Ni and 40 Ca + 64 Ni systems at energies around and below the Coulomb barrier. The 40 Ca beam was delivered by the XTU Tandem accelerator of the Laboratori Nazionali di Legnaro and evaporation residues were measured at very forward angles with the LNL electrostatic beam deflector. Coupled-channels calculations were performed which highlight possible strong effects of neutron transfers on the fusion below the barrier in the 40 Ca + 64 Ni system. Microscopic time-dependent Hartree-Fock calculations have also been performed for both systems. Preliminary results are shown.

Fusion and neutron transfer reactions with weakly bound nuclei within time-dependent and coupled channel approaches

The time-dependent Schrödinger equation and the coupled channel approach based on the method of perturbed stationary two-center states are used to describe nucleon transfers and fusion in low-energy nuclear reactions. Results of the cross sections calculation for the formation of the 198Au and fusion in the 6He+197Au reaction and for the formation of the 65Zn in 6He+64Zn reaction agree satisfactorily with the experimental data near the barrier. The Feynman’s continual integrals calculations for a few-body systems were used for the proposal of the new form of the shell model mean field for helium isotopes.

Quantum coupled-channels model of nuclear fusion with a semiclassical consideration of neutron rearrangement

Background: Significant enhancement of sub-barrier fusion cross sections owing to neutron transfer with positive $Q$ values was observed in many combinations of colliding nuclei. This degree of freedom has not yet been included into the rigorous quantum coupled-channels (QCC) approach. However, the empirical coupled-channels model with neutron rearrangement [Zagrebaev, Phys. Rev. C 67, 061601 (2003)] has already been successfully used in several papers to reproduce and predict cross sections for sub-barrier fusion reactions of stable nuclei.Purpose: The objective of this study is to combine the QCC approach and the empirical model to account for additional channels of neutron rearrangement.Method: Coupling of relative motion to collective degrees of freedom (rotation of nuclei and/or their surface vibrations) are taken into account within the QCC approach. The probability of transfer of $x$ neutrons with a given $Q$ value is estimated semiclassically.Results: The proposed new model was successfully tested on a few combinations of fusing nuclei $^{40}\text{Ca}+^{90,94,96}\text{Zr}, ^{32}\text{S}+^{90,94,96}\text{Zr}$, and $^{60,64}\text{Ni}+^{100}\text{Mo}$. The calculated fusion cross sections and barrier distribution functions agree well with experimental data.Conclusions: The model developed in this work confirms all the conclusions previously made within the empirical coupled-channels model with neutron rearrangement [see Rachkov et al., Phys. Rev. C 90, 014614 (2014)]. Moreover, it has an advantage of a more reliable microscopic account for the coupling between relative motion and the collective degrees of freedom. The proposed model can also be used to reproduce the structure of the barrier distribution function. This is a step forward to a complete solution of the long-term problem of accounting for neutron transfer channels in the QCC model.

Analysis of the role of neutron transfer in asymmetric fusion reactions at subbarrier energies

The excitation functions were measured for the 28Si + 208Pb complete-fusion (capture) reaction at deep subbarrier energies. The results were compared with the cross sections predicted within the quantum diffusion approach. The role of neutron transfer in the case of positive Q values in the 28Si + 124Sn, 208Pb; 30Si + 124Sn, 208Pb; 20Ne + 208Pb; 40Ca + 96Zr; and 134Te + 40Ca complete-fusion (capture) reactions is discussed.

Formation and decay analysis ofCd*4898,104isotopes inCa2040-induced reactions

We have analyzed the fusion dynamics of $_{20}^{40}\mathrm{Ca}+_{28}^{58,64}\mathrm{Ni}$ reactions by using the energy dependent Woods-Saxon potential (EDWSP) model and coupled channel model and subsequently the decay patterns of $_{48}^{98,104}\mathrm{Cd}^{*}$ nuclei are governed via the dynamical cluster-decay model (DCM). The influence of intrinsic degrees of freedom of colliding pairs, such as low lying surface vibrations and neutron transfer channels, are entertained within the context of coupled channel calculations. Interestingly, the energy dependence in the Woods-Saxon potential induces barrier modification effects (barrier height, barrier position, barrier curvature) in a somewhat similar way as that for coupled channel approach, hence adequately explains the observed fusion dynamics of $_{20}^{40}\mathrm{Ca}+_{28}^{58,64}\mathrm{Ni}$ reactions. In addition, the decay analysis of compound nuclei formed in the fusion of $_{20}^{40}\mathrm{Ca}+_{28}^{58,64}\mathrm{Ni}$ reactions is investigated by using DCM. The calculations are done for quadrupole $({\ensuremath{\beta}}_{2})$ deformed fragments having optimum orientations for hot configurations. The experimental data for evaporation residues lying within the wide range of center of mass energy $({E}_{\mathrm{c}.\mathrm{m}.})$ of $64--88$ MeV is nicely addressed using the collective clusterization approach of the DCM. The comparative analysis of decay profiles of $_{48}^{98,104}\mathrm{Cd}^{*}$ is worked out by introducing angular momentum and temperature effects in the fragmentation potential and preformation factor.

Simultaneous analysis of the elastic scattering and breakup channel for the reactionLi11+Pb208at energies near the Coulomb barrier

We present a detailed analysis of the elastic scattering and breakup channel for the reaction of Li-11 on Pb-208 at incident laboratory energies of 24.3 and 29.8 MeV, measured at the radioactive ion beam facility of TRIUMF, in Vancouver, Canada. A large yield of Li-9 fragments was detected by four charged particle telescopes in a wide angular range. The experimental angular and energy distributions of these Li-9 fragments have been compared to coupled-reaction-channel and continuum-discretized coupled-channel calculations. The large production of Li-9 fragments at small angles can be explained by considering a direct breakup mechanism, while at medium-large angles a competition between direct breakup and neutron transfer to the continuum of the Pb-208 target was observed.

Selective properties of neutron transfer reactions in the 90Zr + 208Pb system for the population of excited states in zirconium isotopes

Nuclei produced via multineutron transfer channels have been studied in 90Zr + 208Pb close to the Coulomb barrier energy in a fragment-γ coincident measurement employing the PRISMA magnetic spectrometer coupled to the CLARA γ-array. The selective properties of the reaction mechanism have been discussed in terms of states and their strength excited in the neutron transfer channels leading to 89–94Zr isotopes. A strong population of yrast states, with energies up to ∼7.5 MeV has been observed.

Population of isomeric states in fusion and transfer reactions in beams of loosely bound nuclei near the Coulomb barrier

The influence of the mechanisms of nuclear reactions on the population of 195m Hg and 197m Hg(7/2−), 198m Tl and 196m Tl(7+), and 196m Au and 198m Au(12−) isomeric nuclear states obtained in reactions induced by beams of 3He, 6Li, and 6He weakly bound nuclei is studied. The behavior of excitation functions and high values of isomeric ratios (δ m/δ g) for products of nuclear reactions proceeding through a compound nucleus and involving neutron evaporation are explained within statistical models. Reactions in which the emission of charged particles occurs have various isomeric ratios depending on the reaction type. The isomeric ratio is lower in direct transfer reactions involving charged-particle emission than in reactions where the evaporation of charged particles occurs. Reactions accompanied by neutron transfer usually have a lower isomeric ratio, which behaves differently for different direct-reaction types (stripping versus pickup reactions).