We propose a series expansion similar to that of the Hamiltonian to obtain cluster spectroscopic factors in the vibron model. The reason for this prescription is given by the link between the vibron model and the microscopic cluster model in the harmonic-oscillator limit. The ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+α and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+α systems are discussed as illustrative examples within the dynamic symmetry approach.

The structure and properties of the superdeformed giant dipole resonances (SDGDR) in rotating ${}_{}{}^{146\mathrm{-}152}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{132\mathrm{-}136}{}_{}{}^{}\mathrm{Nd}$, and ${}_{}{}^{80\mathrm{-}84}{}_{}{}^{}\mathrm{Sr}$ even nuclei are studied based on the linear-response theory with self-consistently determined superdeformed mean field. The effect of γ deformation as well as the triaxial superdeformation on the SDGDR is also investigated. The obtained common features may serve as the criterion for the observation of the SDGDR. The features are understood at a microscopic level by analyzing the distributions of the unperturbed p-h pairs connected with E1 operators.

We investigate the structure of the density matrix of relativistic nuclear matter at large momentum (k≫${\mathit{k}}_{\mathit{F}}$) making use of the σ+ω model of Walecka. The density matrix may be written in terms of spinors describing nucleons of modified mass and also has exotic components that contain spinors describing negative-energy states (‘‘antinucleons’’). We calculate the modification of the mean-field density matrix due to the admixture of two-particle, two-hole states in the ground state of the relativistic theory and find that the excitation of the exotic components of the density matrix is so strong and coherent as to preclude the use of perturbation theory. We suggest that an expansion in terms of reaction matrices will not improve the situation and conclude that a consistent picture may be obtained only if one limits oneself to a space spanned by positive-energy spinors (describing nucleons of shifted mass). We also consider the exchange of pions in the calculation of high-momentum components of the density matrix. However, in the case of pion exchange, we find that sensible results may not be obtained (even for the nonexotic components) unless we include tensor and short-range correlations. (The latter calculations have not been performed as yet.) Further, we note that a theory without vertex cutoffs (meson-nucleon form factors) leads to totally unacceptable results, as the depletion of the Fermi sea is again much too large.

Protons and charged pions have been detected at 70°, 90°, and 120° in the reaction induced by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ on various targets at 94 MeV/nucleon incident energy. Measured energy spectra are analyzed in terms of statistical emission from equilibrated sources in a participant-spectator picture. Microscopic dynamical calculations based on the Boltzmann-Nordheim-Vlasov equation are also performed. Experimental data are well reproduced by both models.

We report on a new measurement of the reaction ${}_{}{}^4{}_{}{}^{}\mathrm{He}$(d${,}^3$He${)}^3$H to study isospin breaking effects near threshold. We compared the results with microscopic calculations and infer on the importance of specific isosopin-breaking S-matrix elements. This analysis does not support the idea of an unknown ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ resonance causing the observed effects.

Sequential decay modes for the four-body final-state reaction, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C→3α${+}^{12}$C, are reported at a bombarding energy of 7.5 MeV/u. Position and energy measurement of all three alpha particles allows the kinematic reconstruction of the relative energies of all decay particle combinations. Several known natural parity states are observed from the alpha-particle decay of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_{}^{\mathrm{*}}{}_{}{}^{}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{\mathrm{*}}{}_{}{}^{}$, and in addition unnatural parity states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ never before observed in inelastic heavy-ion scattering are seen. The branching fraction for the alpha-particle decay of the 14.08 MeV $4^{+}$ state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}_{}^{\mathrm{*}}{}_{}{}^{}$, $2^{+}$ state is measured to be 0.83±0.04. Monte Carlo calculations for the effective solid angle for detection of each process are presented. No evidence is found for any spontaneous three alpha-particle decay of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ excited states and no previously unknown states are reported.

Analyzing power ${\mathit{A}}_{\mathit{y}}$ and spin-transfer observables ${\mathit{D}}_{\mathit{i}\mathit{j}}$ have been measured for 500-MeV proton inelastic scattering from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Measured values of the ${\mathit{D}}_{\mathit{i}\mathit{j}}$ for the 9.70-MeV $5^{\mathrm{-}}$, T=0, the 11.58-MeV $6^{\mathrm{-}}$, T=0, and the 14.35-MeV $6^{\mathrm{-}}$, T=1 states are reported at 17° and 22°; values of ${\mathit{A}}_{\mathit{y}}$ cover the range from about 10° to 26°. Nonrelativistic (NRIA) and relativistic (RIA) impulse-approximation calculations are compared with the data. The differences between the two types of calculations are generally small. The RIA yields excellent agreement with the ${\mathit{D}}_{\mathit{i}\mathit{j}}$ data for the $5^{\mathrm{-}}$ state, and both RIA and NRIA do well for ${\mathit{D}}_{\mathit{i}\mathit{j}}$ data for the $6^{\mathrm{-}}$, T=0 state but poorly for the $6^{\mathrm{-}}$, T=1 state. For the ${\mathit{A}}_{\mathit{y}}$ data, both types of calculation give fairly good predictions for the $5^{\mathrm{-}}$ and $6^{\mathrm{-}}$, T=1 states, but not for the $6^{\mathrm{-}}$, T=0 state. Comparison between theory and experiment for the combinations of observables ${\mathit{D}}_{\mathit{K}}$, which are sensitive to individual terms in the nucleon-nucleon interaction, indicates a possible need for medium corrections in the T=1 tensor and spin-orbit forces.

The ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$(p→,γ${)}^{31}$P reaction has been studied in the proton energy range ${\mathit{E}}_{\mathit{p}}$=20–36 MeV. Angular distributions of the cross section and the analyzing power have been measured for γ-ray transitions to the ground state and the first excited state of ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ over the angular range 37.5°–145° at ${\mathit{E}}_{\mathit{p}}$=25.5 MeV. Legendre polynomial fits to both observables yield nonzero coefficients of order k=3,4, suggesting the interference of E2 radiation with the dominant E1 radiation. A transition-matrix-element analysis of the data indicates that ∼26% of the ${\gamma }_1$ cross section at this energy arises from E2 radiation, whereas only 10% of the ${\gamma }_0$ cross section can be attributed to E2 radiation. Direct-semidirect calculations give a direct E2 component of ∼7% for both channels, suggesting significant excess E2 strength in the ${\gamma }_1$ channel at this energy. The energy dependence of the 90° analyzing power for ${\gamma }_1$ shows a resonance structure near ${\mathit{E}}_{\mathit{p}}$=34 MeV which can be reproduced by a direct-semidirect calculation including an E2 resonance at ${\mathit{E}}_{\mathrm{GQR}}$=38.6 MeV with a width of ${\mathrm{\Gamma }}_{\mathrm{GQR}}$=5.0 MeV and a strength of 50% of the isovector E2 energy-weighted sum rule. The current results thus provide strong evidence for collective E2 strength roughly at the expected peak of the isovector giant quadrupole resonance built on the first excited state of ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$.

Cross sections, analyzing powers and spin-flip probabilities have been measured for inclusive inelastic scattering of 290 MeV protons from ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ at laboratory angles between 3.1° and 20°. The momentum transfers vary from small values (q∼0.2 ${\mathrm{fm}}^{\mathrm{-}1}$) where individual giant resonances of low multipolarity are observed, to larger values (q∼1.4 ${\mathrm{fm}}^{\mathrm{-}1}$) where quasielastic scattering dominates. Complete measurements of spin observables at 20° are discussed, which show that present impulse approximation models based on either the Dirac or the Schrödinger equation for the nucleon are not capable of reproducing all the data. At all momentum and energy transfers the measured analyzing powers ${\mathit{A}}_{\mathit{y}}$ are smaller than predictions from nonrelativistic calculations. Relativistic calculations explain this reduction of ${\mathit{A}}_{\mathit{y}}$ for data near the quasielastic point (ω=${\mathit{q}}^2$/2m) as an effect of the attractive scalar field in the nuclear medium; however, they fail to reproduce the observed slopes [d(${\mathit{A}}_{\mathit{y}}$)/dω at fixed angle], assuming for the nuclear response a simple Fermi gas model.

For the observed range of momentum and energy transfers (ω≤96 MeV at 20°; ≤45 MeV at smaller angles) the spin-flip probabilities ${\mathit{S}}_{\mathit{n}\mathit{n}}$ and spin-flip strengths σ${\mathit{S}}_{\mathit{n}\mathit{n}}$ appear to be rather insensitive to assumptions about the reaction mechanism and are qualitatively described by a nonrelativistic model of quasielastic scattering, which approximates the nuclear response by that of a semi-infinite slab with random phase approximation (RPA) correlations. Strongly enhanced ${\mathit{S}}_{\mathit{n}\mathit{n}}$ values are observed for ω>25 MeV and q≃100 MeV/c in agreement with similar observations for several other nuclei. The slab model gives a reasonable account of cross sections and angular distributions for the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$(n,p${)}^{54}$Mn reaction at 298 MeV. The inclusion of damping of the response by two-particle–two-hole excitations and of contributions from two-step processes improves the agreement with the (n,p) data. Using the experimental cross sections for (p,p’) and (n,p) reactions and the measured spin-flip strengths in (p,p’), we have separated the nuclear response into spin (ΔS=0, ΔS=1), isopin (${\mathit{T}}_{\mathit{f}}$=1,2) and angular momentum (L=0,1,2, . . .) components. The distribution and strengths of the Gamow-Teller, the isovector giant dipole, and the (isoscalar) giant quadrupole resonances have been determined from this analysis and are compared to results from complementary reactions. Relative to quasiparticle RPA calculations the Gamow-Teller quenching factors deduced from the σ${\mathit{S}}_{\mathit{n}\mathit{n}}$ data are slightly smaller than those from (p,n) and (n,p) reactions.

Three- and four-nucleon ground-state wave functions are displayed graphically in coordinate space as well as the Faddeev amplitudes from which they are constructed. In the four-body case only two-particle correlations are taken into account in the integro-differential equation approach, which consequently allows us to make a direct comparison between the Faddeev amplitudes for three and four nucleons and to demonstrate their high degree of similarity in shape. We also investigate the effect of the inclusion of the hypercentral potential in the definition of the (modified) Faddeev amplitudes. It is shown that the Faddeev-type components calculated in the adiabatic approximation are rather similar in shape to those calculated by means of the exact solution of the system of coupled integro-differential equations in two variables. The mixed symmetry component of the Faddeev-type amplitudes show the greatest sensitivity to the number of nucleons, the inclusion of the hypercentral potential, and to the adiabatic approximation.

Fission cross sections for a range of targets have been measured by solid-state track detectors following 80 and 100 MeV ${\mathrm{\pi }}^{+}$ bombardment. Fission probabilities have been inferred by comparison to computed reaction cross sections. Fission probabilities for heavy targets agree with those for other probes of comparable energy and with statistical calculations. Probabilities for lighter targets are much above those previously observed or computed. Ternary fission cross sections and multiplicities of light fragments have also been determined.

Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H̃, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian ${\mathit{h}}_1$, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green’s function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.

Average angular momenta deduced from isomer ratio, gamma-multiplicity, and fission fragment angular anisotropy measurements, and the associated cross sections for fourteen systems are analyzed with a barrier penetration model that includes the coupling of inelastic channels. Good agreement was found between the theory and the data obtained from isomer ratio and from gamma-ray multiplicity measurements with the exception of the more symmetric systems. In these cases the discrepancies with theory show correlations in cross section and angular momentum suggesting that a valid model can be found. The measurements of angular momentum using the fission fragment anisotropy technique, however, do not appear reconcilable with the energy dependence of the cross sections. This systematic overview suggests that the origin of this discrepancy lies with the deduction of angular momentum from the measured anisotropy in inclusive fission fragment angular distributions.

The cross section for the (p,${\mathrm{\Delta }}^{++}$) reaction on nuclei is written in a factorized form as the product of an elementary amplitude for the process (pp→n${\mathrm{\Delta }}^{++}$) times a nuclear transition density. The elementary amplitude (τ matrix) is written in the Born approximation, using a relativistic pseudovector Lagrangian for πN coupling (${\mathrm{\tau }}_{\mathit{R}}$) and comparing this with a nonrelativistic version (${\mathrm{\tau }}_{\mathrm{NR}}$). Our results include contributions for ${\mathrm{\Delta }}^{++}$ excitation from the projectile proton (‘‘direct’’ term) as well as the target proton (‘‘exchange’’ term). Using this expression calculations have been made for incident proton kinetic energies 400 MeV, 1 GeV, and 3 GeV for the four-momentum-transfer distribution dσ/dt and the missing-mass spectrum dσ/d(${\mathrm{\mu }}^2$). The magnitude of relativistic effects increases with the proton incident energy. For proton energy around 400 MeV, there is little difference between cross sections calculated using ${\mathrm{\tau }}_{\mathrm{NR}}$ with only a ‘‘direct’’ term and cross sections using ${\mathrm{\tau }}_{\mathit{R}}$ with (direct+exchange) terms. At 1 GeV and beyond, this difference becomes large. It is also found that the overall cross section reaches a maximum around 1 GeV beam energy. When a qualitative estimate of distortions is included, predicted cross sections are in reasonable accord with measured values for proton incident energies around 1 GeV.

The elastic scattering of nuclei belonging to an isobaric multiplet is discussed. These reactions involve at least one unstable nucleus. Such experiments are becoming feasible with the advent of radioactive beams. It is suggested that strong resonances can be found in the scattering of (isobaric) mirror nuclei at energies close to the Coulomb barrier. A simple model for the collision of mirror nuclei composed of identical, inert cores and valence nucleons is considered and the coupled equations, whose solutions yield the direct and charge-exchange amplitudes, are derived.

The purpose of this paper is to understand intuitively the origin of the angular momentum and incident-energy dependence of the nucleus-nucleus interaction on the basis of the totally- antisymmetrized many-body theory. With the aim of understanding the structure of the nucleus-nucleus interaction, we show first that the nucleus-nucleus interaction can be written by the use of the density-distribution function and the phase-space distribution function instead of using the many-body wave function itself. And we show that the structure change of the density-distribution function with the increase of the angular momentum causes the angular momentum dependence of the nucleus-nucleus interaction and that the incident-energy dependence of the nucleus-nucleus interaction originates from the structure change of the phase-space distribution function.

Inclusive excitation spectra for one neutron stripping between heavy ions seem to show contributions from transfer to low-lying unbound states of the target, as well as continuum background due to the breakup of the projectile in the field of the target. We discuss the possibility of calculating the probability distribution for the two processes within the same model with three different methods and compare numerical results obtained in the three ways.

We develop a model for heavy ion collisions that takes place in two stages, the first in which the ions interact through a Coulomb potential and the second in which they form a compound particle. A time-dependent boundary condition between the two stages is proposed at the point of coincidence of the two ions. When applied to stationary states this condition gives the standard single resonance R matrix and the corresponding S matrix shows the usual relation between the actual width of the level and its value when there is no Coulomb interaction. This dynamical model allows us to follow in time the process of scattering of ions for a single resonance, and it can be generalized to more complex situations.

The result of adding the spin density term in heavy-ion interaction potentials is studied for the first time, especially for unclosed shell nuclei. For the energy density functional of Skyrme interaction, the spin density contribution is derived for nuclei with an even number of valence particles (or holes). The calculations are made for light nuclei, using both the shell-model and Fermi-type nucleon densities. The interaction potential is calculated in the proximity theorem, using corrected Thomas-Fermi approximation for the kinetic energy density. Only the repulsive spin density contribution is found to be significant, which cancels a part of attraction in the total interaction potential.

A previously elaborated semiclassical one-body model for the dynamics of a single particle, moving in two potentials, in heavy-ion reactions or in fissioning systems has been extended with respect to the inclusion of angular momenta and more realistic separable potentials. The collective relative motion is assumed to proceed along a trajectory which is calculated from classical equations of motion including conservative and phenomenological friction forces. The formalism has been derived involving three-dimensional trajectories for symmetric as well as for asymmetric nucleus-nucleus systems. The model allows for the calculation of correct quantum-mechanical transition amplitudes to final bound and continuum states. It has been applied for the investigation of the excitation of a neutron during a fission process, covering also nonstatistical differential emission probabilities. From the numerical calculations, using parameters adapted to ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$(sf), one can conclude that in the underlying model without ‘‘sudden’’ processes the energy spectrum consists of two parts. The low-lying component is created in the neck region while a high-lying part seems to be governed mainly by the dynamics of the underlying collective motion rather than by the specific initial conditions.