Spins in Nuclear and Hadronic Reactions

The following sections are included:

• PREFACE

• CONTENTS

Analyses of (p, α) and (p,³He) reactions to the continuum are reviewed, and the importance of analysing powers for determining the reaction mechanism is discussed. Recent analyses using the Feshbach-Kerman-Koonin multistep direct theory of the (p, α) reactions using the alpha-particle knock out model and of the (p,³He) reaction using the deuteron pickup model are described. All this work shows how spin-dependent phenomena provide a powerful tool for the study of nuclear reaction mechanisms.

The semi-classical distorted wave (SCDW) model of nucleon inelastic and charge exchange scattering at intermediate energies is extended to calculate spin observables, making use of the G-matrix parameterized in coordinate representation. The depolarizations in ⁵⁸Ni(p,p′x) at 80 MeV, ⁹⁰Zr(p,p′x) and ⁹⁰Zr(p,nx) at 160 MeV by one- and two-step processes are calculated, and the result for ⁵⁸Ni(p,p′x) is compared with experimental data. The calculated spin flip in (p,nx) on ⁹⁰Zr is analyzed in terms of the effects of in-medium modification of the N-N interaction and the contributions of individual components of the effective interaction.

Spin observables have been measured for (p, 2p) reactions aiming at studying medium effects on NN interactions in nuclear field. Observed strong density-dependent reduction of the analyzing power is consistent with a model calculation where reduction of nucleon and meson masses are taken into account. The spin-transfer coefficients , which data are not reproduced by the model calculation, are found to be sensitive to reduction rate of each meson mass and have a possibility to test scaling lows in mass reductions.

A complete set of polarization transfer coefficients has been measured for quasielastic reactions on ²H, ⁶Li, ¹²C, ⁴⁰Ca, and ²⁰⁸Pb at a bombarding energy of 346 MeV and a laboratory scattering angle of 22° (q_lab ≈ 1.7 fm^-1). The spin-longitudinal R_L and spin-transverse R_T response functions are extracted within a framework of a plane wave impulse approximation with eikonal and optimal factorization approximations. The theoretically expected enhancement of R_L/R_T is not observed. The obversed R_L is consistent with the pionic enhanced R_L expected by random phase approximation (RPA) calculations. On the contrary, a large excess of the observed R_T is found in comparison with R_T of RPA calculations. This excess masks the effect of pionic correlations in R_L/R_T.

Cross sections, analyzing powers and spin rotation parameters of proton elastic scattering from ⁵⁸Ni and ¹²⁰Sn have been measured at intermediate energies. In order to explain the ⁵⁸Ni data, it was necessary to use experimental density distributions deduced from charge distributions and to modify coupling constants and masses of σ and ω mesons. Assuming the same modification was also valid for ¹²⁰Sn and using proton densities deduced from charge densities, neutron density distribution was searched so as to reproduce ¹²⁰Sn data.

We measured polarization transfer (PT) observables in ¹²C, ²⁸Si(p,p′) reactions at 0° with 392 MeV proton beams. The obtained PT observables are compared with DWIA calculations. The strength of the isoscalar central spin-dependent interaction (V_σ) is found to be well described in the Franey and Love effective interaction. A model independent signature of spin transfer, named total spin transfer, is deduced from the measured PT observables for several discrete states.

We construct rotation invariants from polarization transfer coefficients which uniquely specify the magnitude of spin-transfer in nuclear reactions. Forward angle values of the invariants are shown to take restricted values and to provide signatures of spin-dependent excitations in the target nucleus. For nucleon inelastic scattering, for instance, the invariant at 0° takes a value -1 for unnatural parity states, while a deviation from the value 3 for natural parity states implies a mixture of spin-dependent excitations. We show this result first within the plane wave approximation. We then perform an analysis of the nucleon-nucleus scattering amplitude and show that the values of the invariants at 0° are determined by the symmetry properties alone for unnatural parity states, thus confirming the plane wave result.

Inelastic scattering of deuterons by nuclei is investigated in the sudden approximation. Cross section and polarization observables are expressed in terms of amplitudes for the corresponding nucleon-nucleus scattering. They consist of the amplitude of the nucleon-nucleus single collision and that of the double collision. The calculation with single collision term is examined for the excitation of ¹²C to the 2⁺(4.44MeV) and 3^-(9.64MeV) states and is found to give a reasonable description for most of the observables. Contributions of the D-state of the deuteron internal motion and effects of the double collision term of scattering amplitudes are studied.

The electromagnetic M1 operator consists of isoscalar and isovector terms, each containing spin and orbital terms. For the M1 γ transitions in T = 1/2 mirror nuclei, it is shown that the contributions of these terms can be decomposed by combining the strength information from analogous M1 and Gamow-Teller transitions under the assumption that the isospin is a good quantum number. As an example of the decomposition, the analysis is made for M1 γ transitions to the ground states of ²⁷Al and ²⁷Si mirror nuclei by combining the Gamow-Teller transition strengths obtained from the β decay and the charge-exchange reaction of ²⁷Al(³He,t)²⁷Si.

Distributions of the spin-dipole and Gamow-Teller strengths in light nuclei are investigated, and related topics on neutrino scattering and reactions are discussed.

We study the spin excitations of nuclei in the relativistic mean field (RMF) theory. In particular, we discuss the Gamow-Teller strengths and the longitudinal and transverse spin responses, the experimental data of which were taken by the Tokyo group at RCNP. The relativistic description of spin excitations does change largely our picture on the spin correlations in nuclei.

IsoScalar Giant Dipole Resonance (ISGDR) is now a very exciting topic because it is directly related to the nuclear incompressibility, thus we can get another way to know its value, adding to Giant Monopole Resonance (GMR). We attempted to observe the ISGDR using 400 MeV α inelastic scattering at RCNP ring cyclotron laboratory. For ⁵⁸Ni, ⁹⁰Zr, ¹¹⁶Sn, ¹⁴⁴Sm, ¹⁵⁴Sm and ²⁰⁸Pb, we measured angular distributions for ISGDR's at extremely forward angles including 0 degrees. Fitting the spectrum of ²⁰⁸Pb, we derived the energy centroid of ISGDR 21.46MeV.

This presentation contains two subjects on the hadron spin polarization. The first is on the interaction to provide the spin asymmetry. The origin producing spin polarization of hadrons in high energy hadron collisions had been interpreted as a spin-orbit type interaction. However after one theoretical work which pointed out failure of the spin-orbit interaction not providing correct P_T dependence of the spin polarizations, its genuine origin becomes obscure. Here we clearly indicate what sort of spin-orbit interaction we should argue and we solve the existing confusion. The second subject is on the spin transfer mechanism in Λ production reactions. We attempt to resolve an anomaly found in the spin observables; presumably zero analyzing power A_N and spin depolarization D_NN of Λ hyperon production reactions from the quark parton recombination model, whereas apparently non zero in the observation.

We study the origin of the spin polarizations observed in inclusive hadron production, considering the dynamics of quarks in the hadronization process. We obtain the non-trivial spin dependence of the production cross section arising from the interference term of the non-perturbative hadronization amplitudes. Results are in good agreement with experiments. We then apply it to the photo- and lepto-production of hyperons, since the hadronization process itself is independent of the beam. We find large polarizations of hyperons in unpolarized γN collision. Sizable asymmetry is also found for the deep inelastic lepton scattering off a transversely polarized nucleon with a pion in the final state.

We show differential cross sections and the spin transfer coefficient D_nn in the reaction for proton bombarding energy at 1 GeV and π⁰ - p invariant masses spanning the region of the N* (1440) Roper resonance. The present calculation demonstrates that the contribution from the Roper resonance can be clearly identified via D_nn, even under kinematic conditions where cross sections alone exhibit no clear peak structure due to the excitation of the Roper.

We review some simple mechanisms of breakup in nuclear reactions. We mention the spectator breakup, which is described in the post-form DWBA. The relation to other formulations is also indicated. An especially important mechanism is Coulomb dissociation. It is a distinct advantage that the perturbation due to the electric field of the nucleus is exactly known. Therefore firm conclusions can be drawn from such measurements. Some new applications of Coulomb dissociation for nuclear astrophysics are discussed.

Brief description is given on the polarizability of the deuteron. Continuum Discretized Coupled Channels method is applied to the problem of deuteron elastic scattering well below the energy of Coulomb barrier. Experimental data are reasonably well reproduced. Effective polarizability of the deuteron is deduced. Importance of ³S₁ and ³D_I break up channels is explained.

The deuteron breakup reaction at intermediate energies (E_d > 100 MeV) and forward angles (θ_p = θ_n ≃ 0°), where the Coulomb breakup is expected to become dominant, is discussed. Effects of post acceleration and nuclear breakup, which are crucial for application of projectile breakup to astrophysical problems, are enhanced in the deuteron breakup, critically dependent on the incident energy and the target. An attempt has been made to describe the reaction on the basis of the post-form DWBA and the adiabatic approximation.

Evidence for quantum tunneling effect was found in the breakup of ⁷Li via continuum states just above the α - t threshold. The quantum tunneling effect was taken into account to investigate re-acceleration of breakup fragments in the target Coulomb field. It is shown that the previously published astrophysical S-factors are most likely Coulomb distorted. A best effort is made to revise S-factors.

We show how single-nucleon removal reactions with polarised beams can provide information about the detailed structure of nuclear haloes. It is shown that different components of the analysing power probe different components of the halo density matrix. We present numerical estimates of the expected analysing power T₂₀ for the case of neutron stripping from an aligned ¹⁷C beam in experiments in which the final state of the ¹⁶C core is identified.

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANC). These coefficients, which provide the normalization of the tail of the overlap function, determine S-factors for direct capture reactions at astro-physical energies. For example the overlap for ⁸B → ⁷Be + p defines the S-factor for ⁷Be(p,γ)⁸B. A variety of proton transfer reactions have been used to measure ANC's. As a test of the technique, the ¹⁶O(³He,d)¹⁷F reaction has been used to determine ANC's for transitions to the ground and first excited states of ¹⁷F. The S-factors for ¹⁶O(p,γ)¹⁷F calculated from these ¹⁷F → ¹⁶O + p ANC's are found to be in very good agreement with recent measurements. Following the same technique, the ¹⁰B(⁷Be,⁸B)⁹Be and ¹⁴N(⁷Be,⁸B)¹³C reactions have been used, along with optical model parameters for the radioactive beams that were obtained from a study of elastic scattering of loosely bound p-shell nuclei, to measure the ANC appropriate for determining ⁷Be(p,γ)⁸B. The results from the two transfer reactions provide an indirect determination of S₁₇(0).

Proton scattering studies from a halo nucleus ¹¹Li are presented which elucidate its unsual structure. The elastic and inelastic ¹¹Li+p scattering data have been analysed in a coupled channel approach with folded potentials. The analysis delineats that elastic scattering is sensitive to the extent of halo structure at lower incident energy at very forward laboratory angles. The inelastic scattering angular distribution is found to be consistent with the idea of a soft dipole resonance characterising a halo nucleus.

We study the equation of state (EOS) of nuclear matter as well as the properties of unstable nuclei for supernova explosion and r-process in the relativistic many body approach. We provide the EOS table that covers the wide range of density, composition and temperature in supernova explosion by the relativistic mean field (RMF) framework, which is based on the relatlvistic Brückner-Hartree-Fock theory and is checked by the experimental data of unstable nuclei. The relatlvistic EOS table, thus obtained, is applied to the hydrodynamical simulations of supernova explosion. We perform also the r-process simulations of the neutrino-driven wind from the proto-neutron star and show that the neutrino-driven wind in supernova explosion is a promising site for the r-process to create heavy elements.

Effects of spin-orbit force and three-nucleon forces on polarization observables of low-energy three-nucleon scattering are investigated.

For the backward elastic scatterings of deuterons by proton and ³He at intermediate energies, tensor analysing power T₂₀ and polarization transfer coefficient κ₀ are analyzed by PWIA with the assumption of one nucleon exchange model. The PWIA results reproduce rough features of the experimental data and explain the difference of the sign of T₂₀ between the cases of the d+p and d + ³He scatterings. Some theoretical extension from the PWIA is made by taking account of the virtual excitation process phenomenologically and it improves the fit to the data.

We have measured the cross sections and the polarization observables for the ³He(d,p)⁴He reaction at E_d =140, 200, and 270 MeV. This work aims to investigate the high momentum component of deuteron D-state wave function and the mechanism for the one-nucleon transfer reaction at intermediate energies. The measurement was carried out by using the spectrograph SMART at RIKEN Accelerator Research Facility. A cryogenic ³He gas target with a density of 6.6 ×10²⁰ cm^-3 was bombarded by a polarized deuteron beam. The data are compared with the calculation based on the one-nucleon exchange approximation and data from the d + p backward scattering.

We have started a series of experiments of hypernuclear γ-ray spectroscopy to study the ΛN spin-dependent interactions via hypernuclear structure. With a germanium detector system which is newly constructed for this purpose (Hyperball), we succeeded in observing two γ transitions [M1(3/2⁺ → 1/2⁺) and E2(5/2⁺ → 1/2⁺)] in at KEK and two E2 transitions (5/2⁺,3/2⁺ → 1/2⁺) in at BNL. The strengths of the ΛN spin-spin and spin-orbit forces are discussed based on those results.

We provide a systematic analysis of the differential cross section, the tensor analyzing power, T₂₀, and the polarization transfer, κ₀, in 0° inclusive A(d,p) breakup at relativistic energy. It is shown that impulse approximation, multiple scattering and Pauli principle at level of constituent quarks in the deuteron are important to explain such data.

We discuss the possibility of finding polarized antiquark flavor asymmetry in Drell-Yan processes. We find that the difference between polarized proton-proton and proton-deuteron Drell-Yan cross sections should provide valuable information on the polarized flavor asymmetry. Numerical results indicate that the asymmetry effects are conspicuous especially in the large-x_F region. Our analysis is important for the transversity distributions because the flavor asymmetry cannot be found by inclusive lepton scattering and W-production processes.

Polarized parton distribution functions are determined by using asymmetry A₁ data from longitudinally polarized deep inelastic scattering experiments. From our χ² analysis, polarized u-valence, d-valence, antiquark, and gluon distributions are obtained. We propose one set of leading-order distributions and two sets of next-to-leading-order ones as the longitudinally-polarized parton distribution functions.

The β-ray angular distributions from purely spin aligned ¹²B and ¹²N were precisely remeasured to determine a new limit of the G-parity irregular induced tensor form factor in weak nucleon axial vector currents and to study the in-medium mass renormalization of nucleons through the axial charge. Since the major systematic error in the previous result which originated from the intensity fluctuation of the incident beam used for the production of the nuclei was removed in the present measurement, the more reliable result was obtained: 0.01 ≤ 2M f_T/f_A ≤ 0.34 (90% CL). The result is consistent with the theoretical prediction in the framework of which induced tensor form factor is proportional to the mass difference between the up and down quarks. We also determined the axial charge of the weak nucleon current to be y = 4.66 ± 0.12, which may disclose an in-medium mass reduction of the decaying nucleon of 11 ± 4%.

We study the properties of SU(N_f) light quarks in the multi-instanton vacuum of QCD. We formulate the dynamical symmetry breaking for light quarks of various numbers of flavor N_f with the inclusion of the instanton size distribution. We find that the quark mass function increases rapidly toward small Euclidean momenta when the finite size distribution is introduced with a power law fall-off of large instanton size, ρ^-n (n > 3). We observe a confining feature of light quarks for small fall-off parameter n and for large packing fraction in the behavior of the quark mass function extrapolated to the time-like region.

Spontaneous magnetization of quark liquid is examined. It is pointed out that quark liquid has potential to be ferromagnetic at rather low densities.

Bose-Einstein condensates and Fermi-degenerated gas are shortly reviewed, especially for trapped Alkali atoms. We also discuss several properties of Boson-Fermion mixed condensates of potassium atoms: static properties, stabilities and collective excitations, which show similar physical properties with those in the meson condensates in high-density nuclear matter or giant resonances of atomic nuclei.

No abstract received.

The following sections are included:

• Symposium program

• List of participants