The deuteron D-state probability

A method of direct determination of the deuteron D-state probability from the experiment, based on the d ↑ p → ppn reaction analyzis is suggested. Using the known results on the vector analyzing power in elastic NN-scattering, the values of the overall nucleon polarization and the deuteron vector polarization have been obtained. The probability of the deuteron D-state is estimated to be w _D = 0.078 ± 0.046.     

Polarization transfer in deuteron stripping reactions

Polarization phenomena involving the spins of a and b in the A(a, b)B reaction are discussed using a complete set of irreducible tensors carrying definite spin transfer. The linear model independent equations relating the cross section and the polarization observables with these tensors are shown to be particularly appropriate for the study of spin dependent interactions, preferentially associated with particular values of spin transfer. The DWBA theory of polarization transfer in deuteron stripping reactions is thoroughly discussed and among the 17 polarization observables we distinguish those likely to be more sensitive to spin dependent distortion, to have stronger deuteron D-state effects, to exhibit the sign-rule j-dependence and other forms of j-dependence. For certain deuteron polarizations, when the spin transfer is pure $\text{s =}\text{1}\text{2}$, it is shown that deuteron stripping reactions are transparent to vector polarization transfer and the outgoing nucléon polarization independent of scattering angle and deuteron energy. DWBA calculations including contributions from spin transfer $\text{3}\text{2}$ through the deuteron D-state and spin-orbit distortion show that polarization transfer in such deuteron polarizations can be explored as a method of producing fast polarized neutrons with known polarization.     

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.     

The differential cross section and polarization in p + p → d + π+

A coupled-channels approach is used for incorporating NΔ configurations into the mechanism of the meson production reaction p + p → d + π⁺. The differential cross section and the polarization asymmetry are calculated for lab energies ranging from threshold to 750 MeV including the partial waves up to f-wave pions and ³F state nucleons. It is found that the pp state ³F₃ is important in obtaining a reasonable agreement with the existing experimental data. We find a remarkable insensitivity of the differential cross section to the D-state probability of the deuteron, whereas the polarization is somewhat dependent on this.     

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.     

The reaction p + p → d + π+ with a polarized beam and target

Using the method of coupled channels to incorporate NΔ intermediate states into the reaction p + p → d + π⁺ we calculate the differential cross sections, when both the beam and the target are polarized. The results for yy-polarized initial state are given in some detail at 580 MeV. We propose the use of the differential cross section with initial longitudinal polarizations to investigate the D-state probability of the deuteron, P_D. This quantity is found to be very sensitive to P_D.     

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⁺.     

Analysis of large angle p-d elastic scattering: 100–400 MeV

An analysis is presented of large angle proton-deuteron elastic scattering experiments at deuteron energies of 291, 362 and 433 MeV and proton energies of 140 and 316 MeVon the basis of the Kerman-Kisslinger (KK) model (first order). Further analysis is made using the KK model with second order corrections included. The object of the analysis is to determine quantitatively the sensitivity of large angle scattering to the D-state probability (P_D) in the deuteron. It is found that the KK model (first order and also second order corrections included) is not very successful in fitting the data at those energies when used with existing wavefunctions obtained from phenomenological potentials. A value of 6.7% for P_D gives the best fit when the model is used with the modified Moravcsik analytic fit to the Gartenhaus S-state wavefunction (the third approximation). The incoherent contributions of first and second order non-exchange processes are roughly estimated and found to be negligible. An investigation of the ambiguities in the S-state part of the deuteron wavefunction is also presented.     

Polarimetry of the polarized proton and deuteron beams at intermediate energies

Method and results of the beam polarization measurements are presented. The measurements were carried out at the proton polarized beam of Saturne-II accelerator as well as at the JINR (Dubna) synchrophasotron vector polarized deuteron beam. The analysis of the elastic (quasi-elastic) pp-scattering polarization is used as a method of the polarization measurements. The energy range of the measurement is 1.0≤T _p ≤2.8 GeV for polarized proton and 1.66≤T _d ≤7.3 GeV for polarized deuteron beams.     

Polarization of protons in C12(d,p)C13 reaction

The angular distributions of the polarization of protons from C¹²(d,p)C¹³(g.s) reaction were measured at 200 keV intervals for deuteron energies from 1.40 to 2.40 MeV. Elastic scattering on C¹² at 45 ° (lab) was used to analyze the polarization. Positive sign of the polarization corresponds to the vector productK _d ×K _p . The maximum polarization observed is about 30%. The results are not similar to those obtained from the mirror reaction C¹²(d,n)N¹³ in the same deuteron energy range.     

Elastic scattering of vector polarized deuterons by 4He

The vector analyzing power iT₁₁ for deuterons elastically scattered by ⁴He has been measured for c.m. angles between 51.8° and 158.9° and deuteron energies in the range 11.5 to 17 MeV. The results show that d-α scattering is a convenient analyzer for deuteron vector polarization in the energy range investigated, since the angular dependence of iT₁₁ is fairly insensitive to energy and the magnitude of iT₁₁ is quite large at some angles.     

The two-body photodisintegration of the 3He nucleus

The two-body photodisintegration of ³He is calculated using ³He and proton-deuteron wave functions obtained by assuming a separable interaction for the two-nucleon t-matrix. We show that the isotropic component of the cross section is unlikely to yield useful information on the D-state probability densities of the deuteron and ³He. A detailed comparison is made with the data on the cross section at 90°. The separable approximation can account for some of the experimental results, but other experiments suggest that a more sophisticated treatment of the nuclear interactions and wave functions is necessary.     

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.     

Polarization of protons from the Be(d,p)Be reaction at Ed = 12.0 MeV

The polarization of protons from the ⁹Be(d,p)¹⁰Be reaction at E_d = 12.0 MeV was measured for the ground state and first excited state transitions. The results obtained are compared with the predictions of DWBA theory. It was found that better fits to the experimental data can be obtained using volume absorption in the distorting potential of the deuteron elastic channel. A comparison of the present polarization data with the vector analysing power for the same reaction and the same incident deuteron energy has also been made.     

Theoretical study of deuteron polarization in γ+d → π0+d

The state of polarization of the recoil deuteron in γ+d → π⁰+d on unpolarized and target polarized deuterons is analyzed in detail. A new set of statistical tensors is introduced to describe non-oriented systems, such as the recoil deuteron in γ+d → π⁰+d, and their relationships to the vector and tensor polarization parameters are established. The new statistical tensors reduce, in the case of oriented systems, to Fano's statistical tensors. Numerical results are computed using two different deuteron models for polarized photon asymmetry, polarized target asymmetry and the vector and tensor polarizations of the recoil deuteron, and these are presented at various c.m. pion production angles at different energies in the region of the first π-N resonance. The study of these parameters is suggested as a promising source of information on isoscalar pion photoproduction amplitudes.     

OBEP and eikonal form factor: (II). Nuclear matter results

Nuclear matter properties are calculated in a first-order Brueckner-Bethe calculation using a one-boson exchange potential recently proposed by the authors, in which the phenomenological cutoff of dipole type used so far has been replaced by a form factor obtained from an eikonal approximation to multiple vector meson exchange processes. We find ?23.5 MeV saturation energy at a Fermi momentum k_F = 1.77 fm^?1, i.e. about 12 MeV more binding than realistic OBEP using dipole-type cutoffs and about 8 MeV overbinding compared to the empirical value of 16 MeV. On the other hand, estimates suggest that, compared to the Reid soft-core potential, this new OBEP predicts about 1.5 MeV more binding in the case of the triton and about 4 MeV more binding in the case of ¹⁶O, i.e. gives nearly the correct empirical result. The additional binding is traced back to the small deuteron D-state probability of 4.32% predicted by this OBEP, which is a consequence of the special structure of the eikonal form factor. However, taking the effect of the Δ-resonance into account recently given by Green and Niskanen, one arrives at ?14 MeV saturation energy for nuclear matter at k_F = 1.36 fm^?1, whereas the results for the triton and ¹⁶O are changed to a negligible extent only.     

Polarization transfer in the deuteron break-up reaction at 56 MeV

The polarization transfer coefficients K^yy′ of the break-up spectra in the reactions ¹²C, ⁵⁸Ni, ²⁰⁹Bi($\text{d}$, $\text{p}$X) were measured at 56 MeV. In the forwardd angles (13.5° and 20.0°), the K_y^y′ data at the break-up peak are nearly equal to $\text{2}\text{3}$ (the spectator model prediction) and they decrease at both sides of the peak. The deviation due to the deuteron D-state is estimated, using PWBA and DWBA.     

Form factors and polarization in the elasticeD-scattering with inclusion of meson and quark degrees of freedom in a deuteron

A detailed analysis is made of the pair,ρπγ-currents, retardation effects and six-quark admixtures to the charge, quadrupole form factors and to the deuteron polarization. It is shown that the elasticeD-scattering cross section allowing for the meson exchange currents can be described by introducing a six-quark admixture with probability 3.5%. It is predicted that the behaviour of the deuteron polarization tensor at q>4 fm^?1 essentially depends on 6q-admixture.