The magnetic Born and intermediate-Δ contributions to the (γ,p) reaction are calculated for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ targets, within a framework which includes pion rescattering and proton distortions. The results are discussed in light of experimental data, which show no obvious resonant energy dependence for these nuclei. The calculations are also compared to several published theoretical approaches, which disagree with each other regarding the importance of the intermediate-Δ contribution to the (γ,p) reaction at intermediate energies.

The Alt, Grassberger, and Sandhas four-body theory has been used to calculate the differential cross sections for the kinematically complete breakup reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(p,pd${)}^1$H at various proton energies and angles. The two-body input consists of Yamaguchi potentials without Coulomb corrections and the (3+1) and (2+2) amplitudes were expanded using the generalized unitary pole expansion. The resulting effective two-body equations have been solved in the first-order K-matrix approximation. Reasonable agreement with experiment was obtained.

We have calculated the γ-transition strength from the broad $2^{+}$ resonance in α+α scattering at E=2.9 MeV into the ${}_{}{}^8{}_{}{}^{}$Be ${(0\mathrm{}}^{+}$) ground state in a bremsstrahlung model and find a γ width of ${\Gamma }_{\gamma }$=8.3 meV.

The structure of the low-lying states of ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ has been investigated by use of inelastic scattering. Differential cross sections for the elastic and inelastic scattering of 36 MeV α particles and 16 MeV deuterons from ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$ have been measured. Isoscalar transition strengths for l=2, 3, and 4 excitation have been extracted by a coupled-channels distorted wave calculation involving collective model form factors. A number of known levels corresponding to the ground state band, γ band, and octupole bands were seen. Results for the $2^{+}$, $4^{+}$, $6^{+}$, and $8^{+}$ states in the ground state band and $2^{+}$, $4^{+}$, and $6^{+}$ states in the γ band imply the importance of the hexadecapole (${\beta }_4$) and the hexacontatetrapole (${\beta }_6$) shape components. The octupole states at 1431, 1633, and 1913 keV are excited with isoscalar strengths equal to 0.046, 0.058, and 0.023 $e^2$${\mathrm{b}}^3$, respectively, which are comparable with the corresponding B(E3) strengths known from Coulomb excitation of the 1431 and 1633 keV states. The octupole states at 2269, 2324, and 2486 keV with isoscalar E3 transition strengths 0.055, 0.022, and 0.018 $e^2$${\mathrm{b}}^3$, respectively, are newly identified. For quadrupole excitation the results agree in several ways with predictions of the interacting boson approximation model and the geometrical models and for octupole states there is a good agreement with theoretical results of Neergaaumlrd and Vogel.

The distorted wave Born series for inelastic scattering can be formulated as arising from the iteration of an integral equation. The small parameter determining the convergence of the series can then be identified as the spectral radius of the integral kernel. Such a formulation allows a detailed investigation of what controls the accuracy of the distorted-wave Born approximation. Several important questions can then be answered, such as the following: what are the relevant dimensionless parameters, what physics is important, and what is the best distortion potential to use. We consider these questions in a simple, analytically solvable two-channel model.

A closed form version of the two-component exciton model is derived. Discussions of corrections for the Pauli exclusion principle, of the expected behavior of the residual two-body matrix elements, and of the relative merits of different types of reaction calculations within the exciton model are presented. Calculations verify the validity of the equal a priori probabilities assumption underlying exciton model calculations and demonstrate that the one- and two-component models produce very similar results when similar assumptions are made about the relative probabilities of exciting proton and neutron degrees of freedom.

Differential cross sections and analyzing powers of polarized proton elastic and inelastic scattering from ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$, ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$, and ${}_{}{}^{184}{}_{}{}^{}\mathrm{W}$ have been measured at 65 MeV. Analysis has been performed in the framework of the coupled channel formalism of the deformed optical potential for $J^{\pi }$${=0\mathrm{}}^{+}$–$6^{+}$ members of the ground state rotational band. In this analysis, all the deformation parameters of the real central, volume imaginary, surface imaginary, and spin-orbit parts of the deformed optical potential were searched independently. Up to the $6^{+}$ state, excellent fits have been obtained. It is found that the quadrupole moment of the real central part is 6–9 % larger than that of the charge density for all the measured nuclei, but the quadrupole moment of the Woods-Saxon form factor of the spin-orbit part agrees with the charge quadrupole moment within the fitting error. These results are consistent with the difference between the effects of the density dependence of the effective nucleon-nucleon interaction on the real central part and the spin-orbit part of the optical potential. Similar trends are also found for the hexadecapole moments of the real central part and the spin-orbit part. A folding model calculation using a realistic effective interaction has been carried out and its results are compared to those of the coupled channel analysis.

The (p,n) reaction to the analog of the first excited $2^{+}$ state in ${}_{}{}^{56}{}_{}{}^{}$,54Fe at 35 MeV is analyzed with coupled-channel calculations which couple together the ground state, the first $2^{+}$ state, and their analogs. These employ a Lane model optical potential and vibrational model couplings for the inelastic transitions. The potential parameters and transition strengths are constrained by requiring that the calculations simultaneously fit data for the (p,p), (p,p’)$2^{+}$, (n,n), (n,n’)$2^{+}$, (p,n)$0^{+}$, and (p,n,)$2^{+}$ cross sections. At this energy the two-step processes $0^{+}$→$2^{+}$→$2^{+}$ analog, and $0^{+}$→$0^{+}$ analog →$2^{+}$ analog, are essential components of the reaction. Interference between the two-step and the direct one-step ($0^{+}$→$2^{+}$ analog) amplitudes allows both the magnitude and sign of the isovector deformation parameter ${\beta }_1$ to be determined. We find ${\beta }_1$ is negative in ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ but positive or zero in ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$. The results are consistent with β values obtained by comparing measurements with different probes.

Coulomb excitation of states in ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$ up to J=(21/2) has been observed with 160-MeV ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ and 617-MeV ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ ions. Most of these states are grouped into three rotational-like bands based on the ${\mathrm{}(3/2)\mathrm{}}^{+}$ ground state, the ${1/2}^{+}$ first excited state, and the ${\mathrm{}(7/2)\mathrm{}}^{+}$ γ-vibrational-like state at 686 keV. The average deviation between experimental and theoretical energies for 20 states is 45 keV for the particle-asymmetric-rigid-rotor model and 125 keV for the interacting boson fermion approximation model [limited to broken Spin(6) symmetry, and only the $d_{3/2}$ orbital is considered]. The overall agreement of both model predictions with experimental γ-ray yields for transitions within the ${\mathrm{}(3/2)\mathrm{}}^{+}$ band is quite good. For interband transitions originating in the K${=1/2\mathrm{}}^{+}$ and ${\mathrm{}(7/2)\mathrm{}}^{+}$ bands, the interacting boson fermion approximation model tends to underestimate the γ-ray yields by one to two orders of magnitude. These six moderately collective transitions correspond to Δ${\tau }_1$=2 transitions in the U(6/4) and U(6/20) supersymmetry schemes and are strictly forbidden in these schemes. For both supersymmetric schemes there is a lack of detailed agreement with the very collective E2 transitions which have Δ${\tau }_1$=0,±1. The triaxial rotor model description of the experimental energies and the collective E2 transitions is the most successful approach. The B(E3) for excitation of several negative-parity states in ${}_{}{}^{191}{}_{}{}^{}\mathrm{Ir}$ is (4±1)B(E${3)}_{\mathrm{sp}}$.

We study the recent claim that the intranuclear cascade model exhibits collective sidewards flow. 4000 intranuclear cascade simulations of the reaction Nb(400 MeV/nucleon)+Nb are performed employing bound and unbound versions of the Cugnon cascade. We show that instability of the target and projectile nuclei in the unbound cascade produces substantial spurious sidewards flow angles, for spectators as well as for participants. Once the nuclear binding is included, the peak of the flow angle distributions for the participants alone is reduced from 35° to 17°. The theoretical ‘‘data’’ are subjected to the experimental multiplicity and efficiency cuts of the plastic ball 4π electronic spectrometer system. The flow angular distributions obtained from the bound cascade—with spectators and participants subjected to the plastic ball filter—are forward peaked, in contrast to the plastic ball data. We discuss the uncertainties encountered with the application of the experimental efficiency and multiplicity filter. The influence of the Pauli principle on the flow is also discussed. The lack of flow effects in the cascade model clearly reflects the absence of the nuclear compression energy that can cause substantially larger collective sidewards motion—there is too little intrinsic pressure built up in the cascade model.

A constrained-phase-space description of equilibrium in the angular momentum degrees of freedom is used to calculate the spin alignment in deep-inelastic heavy-ion reactions. The phase space is constructed by considering the internal degrees of freedom of the excited fragments and the conservation of angular momentum; the constraint which reflects the reaction dynamics is derived from the classical sticking condition. For several cases of mass-asymmetric heavy-ion reactions, the measured alignments are quantitatively reproduced. It is found that the alignment depends most sensitively on the initial angular momentum and on the fragment deformation at separation so that alignment data are useful to determine these quantities. Angular correlations of sequential-fission fragments from deep-inelastic reactions are also calculated. In the considered example, the measured in-plane anisotropy is explained as mainly resulting from the restrictions, imposed by the experimental setup, on the orientations of the orbital angular momenta in the entrance and exit channels.

Target fragment distributions were measured using radiochemical techniques for 48 different fragments (28≤A≤185) from the interaction of 85 MeV/nucleon ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ with ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The laboratory system angular distributions are forward peaked and generally flat beyond 90°. When compared to similar distributions from the 85 MeV/nucleon ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{197}$Au reaction, the U target fragment distributions are less forward peaked, consistent with lower momentum transfer. The (A=80–120) fission fragment distributions were symmetric about 90° in the moving frame, indicative of a ‘‘slow’’ process in which statistical equilibrium has been established. The average fissioning system angular momentum was deduced to be 25-35 ħ. The observation that the fragments with low N/Z showed more anisotropic distributions than fragments with high N/Z was accounted for in firestreak model calculations as being due to a single reaction mechanism with varying amounts of deposition energy. The lightest (A<60) and heaviest (A=139-169) members of the central fission-like bump in the mass distribution had moving frame angular distributions that were asymmetric in the moving frame. Furthermore, the heavy fragment complement of the ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$ distribution was similar in shape to the ${}_{}{}^{146}{}_{}{}^{}\mathrm{Gd}$ distribution, suggesting these fragments were produced in a new intermediate energy reaction mechanism, a fast, non-equilibrium, very asymmetric fission of a heavy nucleus.

A detailed study of pion production in inelastic and central nucleus-nucleus collisions was carried out using a 2 m streamer spectrometer. Nuclear targets mounted inside the streamer chamber were exposed to nuclear beams of 4.5 GeV/c/nucleon momentum. A systematic study of the influence of the central trigger on observed data is performed. The data on multiplicities, rapidities, transverse momenta, and emission angles of negative pions are presented for various pairs of colliding nuclei. Intercorrelations between various characteristics are studied and discussed. The results are compared with predictions of some theoretical models. It is shown that the main features of the pion production in nuclear collisions can be satisfactorily described by a model assuming independent nucleon-nucleon collisions with subsequent cascading process. However, the observed correlation between Λ and pion characteristics seems to be unexplained by this picture.

Two different quantal approaches to describe relativistic Coulomb excitation are compared and proven to be equivalent in their basic formulations. We reanalyze the Λ${\Sigma }^0$ conversion experiment by means of the plane wave Born approximation and we also discuss the possible applications of this approach to ultrarelativistic Coulomb collision experiments.

Detailed cross sections out to 170° c.m. for elastic scattering and the excitation of states in ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been determined by bombarding ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ targets with 34 MeV ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ beams and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ targets with ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ beams at the same c.m. energy. The present results show that the direct breakup total cross section for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ is about 25 times larger than the sequential total cross section to the ${\mathrm{}(7/2)\mathrm{}}^{\mathrm{-}}$ 4.63 MeV state of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$. In addition, single neutron and proton stripping angular distributions have been measured. The distorted-wave Born approximation is unsatisfactory for the excitation of the ${1/2}^{\mathrm{-}}$ 0.48 MeV state of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, the $2^{+}$ 4.44 MeV state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and the mutual excitation of these two states. Coupled channels calculations, using the rotation-vibration model, describe the excitation of states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ well and find K=3 for the $3^{\mathrm{-}}$ 9.64 MeV state. Poor fits are obtained to the projectile and mutual excitation data with coupled channels calculations. Finite range distorted-wave Born approximation calculations of single-nucleon stripping are in good agreement with the data. Extracted deformation lengths and spectroscopic factors are consistent with those from other studies.

Angular distributions are reported for ${}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$ and ${}_{}{}^{127}{}_{}{}^{}\mathrm{Xe}$ produced by the interaction of 8-GeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and 25-GeV ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions with Au. A shift from a forward to a sideward peaked distribution is observed for ${}_{}{}^{37}{}_{}{}^{}\mathrm{Ar}$, similar to that known to occur for incident protons over the same energy interval. Analysis of these data and those for Z=8 fragments indicate that reactions leading to heavy fragment emission become more peripheral as bombarding energies increase. A mechanistic analysis is presented which explores the ranges of applicability of several models and the reliability of their predictions to fragmentation reactions induced by both energetic heavy ions and protons.

The three-, four-, and five-nucleon transfers were investigated by studying the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$(α,${\mathrm{}}^7$Li${)}^7$Be, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$${(}^3$He${,}^7$Li${)}^7$Be, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(d${,}^7$Li${)}^7$Be reactions, respectively. The measurements were performed in the entire center of mass angular region, at incident energies corresponding to 49.3 MeV in the center of mass system of the exit channel. A distorted-wave Born approximation analysis was performed including second-order transfer contributions for all investigated reactions.

Pion production cross sections in heavy ion-induced reactions at energies close to the absolute threshold are calculated using a generalized version of the compound nucleus model of Aichelin and Bertsch. The calculated results are consistent with the data for laboratory energies per nucleon in excess of 50 MeV. For lower beam energies and for high pion kinetic energies, the model tends to underpredict the data. This indicates the presence of a nonstatistical component in the pion production process.

The energy characteristics and the emission probabilities of the tritons and the α particles emitted in the thermal-neutron-induced ternary fission of ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, and ${}_{}{}^{241}{}_{}{}^{}\mathrm{Pu}$ have been studied at a neutron guide of a high flux reactor, using surface barrier ΔE-E telescope detectors. Within the experimental uncertainties, E${¯}_{\alpha }$ and E${¯}_{\mathrm{t}}$ appear to be constant. On the other hand, the widths of these distributions and the α and t emission probabilities seem to be correlated with $Z^2$/A and with λ (i.e., the constant for radioactive α decay) of the fissioning systems. These results are interpreted and discussed.

Induced nuclear fission is described as a transport process of the fission degree of freedom over the fission barrier. The lifetime of the event is defined in terms of the probability of finding the nuclear system in the potential well corresponding to the ground-state deformation. This definition appears as a natural generalization to nonstationary transport processes of the usual expression for the lifetime. Using the conservation law for the current we relate the lifetime to the time-integrated escape rate across the collective potential barrier.

We envisage a schematic model in which the escape rate attains a constant value only after a certain transient time τ. In this case we show that the lifetime evaluated at the saddle point of the collective potential is made up of two contributions: one—ħ/${\Gamma }_f^{\mathrm{stat}\mathrm{—}}$identified as the quasistationary transition-state expression of the statistical model and one proportional to τ, hence directly related to the transient behavior of the transport process. As long as ħ/${\Gamma }_f^{\mathrm{stat}\mathrm{\gg }\mathrm{\tau }}$, fission can well be described as a quasistationary transport phenomenon. For ħ/${\Gamma }_f^{\mathrm{stat}\ll \mathrm{\tau }}$, which occurs for excitation energies of a few hundreds of MeV and small fission barriers, the fission process becomes a transient phenomenon of duration of the order of τ.

For a single collective variable and its canonically conjugate momentum, we study the transient time τ as a function of the nuclear friction constant β. Thereby we extend and complete the findings of earlier studies. For a specific system of mass A=248, we calculate the lifetime at the saddle point of the collective potential and find results in keeping with our schematic model. We assume further that the collective potential beyond the saddle point can be correctly represented by an inverted parabola and we obtain an analytical expression for the current evaluated at the scission point. We find that this current can be expressed reliably as the current evaluated at the saddle point but delayed by a constant time τ${¯}_1$ which we obtain and interpret. Thereby we bring support to the conjectures made in several studies of fissioning systems within the same framework.

As a result we also extend trivially the schematic model to the escape rate evaluated at the scission point and obtain the lifetime evaluated at scission as the sum of the lifetime evaluated at the saddle point and of the time delay τ${¯}_1$.