Diffraction at backangles

Abstract

The backangle differential cross section is analyzed using an improved analytical approach. The differential cross section smoothed over the frequent angular oscillations is shown to be an oscillating function of the energy in the backangle region. Analogy with the radar scattering of light is pointed out. Angular and energy amplitude functions are introduced and discussed on the basis of general arguments and some simple examples.

A TI-59 model for nuclear reactions between complex nuclei

“…However, the magnitude of the energy oscillations and the energy or, rather, the /c-intervals -where it was observed vary depending upon the specific conditions. Also confirmed was the other conclusion of F4], namely that the deviation from the smooth A~ strongly increases the relative intensity at the large scattering angles as well as period Al,, in this region of l~ equals 2.0~2.5 which should be compared with Al~= 1 for the smooth A(l) [4]. The specific form of the dependence of 6(7r) upon the grazing parameter l~ which in this model determines the energy dependence is, naturally, different for different sequences of random numbers.…”

“…The inaccuracy of the asymptotic approximation for the Legendre polynomials is of no importance for 5(0). It should, however, be noted that the above separation of the cross section into smooth and oscillating components may fail if A t contains contributions in the range of I comparable with I c, see also in [4].…”

“…The amplitude of the angular oscillation of the cross section is determined by the relative magnitudes of (12) and (13). It can be conveniently characterized by a 0-amplitude function oJ(0) determined as the ratio of the difference of the cross sections, taken in the adjacent minima and maxima, to the cross section taken in the local maximum point [4]:…”

“…The interference between the fluctuating and smooth parts of the reaction amplitude may lead to specific effects, particularly in the angular distributions, which might indicate that such an interference was indeed present. In particular, it was expected that the fluctuating amplitude may enhance the energy oscillations in the backangle cross section [4]. As a first step, in this paper a simple model is investigated in which the smooth parts of the partial reaction amplitudes are taken in simple analytical forms and the fluctuating part (considered as a function of the angular momentum l) is produced by a series of normally distributed random numbers.…”

Helicity representation for deep inelastic collisions of heavy ions

“…Note, that the spins of the final nuclei, Jl and J2, may still be either parallel or anti-parallel to each other, S ~Jl +J2' (8) The former case corresponds, probably, to quasifission events whereas the other one can be expected for quasi-elastic collisions involving the surface friction. The Clebsch-Gordan coefficients do, indeed, decrease rather fast with increasing ]~c[ if the momenta are related as in (7).…”