Dispersion relations and low-energy elastic scattering of charged particles from nuclei: (I). Theory

Dispersion relations for the elastic scattering of charged particles from nuclei are deduced for the case of potential scattering. The inclusion of the Coulomb interaction leads to a simple modification of the formalism developed so far for uncharged projectiles only.     

Forward dispersion relations and low-energy elastic scattering of charged particles from nuclei

A forward dispersion relation for charged particle scattering from nuclei is deduced. Inclusion of the Coulomb interaction leads to a simple modification of the formalism for uncharged projectiles. The modified forward dispersion relation is applied to p- scattering below 50 MeV.     

The elastic scattering of 33 MeV He particles from Ni,Cu and Zn

Differential cross sections have been measured for the elastic scattering of 33 MeV ³He particles from targets of ^58,60,62,64Ni,^63,65Cu and ^64,66,68Zn over the angular range 5° to 175°. The data have been analysed with the optical model, with particular emphasis on the investigation of the ambiguities in the real potential, the form of the imaginary potential and the use of a spin-orbit term.     

An experimental study of He elastic,inelastic and charge-exchange scattering from Li

A target of ⁶Li was bombarded with the ³He beam from the University of Illinois cyclotron. Differential cross sections for the elastic scattering, the inelastic scattering to the first two excited states of ⁶Li, and the (³He, t) charge-exchange reaction to the ground state of ⁶Be were determined over angular ranges of approximately 20° to 115° (c.m.) at ³He energies of 24.6 MeV and 27.0 MeV. (The weak inelastic transition to the 3.56 MeV state of ⁶Li, ordinarily obscured by a background of three-body break-up, was observed by requiring a coincidence at most angles between the scattered ³He and the ⁶Li recoil.) The ratio of the integrated charge-exchange cross section between 55° and 115° to the integrated inelastic cross section for this transition (both with ΔT = 1) is somewhat less than expected from isospin considerations (i.e., about 1.6 instead of 2.0).     

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.     

Determination of nuclear spectroscopic factors from data on differential cross sections for elastic neutron scattering on light nuclei

The values of the coupling constants (spectroscopic factors) dpn, ¹²C¹¹Cn and ¹⁴N¹³Nn have been derived by means of the extrapolation of differential cross section data to the corresponding poles. Some general questions concerning the application of this method to light nuclei are considered.     

Target excitations and the optical potential for protons scattering from nuclei

We calculate the contributions to the optical potential for 30 MeV protons due to inelastic excitations of the target nucleus. The scattering due to this non-local potential is calculated exactly and some of the results subjected to conventional optical model analysis. When only one excited state is included, a resonant dependence on the excitation energy is observed. Even with ten excited states, the position of a single one can strongly influence the scattering. It is possible to account for about $\text{3}\text{4}$ of the observed absorption in ⁴⁰Ca and ²⁰⁸Pb, but only by postulating unobserved states which exhaust the remainder of the experimental sum rules at somewhat unreasonably low energies. It was not possible to find simple local potentials which gave the same scattering because of the strong L-dependence of the absorption. The constructed potentials concentrate the absorption at too small radii. It is suggested that rearrangement (pick-up) processes contribute a substantial amount of absorption at larger radii, while compound formation will give rise to a volume term in the imaginary potential.     

Comparison of analyzing power and polarization in the reaction 3H(p,n)3He: (II). New polarization results below 4 MeV

The polarization P^y for the ³H(p, n)³He reaction was measured for energies between 2 and 4 MeV. Special care was given to minimizing the effects of background and to interpreting the experimental spectra. The new values for P^y are significantly higher than previous values, and comparison to the available data for the analyzing power A_y for the same reaction now shows that in this energy range P^y and A_y are equal within experimental uncertainties. This equality negates earlier conclusions that sizeable differences existed between these observables. In particular, our new results demonstrate that in this reaction the effects of charge symmetry breaking on differences between these observables must be small.     

Inelastic scattering of heavy ions from deformed light nuclei at near-barrier energies

Angular distributions have been measured at energies near the Coulomb barrier for the systems ¹⁸O + ²⁴Mg, ¹²C + ²⁸Si and ^{16, 18}O + ²⁸Si for elastic scattering and inelastic scattering to the first 2⁺ states in ¹⁸O, ²⁴Mg and ²⁸Si. Coupled-channel calculations were required in order to reproduce the details of the strong Coulomb-nuclear interference minima. However, a satisfactory account of the main features of the data was obtained in a first-order DWBA analysis and with the closed formalism of Frahn. With the exception of ¹⁸O, it was sufficient to assume equal charge and optical-potential deformation lengths.     

Energy spectra of single neutrons and charged particles emitted following the absorption of stopped negative pions in 4He

Energy spectra have been measured of single neutrons, protons and deuterons emitted following the capture at rest of negative pions in ⁴He. The neutron energy spectrum has been measured with an energy resolution of 4% at 90 MeV. The absolute number of stopped pions has been measured.     

Application of a microscopic interacting boson model to single-closed-shell nuclei

The microscopic treatment of an extended IBM including the pairing vibrational modes is applied to single-closed-shell nuclei with N = 50 or Z = 50. The low-lying spectra in the N = 50 isotones are well described in terms of the quadrupole phonon and the pairing vibration. The Sn isotopes roughly resemble the N = 50 isotones. The behavior of the 0₂⁺, 0₃⁺ and 2₁⁺ levels can be explained fairly well by the present model. Introduction of the pairing-vibrational modes into the IBM is essential for describing the single-closed-shell nuclei.     

Structure study of 12B from the elastic scattering of neutrons from 11B

Differential cross sections for neutrons scattered from ¹¹B have been measured for 2.2 MeV < E_n < 4.5 MeV. The differential cross section σ(θ) is fitted reasonably well by R-matrix parameters for broad states in ¹²B with assignments 1 ^? and (1) ⁺ at excitation energies E_x = 5.8 and 6.8 MeV respectively. The broad 1 ^? state has not been previously observed and is believed to be the 1 ^? member of the $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ particle-hole multiplet predicted to exist by earlier shell model calculations. Its existence completes the identification of all of the levels of this multiplet (3 ^?, 2 ^?, 4 ^?, 1 ^?). The broad (1)⁺ level at E_x = 6.8 MeV has not been previously observed. States at excitation energies E_x = 5.61, 5.73 and 6.6 MeV have been assigned spins and parities of 3⁺, 3^? and (1)⁺ respectively. These states had previously been assigned spins of 2, 3 and $\text{≧ 1}$ respectively. Work on T = 1 states in ¹²C¹ has been compared with the present work.     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

Isospin-forbidden particle decays in light nuclei: (I). T = 32 levels of 9Be, 9B

Absolute branching ratios have been measured for the isospin-forbidden nucleon decays of the lowest $\text{T =}\text{3}\text{2}$ levels of ⁹Be and ⁹B to the ground state and first excited state of ⁸Be. The $\text{T =}\text{3}\text{2}$ levels were populated by the ⁷Li(³He, n) and ⁷Li(³He, p) reactions. The subsequent decay products were observed in coincidence with the neutrons or protons, detected at 0°. Branching ratios of 0.028 ± 0.021 and 0.50 ± 0.11 were determined for the neutron decays of the 14.39 MeV, $\text{T =}\text{3}\text{2}$ level of ⁹Be to the ground state and 2.9 MeV, 2⁺ first excited state of ⁸Be, respectively. Branching ratios of 0.11 ± 0.04 and 0.33 ± 0.09 were determined for the analogous proton decays of the ⁹B, 14.67 MeV $\text{T =}\text{3}\text{2}$ level. The similarity of the decay properties of these analogue levels is in contrast to the large asymmetries observed for $\text{T =}\text{3}\text{2}$ levels in other A = 4N + 1 light nuclei.     

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.     

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.     

Elastic electron scattering from 3He and 4He

The cross sections for elastic electron scattering from ³He and ⁴He were measured for the momentum transfer range from 0.45–2.0 fm^?1. The cross sections were separated into their longitudinal (charge) and transverse (magnetic) contributions using the Rosenbluth formula. The charge and magnetic form factors were obtained model-independently.The rms charge radii were found to be 1.671 (14) fm for ⁴He and 1.976 (15) fm for ³He, and the magnetic rms radius of ³He is 1.99 (6) fm. The mis charge radius for ⁴He is in excellent agreement with the latest muonic data.Comparison of the form factors was made with Faddeev three-body calculations using realistic two-body NN interactions. At present the theoretical calculation is not able to reproduce the experimental data.     

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.