1,631 research outputs found
Spin 1 inversion: a Majorana tensor force for deuteron alpha scattering
We demonstrate, for the first time, successful S-matrix to potential
inversion for spin one projectiles with non-diagonal yielding a
interaction. The method is a generalization of the
iterative-perturbative, IP, method. We present a test case indicating the
degree of uniqueness of the potential. The method is adapted, using established
procedures, into direct observable to potential inversion, fitting ,
, , and for d + alpha scattering over
a range of energies near 10 MeV. The interaction which we find is
very different from that proposed elsewhere, both real and imaginary parts
being very different for odd and even parity channels.Comment: 7 pages Revtex, 4 ps figure
Evidence for <i>L</i>-dependence generated by channel coupling: <sup>16</sup>O scattering from <sup>12</sup>C at 115.9 MeV
Background: In earlier work, inversion of S matrix for 330 MeV 16O on 12C resulted in highly undulatory potentials; the S matrix resulted from the inclusion of strong coupling to states of projectile and target nuclei. L-independent S-matrix equivalent potentials for other explicitly L-dependent potentials have been found to be undulatory.
Purpose: To investigate the possible implications of the undulatory dynamic polarization potential for an underlying L dependence of the 16O on 12C optical potential.
Methods: S matrix to potential, SL
→ V (r), inversion which yields local potentials that reproduce the elastic channel S matrix of coupled channel (CC) calculations, will be applied to the S matrix for 115.9 MeV 16O on 12C. Further, SL for explicitly L-dependent potentials are inverted and the resulting L-independent potentials are characterized and compared with the undulatory potentials found for 16O on 12C.
Results: Some of the undulatory features exhibited by the potentials modified by channel coupling for 115.9 MeV 16O on 12C can be simulated by simple parameterized L-dependent potentials.
Conclusions: The elastic scattering of 16O by 12C is a particularly favorable case for revealing the effective L dependence of the potential modified by channel coupling. Nevertheless, there is no reason to suppose that
undularity is not a generic property leading in many cases to the choice: nucleus-nucleus potentials are (i) smooth and L-dependent, (ii) L-independent and undulatory, or (iii) both
Investigation of the Coupling Potential by means of S-matrix Inversion
We investigate the inelastic coupling interaction by studying its effect on
the elastic scattering potential as determined by inverting the elastic
scattering -matrix. We first address the effect upon the real and imaginary
elastic potentials of including excited states of the target nucleus. We then
investigate the effect of a recently introduced novel coupling potential which
has been remarkably successful in reproducing the experimental data for the
C+C, C+Mg and O+Si reactions over a
wide range of energies. This coupling potential has the effect of deepening the
real elastic potential in the surface region, thereby explaining a common
feature of many phenomenological potentials. It is suggested that one can
relate this deepening to the super-deformed state of the compound nucleus,
Mg.Comment: 12 pages with 3 figure
Emergence of a secondary rainbow and the dynamical polarization potential for <sup>16</sup>O on <sup>12</sup>C at 330 MeV
Background: It was shown recently that an anomaly in the elastic scattering of 16O on 12C at around 300 MeV is resolved by including within the scattering model the inelastic excitation of specific collective excitations of both nuclei, leading to a secondary rainbow. There is very little systematic knowledge concerning the contribution of collective excitations to the interaction between nuclei, particularly in the overlap region when neither interacting nuclei are light nuclei.
Purpose: Our goals are to study the dynamic polarization potential (DPP) generated by channel coupling that has been experimentally validated for a case (16O on 12C at around 300 MeV) where scattering is sensitive to the nuclear potential over a wide radial range; to exhibit evidence of the nonlocality due to collective coupling; to validate, or otherwise invalidate, the representation of the DPP by uniform renormalizing folding models or global potentials.
Methods: S-matrix to potential, SL → V (r), inversion yields local potentials that reproduce the elastic channel S matrix of coupled channel calculations. Subtracting the elastic channel uncoupled potential yields a local L-independent representation of the DPP. The dependence of the DPP on the nature of the coupled states and other parameters can be studied.
Results: Local DPPs were found due to the excitation of 12C and the combined excitation of 16O and 12C. The radial forms were different for the two cases, but each were very different from a uniform renormalization of the potential. The full coupling led to a 10% increase in the volume integral of the real potential. Evidence for the nonlocality of the underlying formal DPP and for the effect of direct coupling between the collective states is presented.
Conclusions: The local DPP generating the secondary rainbow has been identified. In general, DPPs have forms that depend on the nature of the specific excitations generating them, but, as in this case, they cannot be represented by a uniform renormalization of a global model or folding model potential. The method employed herein is a useful tool for further exploration of the contribution of collective excitations to internuclear potentials, concerning which there is still remarkably little general information
Influence of single-neutron stripping on near-barrier <sup>6</sup>He+<sup>208</sup>Pb and <sup>8</sup>He+<sup>208</sup>Pb elastic scattering
The influence of single-neutron stripping on the near-barrier elastic scattering angular distributions for the 6,8He+208Pb systems is investigated through coupled reaction channels (CRC) calculations fitting recently published data to explore the differences in the absorptive potential found in the scattering of these two neutron-rich nuclei. The inclusion of the coupling reduces the elastic cross section in the Coulomb-nuclear interference region for 8He scattering, whereas for 6He its major impact is on the large-angle elastic scattering. The real and imaginary dynamic polarization potentials are obtained by inverting the CRC elastic scattering S-matrix elements. These show that the main absorptive features occur between 11 and 12 fm for both projectiles, while the attractive features are separated by about 1 fm, with their main structures occurring at 10.5 fm for 6He and 11.5 fm for 8He
Velocity distributions in dissipative granular gases
Motivated by recent experiments reporting non-Gaussian velocity distributions
in driven dilute granular materials, we study by numerical simulation the
properties of 2D inelastic gases. We find theoretically that the form of the
observed velocity distribution is governed primarily by the coefficient of
restitution and , the ratio between the average number of
heatings and the average number of collisions in the gas. The differences in
distributions we find between uniform and boundary heating can then be
understood as different limits of , for and
respectively.Comment: 5 figure
Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering
We investigate the properties of the optical model wave function for light
heavy-ion systems where absorption is incomplete, such as Ca
and O around 30 MeV incident energy. Strong focusing effects
are predicted to occur well inside the nucleus, where the probability density
can reach values much higher than that of the incident wave. This focusing is
shown to be correlated with the presence at back angles of a strong enhancement
in the elastic cross section, the so-called ALAS (anomalous large angle
scattering) phenomenon; this is substantiated by calculations of the quantum
probability flux and of classical trajectories. To clarify this mechanism, we
decompose the scattering wave function and the associated probability flux into
their barrier and internal wave contributions within a fully quantal
calculation. Finally, a calculation of the divergence of the quantum flux shows
that when absorption is incomplete, the focal region gives a sizeable
contribution to nonelastic processes.Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The
figures are only available via anonynous FTP on
ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat
Reaction channel contributions to the helion optical potential
Background: The well-established coupled channel and coupled reaction channel processes contributing to direct reactions make particular contributions to elastic scattering that are absent from local density folding models. Very little has been established concerning the contribution of these processes to the optical model potentials (OMPs) for 3He scattering. For studying such processes, spin-saturated closed shell nuclei such as 16O and 40Ca are particularly suitable target nuclei and the (3He, 4He) reaction is easily handled within conventional reaction theory because it avoids complications such as breakup.Purpose: To establish and characterize the contribution to the 3He-nucleus interaction generated by coupling to neutron pickup (outgoing 4He) channels; also to study the contribution of collective states and identify effects of dynamical nonlocality from these couplings.Methods: Coupled reaction channel (CRC) calculations, including coupling to collective states, will provide the elastic channel S-matrix Sl j resulting from the included processes. Inversion of Sl j will produce the local potential that yields, in a single channel calculation, the elastic scattering observables from the coupled channel calculation. Subtracting the bare potential from the CRC calculations yields a local and l-independent representation of the dynamical polarization potential (DPP). From the DPPs, because of a range of combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.Results: Coupling to 4He channels systematically induces repulsion and absorption in the 3He OMP and also a reduction in the rms radius of the real part. The repulsion and absorption is less for 208Pb than for the lighter target nuclei although the qualitative effects, including the general undularity of the DPPs, are similar for all cases; therefore coupling to these channels cannot be represented by renormalizing folding model potentials. Evidence is presented for substantial dynamical nonlocality of the induced DPPs; for 40Ca this modifies direct reaction angular distributions. The local equivalent DPPs for individual couplings cannot be added to give the overall DPP for the complete set of couplings. For the 208Pb case, channel coupling reduces the reaction cross section although it increases it for 16O, with 40Ca an intermediate case. Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of 3He from nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the 3He OMP with implications for direct reactions involving 3He. Departures from a smooth radial form for the 3He OMP should be apparent in good fits to suitable elastic scattering data
Improved +He potentials by inversion, the tensor force and validity of the double folding model
Improved potential solutions are presented for the inverse scattering problem
for +He data. The input for the inversions includes both the data of
recent phase shift analyses and phase shifts from RGM coupled-channel
calculations based on the NN Minnesota force. The combined calculations provide
a more reliable estimate of the odd-even splitting of the potentials than
previously found, suggesting a rather moderate role for this splitting in
deuteron-nucleus scattering generally. The approximate parity-independence of
the deuteron optical potentials is shown to arise from the nontrivial
interference between antisymmetrization and channel coupling to the deuteron
breakup channels. A further comparison of the empirical potentials established
here and the double folding potential derived from the M3Y effective NN force
(with the appropriate normalisation factor) reveals strong similarities. This
result supports the application of the double folding model, combined with a
small Majorana component, to the description even of such a loosely bound
projectile as the deuteron. In turn, support is given for the application of
iterative-perturbative inversion in combination with the double folding model
to study fine details of the nucleus-nucleus potential. A -He tensor
potential is also derived to reproduce correctly the negative Li quadrupole
moment and the D-state asymptotic constant.Comment: 22 pages, 12 figures, in Revte
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