One-nucleon transfer reactions in deformed nuclei

The one-nucleon transfer reaction on deformed nuclei has been computed with the inclusion of indirect inelastic transitions that go through intermediate rotational states. The specific examples considered are¹⁷¹Yb(d, p), ¹⁷²Yb(p, d) and ¹⁸⁶W(p, d). Anomalies in the shapes of of experimental angular distributions with respect to predictions of the distorted-wave Born approximation are shown to be reproduced when these higher-order inelastic processes are taken into account. Consideration is also given to the deuteron optical potential needed for these studies.     

Interfering transfer processes in heavy-ion reactions

Heavy-ion reactions in which two different transfer processes may interfere are analyzed. Angular distributions of the reactions ¹⁴C(¹⁶O, ¹⁷O)¹³C and ¹⁴C(¹⁶O, ¹⁸O)¹²C were measured at incident energies of 20, 25 and 30 MeV. The strong oscillations observed at the Coulomb barrier together with a backward rise at higher energies are taken as evidence for the superposition of two competing transfer reactions. DWBA calculations for the two single transfer processes were performed using the fixed-range approximation, and the two transition amplitudes were summed coherently. The experimental angular distributions are well reproduced. The DWBA also explains the disappearance of the interference structures for higher transferred angular momenta l. Data on the reaction ¹¹B(¹⁶O, ¹⁵N)¹²C measured earlier are included in the analysis in order to show the systematic dependence on l-values.     

Spin-dependence and coherent summations in two-nucleon transfer reactions

The differential cross sections of the ¹⁹F(p, ³He)¹⁷O and ¹⁹F(p, t)¹⁷F reactions leading to the ground and first three excited states have been measured at an incident energy of 42.4 MeV. The polarization analysing powers of two of the (p, ³He) reactions have been measured at a higher energy of 49.5 MeV with a polarized incident beam. The experimental results have been analysed in terms of conventional DWBA theory, and the importance of interference terms arising from the proper coherent summations contained in the definition of the differential cross section and analysing power, have been investigated. It is found that the interference term arising from the coherent summation over the transferred spin S is significant and should not normally be neglected.     

Neutron transfer reactions with very heavy ions

We have studied neutron transfer reactions induced by ¹³²Xe on three rare-earth targets at $\text{E}\text{V}{}_{\mathrm{C}}\text{～ 1.1}$. By using particle-particle-γ coincidence techniques we were able to identify final products and states populated in the one- and two-neutron reactions.The dependence of the transfer probabilities on the distance of closest approach is discussed in terms of effective penetration factors. The results seem to indicate the importance in two-neutron transfer of intermediate states with ? 6 MeV of excitation energy. The effect of excitation energy on the enhancement of the two-neutron transfer is discussed. A qualitative interpretation of the spin dependence of the one-neutron γ-ray yields in terms of the spatial localization of the wave functions involved is given.     

Contribution of decay products of transfer reactions to heavy-ion inelastic and transfer spectra

A study of decay product contributions to inclusive ejectile kinetic energy spectra is presented. Analytical formulae for the positions and widths of these contributions are derived from kinematical considerations. A formal integral expression for the double-differential cross section $\text{d}{}^2\text{σ/}\text{d}\text{Ω}\text{d}\text{E}$ is given in the case of one-particle emission from an excited state of the ejectile. The effects of anisotropic angular distributions are studied. The differential cross sections are then computed by a Monte Carlo method and compared to experimental spectra over a large range of measured systems. The transfer-evaporation mechanism is shown to contribute strongly to the background of the spectra but not to be responsible for the narrow structure observed in some reactions.     

Recoil study of multinucleon transfer reactions: Capture of six charges by Nd targets in Ar induced reactions

Multinucleon transfer reactions induced with Ar ions and involving the capture of six charges by the target have been studied. The targets were all the separated isotopes of Nd, and the observed nuclei were ^149gTb, ¹⁵⁰Dy, ¹⁵¹Dy. The experimental technique involved the measurement of the cross sections, angular distributions, and recoil range at each recoil angle, of the heavy residual nuclei. After transformation of the data into the c.m. system, the angular distributions appear to be peaked backwards, close to 180°. This observation suggests that the present reactions are of the same type as the multinucleon transfer reactions studied by other authors for which the angular distribution of the light fragment was peaked forward in the c.m. system. The energy distributions in the c.m. system were used to check the feasibility of various mechanisms which could lead to the production of the observed isotopes. Each mechanism was supposed to be a two-step process: the first step was the exchange, from the projectile to the target, of a number n of nucléons, leading to an excited intermediate nucleus, and the second step the deexcitation of the intermediate nucleus by nuclear evaporation. This analysis indicates that the most probable mechanisms correspond to n close to 12 (6 protons and 6 neutrons), and to an excitation energy of about 60 MeV for the intermediate nucleus. The distribution of cross sections versus the number of nucléons gained by the target is also in accord with this reaction model.     

Exact finite range calculations of light-ion induced two-neutron transfer reactions

Exact finite-range (EFR) distorted-wave Born approximation calculations were performed for light-ion induced two-neutron transfer reactions, by using a technique to calculate the form factors rather fast. The use of this method made it possible to carry out calculations even when realistic light-ion wave functions and multi-configurational two-neutron wave functions were used and large transferred angular momenta were considered. It was found that, at lower bombarding energies, the predictions of the EFR and zero-range calculations agree very closely both in angular distributions and relative magnitudes of the cross sections, though they differ significantly in absolute magnitude. As the bombarding energy increases, the discrepancy between the predicted absolute magnitude becomes still larger, and noticeable differences are seen even in relative cross sections. For all the energies considered, the EFR calculations predicted the absolute magnitudes of the experimental cross sections to within a factor of several units.     

Two-nucleon T = 0 transfer reactions in the 0p shell

The ¹⁶O(d, α)¹⁴N, ¹⁴N(d, α)¹²C and ¹²C(d, α)¹⁰B reactions at E_d = 40MeV and the ¹²C(α d)1¹⁴N at E_α = 55 MeV were investigated. A total of seventeen transitions are analysed in terms of one-step, zero-range DWBA calculations, using the two-particle coefficients of fractional parentage obtained from the Cohen-Kurath Op shell wave functions. For most transitions, fair agreement is obtained between experiment and calculation, possible exceptions being the transition to the E_x = 4.43 MeV, J^π = 2⁺ state in ¹²C and to the E_x = 2.15 MeV, J^π = 1⁺ state in ¹⁰B, for which the calculations predict too much L = 0 strength. Where possible, a comparison with previous (p, ³He) results is made. In ¹⁴N a state at E_x = 11.04 MeV was observed for which the values (J_π; T) = (3⁺; 0) are suggested. In ¹²C we found, in addition to the well known T = 0 states, two relatively sharp T = 0 states at E_x = 19.50 ± 0.10 and 20.55 ± 0.10 MeV. The shape and strength of the angular distribution for the transitions to these states can be approximately accounted for by the calculations, although no one-to-one correspondence between observed and predicted levels could be established.     

Gross properties of heavy-ion transfer reactions: (I). Formulation

A simple approximation to the semiclassieal theory of heavy-ion transfer reactions is presented. For one-nucleon transfer reactions it reduces to the matching condition model given by Brink. Inelastic scattering and multinucleon transfer reactions can also be treated for either case in which heavy ions follow a straight-line trajectory or temporarily form a dinuclear system. For multistep processes a binary-step approximation is introduced, in which some effects of the time differences between consecutive transfer events are taken into account. Finally the possibility of treating the multinucleon transfer reaction as a Markov process is suggested.     

Heavy ion induced transfer reactions on 148Nd

Transfer reactions induced by ¹⁶O and ¹⁸O beams on ¹⁴⁸Nd were measured with a time-of-flight setup at 72 MeV incident energy. The angular distributions are bell shapes having their maxima at angles somewhat below the grazing angle. The excitation in the final nuclei takes place (if possible) near the optimum Q-value and is spread over 5 MeV for the one-particle transfer reactions and up to 10 MeV for the multiparticle transfers. The cross sections for the individual channels are explained mostly by Q-window considerations. In spite of the differences in the individual channels the total transfer cross section integrated over excitation energy, angle, and all channels turns out to be the same same for both ¹⁶O and ¹⁸O beams. This cross section amounts to 20 % of the total reaction cross section and nicely fills the gap between the measured fusion cross section and the total reaction cross section obtained from optical model calculations based on elastic scattering data.     

Investigations with two-neutron transfer reactions on the even isotopes of samarium

The (p, t) reaction on the even isotopes of samarium has been investigated at a proton energy of 25.5 MeV. Angular distributions were obtained in the range 18° ≦ θ ≦ 148° with angular steps between 2° and 5°. The experimental energy resolution varied between 35 keV and 50 keV FWHM. Spin and parity assignments are performed by comparing the measured angular distributions to zero-range DWBA calculations. Some difficulties of DWBA calculations for (p, t) reactions are pointed out. The relative cross sections for transitions to different levels of the final nuclei are compared with other (p, t) and (t, p) measurements in the same region of the rare earth isotopes. The dependence of the (p, t) cross sections for different transitions on the neutron number of the final nuclei is discussed. Some 2⁺ states observed in (p, t) and (t, p) reactions are described in the quadrupole pairing vibrational picture.     

Evidence on the influence of fission channels on fission phenomena

Partial fission channel widths can be extracted from fission cross-section analysis only up to a rotation in the space of fission vectors. We propose to obtain a physically significant basis for fission vectors taking into account information from other fission characteristics such as the valley-to-peak ratio of the mass distribution and the number of prompt neutrons emitted per fission event. Fission widths and other channel characteristics are calculated for 0⁺ resonances in low energy neutron induced fission of ²³⁹Pu.     

Fast fission phenomenon

We review some experimental results which cannot be understood within the usual concepts of dissipative collisions. We present a dynamical model in which fast fission phenomenon appears in a natural way if certain conditions are fulfilled. Two kinds of fast fission are described, according to the size of the system. An extended notion of the so called fusion process is proposed and calculations of fusion cross sections are compared with experimental data. The fluctuations associated with the collective variables which are involved during fast fission and compound nucleus fission are treated within the framework of the linear response theory. The study of mass distributions supports the existence of fast fission with medium systems as an intermediate mechanism between the deep inelastic collisions and the compound nucleus formation.     

Microscopic form factor for DWBA analysis of light-ion induced three-nucleon transfer reactions

A modified zero-range distorted-wave Born approximation calculation was performed for the (p, α) reactions. The form factor is calculated by a first method, which is an extension of the Bayman and Kallio method to extract the relative l = 0 part of two-nucleon shell-model wave functions. The method includes some of the range effects so that one can predict the absolute magnitudes of the cross sections. A second method in finite range involves the ³He cluster expansion of the α-particle where the known (³He, α) transfer normalization may be used to estimate the absolute cross sections. The ¹¹⁸Sn(p, α)¹¹⁵In reactions are analyzed using the hole-vibration coupling model for ¹¹⁵In. The shapes of the experimental cross sections and the analyzing powers can be fitted by the calculations but the magnitudes of the cross sections are predicted to be too small.     

Symmetric and asymmetric fission in electron induced fission of 232Th

We have measured fragment kinetic energies in electron induced fission of ²³²Th for electron energies in the range 7 MeV ≦ E_e ≦ 66 MeV. The relative contribution of the distribution peak associated with high fragment kinetic energies decreases continuously with electron energy. This is interpreted as a relative increase of the symmetric fission yield as compared to the asymmetric fission yield; this fact in turn indicates a non-negligible increase in the average excitation of the fissioning nucleus, with the energy of the bombarding electrons, even above the giant dipole resonance.     

A study of three-nucleon transfer reactions on 18O

The reactions ¹⁸O¹¹B, ⁸Li)²¹Ne, ¹⁸O(¹²C, ⁹Be)²¹Ne and ¹⁸O(¹³C, ¹⁰B)²¹F have been studied, using beams of 115 MeV ¹¹B and ¹²C and 105 MeV ¹³C incident on a gas target. Shell-model calculations have been performed for ²¹Ne and ²¹F, for comparison with the experimental data. It is found that the data can be interpreted using the shell-model spectroscopic factors and a semiclassical reaction theory. Assignments are suggested for several previously unidentified high-spin states in ²¹Ne and ²¹F.     

Recoil effect and kinematics of the molecular states approach to heavy-ion transfer reactions

The kinematic properties of the adiabatic representation of the total wave function which can be useful to demonstrate the molecular features in the heavy-ion transfer reactions are discussed. The matrix transformation of the adiabatic Hamiltonian which simplifies its asymptotic form is then constructed. This allows one to treat the recoil effect in the form of a simple matrix transformation of the adiabatic S-matrix.     

Angular momentum transfer in 12C-, 20Ne- and 40Ar-induced fission

Angular momentum transfer in a variety of ¹²C-, ²⁰Ne- and ⁴⁰Ar-induced fission reactions has been investigated using γ-ray multiplicity techniques. Fission fragments were detected in coincidence using a pair of solid-state detectors. The fragment masses were deduced from the kinetic energies and emission angles using two-body kinematics. The γ-ray multiplicities (M_γ) of the fission fragments were measured utilizing an array of eight NaI detectors. For most of the systems studied, M_γ is nearly independent of the exit-channel mass asymmetry. The strongest dependence on mass is observed in the systems ¹⁵⁴sm + 240 MeV ⁴⁰Ar, where a minimum exists at symmetry, and ¹⁹⁷Au + 164 MeV ²⁰Ne, where nuclear structure effects are suggested by the data. For all the reactions the quantity M_γ tends to decrease gradually with increasing fragment kinetic energy. The magnitude of M_γ generally appears to be larger than expected on the basis of rigid rotation, suggesting a spin enhancement effect. The data are compared with a simple model which assumes the statistical excitation of a variety of angular momentum bearing collective modes. Reasonable agreement is obtained with the experimental results. The roles of other collective effects, such as shape fluctuations and angular momentum fractionation, are also considered.