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Register a new userSurface-integral formalism of deuteron stripping
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The purpose of this paper is to develop an alternative theory of deuteron stripping to resonance states based on the surface integral formalism of Kadyrov et al. [Ann. Phys. 324, 1516 (2009)] and continuum-discretized coupled channels (CDCC). First we demonstrate how the surface integral formalism works in the three-body model and then we consider a more realistic problem in which a composite structure of target nuclei is taken via optical potentials. We explore different choices of channel wave functions and transition operators and show that a conventional CDCC volume matrix element can be written in terms of a surface-integral matrix element, which is peripheral, and an auxiliary matrix element, which determines the contribution of the nuclear interior over the variable $r_{nA}$. This auxiliary matrix element appears due to the inconsistency in treating of the $n-A$ potential: this potential should be real in the final state to support bound states or resonance scattering and complex in the initial state to describe $n-A$ scattering. Our main result is formulation of the theory of the stripping to resonance states using the prior form of the surface integral formalism and CDCC method. It is demonstrated that the conventional CDCC volume matrix element coincides with the surface matrix element, which converges for the stripping to the resonance state. Also the surface representation (over the variable $r_{nA}$ of the stripping matrix element enhances the peripheral part of the amplitude although the internal contribution doesnt disappear and increases with increase of the deuteron energy. We present calculations corroborating our findings for both stripping to the bound state and the resonance.
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Theories of $(d,p)$ reactions frequently use a formalism based on a transition amplitude that is dominated by the components of the total three-body scattering wave function where the spatial separation between the incoming neutron and proton is confined by the range of the $n$-$p$ interaction, $V_{np}$. By comparison with calculations based on the CDCC method we show that the $(d,p)$ transition amplitude is dominated by the first term of the expansion of the three-body wave function in a complete set of Weinberg states. We use the uc{132}{Sn}(d,p) uc{133} {Sn} reaction at 30 and 100 MeV as examples of contemporary interest. The generality of this observed dominance and its implications for future theoretical developments are discussed.
Deuteron-deuteron elastic scattering and transfer reactions in the energy regime above four-nucleon breakup threshold are described by solving exact four-particle equations for transition operators. Several realistic nuclear interaction models are used, including the one with effective many-nucleon forces generated by the explicit $Delta$-isobar excitation; the Coulomb force between protons is taken into account as well. Differential cross sections, deuteron analyzing powers, outgoing nucleon polarization, and deuteron-to-neutron polarization transfer coefficients are calculated at 10 MeV deuteron energy. Overall good agreement with the experimental data is found. The importance of breakup channels is demonstrated.
While it is well established that the ground state reorientation coupling can have a significant influence on the elastic scattering of deformed nuclei, the effect of such couplings on transfer channels has been much less well investigated. In this letter we demonstrate that the 208Pb(7Li,6He)209Bi proton stripping reaction at an incident energy of 52 MeV can be well described by the inclusion of the 7Li ground state reorientation coupling within the coupled channels Born approximation formalism. Full finite-range distorted wave Born approximation calculations were previously found to be unable to describe these data. Addition of coupling to the 0.478-MeV 1/2- excited state of 7Li, together with the associated two-step transfer path, has little or no influence on the shape of the angular distributions (except that for stripping leading to the 1.61-MeV 13/2+ level of 209Bi which is significantly improved) but does affect appreciably the values of the 209Bi -> 208Pb + p spectroscopic factors. Implications for experiments with weakly-bound light radioactive beams are discussed.
It is shown that the ratio of the deuteron and proton analysing powers in proton-deuteron elastic scattering at small angles is sensitive to subtle effects in a theoretical description. These include the transverse spin-spin term in the elementary nucleon-nucleon amplitudes and double-scattering corrections. On the other hand there is far less sensitivity to the spin-orbit amplitude and to binding or other kinematic effects associated with the use of the deuteron, as either target or projectile. The available data are in agreement with the results of a refined Glauber theory model.
Based on Bohr model, we have presented a general formalism describing the collective motion for any deformed system, in which the collective Hamiltonian is expressed as vibrations in the body-fixed frame, rotation of whole system around the laboratory frame, and coupling between vibrations and rotation. Under the condition of decoupling approximation, we have derived the quantized Hamiltonian operator. Based on the operator, we have calculated the rotational spectra for some special octupole and hexadecapole deformed systems, and shown their dependencies on deformation. The result indicates that the contribution of octupole or hexadecapole deformations to the lowest band is regular, while that to higher bands is dramatic. These features reflecting octupole and hexadecapole deformations are helpful to recognize the properties of real nuclei with octupole and/or hexadecapole deformations coexisting with quadrupole deformations.
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