Low energy α+<Superscript>16</Superscript>O scattering in the orthogonality condition model

The orthogonality condition model (OCM) is used to describe α+¹⁶O scattering at low energies. A double folding potential with density-dependent effective NN interactions is used as the local potential of the model. The energies and widths of α-cluster resonances and differential cross sections are calculated. The results are compared to one obtained using the standard potential approach, without the nonlocal interaction of the OCM.     

Effective nucleus-nucleus potentials derived from the generator coordinate method

The equivalence of the generator coordinate method (GCM) and the resonating group method (RGM) and the formal equivalence of the RGM and the orthogonality condition model (OCM) lead to a relation connecting the effective nucleus-nucleus potentials of the OCM with matrix elements of the GCM. This relation may be used to derive effective nucleus-nucleus potentials directly from GCM matrix elements without explicit reference to the potentials of the RGM. In a first application local and l-independent effective potentials are derived from diagonal GCM matrix elements which represent the energy surfaces of a two-centre shell model. Using these potentials the OCM can reproduce the results of a full RGM calculation very well for the elastic scattering of two α-particles and fairly well for elastic ¹⁶O-¹⁶O scattering.     

Microscopic calculations for the 8Li system

A microscopic multi-channel cluster model calculation for the ⁸Li scattering system has been performed. Diagonal phase shifts, channel coupling strengths, and eigenphases are presented. For comparison, the ⁸Li bound and quasibound states have been investigated by a refined resonating group calculation. The results of both types of calculations are in excellent agreement. In the energy region up to the ⁵He-t threshold the calculated S-matrix elements, the energy eigenvalues, and the overlaps of the normalized functions with the eigenvectors explain the origin of the experimentally detected levels and moreover give predictions for the existence of additional levels.     

On the nuclear polarization potential for heavy-ion scattering

The real polarization potential ΔV due to transfer reactions is studied using a microscopic semiclassical formalism. It is found that ΔV is typically of the same order of magnitude as the corresponding absorptive potential W. Different types of possible energy dependences for ΔV and W are explored qualitatively. Specific calculations for ¹⁶O + ²⁰⁸Pb and ¹⁶O + ⁶⁰Ni scattering show features similar to those which have been deduced empirically.     

Analysis of elastic scattering of pi-mesons by nuclei within the microscopic optical potential

The microscopic pion-nucleus optical potential defined by the pion-nucleon scattering amplitude and the density distribution function of the target nucleus is applied to obtain the differential cross section of the elastic pion-nucleus scattering based on the solution to the relativistic wave equation. This allow one to account for effects of the relativization and distortion by the potential field. Data on π^±-meson scattering on ²⁸Si, ⁵⁸Ni, and ²⁰⁸Pb nuclei at T _lab = 291 MeV are analyzed and the parameters of the in-medium πN-amplitude are obtained. The parameters are compared with similar parameters for scattering on free nucleons.     

Distortion effects in light hypernuclei

We have studied the particle-bound levels in the hypernuclei_Λ ^3,4H,_Λ ⁵He,_Λ ⁸Li and_Λ ^8,9Be in the framework of the full microscopic Resonating Group Method (RGM). In a first step we have solved the respective nuclear many-body problem within the RGM. For each hypernucleus we have then performed a static calculation, in which the nuclear degrees of freedom were kept fixed, and a dynamical calculation in which nuclear degrees of freedom were allowed to vary. The differences between these two studies allowed us to investigate nuclear distortion effects caused by the presence of theΛ-particle. We find the nuclear distortion effects to be inverse proportional to the binding of the nuclear constituents. Thus, the strongest effects are observed for_Λ ³H and for_Λ ⁹Be. Our dynamical approach does not show the strong overbinding of_Λ ³H and_Λ ⁹Be as reported in other cluster model studies. Our results for thep-shell hypernuclei agree reasonably well with those obtained in a semi-microscopic Orthogonal Condition Model (OCM) study which used the same effectiveΛN-interaction as employed in our calculation.     

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, ¹²C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E_α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A_t^{?5 ± 1}. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ_T < 10^?34 cm² consistent with present experimental limits. The data for ²⁴Mg(α, ¹²C)¹⁶O has been studied in more detail and indicates a selective population of final states including ¹⁶O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct ⁸Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2⁺, E_x ≈ 7 MeV; 4⁺, E_x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated ⁸Be cluster overlaps and the calculated and measured (α, ¹²C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.     

Analytic expressions for energy centroids and widths in the microscopic collective model

Analytic formulae are given for the U(3) centroids of the collective Bohr-Mottelson potential in the microscopic collective model. In particular, formulae are reported for the centroids of the quadratic [Q · Q ～ β²] and cubic [Q · (Q × Q ～ β³cos 3γ] rotational scalars in the microscopic quadrupole operator. Favorable comparisons for ground-state intensities are achieved between shell-model diagonalizations and statistical predictions based upon the gaussian approximation to the energy density. These results suggest that statistical measures can be used reliably for truncation of the infinite-dimensional representation spaces of the microscopic symplectic collective theory.     

Virtual coupling potential for elastic scattering of Be on proton and carbon targets

The ^10,11Be(p, p) and (¹²C, ¹²C) reactions were analyzed to determine the influence of the weak binding energies of exotic nuclei on their interaction potential. The elastic cross sections were measured at GANIL in inverse kinematics using radioactive ^10,11Be beams produced at energies of 39.1A   and 38.4A MeV$38.4A\text{ MeV}$. The elastic proton scattering data were analyzed within the framework of the microscopic Jeukenne–Lejeune–Mahaux (JLM) nucleon–nucleus potential. The angular distributions are found to be best reproduced by reducing the real part of the microscopic optical potential, as a consequence of the coupling to the continuum. These effects modify deeply the elastic potential. Including the Virtual Coupling Potential (VCP), we show the ability of the general optical potentials to reproduce the data for scattering of unstable nuclei, using realistic densities. Finally, the concepts needed to develop a more general and microscopic approach of the VCP are discussed.     

Low-collective scissors mode

Realistic microscopic RPA calculations for¹⁵⁶Gd with a deformed Woods-Saxon mean field, quadrupole-quadrupole, spin-spin and symmetry-restoring residual interactions show that the purely collective scissors mode of the two-rotor model is fragmented over orbital isovector 1⁺ states, lying at 2–7 MeV. The strongest experimentally observed magnetic dipole state is interpreted as performing a low-collective scissors-type of geometrical motion. This conclusion evolves from the identification of the above state with the strongest RPA excitation, which reproduces well the experimental energy,B(M1) value and (e, e′) form factor, has the largest overlap with the scissors state and can be represented as a low-collective scissors type vibration.     

The shell correction and self-consistent deformation energies

The Hartree-Fock deformation energy of the nucleus is represented as the sum of two terms one of which (E^σ) is due to the re-distribution of the nuclear density and depends on the microscopically non-self-consistent parameters σ of the nuclear shape. The other component (E^π) is related to the coherent distortion of the quasiparticle wave functions in the occupied states and is the same as the deformation energy considered in theories of microscopic vibrations for a fixed quasiparticle distribution. Quantities averaged over the particle-hole distribution are introduced which satisfy the condition of statistical self-consistency. It is shown that the shell correction energy represents the averaged effect of the re-distribution of the single-particle states. Finally, corrections are formulated for the shell-model potential which does not satisfy the condition of statistical self-consistency.     

Structure of the deformed terms of the rotational-model optical potential (II)

The microscopic optical matrix potential (OMP^m) for rotational nuclei is constructed. The structure of the non-diagonal elements of OMP^m is investigated and compared with the deformed part of the phenomenological optical potential (OMP^p) employed in analyses of nucleon inelastic scattering data. The deformed form of OMP^p relates the real parts of the phenomenological form factors. This relation is shown to be approximately satisfied by the microscopic form factors. It is proved that the decay amplitudes of complicated compound states to similar channels are correlated, which we call the similar channels effect (SCE). Some channels are similar since the rotational states of the target are obtained from the same intrinsic state. The commonly used deformed imaginary part of OMP^p at very low energies (few MeV or Iess) may be justified as being due to the similar channels effect.     

Anl-independent representation of a Majorana potential

The local andl-independent potential which isS-matrix equivalent to the parity dependent potential of Michel and Reidemeister forα scattering from²⁰Ne has been determined by inversion. The two potentials which fit elastic scattering produce radically different wavefunctions where the nuclei overlap. Phenomenological consequences are discussed.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.