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.     

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.     

On the use of a noncentral velocity dependent potential for the interpretation of the nucleon-nucleon scattering data

A phenomenological nucleon-nucleon potential containing a noncentral velocity dependent term of the form (σ ₁ ·p)(σ ₂ ·p) is used to fit the solutions YLAM and YLAN 3 M of the phaseshift analysis ofBreit et al. andHull et al. for protonproton and neutron-proton scattering respectively. The potential contains altogether 20 parameters. The fit is carried through in the range from 10 to 300 MeV laboratory energy. While the results for thep-p phase parameters are useful only in some cases the results for then-p phase parameters are in general quite satisfactory.     

Measurement ofD(\vec p,p)D elastic scattering at 10.0, 12.0, 14.1 and 16.5 MeV especially for small forward and extreme backward scattering angles

The elastic scattering was investigated especially in the Coulomb sensitive scattering regions. Angular distributions of the differential cross section and of the analyzing powerA _y, with emphasis on small scattering angles, were measured at 10.0 and 14.1 MeV. For extreme backward angles up toJ _c.m.=179° the differential cross section was measured at 12.0, 14.1 and 16.5 MeV. The data have been compared with recent Faddeev calculations based on the realistic meson-exchange Paris potential and including an approximate Coulomb correction. There are discrepancies between the data and the calculations especially for the analyzing power. This indicates that the approximate treatment of Coulomb effects and possibly also the purely nuclear part of the calculations need to be improved.     

Electron-cluster interactions

Beam depletion spectroscopy has been used to measure absolute total inelastic electron-sodium cluster collision cross sections in the energy range fromE0.1 toE6 eV. The investigation focused on the closed shell clusters Na₈, Na₂₀, and Na₄₀. The measured cross sections show an increase for the lowest collision energies where electron attachment is the primary scattering channel. The electron attachment cross section can be understood in terms of Langevin scattering, connecting this measurement with the polarizability of the cluster. For energies above the dissociation energy the measured electron-cluster cross section is energy independent, thus defining an electron-cluster interaction range. This interaction range increases with the cluster size.     

Calculations of Three-Nucleon Reactions

Faddeev calculations using the chiral three-nucleon force in next-to-next-to-next-to-leading-order show that this force is too weak to provide an explanation for the low-energy A _y puzzle. The large discrepancy between data and theory for the neutron–neutron quasi-free-scattering cross section in low energy neutron–deuteron breakup requires a modification of the ${^{1}S_0}$ neutron–neutron force. We discuss the consequences that a bound ${^{1}S_0}$ state of two neutrons has on neutron–deuteron scattering observables. At higher energies we compare the solutions of the non-relativistic three-nucleon Faddeev equations with three-nucleon force included to the solutions of its Poincaré invariant version.     

Off-shell effects inpp↔πd spin observables

We show that spin observables inppd are fairly sensitive to small changes in the off-shell N helicity amplitudes. This is illustrated at proton laboratory kinetic energies ofT _p=515 MeV andT _p=578 MeV. A reduction of the helicity-flip amplitude by 13% brings the predictions of the relativistic rescattering model much closer to experiment.     

Faddeev partial-wave calculations with a three-nucleon potential for the triton ground state

The triton binding energy, the percentages ofS, S, andD states, and the asymptotic normalization constants are presented for 5-, 18-, 26-, and 34-channel Faddeev calculations with some realistic two-nucleon potentials and the Tucson-Melbourne three-nucleon potential. For the two-nucleon interaction, we take the Reid soft-core, the Argonne, the Paris, and the de-Tourreil-Rouben-Sprung potentials. The convergence properties of these calculations are discussed in detail. It turns out that five-channel calculations are decisively insufficient. We also discuss some asymptotic properties, such as the asymptotic normalization constants, the charge radius, and the momentum distribution in the long-wave-length region. It is shown that these quantities do not depend on the specific dynamics of the system, but only on the binding energy.     

New attempt to determine the n-n scattering length with the 2H(n, np)n reaction

The n-n final-state interaction (FSI) was investigated via the 2H(n, np)n reaction at 25 MeV, using a geometry which enables the simultaneous observation of n-p quasifree (QFS) scattering. The data were analyzed with Monte Carlo simulations based on rigorous Faddeev calculations with realistic nucleon-nucleon potentials. The value of a(nn) deduced from the absolute yield in the FSI peak is -16.27+/-0. 40 fm while the relative data, normalized in the QFS region, give -16.06+/-0.35 fm. Thus our results differ from the "recommended" value of a(nn) = -18.5+/-0.3 fm by more than 5 standard deviations.     

Measurements of the two and three spin-index observables inn p elastic scattering between 0.80 and 1.10 GeV

We present data of several rescattering observables measured inn p elastic scattering between 0.80 and 1.10 GeV. The SATURNE II polarized beam of free neutrons obtained from the break-up of polarized deuterons was scattered on the Saclay polarized frozen-spin proton target. Three different configurations of beam and target polarization directions were used: the observablesD _onon andK _onno were measured with the normal-normal spin configuration at eight energies;N _onkk ,D _os″ok andK _os″ko were determined with the longitudinal-longitudinal configuration at six energies;N _onsk ,D _os″ok andK _os″so with the sideway-longitudinal configuration at six energies. Part of the data was obtained with an unpolarized CH₂ target where only the two spin-index polarization transfer parametersK _os″ko andK _os″so were determined. Data are compared with phase shift analyses predictions and with the LAMPF results at 0.788 GeV. Present results are the first measurements of rescattering observables above 0.80 GeV. They provide an important contribution to any future theoretical or phenomenological analysis.

     

Developing a generalized diffraction model for elastic pd scattering at intermediate energies

A generalization of the Glauber-Sitenko diffraction model that includes the spin dependence of NN amplitudes, the D-wave of the deuteron, and the charge exchange effects is constructed for elastic pd scattering at intermediate energies. The developed model was used to analyze differential cross sections and some spin observables (analyzing powers) at the incident proton energies T _p = 1 GeV, 440 and 250 MeV. It was shown that predictions of the generalized diffraction model agree both with the experimental data and with the exact Faddeev calculations at low transfer momenta.     

Gluonic transverse spin structure functions and their possible measurement inχ 2 production

Gluonic parton distributions in a transversely polarized proton are identified and their classification according to twist is discussed. We find that there are two twist-three transverse spin gluonic structure functions, called hereinH ₁(x, Q ²) andH ₂(x, Q ²). These are potentially measureable in ₂ production in hard polarizedp-p collisions. Crossection formulae are calculated for a variety of polarization states, assuming a simple effective interaction for ₂ production from gluon fusion.     

Comparisons of vector analyzing-power data and calculations for neutron-deuteron elastic scattering from 10 to 14 MeV

High-accuracy analyzing-powerA _y() data forn-d elastic scattering at 12 MeV have been measured using the polarized-neutron facilities at the Triangle Universities Nuclear Laboratory (TUNL). The present data have been combined with our previousn-d measurements at 10, 12, and 14.1 MeV to form the highest-accuracyA _y() data set forn-d elastic scattering below 20 MeV. These data are compared to recent Faddeev-based neutron-deuteron (n-d) calculations which use the Paris and Bonn equivalent separable potentials PEST and BEST, as well as Doleschall's representation of theP- andD-wave nucleon-nucleon interactions. None of these models adequately describe the data in the angular region around the maximum ofA _y(). Possible reasons for the discrepancies are discussed. The sensitivity of the present Faddeev-based calculations to various angular momentum components of the nucleon-nucleon interaction are examined.     

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.     

Second and third virial coefficient of a quantum gas from two-particle scattering amplitude

Starting from the cluster expansion of the partition function the second and third virial coefficient of a quantum gas is expressed in terms of the two-particle scattering amplitude. In the case of spherically symmetric interaction the result forB(T) agrees with the well known expression ofBeth andUhlenbeck, but the method given here is also valid for non-spherically symmetric and even for non-local potentials. For the third virial coefficientC(T) an expression is derived in lowest order in the two-particle scattering amplitude which is suitable for numerical calculations.     

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.     

Variational calculations of resonant states in 4He

We present a modified R-matrix method which allows microscopic calculations of nucleon-nucleus scattering at low energies. This method may be applied in conjunction with any of the commonly used methods for the ground states of few-body systems, i.e. the Green function Monte Carlo, Faddeev and variational techniques. We then report results of variational calculations of low-energy tp scattering in the region of 0⁺, 0^? and 2^? resonances in ⁴He. The energies and widths of these resonances are calculated using realistic two- and three-nucleon interactions; but, the Coulomb interaction is neglected. The three-nucleon interaction is found to have a much smaller effect on the energies of the resonances than on the ground-state energy.     

The second order optical potential for theπd system at the threshold

The second order optical potential for thed system is derived in the framework of the Watson formalism and applied to the calculation of the 1s-state energy shift of the atom and thed scattering lengtha _d . The results are in good agreement with those of the Faddeev type calculations.The authors wish to thank V. B. Belyaev, R. Mach, M. G. Sapozhnikov and R. A. Eramzhyan for stimulating discussions and helpful advice.     

<Emphasis Type="Italic">η</Emphasis><Superscript>7</Superscript>Li Scattering in the <Emphasis Type="Italic">αt</Emphasis>-Cluster Model

The cross sections for elastic and inelastic η-meson scattering on ⁷Li nuclei are obtained on the basis of the αt-cluster representation of the target nucleus. The experimentally known values of the parameters of elastic ηα and αt scattering are used in exactly solving three-body Faddeev equations with separable two-body potentials. The η⁷Li elastic-scattering scattering length found from respective calculations is a_η7Li = ?0.310 ? i0.198 fm.