One- and two-step processes in natural- and unnatural-parity 208Pb(p,t)206Pb reaction at Ep = 22 MeV

Reaction mechanism and nuclear-structure dependence of the natural- and unnatural-parity ²⁰⁸Pb(p, t)²⁰⁶Pb(2⁺, 3⁺, 4⁺, 5⁻ and 7⁻) reaction are studied by using a 22 MeV polarized proton beam. Angular distribution of the analyzing power for the second 3⁺(3₂⁺) transition has an opposite sign to that for the 3₁⁺ one and the difference is explained in terms of the j-dependence in the sequential two-step (p, d)(d, t) process. The observed analyzing powers and cross sections for the two 3⁺ transitions are reproduced by the finite-range first- and second-order DWBA calculation. Two-step analysis is necessary to explain the variety of angular distributions of the analyzing powers for the natural-parity transitions. Microscopic analysis in terms of the one- and two-step (p, t) calculation is made for the transitions to the 2_1–5⁺, 4_1–3⁺, 5_{1, 2}⁻ and 7₁⁻ states in ²⁰⁶Pb. The calculation reproduces the absolute values of the observed cross sections within a factor of 2.     

7Li(p,n)7Be reaction with polarized protons from the threshold to 3.0 MeV

A polarized beam was used to measure angular distributions of the proton analyzing power of the ⁷Li(p,n)⁷Be reaction at 11 energies from 2.05 to 3.00 MeV. The analyzing power is generally large and positive. The analyzing power can be fitted with associated Legendre polynomials. The coefficient of P₁¹ rises rapidly from threshold to a maximum near the 3⁺ state at 2.25 MeV from which it drops to a minimum at 2.42 MeV, whence it gently rises to 3.00 MeV; the coefficient of P₂¹ has small values that increase with energy. The data were measured typically to an accuracy of 0.02 with a target 20 keV thick at 2 MeV bombarding energy. Polarization contour maps are given. Comparison of these analyzing power measurements with previous data for the neutron polarization induced with unpolarized protons shows equality at some energies and slightly higher values at others.     

Two-pion production in proton-proton collisions with a polarized beam

The two-pion production reaction pp → ppπ⁺π⁻ was measured with a polarized proton beam at T _p ≈ 750 and 800MeV using the short version of the COSY-TOF spectrometer. The implementation of a delayed-pulse technique for Quirl and central calorimeter provided positive π⁺ identification in addition to the standard particle identification, energy determination as well as time-of-flight and angle measurements. Thus all four-momenta of the emerging particles could be determined with 1–4 overconstraints. Total and differential cross-sections as well as angular distributions of the vector analyzing power have been obtained. They are compared to previous data and theoretical calculations. In contrast to predictions we find significant analyzing-power values up to A _y = 0.3. The data taken in the energy region of the excitation of the Roper resonance confirm that its dominant ππ decay channel is N ^* → Nσ.     

Observation of deuteron D-state and compound nucleus effects in (d,p) reactions on 46Ti and 52Cr with a polarized deuteron beam

The cross section and the vector and tensor analyzing powers have been measured for ⁴⁶Ti(d, p)⁴⁷Ti at deuteron energies of 6 and 10 MeV and ⁵²Cr(d, p)⁵³Cr at 6 MeV. Transitions were observed to the states at E_x=0.159, 1.549 and 1.793 MeV in ⁴⁷Ti and the states at E_x=0.0, 0.564, 1.006 and 2.321 MeV in ⁵³Cr. In addition, the cross sections and vector analyzing powers for deuteron elastic scattering were measured for the same targets and deuteron energies and compared to optical model calculations. The choice of optical parameters for the DWBA analysis of the (d, p) reactions is discussed. Calculations made with the DWBA method show that the deuteron D-state must be included to reproduce even qualitatively the (d, p) tensor analyzing power measurements. The j-dependence of the tensor analyzing power T₂₂ is discussed. The validity of the local energy approximation (which was used to incorporate the deuteron D-state into the DWBA calculations) is evaluated by comparison to finite range calculations. The contribution of compound nucleus reactions to the measured cross sections and analyzing powers was investigated. In order to determine the compound cross section, the Ericson fluctuations in excitation functions of cross section and vector analyzing power were measured from 5 to 7 MeV on each target. The formulas used to calculate the polarization observables from the Hauser-Feshbach theory are presented.     

Investigation of the 58Ni(7Li, 6Li)59Ni reaction with vector polarized 7Li

Angular distributions of the cross section and of the vector analyzing power for the ⁵⁸Ni(⁷$\text{Li}$, ⁶Li)⁵⁹Ni reaction leading to several groups of levels in the final nucleus have been measured at E_Li = 20.3 MeV. The observed Q-value dependence of the vector analyzing power can to a large extent be attributed to a kinematical effect caused by the polarization of the orbital angular momentum of the transferred neutron in ⁷Li.     

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.     

The PbPb collision

The reaction ²⁰⁸Pb on ²⁰⁸Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the ²⁰⁸Pb on ²³⁸U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ_z² versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.     

Investigation of low-lying states of 15N via 14N(d,p)15N reactions with vector polarized deuterons

Angular distributions of cross section and vector analyzing power have been measured for the ¹⁴N(d, p)¹⁵N reaction at E_d = 10 MeV for transitions to levels up to 8.6 MeV excitation in ¹⁵N. Distorted wave Born approximation calculations and calibration curves were used to determine total and orbital angular momenta and spectroscopic factors of the transferred neutrons. The results were compared with different theoretical approaches.     

Measurements of the inclusive pd breakup cross section at low and intermediate energies

Inclusive measurements of the D(p, p)pn reaction were made at incident proton energies of 248?MeV and 13?MeV, to investigate the global feature of the pd breakup reaction at intermediate and low energies. At 248?MeV, the cross section and analyzing power A _y were measured at four angles from 7° to 20°. The data largely disagree with Faddeev calculations even if 2π-exchange three-nucleon force (2π3NF) or Δ-isobar is included, and the disagreement increases at forward angles. At 13?MeV, the cross section was measured at eight angles from 10° to 70°. The data are well reproduced by a recent pd Faddeev calculation, and the effects of Δ-isobar at 13?MeV are very small.     

Study of low-lying levels in 47Ca with the 48Ca(d, t)47Ca reaction

Angular distributions of cross sections [α(θ)] and vector analyzing powers [iT₁₁(γ)] have been measured for seven low-lying states or groups of states excited by the ⁴⁸Ca($\text{d}$, t)⁴⁷Ca reaction with 13.5 MeV deuterons and analyzed by the DWBA. On the basis of comparison of vector analyzing powers with DWBA calculations, spin-parity assignments have been made or confirmed for several states. Spectroscopic factors have been extracted. Angular distributions for weak states at 3.30 and 3.57 MeV excitation in ⁴⁷Ca could not be reproduced by DWBA calculations. Investigations of compound nucleus and multi-step contributions to the cross sections and analyzing powers for these states have been made by means of Hauser-Feshbach and CCBA calculations. Optical model parameters were obtained from analysis of 13.5 MeV deuteron elastic scattering cross sections and analyzing powers.     

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.     

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.     

Particle-hole excitations in the208Pb mass region

Spectra, magnetic dipole moments and spectroscopic factors of a number ofA=205–209 nuclei as well asM1 transitions in²⁰⁸Pb are investigated in terms of large-scale shell-model calculations which include 1p ?1h excitations and for some nuclei 2p ?2h excitations. The calculated spectra agree well with the data. The calculatedg-factors are in fair agreement with the data in most cases. The predicted strength forM1 transitions to low-lying states in²⁰⁸Pb is less than that obtained from previous calculations. Spectroscopic factors forl=0 proton pick-up from²⁰⁸Pb and²⁰⁶Pb agree very well with recent experimental data from (e, e′p) reactions.     

Measurement of the differential cross section and of the tensor and vector analyzing powers for the fragmentation of 4.5-GeV/c deuterons on beryllium in the reaction involving proton emission at an angle of 80 mrad

The invariant differential cross section, the tensor analyzing power A _yy , and the vector analyzing power A _y for the reaction ⁹Be(d, p)X are measured at an initial deuteron momentum of 4.5 GeV/c and a proton detection angle of about 80 mrad. The data obtained for the differential cross section are consistent with the results of measurements at 3.5 and 5.78 GeV/c and a proton emission angle of 2.5°. The values found for the tensor analyzing power A _yy are compared with similar data obtained previously for the deuteron-fragmentation process occurring on a carbon target at various values of the initial deuteron momentum and leading to proton emission at zero angle. The data on the differential cross section for the reaction ⁹Be(d, p)X can be satisfactorily described within the relativistic impulse approximation by using standard deuteron wave functions; however, the approach based on this conceptual framework proves to be inadequate in dealing with data on the tensor analyzing power. These results indicate that it is necessary either to change the method for describing the relativistic deuteron or to take into account additional mechanisms.     

Charge-changing cross sections of the neutron-rich isotopes8,9,11Li

Total charge-changing cross sections have been measured for⁸Li on C and Pb targets, for⁹Li on C, Al, Cu, Sn and Pb targets, as well as for¹¹Li on C, Sn and Pb targets at about 80 MeV/nucleon. These data are compared to measured total reaction cross sections and Glauber-type calculations using Hartree-Fock density distributions. These comparisons allow to draw conclusions on the proton density distribution of the neutronrich lithium isotopes. The results show that even for the most exotic nucleus¹¹Li the proton distribution is only very weakly influenced by the long tail in the neutron density distribution already established in several experiments.     

Polarization of single particle states in heavy ion induced nuclear reactions within the two center shell model

In “slow” nucleus-nucleus collisions the single particle states will adjust continuously to an instantaneous two center potential. Transfer reactions will occur between polarized rather than between asymptotic states. In order to employ two center states in reaction calculations, an expansion in terms of asymptotic states with good angular momentum is required. This expansion is formulated, and equations for the expansion coefficients are derived. Model calculations for the system ⁴⁰Ca+¹⁶O indicate that the polarization of unoccupied proton states in ⁴⁰Ca is strong, while it is very weak for the tightly bound 1p_{$\text{1}\text{2}$} proton in ¹⁶O. The dependence of the polarization effect on several relevant parameters is discussed.     

Complex microscopic effective interaction for (p,n) reactions

A simple recipe for generating a complex effective interaction for distorted wave Born approximation calculations from a real, microscopic charge-exchange form factor is investigated. The recipe is tested against angular distribution data for ²⁰⁸Pb(p, n) and ²⁰⁹Bi(p, n) from 25 to 50 MeV incident proton energy. The form factor resulting from the recipe is also compared qualitatively to complex effective coupling potentials, resulting from a charge-independent Lane-model formalism and from coupled-channion-channels calculations for a suggested multistep (p, d)—(d, n) reaction mechanism.     

The distribution of205Tl proton hole states and estimation of the root mean square radii of206Pb and208Pb from their charge distributions

The fragmentations of the 3s _1/2, 2d _3/2, 2d _5/2 and 1.h _11/2 proton states were deduced using the hole-core coupling model calculation and compared with recent²⁰⁶Pb ( \(\vec d\) ,³He) reaction data. The energies of the proton fragments carrying the main shell-model strengths were used to deduce the radial wave functions of²⁰⁵T1 and²⁰⁷Tl that give rise to charge distributions of these nuclei. From their respective charge distributions, root mean square radii of²⁰⁶Pb and²⁰⁸Pb were extracted.     

Breakup of 4He with polarized protons at 65 MeV

For the ⁴He(p, p³H)¹H reaction, large negative analyzing powers are observed in the FSI regions. For the inelastic scattering of protons, the angular dependence of the analyzing power is well reproduced by the single and double scattering terms of the Faddeev breakup theory.