Liquid-drop model description of heavy ion fusion at sub-barrier energies

The enhancement of the heavy ion fusion cross section at sub-barrier energies is studied in the liquid-drop model approach. The shape of the system is described by two spheres smoothly connected by a neck, and the kinetic and potential energies are calculated within this parametrization. Underbarrier fusion cross sections for symmetric projectile-target combinations are calculated in the WKB approximation and a comparison with the available data is made. The agreement is quite satisfactory, except for those systems in which the reaction is strongly affected by the details of the nuclear structure of the collision partners.     

Puzzling features of heavy-ion fission at sub-barrier energies

Elastic and inelastic scatterings cross-sections of¹²C+¹²C in the energy range 11–24 MeV/n have been analyzed within the coupled channels framework including appropriate symmetrization. The set obtained withr ₀=1.01 fm,r _I =0.86 fm for seven incident energies gave the best agreement with the data and could be, therefore, considered as really significant when compared with other sets. Coupled channels calculations have been made to fit the data and it has been found that they require a reduction of the imaginary potential. The total reaction cross-sectionσ _R (E) determined from this analysis is in good agreement with a direct and recent measurement of σ _R . Quadrupole deformation parameterβ ₂ has been extracted and compared with those obtained for proton and alpha scatterings. Some small energy dependence of β₂ over this energy range has been found, ¦β ₂¦ ～0.39–0.47. Finally, these calculations further confirm that β₂ depends on the probe used in the various scattering experiments. For composite projectile such asα or¹²C,β ₂ is clearly smaller than that one for nucleon as projectile.     

Puzzling features of heavy-ion fission at sub-barrier energies

The heavy-ion induced fission fragment angular distributions measured for systems with Th, U and Np as targets have revealed “anomalous” values of anisotropies at energiesE≤V _B (fusion barrier) and this feature is observed to be independent of the entrance channel mass-asymmetry. While this puzzling feature is exhibited by the deformed targets like Th, U and Np, most of the fission data measured for the spherical targets like Pb and Bi can be satisfactorily explained using the standard saddle point statistical model with moderate correction for pre-fission neutron emission. Plausible reasons for this anomalous behaviour are explored.     

Study of deuteron breakup in light targets at intermediate energies

Reaction cross-sections and proton removal cross-sections in deuteron-induced reactions with carbon and beryllium targets are studied at intermediate energies. The cross-sections calculated in eikonal approximation show a good agreement with experimental data. The sensitivity of the cross-sections to the target structure, the nucleon-target interaction potential, and the spatial distribution of nucleons in the deuteron is discussed. Received: 30 May 2001 / Accepted: 2 October 2001     

Sputtering and backscattering of keV light ions bombarding random targets

The fission fragment fluence required to render CaUO₄, Na₂U₂O₄, MgUO₄, Sr₂U₃O₁₁ and u₃O₈ x-ray amorphous was deduced as ～5 × 10¹⁵ events cm³. Significant annealing of the structural damage occurred in the 300–-500°C range.     

14N fusion with 13C and 16O at sub-barrier energies

Total fusion cross sections for the ¹⁴N+¹²C and ¹⁴N+¹⁶O reactions have been measured in the c.m. energy ranges 3.6–9.2 MeV and 5.6–12.6 MeV, respectively. Cross sections are also reported for important individual exit channels which were studied by observing discrete γ-ray transitions in the evaporation residues with a Ge(Li) detector. Excitation functions reveal no evidence of intermediate structure in these reactions. The fusion cross sections for ¹⁴N induced reactions on ¹²C, ¹⁴N and ¹⁶O are compared with an IWB calculation using recently published semi-empirical parameters for the real ion-ion interaction potential. Such a comparison supports the view that low-energy fusion studies may be sensitive probes of the nuclear potential in the interior of the interaction barrier.     

Unexpected behavior of heavy-ion fusion cross sections at extreme sub-barrier energies

The excitation function for fusion evaporation in the (60)Ni+ (89)Y system was measured over a range in cross section covering 6 orders of magnitude. The cross section exhibits an abrupt decrease at extreme sub-barrier energies. This behavior, which is also present in a few other systems found in the literature, cannot be reproduced with present models, including those based on a coupled-channels approach. Possible causes are discussed, including a dependence on the intrinsic structure of the participants.     

Coherent backscattering of polarized light from a turbid medium

Approximate analytical expressions for the intensities of the polarized components of light reflected from a disordered medium with large discrete particles (larger than the wavelength) have been derived with the use of the method of decoupling of the vector transfer equation that is based on separate treatment of basic and additional polarization modes. The results obtained provide the relation between the peak shape in the angular distribution of the backscattered radiation with a given polarization and the optical characteristics of the medium and are in good agreement with experimental data and numerical calculations.     

Inelastic scattering of heavy ions from deformed light nuclei at near-barrier energies

Angular distributions have been measured at energies near the Coulomb barrier for the systems ¹⁸O + ²⁴Mg, ¹²C + ²⁸Si and ^{16, 18}O + ²⁸Si for elastic scattering and inelastic scattering to the first 2⁺ states in ¹⁸O, ²⁴Mg and ²⁸Si. Coupled-channel calculations were required in order to reproduce the details of the strong Coulomb-nuclear interference minima. However, a satisfactory account of the main features of the data was obtained in a first-order DWBA analysis and with the closed formalism of Frahn. With the exception of ¹⁸O, it was sufficient to assume equal charge and optical-potential deformation lengths.     

Influence of the boundary of a medium on the coherent backscattering of light

The multiple scattering of light from an inhomogeneous medium occupying a half-space is investigated on the basis of the Bethe-Salpeter equation. The latter is integrated over the spatial variables to obtain an identity having the significance of the energy balance of the incident and scattered radiations. This relation is then used to derive a length parameter that plays the role of the Milne interpolation length. The use of this parameter in the method of mirror images for describing the shape of the coherent backscattering peak in isotropic single scattering yields results in almost perfect agreement with the predictions of the Milne theory. The application of the given approach for an anisotropic single-scattering diagram yields quantitative agreement of the theory with experiments on the angular dependence of coherent backscattering. The new approach is generalized to an electromagnetic (vector) field, and backscattering polarization effects are investigated. Zh. éksp. Teor. Fiz. 116, 1912–1928 (December 1999)     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

Time-resolved backscattering of circularly and linearly polarized light in a turbid medium

Time-resolved backscattering profiles of circularly and linearly polarized light were measured from a turbid medium composed of small and large polystyrene sphere particles in water. It is shown that, based on the measurements of the time-resolved backscattered copolarized and cross-polarized components of the incident polarized light, either linearly or circularly polarized light can be used to effectively image an object that is deep inside a turbid medium composed of small particles, depending on the depolarization properties of the object itself. For large particles such as in tissue, fog, and clouds, the experimentally observed polarization memory effect on the backscattering temporal profiles suggests that a significant improvement in the image contrast can be achieved by use of circularly polarized light.     

Total backscattering of keV light ions from solid targets in single-collision approximation

The reflection of light ions from heavy random targets has been calculated within the single-collision approximation on the basis of essentially the same physical model as Schiøtt's adaptation of the LSS range theory to light ions. An accurate effectivepower approximation has been utilized to evaluate a number of physical quantities relating to reflected ions under the assumption of Thomas-Fermi scattering. Analytical results as well as universal curves are presented for reflected-energy spectra integrated over ejection angle, particle and energy reflection coefficients, and quantities derived from these. Good agreement with experimental results is obtained for ε?, where ε is Lindhard's energy parameter. The results are compared with those from previous calculations on the basis of transport theory and computer simulation. An estimate is given of the single-collision tail of the light-ion range profile. Qualitative corrections for beam attenuation and recoil energy loss are presented in appendices.     

Fusion and peripheral reactions in the systems 16O + 148,152Sm at sub-barrier energies

Cross sections for fusion and peripheral reactions in the sub-barrier region obtained with the coupled-channel and equivalent-spheres methods are compared for the systems ¹⁶O + ^148,152 Sm. A barrier-like real potential plus a residual surface-imaginary potential is introduced as an alternative approach which allows the simultaneous fit of elastic, inelastic, fusion and peripheral reaction cross sections.     

Elastic hadron scattering on Li isotopes at intermediate energies

The elastic scattering of hadrons (protons, charged pions, and positively charged kaons) on ^6,7,8Li nuclei is analyzed on the basis of Glauber-Sitenko diffraction theory. A few nuclear-wave-function versions found within two-and three-particle potential cluster models are used in the calculations. It is shown that the application of these wave functions in diffraction theory makes it possible to describe adequately the experimental differential cross sections and analyzing powers in hadron scattering at intermediate energies. In this study, particular attention is given to a comparison of the scattering of different particles on the same target nucleus, as well as to a comparison of scattering of particles of the same sort on different target nuclei.     

Scattering of α-particles at medium energies

Elastic scattering of α-particles is treated within the context of high energy multiple diffraction theory. Terms up to fourth order in the expansion of the optical phase-shift function are retained (when necessary). The theoretical predictions are compared with the recent 5.05 and 4.30 GeV/c α-α measurements. The effects of short-range dynamical correlations are discussed.     

Coherent backscattering of a light pulse by a slab of disordered medium

We obtain an exact analytical solution to the problem of the enhanced backscattering of a short pulsed signal from a two- and three-dimensional medium with isotropically scattering centres. The angular spectrum is expressed in terms of the solution to the corresponding stationary problem. The intensity oscillations are shown to appear on the tails of the angular spectrum. The origin of these oscillations is associated with the ballistic phase shift between the interfering waves arriving at the detector. It is shown that the finiteness of the slab thickness influences the magnitude of the backscattering intensity and does not change the shape of the angular spectrum. The range of validity for the diffusion approximation is pointed out.

The results obtained in the paper also contain a generalization of the well known solution to the problem of incoherent transfer to a pulsed signal to the case of two-dimensional disordered media.     

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.