Strong pickup-channel coupling effects in proton scattering: the case of p + Be-10

The dynamic polarization potential (DPP) contribution to the effective proton-nucleus interaction, that is due to the coupling of deuteron channels, is evaluated by applying $S_{lj} \to V(r)$ inversion to the elastic channel $S$-matrix from coupled reaction channel calculations of proton elastic scattering. This was done for protons scattering from $^{10}$Be at 12, 13, 14, 15, and 16 MeV; non-orthogonality corrections were included. We find a consistent pattern of a repulsive real and an absorptive imaginary DPP, with the absorption shifted to a larger radius. This is consistent with what has been found for proton scattering from the neutron skin nucleus $^8$He. The DPP is not of a form that can be represented by a renormalization of the bare potential, and has properties suggesting an underlying non-local process. We conclude that deuteron channels cannot be omitted from a full theoretical description of the proton-nucleus interaction (optical potential).Comment: 14 pages, 4 figures, RevTeX4, accepted by Phys Rev

Coupling effects in proton scattering from ⁴⁰Ca

Recent studies showed that neutron pickup makes a substantial contribution to the proton optical model potential (OMP) for light, mostly halo, target nuclei. Here, we extend those studies to a more “normal” target nucleus: 40Ca. We present coupled reaction channel (CRC) calculations with the coupling of 30.3 MeV incident protons to deuterons and up to 12 states of 39Ca. The proton elastic scattering S matrix from the CRC calculation is subject to Slj→V(r)+l·s VSO(r) inversion and the bare potential of the CRC calculation is subtracted, directly yielding a local and L-independent representation of the dynamic polarization potential (DPP). This is appropriate for comparison with phenomenological OMPs and local OMPs derived in local density folding models. The real-central part of the DPP is repulsive and cannot be represented as a uniform normalization of the bare potential, changing the rms radius. A series of model calculations reveal the dependence of the DPP on a range of parameters illuminating (i) departures of nucleon potentials of specific nuclei from global properties, (ii) the generation of repulsion, and (iii) the requirements for all-order CRC and deuteron breakup. Light is thrown on the nonlocality of the underlying DPP

Dynamic polarization potential due to ⁶Li breakup on ¹²C

For 6Li scattering from 12C at five laboratory energies from 90 to 318 MeV, we study the dynamic polarization potential, DPP, due to the breakup of the projectile. The breakup is evaluated using standard continuum discretized coupled-channels formalism applied to a two-body cluster model of the projectile. The DPP is evaluated over a wide radial range using both direct S-matrix-to-potential inversion and trivially equivalent local potential methods which yield substantially and systematically different results. The radius at which the real DPP changes from external repulsion to interior attraction varies systematically with energy. This should be experimentally testable because, according to notch tests, this crossover radius is within a radial range to which elastic scattering should be sensitive. The imaginary DPP has an emissive (generative) region at the lower energies; this may be associated with counterintuitive properties of |SL|

Significant features of ⁸B scattering from ²⁰⁸Pb at 170.3 MeV

The scattering of proton-halo nucleus 8B from 208Pb at 170.3 MeV is shown to reveal a distinctive pattern in the change in |SL| that is induced by coupling to breakup channels. The same pattern had been found for 8B scattering from 58Ni at 30 MeV, an energy near the Coulomb barrier, and has been linked to various other respects in which scattering for this proton-halo nucleus differs from that of other light, weakly bound nuclei. The increase in |SL | forL < 80, induced by breakup coupling, is associated with a substantial repulsive region in the dynamic polarization potential as determined by exact inversion. This repulsion appears to reduce the penetration of the projectile into the absorptive region of the interaction. This accounts for the fact that the increase in the total reaction cross section, due to breakup, is much less than the breakup cross section, and is consistent with the relatively small effect of breakup on the elastic scattering angular distribution compared with the large breakup cross section

Evidence for <i>L</i>-dependence generated by channel coupling: ¹⁶O scattering from ¹²C 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

Breakup coupling effects on near-barrier ⁶Li, ⁷Be and ⁸B + ⁵⁸Ni elastic scattering compared

New data for near-barrier 6Li, 7Be and 8B + 58Ni elastic scattering enable a comparison of breakup coupling effects for these loosely-bound projectiles. Coupled Discretised Continuum Channels (CDCC) calculations suggest that the large total reaction cross sections for 8B + 58Ni are dominated by breakup at near-barrier energies, unlike 6Li and 7Be where breakup makes a small contribution. In spite of this, the CDCC calculations show a small coupling influence due to breakup for 8B, in contrast to the situation for 6Li and 7Be. An examination of the S matrices gives a clue to this counter-intuitive behaviour

Emergence of a secondary rainbow and the dynamical polarization potential for ¹⁶O on ¹²C 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

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 $S^j_{ll'}$ yielding a $T_{\rm R}$ 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 $\sigma$, ${\rm i}T_{11}$, $T_{20}$, $T_{21}$ and $T_{22}$ for d + alpha scattering over a range of energies near 10 MeV. The $T_{\rm R}$ 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