Microscopic analysis of the breathing mode in 40Ca and 58Ni

Recent experimental studies of the giant electric resonance region in ⁵⁸Ni and ⁴⁰Ca with inelastically scattered α-particles of energy E_α= 240 MeV are analyzed within a microscopic nuclear structure model. The model includes the continuum RPA and more complex 1p1h⊗phonon configurations. By superimposing the contributions of different multipoles up to L = 4 we obtain good agreement with the newest (reanalyzed) data for the isoscalar monopole strength and for the total (α,α′) cross section in ⁵⁸Ni. Agreement with experiment for the isoscalar monopole resonance in ⁴⁰Ca is obtained too. We emphasize the necessity of using microscopic transition densities and discuss consequences for the analyses of such experiments in light and medium mass nuclei. It is shown that the gross structure of the isoscalar monopole resonance in ⁴⁰Ca is caused by the 1p1h⊗phonon configurations. Received: 23 December 1999 / Revised version: 28 February 2000     

Evidence of non-statistical structures in the elastic and inelastic scattering of58Ni+58Ni and58Ni+62Ni and intermediate dinuclear states

Excitation functions and angular distributions of⁵⁸Ni+⁵⁸Ni and⁵⁸Ni+⁶²Ni scattering at energies just above the Coulomb barrier have been measured aroundθ _cm=90° in energy stepsΔE _cm=0.25 MeV fromE _cm ? 110 MeV toE _cm ? 120 MeV for⁵⁸Ni+⁵⁸Ni and fromE _cm ? 110 MeV toE _cm ? 118 MeV for⁵⁸Ni+⁶²Ni. Evidence for structure of non-statistical character has been found in the angle-summed excitation functions; this evidence is corroborated by the analysis of the angular distributions. This is the first time that non-statistical structure in elastic and inelastic scattering is reported with high confidence level for this mass and excitation energy ranges. Attempts are presented to understand the nature of this structure, including the presence of intermediate dinuclear states and virtual states in a potential well.     

Damped oscillations in the energy autocorrelation functions of the 58Ni+46Ti elastic and 58Ni+62Ni elastic and inelastic scattering cross sections

Structures of non-statistical character, recently observed in ⁵⁸ Ni +⁴⁶ Ti elastic and ⁵⁸ Ni +⁶² Ni elastic and inelastic excitation functions, produce damped oscillations in the cross section energy autocorrelation functions. The analysis of these damped oscillations in terms of S-matrix spin and parity decoherence indicates, as a possible interpretation, damping of the coherent rotational motion of the intermediate dinuclear system formed in the reaction.     

Optical potentials for elastic heavy ion scattering

The zero-field level crossing effect in selective reflection from an atomic vapour is calculated for normally incident radiation using a theory which, unlike the conventional dispersion theory, includes the effect of transient polarization behaviour due to diffuse wall collisions of vapour atoms. Both longitudinal and transverse magnetic fields are considered. At low vapour densities we find a narrowing of the level crossing curve in selective reflection relative to its width in the conventional dispersion theory. The narrowing is calculated as a function of the ratio of the homogeneous and inhomogeneous line width of the vapour for a Maxwellian velocity distribution of the vapour atoms and spectrally uniform incident radiation. The theory of this paper offers an explanation for recent observations of narrowing of level crossing curves in selective reflection.     

Semiclassical treatment of heavy ion elastic scattering

A generalized semiclassical treatment for the elastic scattering of heavy ions is developed in the presence of a complex optical potential. The scattering phase shift and its derivatives with respect to the impact parameter are calculated after extending the JWKBL approximation. The results are compared with experimental data for the elastic scattering of¹⁶O from medium and heavy target nuclei and relation between the present treatment and that of the optical model and Regge pole analysis is established     

Mode shaping in mixed ion crystals of 40Ca2+ and 40Ca+

We present studies of mixed Coulomb crystals of ⁴⁰Ca⁺ and ⁴⁰Ca²⁺ ions in a linear Paul trap. Doubly charged ions are produced by photoionization of trapped ⁴⁰Ca⁺ with a vacuum ultraviolet laser source and sympathetically cooled via Doppler cooled ⁴⁰Ca⁺ ions. We investigate experimentally and theoretically the structural configurations and the vibrational modes of these mixed crystals. Our results with ⁴⁰Ca²⁺ are an important step towards experimental realization of the proposals for mode shaping in a linear crystal and spin-dependent configuration changes from zigzag to linear as proposed by Li et al. (Phys Rev A 87:052304, 2013) and Li and Lesanovsky (Phys Rev Lett 108:023003, 2012) using ions excited to Rydberg states.     

Rainbow interference effects in heavy ion elastic scattering

It is shown that the oscillatory behaviour of differential cross section of heavy ion elastic scattering, which satisfies the semi classical conditions, is well described in terms of interference effects due to a rainbow.     

The transition between quasi elastic and completely damped collisions studied in the40Ar (280 MeV)+58Ni reaction

A careful exploration of the angular distribution for the products emitted mainly below the grazing angle shows the continuous evolution from Q.E. to completely damped collisions. The relative relaxation time of the collective degrees of freedom is considered.     

Two-particle transfer contributions to elastic and inelastic heavy ion scattering

The contributions of two-particle transfer to elastic and inelastic scattering of heavy ions are treated simultaneously in the coupled channels framework using microscopic transfer form factors. As an example, the reaction ¹⁸O(¹⁶O, ¹⁶O)¹⁸O(g.s. and 2₁⁺) is investigated at three energies near the Coulomb barrier. The interference between scattering and transfer leads to a consistent interpretation of both elastic and inelastic data. Indirect transfer contributions give relatively small, but non-negligible corrections to the direct scattering plus transfer result, removing a previously reported energy dependence of the spectroscopic factor.     

Zero-motion flucton correlations in high-energy proton elastic scattering on40Ca

The 1.04 GeV-proton elastic scattering from⁴⁰Ca is studied in the framework of the coherent density fluctuation model (CDFM). The calculations are carried out in the Glauber theoretical scheme with three different charge densities. It is shown that:i) the account of the flucton correlations leads to results considerably different from those obtained in the independent particle Glauber approach (IPGA);ii) in contrast to the case of IPGA the use of a more realistic density improves the agreement of CDFM-results with the experimental data.     

The optical potential for the elastic heavy ion scattering

For the elastic scattering of heavy ions a microscopic model is developed which uses shell model wave functions which are localised at a certain distance both in coordinate and momentum space. The antisymmetrization is treated exactly. Using oscillator functions and the Brink-Boeker force the energy dependent real part of the optical potential for O₁₆- O₁₆ scattering is numerically determined. The results are compared with the analysis of experiments.     

Total reaction cross sections from heavy ion elastic scattering

A model-independent method of obtaining total reaction cross sections has been applied to α-particle and ¹⁶O, ⁴⁰Ar and ⁸⁴Kr elastic scattering. Results are compared with total reaction cross sections determined by other means.     

Effects of relativistic kinematics in heavy ion elastic scattering

Relativistic corrections to the reaction kinematic parameters were made for elastic scattering of ⁶Li, ¹²C and ⁴⁰Ar from ⁴⁰Ca, ⁹⁰Zr and ²⁰⁸Pb targets at incident energies between 20 and 100 MeV/nucleon. The results of optical model calculations show that the effects of such corrections are important when describing the angular distributions of elastic scattering cross sections for heavy ion scattering at incident energies as low as around 40 MeV/nucleon. The effects on the total reaction cross sections on the other hand, were found to be small within the energy range studied when the optical model potential is fixed.     

Nucleon elastic scattering from 40Ca between 11 and 48 MeV

Differential cross sections for the elastic scattering of neutrons from ⁴⁰Ca have been measured in the 19–26 MeV region. The neutron elastic scattering data, previous neutron measurements and additional proton elastic scattering data are analyzed using three different approaches to the optical model potential: Woods-Saxon parameterization, model independent analysis and microscopic calculations. The difference between the phenomenological neutron and proton real potentials is studied in terms of Coulomb effects, nuclear polarization and charge symmetry breaking in the nuclear mean field.     

Diffractive,refractive and interference effects in heavy ion elastic scattering

The elastic scattering amplitude is divided into contributions arising from the “near” and “far” sides of the interaction region. Each of these contributions is further divided into a diffractive component arising from strong absorption and refractive components arising from the repulsive Coulomb and attractive nuclear fields. Damped orbiting of the projectile around the target is also allowed for. Simple closed form expressions are derived for the various contributions by assuming specific forms for the elastic scattering matrix. The results are discussed by analysing several typical elastic scattering data.     

Shape effects in heavy ion (Li) elastic scattering

The elastic scattering of aligned ⁶Li and ⁷Li on ⁵⁸Ni at E_cm = 12.7 MeV displays an “isotopic” effect which can be traced to the very different (mass) quadrupole moments of both isotopes. The elastic scattering of aligned ⁶Li and ⁷Li on ^12,13C at E_Li = 9 MeV displays large effects, but the angular dependence is much more complicated compared to the scattering on ⁵⁸Ni.     

Comment on fusion cross sections in the40Ar+40Ca and40Ca+40Ca systems

Using a strongly mismatched transfer reaction,¹³⁸Ba (¹⁴C,¹⁵N), the spin orbit potential for¹⁵N projectiles has been derived in terms of the reaction asymmetry. The strength and sign of the L·S-potential are consistent with a previous determination using an (¹⁶O,¹⁵n) reaction; the signis opposite to that for nucleons and agrees with a model where the last P_1/2 nucleon is responsible for the L·S potential.     

Data on light-fragment correlations in 40 Ar + 58 Ni at 77 MeV/nucleon

Results of the experimental study of p ⁴ He, d ³ He, dT, pT, p ³ He and, for the first time, nT, n ³ He, n ⁴ He correlations in the region of small relative momenta are presented. The data analysis provides an estimate of the effective source size or emission time.Received: 26 May 2003, Published online: 2 December 2003PACS: 25.70.Pq Multifragment emission and correlations     

Large angle elastic alpha scattering on a N=Z nucleus above A=40

Scattering of alpha particles from 44Ti, the lightest unstable alpha-particle nucleus above A=40, has been measured at backward angles. The "anomalous" order-of-magnitude enhancement that is characteristic of 40Ca and other light alpha-particle nuclei is not observed. Instead, the backward yield is similar to that observed for other nuclei heavier than 40Ca, and is well described with average optical model parameters.