Competition between neutron-proton rescattering and deuteron break-up in (d, np) reactions

Existing final-state interaction (FSI) theories predict observable rescattering effects in low-energy nuclear reactions with three or more particles in the final state. Obvious yields which could be attributed to this effect have only been reported in (d, np) reactions. However,n-p rescattering might be confused with the neutron-proton FSI following deuteron break-up since both contribute strongest at low relative neutron-proton energies. We have re-examined the (d, np) reactions on¹²C and⁴⁰Ca in a kinematically complete experiment making special effort to try to distinguish between rescattering and then-p FSI. Data have been taken within and outside the reaction plane at different bombarding energies. Attempts to simultaneously fit the detailed shapes of the proton spectra and the azimuthal angularn-p correlations with theoretical predictions in a consistent way were unsuccessful forboth reaction mechanisms. Improvements in the fits at particular energy and angle combinations were always at the expense of the agreement at other angles or energies. Therefore it must be concluded from our analysis that on the basis of calculations available at present the contributions fromn-p rescattering and deuteron break-up cannot be distinguished in a conclusive manner in the (d, np) experiments performed to date.     

Quasi-free scattering in the 3-N continuum

The interaction of a nucleon with the deuteron leading to break-up at the quasi-free scattering (QFS) condition is studied atE _N ^lab =12.0, 22.7, 68.0, and 140.0 MeV. Results of rigorous Faddeev calculations and of the impulse approximation (IA) are compared at these energies for bothn-p andp-p QFS in order to study the importance of rescattering terms. For the two-nucleon interaction the Paris potential is used. It is restricted to act in two-body states with total angular momentumj2. Also we compare the Faddeev calculations with experimental data for the QFS cross section and analyzing powerA _y and find overall agreement. The behaviour of scattering observables turns out to be different forn-p andp-p QFS. Also the energy dependence of rescattering terms is different in the two cases. For all energies studied the IA is not reliable.     

πo photoproduction on quasi-free neutrons in the reaction γd → πo np in the Δ region

The possibility of obtaining information about the reaction γn → π^on in the Δ resonance region from the reaction γd → π^onp is analyzed. To this aim, the differential cross sections d³σ/dE_ndΩ_πdΩ_n both for unpolarized particles and in case of polarized photons and deuterons as well as the asymmetry Σ for linearly-polarized photons are calculated at photon energies from 250 to 400 MeV in the diagrammatic approach. The contributions from the pole diagrams as well as one-loop diagrams both with n-p and π-N-rescattering are taken into account. The main contribution to the differential cross sections of π^o photoproduction on the neutron in the quasi-free kinematics arises from the neutron pole diagram. The correction due to n-p rescattering decreases with increasing pion angle and becomes to be less than 8% at Θ_π ≥ 90°. The contributions of the proton pole diagram and the one of π -N rescattering were found to be negligible. Background effects are more pronounced in the case of the asymmetry Σ. However, they are also strongly suppressed in the neutron quasi-free kinematics at photon energies above 300 MeV.     

The neutron-proton scattering length in the reaction9Be(p,np)8Be at 7.5 MeV

The relative differential cross section of the⁹Be(p, np)⁸Be _gs reaction at 7.5 MeV has been measured in an FSI geometry. A strongn-p FSI peak was observed with virtually no sequential decay modes interfering. The Watson-Migdal analysis of this peak yields the scattering lengtha _np =–23.8_–1.2 ^–1.1 fm with the effective ranger _np =2.76 fm.     

The reactiond+d→p+t and elastic deuteron-deuteron scattering at 51.5 Mev

The elastic deuteron-deuteron scattering and the reactionsd(d,p)t andd(d,³He)n have been investigated at an incident deuteron energy of 51.5 MeV. Time-of-flight technique was used for the particle identification. The observed angular distributions for the (d, p) and (d, n) reaction are identical within the accuracy of the experimental data. The experimental results for the reactiond(d, p)t are compared with a theoretical prediction based on the application of a generalized separable potential model to the four nucleon systems. Information on the single deuteron break-up reactiond+d→d+p+n and on the double deuteron break-up reactiond+d→p+p+n+n is contained in the observed continuous proton and deuteron spectra. The double break-up seems to be contribute only with a rather small amount to the whole break-up cross section.     

Neutron-proton final state interaction in the 3H(3He,pα)n reaction at low bombarding energies

The ³H(³He, pα)n reaction has been studied in a kinematically complete experiment at ³He bombarding energies between 0.31 and 2.80 MeV in order to detect a possible resonant energy dependence of the spin singlet (T = 1) neutron-proton final state interaction (FSI). The data in the region of low n-p relative energies have been analyzed in terms of the Watson-Migdal formalism. Only a slight relative increase of the ¹S₀ n-p FSI is observed with increasing bombarding energy. This result is not easily related to the strong isospin violations found in the two-body reaction ³H(³He, d)⁴He at similar ³He energies.     

The break-up reactionp+d→p+p+n

The three-particle reactionp+d→p+p+n has been investigated at a deuteron bombarding energy of 52.0 MeV. Single counter experiments as well as coincidence measurements have been carried out. The laboratory angular distribution of the break-up reaction and the total break-up cross-section have been determined by means of the single counter experiments. The angular distribution for final-state interacting neutron-proton pairs was obtained by means of coincidence measurements. The coincidence experiments provide a strong evidence for very different shapes of the angular distributions for neutron-proton singlet and triplet final-state interaction.     

π° photoproduction on quasi-free neutrons in the reactionγd→π°np in theΔ region

The possibility of obtaining information about the reactionγn→π°n in theΔ resonance region from the reactionγd→π°np is analyzed. To this aim, the differential cross sectionsd ³ σ/dE _n dΩ _π dΩ _n both for unpolarized particles and in case of polarized photons and deuterons as well as the asymmetryΣ for linearly-polarized photons are calculated at photon energies from 250 to 400 MeV in the diagrammatic approach. The contributions from the pole diagrams as well as one-loop diagrams both withn-p andπ-N-rescattering are taken into account. The main contribution to the differential cross sections ofπ° photoproduction on the neutron in the quasi-free kinematics arises from the neutron pole diagram. The correction due ton-p rescattering decreases with increasing pion angle and becomes to be less than 8% atΘ _π ≥ 90°. The contributions of the proton pole diagram and the one ofπ-N rescattering were found to be negligible. Background effects are more pronounced in the case of the asymmetryΣ. However, they are also strongly suppressed in the neutron quasi-free kinematics at photon energies above 300 MeV.     

Rescattering and neutron-proton final-state interaction in the 12C(d,pn)12C reaction

The ¹²C(d, pn)¹²C reaction has been studied in a kinematically complete experiment at several energies and angles suitable for observing proton-neutron rescattering and sequential decay final-state interactions (FSI), with the aim of investigating the relative importance of the two reaction mechanisms. An increase of yield has been observed for all spectra in the region of low relative proton-neutron energy where both rescattering and sequential decay leading to the ¹S₀ final-state interaction are possible. No consistent fits to the data using only the rescattering graph were found and interference with other diagrams must be assumed to occur. The effect of isospin non-conservation is discussed. It is concluded that no reported measurements on this reaction require an exclusive interpretation in terms of a rescattering mechanism and therefore no reliable information on nuclear lifetimes can be obtained from these experiments.     

The (2H-d)-reactions below 200 keV

The²H(d, n)- and²H(d, p)-reactions are studied for deuteron energies below 200 keV. It is shown that theR-matrix approach of Konopinski and Teller, which is very sensitive to the channel radius used, can be approximated in a way that the dependence on the channel radius does not appear explicitly. This approach appears to be formally equivalent to a kind of “direct approach” of Boersma. This equivalence answers the question why a direct approach to these reactions works at all at low energies. Each reaction is described by three parameters which are determined in a fit to the up to now available data.     

Qualitative features of Pauli break-up from the configuration space viewpoint

A dimensionless measure of the effect of Pauli exclusion upon the neutron-proton interaction in a projectile deuteron is calculated in the zero range approximation for a Hulthen deuteron. One learns thereby that the Pauli break-up matrix element is distributed differently in space from that for nuclear break-up and that the effect with decreasing energy to a large value at the lowest deuteron energies.     

The (d,p) Reactions below 3.0 MeV

Excitation functions for a number of proton groups for the reactions ²³Na(d, p)²⁴Na and ²⁷Al(d, p)²⁸Al were measured in the energy range E_d = 1.5 to 3.0 MeV. The angular distributions for a number of proton groups were measured at a number of deuteron energies below 3.0 MeV for the three reactions ¹²C(d, p)¹³C, ²³Na(d, p)²⁴Na and ²⁷Al(d, p)²⁸Al. The theory of deuteron stripping reactions at incident energies below the Coulomb barrier has been considered. A closed analytical form for the differential cross-section has been obtained considering three cases according to the incident deuteron and outgoing proton energies. An attempt has been made to fit the angular distribution measurements at a number of deuterons bombarding energies accordingly.     

The dp → ppn reaction as a method to study neutron-proton charge-exchange amplitudes

The differential cross section and deuteron analysing powers of the p → {pp}n charge-exchange reaction have been measured with the ANKE spectrometer at the COSY storage ring. Using a deuteron beam of energy 1170MeV, data were obtained for small momentum transfers to a {pp} system with low excitation energy. A good quantitative understanding of all the measured observables is provided by the impulse approximation using known neutron-proton amplitudes. The proof of principle achieved here for the method suggests that measurements at higher energies will provide useful information in regions where the existing np database is far less reliable.     

The level structure of 189Os

The level structure of ¹⁸⁹Os has been studied by (d, p), (d, t) and (d, d') reaction spectroscopy at E_d = 12.1 MeV. Assignments of a number of levels at excitation energies below ≈ 1700 keV are given. The assignments are discussed in terms of a unified model based on the Nilsson model including pairing, rotational motion and attenuated Coriolis coupling. Deviations between predicted and experimental excitation energies and wave functions are generally found to be consistent with trends observed in ¹⁸⁷Os and in the odd W isotopes. Evidence for the existence of collective non-rotational states is found from the (d, d') reactions. Results of (³He, α) and high resolution γ-ray and conversion electron studies were also included at various stages of the investigation to supplement the data from the deuteron induced reactions. Comparisons between calculated and measured B(E2) values are found to indicate an intrinsic quadrupole moment of the ground-state band of ≈ 5.0 b, in agreement with values in adjacent even Os isotopes. Details of the Coriolis coupling calculations are given.     

Peculiarities of deuteron splitting by the Coulomb field of heavy nuclei

It is shown that the (d, pf) reaction occurs through two channels. The second channel is related to the deuteron splitting in the Coulomb field of the nucleus and the formation of a singlet deuteron with a kinetic energy lower than the incident-deuteron energy by 2.3 MeV, sizes exceeding > a _np, and an isospin equal to 1. The interaction of a singlet deuteron with the initial nucleus leads to occupation of the shape isomer states.     

Total cross-section measurements for the production of nuclear gamma rays from light nuclei by low-energy deuterons

The thick target yields of the reactions ⁶Li, ⁹Be, ¹⁰B(d, nγ) for specific final nucleus γ-rays have been measured between deuteron bombarding energies of 48 and 170 keV. The measured thick target yields are used, together with recently published values of the stopping power of low-energy deuterons in matter, to infer the total reaction cross sections for the production of the specific γ-rays between deuteron energies of 65 and 160 keV. The cross sections are compared to appropriate Coulomb barrier penetration probabilities and the astrophysical functions S(E) are deduced.     

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.     

Neutron polarizations from the9Be(d,n)10B and11B(d,n)12C reactions

Neutron polarization angular distributions were measured for the⁹Be(d,n)¹⁰B and¹¹B(d,n)¹²C reactions for deuteron energies of 5.47 and 5.34 MeV, respectively. Using neutron time-of-flight techniques, polarizations to eight states in¹⁰B and to six states in¹²C have been measured. Neutron polarization energy excitation functions for both reactions were measured for deuteron energies from 3.0 to 5.5 MeV in 0.25 MeV steps at 30° (lab). Distorted wave method calculations carried out to compare theoretical calculations against experimental results were not in good agreement with the data.     

Cross Sections for Neutron–Deuteron Elastic Scattering in the Energy Range 135–250 MeV

We report new measurements of the neutron–deuteron elastic scattering cross section at energies from 135 to 250 MeV and center-of-mass angles from 80^? to 130^?. Cross sections for neutron-proton elastic scattering were also measured with the same experimental setup for normalization purposes. Our nd cross section results are compared with predictions based on Faddeev calculations including three-nucleon forces, and with cross sections measured with charged particle and neutron beams at comparable energies.     

Complete and incomplete fusion in reactions of 7Li + 56Fe at E(7Li) = 50 and 68 MeV from analysis of recoil range and light-particle measurements

Excitation functions for the production of eight radioactive products of the reactions of ⁷Li on ⁵⁶Fe have been measured up to E(⁷ Li) = 89 MeV. Recoil range distributions for these products, together with inclusive proton, deuteron, triton and alpha spectra, have been measured at energies of 50 and 68 MeV. The α, t and d spectra show characteristic “break-up” components at forward angles, while the recoil distributions show evidence of complete fusion and incomplete-fusion process ⁵⁶Fe( ⁷Li,α) ⁵⁹Co ^* . A parallel study on ⁵⁵Mn shows some evidences of the ( ⁷Li,t) incomplete-fusion process, but the cross-section for this process is significantly less than for the triton fusion process. The recoil distributions can be reproduced on the assumption that essentially all the observed break-up fragments are in fact associated with incomplete fusion, but uncertainties in normalisation leave open the possibility of a significant contribution of pure break-up. A diffraction model of the ( ⁷Li,α) transfer process reproduces the observed break-up α spectra with some success. Received: 29 March 2001 / Accepted: 12 November 2001