Deuteron Stripping Research Articles

Three-body calculations of elastic scattering and stripping of deuterons on 16O

A calculation is presented in which a reaction of complex nuclei is approximated by a model three-body problem. The results of such a calculation, for elastic scattering and stripping of deuterons from 16O, are compared to the results obtained from conventional distorted-wave Born approximation (DWBA) calculations. Since severe limitations had to be imposed on the three-body calculation, for computational reasons, and the Coulomb force was neglected, the problem is to be considered a model problem. Experimental data were used to guide the selection of the two-body interactions, but the results cannot meaningfully be compared with data. A comparison of the three-body results to those given by the DWBA show qualitatively good agreement in the differential cross sections for both elastic scattering and stripping, but quantitative agreement is obtained only for the elastic scattering results. Polarization observables show no similarity between the two calculations. Several possible reasons for this discrepancy are discussed, but more work is needed to separate various contributing factors.

Deuteron stripping reactions at intermediate energies

The deuteron stripping reaction A(d,p)B is estimated in terms of the cross section for pion production with a proton beam A(p, pi +)B for the same nuclear states A and B. Extending the triangle graph model, which was constructed to explain large-angle proton-deuteron elastic scattering, data on 2H, 3He and 11C are described successfully for deuteron energies of about 800 MeV.

Does deuteron stripping in nuclear collisions test the wave function?

In a simple, parameter-free model for deuteron stripping we calculate the inclusive proton spectrum in the deuteron fragmentation region. The spectrum does not reflect in any simple manner the behavior of the deuteron wave function. We find that in the deuteron rest frame the transverse distribution is substantially wider than the longitudinal one. The physical reasons for this result are discussed. We obtain good agreement with existing data and make predictions for expected ones.

Validity of Neglecting Continuum Contributions in Two-Body Rearrangement Collisions

The neglect of $n$-body breakup contributions, $n>~3$, is a widely used but previously untested approximation occurring in the analysis of almost all atomic, molecular, and nuclear collisions. A simple three-body model of deuteron stripping is used to study this approximation. Below the breakup threshold, use of this approximation accounts for the overall shape of the angular distributions and fits the exact transfer cross section at forward angles. With increasing energies, continuum effects render this approximation much less accurate.

Effects of imaginary potentials in a three-body deuteron-nucleus scattering model

We test the sensitivity of a three-body theory of deuteron-nucleus reactions to the imaginary parts of the nucleon-nucleus potentials on which the theory is based, by switching off the imaginary potentials in a previous approximate three-body model. Absorption due to deuteron breakup tends to replace the omitted optical potential absorption, with the result that the ${l}_{n}=2$ deuteron stripping cross section remains qualitatively unchanged. However, the mechanism of absorption is entirely different.NUCLEAR REACTIONS Scattering theory, effects of imaginary potentials in three-body deuteron-nucleus model.

Three-body model of deuteron breakup and stripping, II

A previously investigated three-body model of the deuteron-nucleus system, limited to relative angular momentum l = 0 for the two active nucleons, is reevaluated. Full attention is given to self-consistency between elastic and breakup channels. Introduction of the reaction of breakup on the elastic channel now reduces the elastic reflection coefficients in low partial waves by nearly a factor of 2 and causes substantial shifts in phase. Breakup amplitudes in low partial waves are also greatly reduced. As before, the breakup part of the wavefunction contains a broad spectrum of n- p continuum states. The breakup part of the wavefunction at zero n- p separation is localized at small radii, within and just outside the target nucleus, where it is comparable in magnitude with the projected elastic channel wavefunction. As a result, the projected elastic channel wavefunction is a poor approximation to the full wavefunction at n- p coincidence. Deuteron stripping theories that use the projected elastic wavefunction in a truncated waves Born series must correspondingly be quite misleading. To investigate deuteron stripping further, the exact result of the coupled channels calculation is compared with several standard approximate models. Although there is a close qualitative resemblance among the results of all the approaches, the best single approximation to the coupled channels result is found from the familiar phenomenological approach, in which a local optical potential is fitted to the elastic scattering “observed” in the coupled channels calculation. The coupled channels results are also used to analyze the approximations in the Johnson-Soper method. Several formal aspects of the three-body model are discussed.

Slowly converging integrals in the analysis of deuteron stripping to decaying states

The slowly converging overlap integral appearing in the distorted wave Born approximation analysis of deuteron stripping to decaying states is treated by employing a Gaussian convergence factor to ensure proper convergence. Numerical results are presented and the usefulness of the above technique in handling stripping overlap integrals in the continuum region is discussed.NUCLEAR REACTIONS $^{32}\mathrm{S}(d, p)$ reactions, unbound state, calculated $\ensuremath{\sigma}({E}_{p}, {\ensuremath{\theta}}_{p})$, ${E}_{D}=12.0$ MeV, method of handling the divergent integrals discussed.

A new approximation for Glauber theory on stripping of relativistic deuterons

Abstract The momentum distribution of forward protons from relativistic collisions of deutrons with nuclei is computed from a Glauber theoretical ansatz of Bertocchi and Tekou. In this paper we approximate the outgoing proton-neutron scattering state (disintegrated deuteron) with a plane wave minus the component of this plane wave along the deuteron bound state vector. With no fitted parameters we find good agreement with data from the reaction d+C 12 →p+X in the region corresponding to non-relativistic Fermi momenta in the forward direction. At more relativistic Fermi momenta, the model deviates more from the data, which can be due to an incorrect choice of the short distance part of the deuteron wave function as well as to off-shell effects in the deuteron.

A comparison between exact and DWBA stripping to a resonance

Exact cross sections for deuteron stripping to a resonance from a heavy target were obtained by solving the Faddeev-Lovelace equations for separable s-wave potentials. The s-wave resonance in the neutron-target subsystem is described by an energy-dependent term in the potential, of the type arising from a BSEC. The DWBA is derived without recourse to an adjustable optical potential. The DWBA and exact cross section, without the background contribution, are evaluated and compared. Interference effects between the resonance and background amplitudes turned out to be important and of the kind observed experimentally.

Deuteron stripping reactions with the Tabakin potential

Deuteron stripping reactions are considered. Due to the strong repulsion between nucleons at very short distances, we have investigated the nuclear short-range correlations. The neutron-proton nuclear potential in the deuteron is taken as a short-range repulsive core surrounded by a long-range attractive potential. The neutron-proton potential is taken as the Tabakin separable potential to take into account the short-range correlations. The differential cross-sections for deuteron stripping reactions have been calculated in two different cases by taking Yamaguchi or Breitet al. type parameters for the Tabakin potential used. The angular distributions for different (d, p) stripping reactions on the different target nuclei28Si,32,34S,36Ar,40,48Ca,50,52,54Cr have been calculated by means of the DWBA calculations. Our present theoretical calculations for the angular distributions of the different reactions considered have been fitted to the experimental data, with which good agreement is obtained. The extracted spectroscopic factors from the present work are found to be more reliable.

Stripping-theory analysis of thick-target neutron production for D+Be (and tissue dose calculation)

The Serber theory for deuteron stripping is employed to predict the shape of the neutron energy spectrum produced by 35 MeV deuterons (D+) on a thick beryllium target. In particular, the observation that the maximum of the neutron energy spectrum (at O degrees relative to the deuteron beam direction) occurs at approximately 0.4Ed, where Ed is the incident deuteron energy, is explained reasonably well by the calculations. The application of this theory also accounts for the previously observed Ed2.99 dependence of the absorbed dose in tissue, per unit charge of D+ ions on target, in the direction of the incident beam. This approximate Ed3 dependence is shown to be a characteristic property of deuteron stripping in a thick target and follows directly from the calculations that predict the neutron energy spectrum.

Coulomb (d, p) stripping reactions

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 by considering three cases, according to the incident-deuteron and outgoing-proton energies. The agreement between our theoretical calculations and the experimental data is satisfactory. By fitting our theoretical calculations with the experimental data, more reliable values for the spectroscopic factors are extracted.

Neutron spectrum at 0° from 83.7 MeV deuterons on beryllium

The neutron spectrum measured at 0\ifmmode^\circ\else\textdegree\fi{} from 83.7 MeV deuteron bombardment of a thick beryllium target is bell-shaped with a peak at about 34 MeV and a full width at half maximum of about 22 MeV. Measurements down to 4 MeV show no indication of an evaporation peak. While the shape of the spectrum calculated on the basis of the Serber model for deuteron stripping is similar to the observed shape, the width of the calculated spectrum is broader than that observed. The broadening occurs primarily on the low-energy side of the spectrum. The same features are revealed in further calculations of the 0\ifmmode^\circ\else\textdegree\fi{} spectrum from 53.8 MeV deuterons on a thick beryllium target.

Deuteron stripping reaction to unbound states

Two features of the (d, p) stripping reaction to the continuum, the parallelism between the excitation functions of energy-differential stripping cross section d/sup 2/sigma/d..cap omega..dE and the total neutron-target elastic scattering cross section delta/sub tot/(n n), and the dependence of the ratio (d/sup 2/sigma/d..cap omega..dE) sigma/sub tot/(n, n) on transferred angular momentum (1), are explained satisfactorily by a plane wave Butler approximation for a /sup 32/S target nucleus. It appears that the l dependence of the above ratio is so dominant that even the crude Bulter approximation suffices for identification of l values. The (d, p) and (d, n) angular distributions are also calculated with experiment and with these obtained by distorted wave Born approximation method employing an extrapolation technique to treat the neutron wave in the continuum. (AIP)

Spectroscopic factors for (d,p) stripping reactions with different repulsive core nucleon-nucleon potentials

Deuteron stripping reactions are considered. The short-range correlations for the nucleons in the nuclei are taken into account. The neutron-proton nuclear potential in the deuteron is taken as a long-range attractive potential surrounded by a short-range repulsive potential. We take different forms for the two parts of the neutron-proton nuclear potential. The differential cross sections for the two nuclear reactions $^{28}\mathrm{Si}(d,p)^{29}\mathrm{Si}$ and $^{40}\mathrm{Ca}(d,p)^{41}\mathrm{Ca}$ have been calculated for each of the nuclear potential forms. Fitting our theoretical calculations, with the experimental data, using the distorted-wave Born-approximation calculations, a good agreement is obtained. The more reliable spectroscopic factors for these reactions have been extracted.NUCLEAR REACTIONS $^{28}\mathrm{Si}(d,p)$, $E=18.0$ MeV; $^{40}\mathrm{Ca}(d,p)$, $E=7.0$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; optical-model parameters; DWBA analysis; extracted spectroscopic factors.

11C total production cross section in n 12C interactions between 1 and 2 GeV/c

A quasi-monokinetic neutron beam, obtained by deuteron stripping has been used to measure the 12C(n, X) 11C cross section, for fifteen incident neutron momenta between 1 and 2 GeV/ c. The absolute calibration of the incident neutron intensity was obtained by measuring the rate of the reaction np→d π 0 of known cross-section. The cross-section σ(n, X) for the 12C(n, X) 11C reaction was determined by a measurement of the 11C's β + activity.

Nuclear rearrangement scattering. II scattering of composite projectiles with application to deuteron elastic scattering, the deuteron optical model, and deuteron stripping

Methods developed for the description of scattering from correlated nuclei and applied previously to the elastic scattering of nucleons, and to quasifree ( p, 2 p) reactions, are extended to include the possibility of describing composite nuclear projectiles. These methods are then applied to obtain a unified description of deuteron scattering. We consider the elastic and the stripping final channels explicitly. The correlated structure of the deuteron and of the target nucleus and the influence of these correlations on the off-shell character of the appropriate channel interactions are taken fully into account. So too are the Pauli and exchange effects due to the identity of the nucleons of the deuteron and the target nucleus. Our methods, however, do not contain any treatment of target recoil effects. The theory leads to a two-potential formulation for the optical potential for deuteron elastic scattering. The first potential describes the deuteron breakup and scattering resulting from the Pauli principle as it applies to the constituents of the target and is expressed entirely in terms of well-behaved quantities, even in the case of singular nucleon-nucleon interactions. The second potential contains the remaining deuteron-nucleus interaction and is evaluated in terms of a fully renormalized perturbation expansion. While this expansion involves the usual Brueckner reaction matrices and occupation probabilities for the bound orbitals it cannot in general be expressed solely in terms of such quantities. It requires the introduction of more complicated two-body interaction matrices as well. These are quite distinct from the reaction matrix because they involve the entire two-body Hamiltonian and because the projction operator accompanying the intermediate state propogator cannot be factorized into a product of one-body projection operators. At high energy, however, the latter interaction becomes negligible and, to lowest order, the deuteron optical potential reduces to the sum of two one-body optical potentials, as expected. The correct energy dependence of these potentials is explicitly exhibited. Deuteron stripping is also discussed in some detail within the context of our formalism. We obtain the lowest-order expression for the stripping amplitude and we indicate a certain class of corrections to this lowest-order term. The various approximations which are necessary to make contact with phenomenological distorted-wave treatments are indicated.

Test of a relation between deuteron stripping to unbound levels and elastic scattering measurements

The work concerns a simple 'model-independent' approximation to the energy-differential cross section d2 sigma /dEd Omega for a stripping reaction A(d,p)B* into the continuum. For specified angular momentum of B*, this is given by a single-particle cross section calculable with DWBA, multiplied by sin2 delta , where delta is the phase shift for n-A scattering at a corresponding energy. Though previously applied only to isolated resonances in B*, and for the cross section integrated over energy, the approximation is tested in detail and as to absolute magnitude across two broad, overlapping resonances of the same spin and parity. Experimental phase shifts of Demanins et al. (1971) for n-12C scattering are used to calculate the spectra of protons as observed by Darden et al. (1973) at various angles in the 12C(d,p)13C* reaction. The principal resonances in 13C are two d3/2 ones, levels 7 and 8. Agreement between calculated and observed spectra is quite good. The spectroscopic factors of the levels are discussed.

Nuclear rearrangement scattering. II: Scattering of composite projectiles with application to deuteron elastic scattering, the deuteron optical model, and deuteron stripping: Robert R. Scheerbaum. Department of Physics, Texas A&M University, College Station, Texas 77843, and C. M. Shakin. Lawrence Livermore Laboratory, University of California, Livermore, California 94550

Nuclear rearrangement scattering. II: Scattering of composite projectiles with application to deuteron elastic scattering, the deuteron optical model, and deuteron stripping: Robert R. Scheerbaum. Department of Physics, Texas A&M University, College Station, Texas 77843, and C. M. Shakin. Lawrence Livermore Laboratory, University of California, Livermore, California 94550

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 s = 1 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 3 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.