Deeply inelastic transfer reactions induced by heavy ions in rare-earth targets

Recoil techniques have been used for a systematic study of deeply inelastic transfer reactions induced in rare earth targets by⁴⁰Ar,⁵²Cr,⁵⁶Fe and⁶³Cu projectiles. The targets were separated isotopes of Eu, Sm, Nd and Pr. The residual nuclei^149gTb,¹⁵⁰Dy and¹⁵¹Dy were identified by their radioactive properties. The reactions studied involved the transfer of 3 to 7 charges from projectile to target. The c.m. angular and energy distributions were measured over the whole angular range from 0 to 180° (c.m.). A special device was used to measure accurately the c.m. energy of products emitted in the angular range 170–180° in the c.m.s. The c.m. angular distributions depend strongly on the ratio of the incident energy to the strong interaction barrier, and slightly on the number of transferred charges. The c.m. energy distributions are typical of completely damped collisions for 6-charge transfer reactions, and include a contribution of partially damped collisions for 4-charge transfer reactions. A kinematic analysis was used to determine the most probable number of neutrons transferred in the first reaction step with a given number of protons. The numbers found correspond to equilibration of the neutron to proton ratio in the composite system.     

Time-dependent Hartree-Fock calculation of 12C + 12C with a realistic potential

We have used a realistic single-panicle K-matrix model to compute the head-on scattering of ¹²C + ¹²C at incident projectile lab energies of 3.2, 6.4, 12.8, 19.2, 25.6, 32, 51.2 and 64 $\text{MeV}\text{nucleon}$, above the Coulomb barrier, in the time-dependent Hartree-Fock approximation. Direct and exchange Coulomb forces as well as spin-orbit forces are included. A large deformed harmonic oscillator basis is used. Spatial density and current distributions at various times are shown. The outgoing energy is found to be E₀ = 0.8E_in?28 (MeV), in the c.m. system. Fusion and fully relaxed scattering are observed at low energy. Some compression is seen at higher energies but no shock waves can be detected. Consequences for heavy-ion reactions are discussed.     

Quasi-fission — The mass-drift mode in heavy-ion reactions

The binary and ternary products from reactions of ²³⁸U beams with targets of ¹⁶O, ²⁷Al, ⁴⁸Ca, ⁴⁵Sc, ⁴⁸Ti, ⁵⁸Fe, ⁶⁴Ni and ⁸⁹Y have been recorded at 6.0 MeV/u bombarding energy with four position-sensitive avalanche detectors, operated in coincidence. A few runs at 5.4 MeV/u have also been performed. Accurate triple-differential cross sections, $\text{d}{}^3\text{σ}\text{d}\text{A}\text{d}\text{θ}{}_{\mathrm{<mtext>c.m.</mtext>}}\text{dTKE}$, are obtained for the binary events within the full range of mass A and total kinetic energy TKE, and within almost the full range of center-of-mass angle θ_c.m.. Similar cross sections are obtained with somewhat less accuracy for triple events stemming from the sequential fission of uranium-like products. The distributions are discussed in terms of quasielastic and strongly damped scattering, where the products have partially relaxed energies and negligible average drift in mass, as opposed to capture where the products emerge with fully relaxed energies after a more or less pronounced mass drift towards symmetry. Apart from the reaction with ¹⁶O, all the capture product distributions are dominated by the non-equilibrium quasi-fission (or fast fission) process. The central feature of this reaction mechanism is the evolution of the reaction complex towards mass symmetry. With the ²⁷Al target the evolution towards symmetry is almost complete, whereas the heavier targets show very broad mass distributions with clear evidence of dissociation taking place before symmetry is reached. At the same time, the cross section for quasi-fission diminishes as the target Z-value increases. With the ⁸⁹Y target the strongly damped scattering component dominates completely. The capture cross sections are discussed in terms of the extra-push concept, and the mass and angular distributions in quasi-fission are analyzed in terms of interaction time and mass rearrangement as functions of target Z-value and excess kinetic energy in the entrance channel.     

In-beam γ-ray studies of complex band structures and of isomeric states in 152, 153Dy nuclei

The high-spin level structures of ¹⁵²Dy and ¹⁵³Dy were studied experimentally with ^{154, 155}Gd(α xnγ) in-beam reactions, and for ¹⁵²Dy also with ${}^{\mathrm{144,\; 146}}\text{Nd}\text{(}{}^{12}\text{C, x}\text{n}\text{γ)}$ reactions. The experiments included measurements of singles γ-ray and conversion-electron spectra, γ-ray angular distributions and E_γ-t and E_γ-E_γ-t coincidences. A multiplicity filter set-up was used to study the feeding and decay of isomeric states in ¹⁵²Dy. In ¹⁵²Dy about twenty so far unknown levels were found, including two high-spin isomeric states with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{≈ 60}\text{and}\text{≈ 13}\text{ns}$ at excitation energies E_x ≈ 5.04 and 6.08 MeV, respectively. These states are compared with recent calculations on yrast traps. The level scheme of ¹⁵³Dy contains 28 levels up to E_x = 4.1 MeV and $\text{J}{}^{\mathrm{\pi }}\text{= (}\text{37}\text{2}{}^{\mathrm{+}}\text{)}$. Band structures in both nuclei are discussed in comparison with other N = 86 and N = 87 isotones.     

Measurement of the 11B(11B, 10Be)12C proton transfer reaction at low energies

Differential cross sections for the ¹¹B(¹¹B,¹⁰Be)¹²C proton transfer reaction leading to the ¹⁰Be(g.sO+¹²C(4.43 MeV) $\text{(Q = 0.289}\text{MeV}\text{)}\text{and}{}^{10}\text{(3.37}\text{MeV}\text{) +}{}^{12}\text{C}\text{(g.s.) (Q = 1.36}\text{Me V}\text{)}$ final channels have been measured at E_c.m. = 5.5 MeV by coincident detection of the ¹⁰Be and ¹²C nuclei. The integrated cross sections for the ¹⁰Be + ¹²C(4.43 MeV) channel have been obtained for incident energies between E_c.m. = 2.66 and 3.64 MeV from the yields of the 4.43 MeV γ-ray emitted in the ¹²C 4.43 MeV → g.s. transition. The cross-section magnitudes compare well with the DWBA calculations. The sub-barrier transfer cross sections exhibit an unusual energy dependence: their ratio to the total reaction cross section is decreasing with decreasing incident energy.     

An experimental survey of 8Li emission in 50 GeV/cπ− interactions with emulsion nuclei

From the NIKFI-R emulsions exposed to 50 GeV/cπ^? beam, 82 events of hammer tracks (HTs) are collected. Energy spectra, total number of heavy prongs (N_h) versus average energy spectra and forward to backward ratio ($\text{F}\text{B}$) in different cases are studied. The angular distribution of the events is found anisotropic. The process of jet formation affects the direction of emission of the intermediate mass nuclei.     

A study of diffusion phenomena in the rare earth region: The reaction 159Tb + 620 MeV 86Kr

Kinetic energy spectra, charge and angular distributions have been measured with ΔE-E telescopes for over twenty-five identified elements from the reaction ${}^{159}\text{Tb}\text{+ 620}\text{MeV}{}^{86}\text{Kr}$. At all angles and for all observed atomic numbers, the energy spectra indicate the presence of energetically relaxed products in the vicinity of the Coulomb barrier. Elements near the projectile also show a sizable contribution from incompletely damped events at angles close to the grazing angle. The charge distributions are peaked near the projectile Z and demonstrate a strong shape dependence on the angle of observation. The angular distributions show a weakening of the side peaking with increasing proton transfer to or from the projectile. Angular distributions and angle-integrated charge distributions have been calculated with a diffusion model which assumes the formation of a rotating intermediate complex with an l-dependent lifetime. The mass exchange between the two segments of the intermediate complex is treated as a diffusive process which is described by the master equation. Values for the diffusion constant, the overlap of the two density distributions, the mean lifetime of the intermediate complex and the spread in the average lifetime were used which semiquantitatively reproduced data from the 620 MeV ⁸⁶Kr reaction on ¹⁸¹Ta and ¹⁹⁷Au targets. Satisfactory agreement was obtained between these calculations and the data from the ¹⁵⁹Tb target. In addition, by increasing the lifetime of the complex by 30 %, the previously measured data for the ^{107, 109}Ag + 620 MeV ⁸⁶Kr reaction was semiquantitatively reproduced.     

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.     

Investigation of the reaction 208Pb(18O, f): Fragment spins and phenomenological analysis of the angular anisotropy of fission fragments

The average multiplicity of gamma rays emitted by fragments originating from the fission of ²²⁶Th nuclei formed via a complete fusion of ¹⁸O and ²⁰⁸Pb nuclei at laboratory energies of ¹⁸O projectile ions in the range E _lab = 78–198.5 MeV is measured and analyzed. The total spins of fission fragments are found and used in an empirical analysis of the energy dependence of the anisotropy of these fragments under the assumption that their angular distributions are formed in the vicinity of the scission point. The average temperature of compound nuclei at the scission point and their average angular momenta in the entrance channel are found for this analysis. Also, the moments of inertia are calculated for this purpose for the chain of fissile thorium nuclei at the scission point. All of these parameters are determined at the scission point by means of three-dimensional dynamical calculations based on Langevin equations. A strong alignment of fragment spins is assumed in analyzing the anisotropy in question. In that case, the energy dependence of the anisotropy of fission fragments is faithfully reproduced at energies in excess of the Coulomb barrier (E _c.m. ? E _B ≥ 30 MeV). It is assumed that, as the excitation energy and the angular momentum of a fissile nucleus are increased, the region where the angular distributions of fragments are formed is gradually shifted from the region of nuclear deformations in the vicinity of the saddle point to the region of nuclear deformations in the vicinity of the scission point, the total angular momentum of the nucleus undergoing fission being split into the orbital component, which is responsible for the anisotropy of fragments, and the spin component. This conclusion can be qualitatively explained on the basis of linear-response theory.     

Pion production from deuterium bombarded with polarized protons of 277 and 500 MeV

Analyzing power measurements of the $\text{p}\text{→ tτ}{}^{\mathrm{+}}$ reaction are reported at incident proton energies of 277 and 500 MeV. The 277 MeV results span the angular range from 70° to 130° in the centre of mass while the two 500 MeV measurements at large angles were taken as a check of published results. With the angular distribution of the analyzing power at 277 MeV now known, it is possible to show that the energy dependence of the analyzing power exhibits characteristics closely resembling the shape and magnitude of the analyzing power distribution observed for 1p shell nuclei of similar excitation energies.     

Small-angle neutron scattering from Pb and 238U between 0.6 and 2.2 MeV

Differential cross sections for neutrons scattered from natural Pb and 99.9 % isotopically pure ²³⁸U have been measured at 0.5°, 1.0°, and 1.5°. A neutron energy continuum was produced by bombarding a thick natural lithium target with a 4 MeV, nanosecond-pulsed proton beam. Neutron energies were determined by time-of-flight techniques. Flight paths from the neutron source to the scatterer and from the scatterer to the detector were each about 5 m. For the 0.5° measurements an annular detector geometry with an angular resolution of ± 0.1° was developed to maximize detection solid angle. Data were averaged over 100 keV intervals from 0.6 to 2.2 MeV and were corrected for backgrounds, multiple scattering and inelastic scattering. Measured cross sections were compared to optical-model calculations which included electromagnetic interactions of neutrons with the nuclear Coulomb field. Inclusion of an induced neutron electric dipole moment interaction was not warranted by the data. The angular dependence of the cross section was fitted with a function $\text{A + B}\text{cot}{}^2\text{case1}\text{2}$θ at each energy. Mean values of B for ²³⁸U are in agreement with theoretical predictions. Values of B for Pb are apparently 15 % too low.     

Longitudinal polarization transfer in the T→p, →n)3He reaction

The longitudinal polarization of neutrons has been measured for the reaction $\text{T}\text{→p}\text{,}\text{→n}\text{)}{}^3\text{He}$ with the incident proton beam longitudinally polarized. Measurements were performed at 0° for proton energies from 4 to 15 MeV and an angular distribution was measured at 10 MeV. The data determine the polarization transfer coefficient K_z^z′, which is equivalent to the Wolfenstein A′ parameter for nucleon-nucleon scattering. The quantity K_z^z′ at 0° increases from about 0.3 at 3 MeV incident energy to 0.9 at 9 MeV, and then decreases to 0.5 at 15 MeV. The data are computed with R-matrix calculations which reproduce the qualitative shape of the data at 0° and the angular distribution at 10 MeV.     

Multiple coulomb excitation of 167Er

The ground-state rotational band in ¹⁶⁷Er has been investigated through multiple Coulomb excitation with a 160 MeV ³⁵Cl beam. Excited states up to $\text{25}\text{2}{}^{\mathrm{+}}$ were established by measuring γγ coincidences and γ-ray angular distributions. Gamma-gamma angular correlations were also measured. Nuclear lifetimes of levels up to spin $\text{23}\text{2}$ have been determined from Doppler-broadened γ-ray lineshapes, and B(M1) and B(E2) values of intra-band transitions deduced. Considerable signature dependence was observed for level energies and M1 transition probabilities. A Coriolis band-mixing calculation was carried our for comparison with the experimental results. The measured M1 transition probabilities are compared to calculations based on a particle-rotor model, a cranking model, and a microscopic model with quantum-number projection.     

Strong change in the mass distribution of fission-like processes around ACN = 100

The completely relaxed reaction products resulting from bombardment of ⁵⁹Co, ⁶⁵Cu, ⁷⁴Ge, ⁷⁹Br, ⁸⁵Rb and ⁸⁹Y with ³²S have been studied. At incident energies from 153 MeV to 184 MeV, compound of composite nuclei with masses, A_CN, between 91 and 121 are formed with excitation energies of 80–100 MeV. Their spins might be as high as 60–70 $\text{h}\text{?}$ which allows for fission decay. The mass distribution from the reaction ³²S on ⁸⁹Y exhibits a sharp peak corresponding to symmetric fragmentation and consistent with a fission mechanism. The mass distribution over the above range range of decaying composite nuclei continuously broadens with decreasing mass, A_CN. Maxima around the projectile and target mass gradually become more predominant and finally dominate the mass spectrum obtained in the reaction ³²S on ⁵⁹Co. These changes in the overall character of the mass distribution are discussed in terms of various mechanisms.     

Incomplete fusion in 12C+160Gd collisions

The mechanism of the production of fast α-particles in ¹²C induced reactions was studied over a wide range of bombarding energies (7.5–16.7 MeV/A) by measuring α-γ coincidences. Absolute cross sections for ${}^{160}\text{Gd}\text{(}{}^{12}\text{C}\text{, αx}\text{n}\text{)}{}^{\mathrm{168?x}}\text{Er and}{}^{160}\text{Gd}\text{(}{}^{12}\text{C}\text{, 2αx}\text{n}\text{)}{}^{\mathrm{164?x}}\text{Dy}$ reactions, as well as inclusive α-particle production cross sections, have been determined. Depending on the bombarding energy, a fraction of 0.2–0.4 of the singles α-particles can be explained as resulting from incomplete fusion reactions (¹²C, α) and (¹²C, 2α) which correspond to a capture of “⁸Be” and “⁴He”, respectively. The remaining fragments of the projectile have, on the average, the beam-velocity energies and their angular distributions are forward peaked. Distributions of side-feeding to the yrast bands in the target-residue nuclei indicate that low partial waves are strongly hindered in the incomplete fusion reactions. The energy dependence of the cross sections for (¹²C, α) and (¹²C, 2α) incomplete fusion as well as for (¹²C, 3α) projectile breakup is given. A generalized concept of critical angular momentum which explains a competition between complete fusion, incomplete fusion and breakup reactions is proposed.     

Finite-range DWBA analyses of (dt) and (d3He) reactions on 64Zn at Ed = 13 MeV

Exact finite-range DWBA analyses of ($\text{d}\text{, t}\text{)}$ and $\text{(}\text{d}\text{d}$, ³He) reactions have been performed for an ⁶⁴Zr target at an incident deuteron energy of 13.0 MeV, leading to the ground states of the residual nuclei. The microscopic overlap functions for (d, t) and (d, ³He) systems obtained by using the Phillips triton wavefunctions have been used as projectile form factors into the calculation. The results are compared with zero-range DWBA calculations taking the finite-range effects into account by means of a local energy approximation. The results obtained by finite-range and zero-range calculations for differential cross sections as well as vector and tensor analysing powers are compared with the experimental data. The range of validity of the local energy approximation is discussed.     

Measurement of polarization in K−p elastic scattering between 0.955 GeV/c and 1.272 GeV/c

The polarization parameter has been measured for K^?p elastic scattering at nine incident beam momenta between 0.955 and 1.272 GeV/c covering the c.m. angular range $\text{?0.9 < cos θ}{}^1\text{< + 0.9}$. Experimental results and coefficients of Legendre polynomial fits to the data are presented and compared with other measurements and a partial-wave analysis.