Elastic scattering of 56 MeV polarized deuterons on 4He

The differential cross section and the vector and tensor analyzing powers A_y, A_xx, A_yy and A_xz were measured for the d-⁴He elastic scattering at 56 MeV. The measurement of A_xz was performed using a deuteron beam polarized in the horizontal plane. An optical-model analysis of the experimental data was carried out. The magnitude of the tensor analyzing powers could not be reproduced without the tensor potential. By including the T_R type tensor potential, the optical-model calculations give a reasonable reproduction of the experimental data at θ_c.m. < 120°. The obtained T_R tensor potential was much stronger than that predicted by the folding model. The strength of the real T_R potential was roughly in accordance with that obtained from the optical-model analysis of d-⁴He elastic scattering at 20.2 MeV.     

Spectroscopy of the 50Cr(d, p)51Cr reaction and the deuteron D-state effects

Analyzing powers (T₁₁, T₂₀ and T₂₂) were measured for the (d, p) reaction leading to several states of ⁵¹Cr using 12.3 MeV polarized deuterons. The experimental results were analyzed in terms of distorted-wave theory with the inclusion of the deuteron D-state. Spin assignments to several states of ⁵¹Cr were made on the basis of j-dependence of the vector and tensor analyzing powers.     

Deuteron d-state effects for the reactions 117Sn(d, p)118Sn and 119Sn(d, p)120Sn

Angular distributions of the differential cross section and the three tensor analyzing powers were measured for the reactions ¹¹⁷Sn($\text{d}$, p)¹¹⁸Sn and ¹¹⁹Sn($\text{d}$, p)¹²⁰Sn at E_d = 12 MeV. In addition, excitation functions of the tensor analyzing power T₂₀ were measured at proton lab angles of 0° and 5° for energies ranging from 10 to 12 MeV. At forward angles, the tensor analyzing powers for the ground state (l_n = 0) transitions are more than an order of magnitude larger than the predictions of distorted-wave calculations which neglect the deuteron D-state. Qualitative agreement with the measurements is obtained when the D-state is included.     

Measurement of the tensor analyzing power components in the coherent photoproduction of a π 0 meson on a deuteron

The components of the tensor analyzing powers, T ₂₀, T ₂₁, and T ₂₂, of the coherent photoproduction of a π₀ meson on a deuteron have been measured for photon energies of 250–450 MeV and pion emission angles of 90°–145°. The results are compared with the theoretical predictions.     

Analyzing powers Ayy , Axx , Axz and Ay in the dd → 3Hen reaction at 270 MeV

The data on the tensor A_yy, A_xx, A_xz and vector A_y analyzing powers in the dd → ^3Hen obtained at T _d = 270 MeV in the angular range 0^° - 110^° in the c.m. are presented. The observed negative sign of the tensor analyzing powers A_yy, A_xx and A_xz at small angles clearly demonstrate the sensitivity to the ratio of the D - and S -wave component of the ³He wave function. However, the one-nucleon exchange calculations by using the standard ³He wave functions have failed to reproduce the strong variation of the tensor analyzing powers as a function of the angle in the c.m.     

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.     

Analysis of scattering and reactions of aligned7Li-nuclei in a double folding model

Previously measured angular distributions of the differential cross section and the tensor analyzing powerT ₂₀ for the scattering of⁷Li from⁵¹V in the energy range from 10 to 18 MeV were analyzed with the double folding model using the effective nucleon-nucleon interaction M3Y as well as a zero range effective nucleon-nucleon interaction. Due to the spectroscopic deformation of the⁷Li-nucleus the interaction potential contains a central and aT _R -tensor part. The latter one is the origin of the observed tensor analyzing powers. Within the same model the scattering of aligned⁷Li-nuclei from⁵⁸Ni at 14.2 and 20.3 MeV is well described. The strength of theT _R -tensor potential in relation to the spectroscopic mass deformation of⁷Li is discussed. Using the real interaction potential obtained by the double folding model the energy dependence of the total reaction cross sectionσ ^r and its tensor analyzing powerT ₂₀ ^r for the system⁷Li?⁵¹V is well described within a barrier penetration model.     

Alpha-particle D-state and configuration-mixing effects in the 89Y(d, α)87Sr reaction

Angular distributions of cross sections and vector and tensor analyzing powers have been measured for low-lying levels populated by ⁸⁹Y(d, α)⁸⁷Sr reaction at 9.0, 12.0, and 16.0 MeV. Full finite-range DWBA calculations that include the effects of an α-particle D-state component and (L, J) mixing have been performed. The ground-state transition indicates that the D-state parameter D₂ = −0.30 ± 0.1 fm². The angular distributions of the tensor analyzing powers are very sensitive to the magnitude and sign of the mixing amplitudes and can be used to determine the neutron-proton configurations transferred. The mixing amplitudes for the 0.388 MeV and 0.873 MeV states in ⁸⁷Sr are established from the analysis.     

The three-nucleon system near the N-d threshold

The three-nucleon system is studied at energies a few hundred keV above the N-d threshold. Measurements of the tensor analyzing powers T₂₀ and T₂₁ for p-d elastic scattering at E_c.m. = 432 keV are presented together with the corresponding theoretical predictions. The calculations are extended to very low energies since they are useful for extracting the p-d scattering lengths from the experimental data. The interaction considered here is the Argonne V18 potential plus the Urbana three-nucleon potential. The calculation of the asymptotic D- to S-state ratio for ³H and ³He, for which recent experimental results are available, is also presented.     

Angular dependences of the tensor analyzing powers in the dd → 3Hen reaction at intermediate energies

The tensor analyzing powers A _yy, A _xx, and A _xx in the dd → ³Hen reaction at intermediate energies are considered in the framework of the one-nucleon-exchange approximation. Their strong sensitivity to the ³He and deuteron spin structure at short distances is shown.     

Elastic and inelastic scattering of 15 MeV polarized deuterons from isotopes of Ca,Cu, Sr,Zr, and Mo

The elastic and inelastic scattering of 15 MeV polarized deuterons from ⁴⁸Ca, ⁶³Cu, ⁸⁸Sr, ⁹⁰Zr, ⁹²Zr, and ⁹²Mo has been investigated. Angular distributions of the cross section and vector analyzing power iT₁₁ have been measured for all these nuclei; the tensor analyzing powers T₂₀ and T₂₂ have been studied for ⁹²Zr. Cross sections and vector analyzing powers are generally well explained by the optical model for elastic scattering and by the DWBA with a macroscopic form factor for the inelastic scattering; this is consistent with previous work. Distributions for ⁴⁸Ca, however, are poorly fitted. Anomalous behavior of the N = 50 nuclei found in the inelastic scattering of polarized protons is not present for deuterons. Tensor analyzing powers are not well explained by standard procedures: use of approximate folding model optical parameters did not improve the fits. The distribution of iT₁₁ for the $\text{1}\text{2}$^? state in ⁶³Cu is significantly different from the distributions for the $\text{5}\text{2}$^? and $\text{7}\text{2}$^? states.     

Tensor interactions and polarization phenomena in heavy-ion scattering

Elastic and inelastic scattering of ⁷Li by ⁵⁸Ni at E_lab = 14.2 and 20.3 MeV is investigated theoretically, special emphasis being laid on polarization phenomena. A parameter-independent study shows second-rank tensor interactions to be the main origin of tensor analyzing powers for both elastic and inelastic scattering. Coupled-channel (CC) calculations using cluster-folding interactions which include the tensor terms are found to be successful in reproducing the data for cross sections and vector and tensor analyzing powers, when projectile excitation effects are sufficiently taken into account. Scattering of ⁶Li by ⁵⁸Ni at E_lab = 20.0 MeV is also investigated by the CC calculation, where successes similar to the ⁷Li case are obtained in understanding experimental data.     

The 4He(d, αp)n reaction at 12 and 17 MeV

The cross section and the analyzing powers A_y, A_xx and A_yy for the reaction ⁴He($\text{d}$, αp)n are studied with kinematically complete measurements at incident energies of 12 and 17 MeV. Spectral structures due to the final-state interactions and quasifree scattering are measured. A three-body model of the Faddeev type gives a satisfactory fit to the cross-section and A_y data, but it fails to fit adequately the tensor analyzing-power data. The tensor analyzing powers in the breakup process should be sensitive to the input two-body force, and that sensitivity seems to be somewhat greater near the three-body 1⁺ resonance.     

Scattering of polarized 7Li by 120Sn and projectile-target spin-dependent interactions

Scattering of ⁷Li by ¹²⁰Sn targets at E_lab = 44 MeV is investigated in the coupled-channel frame by taking account of the projectile virtual excitations to the lowest three excited states. Calculations are performed by the cluster-folding (CF) interactions and the double-folding (DF) one. Both interactions reproduce very well the experimental data on the cross section, the vector analyzing power, the second-rank tensor ones and the third-rank tensor one in elastic and projectile inelastic scattering, although some differences are found between the CF results and the DF ones. In the calculation, the virtual excitations of the projectile are important for most of the analyzing powers and the spin-orbit interaction is indispensable for the vector analyzing power. These features are in contrast to those in ⁷Li-⁵⁸Ni scattering at 20 MeV and are interpreted as over-Coulomb-barrier effects. The scattering amplitudes and the analyzing powers are investigated by the invariant amplitude method, which provides a key connecting the spin-dependent interactions to the analyzing powers. The method proposes an important relationship between the tensor analyzing powers, which is useful in analyses of both theoretical and experimental results. Finally, it is found that in the elastic scattering the second-rank tensor analyzing powers are proportional to the strength of the second-rank tensor interaction and the vector and third-rank tensor analyzing powers to the square or cube of the strength of this interaction, while in the inelastic scattering the cross section is proportional to the square of the strength of the tensor interaction, other quantities being weakly dependent on the strength.     

Measurement of the analyzing power of the 3He(d, p)4He reaction below 1 MeV

The analyzing powers iT₁₁, T₂₀, T₂₁ and T₂₂ have been measured for the reaction ³He(d, p)⁴He at laboratory energies of 344, 465 and 727 keV. A polarized deuteron beam was used with quantization axis oriented perpendicular to and at 54.7° to the incident beam direction. With semi-conductor proton detectors in two perpendicular planes all four analyzing powers could be determined. The beam polarization was determined using the ³H(d, n)⁴He reaction at a mean energy of 130 keV. The uncertainty in this analyzing power and the effect on the results is discussed. The analyzing powers have been fitted to a Legendre polynomial expansion to four or five terms and the resulting coefficients tabulated. The results indicate that d-waves contribute to the reaction only through the ${}^4\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ entrance channel and their contribution falls off both above and below the $\text{3}\text{2}{}^{\mathrm{+}}$ resonance at 430 keV.     

Tensor analysing powers of (d,p) reactions on 28Si, 67Zn, 90Zr and 208Pb at 12.3 MeV

The tensor analysing powers T₂₀ and T₂₂ of(d, p) reactions leading to several states of the final nuclei ²⁹Si, ⁶⁸Zn, ⁹¹Zr and ²⁰⁹Pb were measured at 12.3 MeV deuteron beam energy. The measured tensor analysing powers together with the vector analysing power and cross-section data are compared with DWBA calculations with and without the deuteron D-state. The D-state effects and j-dependence of the tensor analysing powers are discussed. The spin transfers involved in populating the 1.08, 1.88 and 3.30 MeV states in ⁶⁸Zn in the ⁶⁷Zn(d, p)⁶⁸Zn reaction are deduced to be predominantly $\text{1}\text{2}{}^{\mathrm{?}}$. This implies an assignment for the 3.287 MeV level of ⁶⁸Zn of J^π = 2⁺.     

Elastic scattering of polarized deuterons by protons at intermediate energies

The tensor analyzing power T₂₀(θ) in dp backward scattering has been measured at or near center-of-mass angle θ = 180° in the energy range 0.3–2.3 GeV. A pronounced structure is observed around T_d = 0.5 GeV which is explained by a predominant one-neutron-exchange mechanism. Other structures appear around 1 GeV and higher. They are not explained by calculations which include Δ-excitations in intermediate states. In addition, full angular distributions of vector A_y and tensor A_yy analyzing powers and differential cross sections have been obtained at 1.2 GeV and limited angular ranges explored at 0.5 GeV (back angles) and 1.6 GeV (forward angles).