Three-step analytic model for high-energy heavy-ion collisions

We discuss within the framework of an analytical model central collisions between large nuclei at an intermediate energy. The model assumes three stages: the ignition stage in which thermalized nucleons are created within the reaction volume; the expansion phase in which the hot nuclear matter expands and cools; and finally, the evaporation stage in which the system disintegrates through a surface evaporation. The model provides a qualitative insight into the connections between the main physical processes throughout the collision event.     

Classical many-body model for heavy-ion collisions (II)

A four-parameter classical many-body model, specifically designed for heavy-ion collisions, is presented. Binding energies and densities of infinite and finite nuclei (N = Z) are satisfactorily reproduced. So also is the viscosity moment of the two-body scattering cross section at lab energies between 100 and 300 MeV.     

Quasi-linear response theory of statistical heavy-ion collisions: (II). Analysis of the friction tensor and the energy transport

We apply the recently proposed quasi-linear response theory to the study of energy transport in deep inelastic heavy-ion collisions. By solving a master equation, we show how quickly the canonical distribution function becomes a good representation of the intrinsic state in the case of the random intrinsic excitations proposed by Weidenmüller and co-workers. We numerically analyze the properties of the corresponding friction tensor. In addition, we demonstrate that the known fluctuation dissipation theorem in the linear response theory is considerably violated for large part of deep inelastic collisions. We then calculate the double differential cross section for three typical examples. The results agree well with the experimental data if we phenomenologically introduce a time-dependent potential. We remark on the difference of the present calculation from that of the linear response theory. We comment also on the validity of a time-dependent theory, which derives the basic equations from time-independent equations by assuming a one-to-one correspondence between the time and the relative distance.     

Statistical model calculations of continuum feeding times in heavy-ion fusion reactions

The time development of oxygen-induced compound reactions on ²⁷Al and ⁵⁸Ni targets at 30–70 MeV beam energy has been calculated in the framework of the statistical model. Feeding times associated with the population of yrast states in the evaporation residues have been estimated. It is shown that the experimental feeding times τ₁ < 0.2 ps, when combined with measured evaporation residue cross sections and/or absolute γ-ray yields, put restrictions on the spin dependence of the level density. Furthermore, it has been found that the dipole strength of continuum transitions between high-spin states is of the same order of magnitude as that obtained in radiative neutron capture reactions.     

Classical many-body model for heavy-ion collisions incorporating the Pauli principle

A classical model for heavy-ion collisions, introduced previously, has been extended to include certain effects of the Pauli principle. All nucleons are treated equally. They obey classical dynamics and interact through an ordinary two-body force and through a momentumdependent two-body “Pauli core” which satisfies, approximately, that $\text{p}{}_{\mathrm{ij}}\text{r}{}_{\mathrm{ij}}\text{≧ξ}\text{h}\text{?}$, where ξ is a dimensionless constant. A form for the Pauli core is presented. The ordinary two-body force has been adjusted to fit bulk properties of nuclei and to reproduce that moment of nucleon nucleon scattering cross sections which is relevant to hydrodynamics. The parameters of the forces are given.     

Investigation of 36Ar with the 35Cl(p, γ)36Ar reaction: (II). Angular distributions and shell model calculations

The angular distributions of primary and secondary γ-ray transitions at eight resonances in the ³⁵Cl(p,γ)³⁶Ar reaction have been measured with a 60 cm³ Ge(Li) detector. The measurements lead to unambiguous J^gp assignments for 17 states of ³⁶Ar and to J^π limitations for seven other states. A large number of γ-ray multipole mixing ratios were obtained. Many of the resonances are analogues of ³⁶Cl levels. The lifetime of the E_x = 6.36 MeV level has been determined as τ_m = 440 +-150 fs. A simple shell model calculation has been performed to study the odd-parity levels of ³⁶Ar and ³⁶Cl. Coulomb displacement energies have been computed. Spectroscopic factors have been calculated and compared with the experimental data for the ³⁵Cl(d, p)³⁶Cl and ³⁵(τ, d)³⁶ reactions.     

Atomic capture of negative mesons: (I). The Fermi-Teller model

We develop the Fermi-Teller model for describing the initial atomic capture and subsequent deexcitation of negative mesons. This enables us to predict an “initial” distribution for the lowest, quantum-mechanical part of the cascade. Our results are fairly close to the traditional ad hoc “statistical” distribution. Advantages and shortcomings of the Fermi-Teller model are discussed.     

Sequential calculations for heavy-ion induced two-nucleon transfer on 14N, 15N and 16O

¹¹B and ¹³C induced two-nucleon transfer data on ¹⁴N, ¹⁵N and ¹⁶O are compared with exact finite-range sequential transfer calculations. The data appear to be consistent with this reaction model and the assumed shell-model structure of the states populated. Single-nucleon transfer data on these targets is also analyzed using the DWBA. Modifications to the exit channel optical potential are required to obtain agreement with shell-model spectroscopic factors.     

Classical trajectory calculations with time-dependent forces in heavy-ion collisions

The applicability of a phenomenological time-dependent nucleus-nucleus potential to deep inelastic collisions is studied. We present its general shape and make a particular choice of the diabatic and adiabatic parts. From trajectory calculations we find that the angle-energy correlation is well described when a time-dependent friction force is used. We also compare our results to some TDHF calculations.     

Heavy-ion one-neutron transfer reactions involving 13C: (I). Spectroscopic factor products

The total cross sections of some heavy-ion one-neutron transfer reactions involving ¹³C, which lead to excited states of one of the final nuclei, have been measured at energies below the Coulomb barrier. Products of the neutron spectroscopic factors in the initial and final states have been extracted using a Coulomb wave Born approximation, and have been compared with theory.     

The structure of 209Bi: (I). Microscopic structure from analog resonances

Excitation functions for the ²⁰⁹Bi(p, p′) reaction have been measured for incident proton energies from 14.0 to 15.5 MeV to study the population of states in ²⁰⁹Bi via decay of the isobaric analog resonances in the compound nucleus ²¹⁰Po. The analogs correspond to parent states in the lowest one MeV of excitation in ²¹⁰Bi. Strong resonances are observed in the excitation functions for twenty proton groups corresponding to levels between 2.75 and 3.65 MeV in ²⁰⁹Bi. From these results, levels which possess microscopic 2p-1h structure involving the orbitals are identified and their ²¹⁰Bi parentage determined. The resonant scattering results together with other direct inelastic scattering data allow the spins and parities for many of the levels to be deduced. The results of a microscopic calculation, in which empirical two-body matrix elements are employed to describe the interactions between the orbitals, are also reported and compared with the experimental results for levels in ²⁰⁹Bi. The excellent agreement between theory and experiment demonstrates that the general character of these levels can be understood microscopically in terms of their 2p-1h structure.     

Direct reactions to many-channel, many-level final states : (II). (d, p)n and (He, d)p

In an earlier paper, the cross section for a direct reaction to a generalised positive-energy final state, described by an R-matrix wave function, was derived. Here a distinction is emphasised between two classes of such a reaction, depending on whether it can or cannot decay back to the target state. A major contribution in the latter case can be via direct break-up. This is computed for the reaction ⁷Li(³He, d)⁸Be(p)⁷Li, treated by a stripping mechanism. The dependence of the cross section on the final-state (⁸Be) channel energy is discussed. The present work uses shell-model wave functions for R-matrix basis states, and this is shown to be appropriate and useful for direct reactions.     

High-spin states in 24Mg and upper limits for particle spectroscopy of high spins by heavy-ion compound reactions

High-spin states in ²⁴Mg have been investigated by the reaction ¹⁰B(¹⁶O, d)²⁴Mg up to $\text{E}{}^1\text{≈ 24}\text{MeV}$. High-spin states with $\text{I ≧ 9}$ have been identified at $\text{E}{}^1\text{= 19.20, 20.26, 20.8, 21.6, 23.1,}\text{and}\text{23.5}\text{MeV}$. The 10⁺ yrast state in ²⁴Mg is probably located at 20.26 MeV. The upper limits with respect to spin and excitation energy of the applicability of heavy-ion compound reactions for particle spectroscopy of high-spin states are discussed. The main limitations result from the increasing continuum and from a decrease of the high-spin selectivity when the final spins approach the critical angular momentum for compound-nucleus formation. It will be shown that the difficulty in the analysis of the experiments arising from the decreasing probability of finding isolated yrast states at high excitation energies, i.e. from the increasing level density, can be overcome in such experiments. The decrease in the high-spin selectivity of the total cross section is compensated for spins up to J_max by the fact that the shape of the angular distributions depends on the final spin for states with I ～ J_max. This is caused by the decreasing alignment of the final nucleus with decreasing values of |I ? J_max| and can be used for high-spin spectroscopy.     

Structure calculations for 25Mg-25Al

The results of a shell model calculation for ²⁵Mg-²⁵Al are presented in which the Hamiltonian for the system was taken to be that of an inert ¹⁶O core plus nine s-d shell particles interacting through the usual one-body l² and l · s terms plus general two-body residual interactions of the Kuo-Brown type. The basis was truncated to include nine favored representations of SU(3) in each of the two leading spatial symmetries ([441]: (66), (93), (74), (82)², (55)², (28), (90); [432]: (10,1), (74), (82)², (55)², (28), (47), (90)). It is found that a (λμ)-dependent renormalization of the type proposed by Harvey but empirically modified for axially asymmetric shape distributions is required to reproduce the experimentally observed ordering of the three lowest rotational bands. The goodness of K_J as a band label for the calculated eigenstates is investigated by comparing calculated quadrupole moments with simple rotational model predictions. Calculated B(E2) and B (M1) rates are compared with the available data. Results for relative spectroscopic factors from (d, p) stripping on the ground state of ²⁴Mg are also presented.     

The reaction 36S(p, γ)37Cl: (II). Lifetimes,spins and parities of 37Cl levels

Analysis of the γ-ray angular distributions measured at 16 ³⁶S(p, γ)³⁷Cl resonances yields the spins and/or parities of 21 bound states of ³⁷Cl in addition to the resonance spins. Among the latter are four $\text{J =}\text{1}\text{2}$ resonances. For several other bound states the possible spins have been restricted. Multipolarity mixing ratios have been deduced from the same data. Lifetimes (or lifetime limits) of 29 bound states have been deduced from DSA measurements.This extensive experimental information allows a comparison with the results of a shell-model calculation for both the even- and odd-parity states of ³⁷Cl. In this calculation either zero, one or two particles are promoted from the 2s_{$\text{1}\text{2}$} or 1d_{$\text{3}\text{2}$} to the 1f_{$\text{7}\text{2}$} or 2p_{$\text{3}\text{2}$} subshells. Up to an excitation energy of about 5 MeV a one-to-one correspondence is found between experimental and calculated levels.     

Dispersion relations and low-energy elastic scattering of charged particles from nuclei: (II). Application to N-4He scattering

A “Coulomb-modified” dispersion relation is applied to low-energy p-⁴He forward elastic scattering. To check the validity of the modification, the results are compared with those deduced from n-⁴He elastic scattering. Completely analogous information is obtained for the two processes. The exchange of three bound nucleons is found to contribute strongly to N-⁴He forward scattering. The corresponding ⁴He-³H-p and ⁴He-³He-n coupling constants are evaluated as R_p = 3.8±0.3 and R_n = 3.0±0.3, respectively. These constants are related to the strength of the asymptotic wave function of nucleons in ⁴He and thus to the tail of the nucleon distribution. A comparison of R_p with the empirical proton distribution in ⁴He as deduced from e-⁴He elastic scattering shows excellent agreement. From R_p and R_n the effective ranges of the singlet ³H-p and ³He-n interactions in the ground state of ⁴He are determined to be equal, in accordance with charge symmetry, and to have a value of r_eff = 1.072±0.006 fm.     

Neutral-pion production in central collisions of relativistic C and Ar on Pb

The production of π⁰ mesons in central collisions of ¹²C and ⁴⁰Ar on ²⁰⁸Pb has been examined at a number of energies from 1. to 2.1 GeV/N, as part of the first systematic study as a function of beam energy and charged-particle multiplicity of the rate of neutral-pion production in relativistic heavy-ion collisions. For comparison, corresponding π^± data acquired with the same detector system have also been presented. The results indicate that, for a given target-projectile combination, both neutral- and charged-pion production increase smoothly by a factor of approximately 2.9 in this energy range. The measurement of charged-particle multiplicity is discussed in order to indicate how the characteristic distributions observed in this study were used to parameterize the experimental results. The average multiplicity of both pions and nucleons projected from these data is found to disagree with statistical models of particle production. The significance of the N_π^±/N_charge and N_π^±/N_π⁰ ratios observed as a function of beam energy and charged-particle multiplicity is discussed in the context of understanding the nature of the collision process.