Use of the momentum representation in the local DWA description of inelastic scattering

doi:10.1016/0375-9474(75)90706-X

Nuclear Physics A

Volume 251, Issue 1, 13 October 1975, Pages 143-155

https://doi.org/10.1016/0375-9474(75)90706-X Get rights and content

Abstract

Applications of a discrete momentum representation in the microscopic description of inelastic scattering are described. Specifically, a method for computing folded form factors is given. This method should be particularly useful in obtaining the double folded form factors required in the microscopic treatment of heavy-ion inelastic scattering. The problem of evaluating the local DWA transition amplitude in momentum space is also examined. It is argued that for many applications this is a useful alternative to the standard coordinate space method.

References (8)

A. Scott et al.
Bull. Am. Phys. Soc.
(1968)
A. Scott, N.P. Mathur, F. Petrovich and G.R. Hammerstein, to be...
D. Robson et al.
Phys. Rev.
(1972)
L.A. Charlton
Phys. Rev.
(1973)
T.H. Lee and F. Tabakin, to be...T.H. Lee
F. Petrovich et al.
Bull. Am. Phys. Soc.
(1974)

There are more references available in the full text version of this article.

Cited by (52)

Stability of matter-antimatter molecules
2011, Annals of Physics
We examine the stability of matter–antimatter molecules by reducing the four-body problem into a simpler two-body problem with residual interactions. We find that matter–antimatter molecules with constituents $(m_{1}^{+}, m_{2}^{-}, {\bar{m}}_{2}^{+}, {\bar{m}}_{1}^{-})$ possess bound states if their constituent mass ratio m₁/m₂ is greater than about 4. This stability condition suggests that the binding of matter–antimatter molecules is a rather common phenomenon. We evaluate the binding energies and eigenstates of matter–antimatter molecules $(μ^{+} e^{-}) - (e^{+} μ^{-}), (π^{+} e^{-}) - (e^{+} π^{-}), (K^{+} e^{-}) - (e^{+} K^{-}), ({pe}^{-}) - (e^{+} \bar{p}), (p μ^{-}) - (μ^{+} \bar{p})$ , and (K⁺μ⁻) − (μ⁺K⁻), which satisfy the stability condition. We estimate the molecular annihilation lifetimes in their s states.
Consistent folding model description of nucleon elastic, inelastic, and charge-exchange scattering from 6,7Li at 25-50 MeV
1993, Nuclear Physics, Section A
The results of a consistent theoretical microscopic single scattering model study of nucleon elastic, inelastic, and charge-exchange scattering from ^6,7Li at E_p(n) = 25–50 MeV are reported. A realistic effective nucleon-nucleon interaction, adopted from the work of Mahaux and collaborators and Bertsch and coworkers, has been employed in the model calculations. The density distributions needed to describe the structure of the mass 6 and 7 systems in the calculations are the same as those used in recent proton-nucleus scattering studies of these targets at E_p = 200 MeV. The present, parameter-free model calculations provide an excellent description of the available low-energy nucleon-nucleus scattering data on ^6,7Li.
Consistent description of the (t, 3He) reaction for A = 12-89
1991, Nuclear Physics, Section A
New differential cross section data for seven target nuclei were analysed using a microscopic model. Particular care was taken to ensure that the absolute magnitude of the cross sections was correctly measured. The predicted direct or one-step (t, ³He) reaction did not account for the magnitude of the data except for forward angles and A⩾40. The calculations were estended to include the contributions from two-step or sequential single-nucleon transfers. Calculations were made using the second-order DWBA and zero-range or full finite-range forms. In the latter the non-orthogonality between the basis states in the two-step transfers was included. The transfer amplitudes were deduced from comparisons of predicted angular distributions with data obtained from the (t, α) and (t, d) reactions, and from amplitudes determined by repeating previously reported shell-model calculations. The full finite-range DWBA calculations which included non-orthogonality terms, accounted for both the shape and magnitude of the data within a factor of 3 in the worst case. The (t, α) reaction angular distributions are, however, poorly predicted.
Further studies of density-dependent interactions for the excitation of collective states
1988, Nuclear Physics, Section A
The density-dependent DDM3Y effective nucleon-nucleon interaction was used in a double-folding model with macroscopic transition densities to explore further density-dependent effects on the inelastic scattering of α-particles and protons. In particular, we investigate whether transition densities with a node near the nuclear surface, such as occurs for the giant monopole (breathing mode) resonance, are particularly sensitive to density dependence in the interaction. We also study the imposition of a consistency condition on the use of density dependence for inelastic scattering. In both situations, the effects are small (≲20%) for α-particles but large for protons. The consistency condition is discussed further in an appendix.
The (3He,t) reaction at intermediate energies: Spin-isospin transitions to states in 12N and 13N
1987, Nuclear Physics, Section A
The (³He, t) reaction has been studied at intermediate energies, 600 MeV–2.3 GeV. The reaction is a single-step direct reaction, and the angular distributions are well described by DWIA calculations. At these energies the σρ component of the interaction dominates. The ratio of the isovector strengths $¦J_{σρ} /_{ρ} ¦$ derived from the data on ¹³C appears to remain roughly constant in the energy range 300–700 MeV per nucleon.
The triton spectra exhibit a prominent quasi-free peak. The data at momentum transfers q ⪢ 1.7 fm⁻¹ show a shift of the peak towards smaller energy loss than observed in (e, e') experiments at corresponding four-momentum transfers. The shift becomes progressively larger with increasing q and is about 45 MeV at q = 2.5 fm⁻¹. The shift may be caused by particle-hole correlations in the spin-longitudinal channel.
Investigation of the one-step direct contribution to the 28Si(18O, 18F)28Al reaction at 19.6 MeV/nucleon
1986, Physics Letters B

View all citing articles on Scopus

^☆: Supported in part by the National Science Foundation Grants no. NSF-GJ-367, NSF-GU-2612, and NSF-GP-41834X.

View full text

Article preview

Nuclear Physics A

Abstract

References (8)

Bull. Am. Phys. Soc.

Phys. Rev.

Phys. Rev.

Bull. Am. Phys. Soc.

Cited by (52)

Stability of matter-antimatter molecules

Consistent folding model description of nucleon elastic, inelastic, and charge-exchange scattering from <sup>6,7</sup>Li at 25-50 MeV

Consistent description of the (t, <sup>3</sup>He) reaction for A = 12-89

Further studies of density-dependent interactions for the excitation of collective states

The (<sup>3</sup>He,t) reaction at intermediate energies: Spin-isospin transitions to states in <sup>12</sup>N and <sup>13</sup>N

Investigation of the one-step direct contribution to the <sup>28</sup>Si(<sup>18</sup>O, <sup>18</sup>F)<sup>28</sup>Al reaction at 19.6 MeV/nucleon

Nuclear Physics A

Use of the momentum representation in the local DWA description of inelastic scattering☆

Abstract

Bull. Am. Phys. Soc.

Phys. Rev.

Phys. Rev.

Bull. Am. Phys. Soc.

Stability of matter-antimatter molecules

Consistent folding model description of nucleon elastic, inelastic, and charge-exchange scattering from <sup>6,7</sup>Li at 25-50 MeV

Consistent description of the (t, <sup>3</sup>He) reaction for A = 12-89

Further studies of density-dependent interactions for the excitation of collective states

The (<sup>3</sup>He,t) reaction at intermediate energies: Spin-isospin transitions to states in <sup>12</sup>N and <sup>13</sup>N

Investigation of the one-step direct contribution to the <sup>28</sup>Si(<sup>18</sup>O, <sup>18</sup>F)<sup>28</sup>Al reaction at 19.6 MeV/nucleon