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The depth of the imaginary part of the optical potential is derived from the assumption that, at a given energy and for each partial wave L, it is proportional to the compound nucleus density level up to a given excitation energy above the yrast level corresponding to the angular momentum L, and remains a constant for smaller values of L. The prescription is successfully tested for the system 160 + 28Si at nine different projectile energies between 33 and 81 MeV; it fails however at 141.5 MeV, as expected, because other channels, besides elastic scattering and fusion, are important.In heavy-ion physics the large decrease of the elastic cross section at energies where the nuclei begin to penetrate each other points to a large absorption out of the elastic channel. This is usually described by means of the imaginary potential in the optical model. During the last decade much effort has been made to derive this potential from different approaches [l-4] . In this paper, following a suggestion by Arima and Hodgson [5], we present a method to construct the imaginary part of the optical potential. This is inspired, in part, in the model proposed by Helling et al. [6] where that potential is given by the transition probability from the elastic channel into a precompound state which is a doorway state for the formation of the compound nucleus. This transition probability is given in first order by Fermi's golden rule:where p(E* , L) is the level density of the precompound nucleus with excitation energy E* and angular momentum L. ~iin+ is the interaction between the pre-_-. I compound state Gcomp and the elastic channel +elas. To estimate the magnitude of the transition matrix element it is necessary to introduce microscopic wave functions. Because the nucleons in the overlap region contribute most to the transition probability, Fink et al. [7] assume that the radial dependence of the square of the matrix element in (1) is proportional to 14 the number of nucleons in the overlap region. This suggests a factorization of the imaginary potential:where W(r) contains the radial dependence and W(E, L) the energy and angular momentum dependence through the level density p(E* , L) of the compound nucleus. This approximation implies that the formation of the compound nucleus is the dominant reaction mechanism. Such an assumption is reasonable only for not too high energy and not very heavy ions. This is one first limitation of our model. The yrast level is the state of highest possible angular momentum for a given excitation energy. Since angular rotations have usually the highest angular momentum, for a given energy the yrast level is reached if all excitation energy is converted into rotational energy. Bellow the yrast line of the compound nucleus the imaginary potential (2) is exactly zero since no compound states can be reached. Based on these ideas the imaginary part (2) of the optical potential may be expressed as follows: W(r) = { 1 + exp [(r -R)/a] }-l , R =Q,@;'~ +Ati3),

The energy dependence of the fusion cross section and its maximum value are well predicted, for a wide range of nuclei and energies, by introducing information on the nuclear matter density distribution into a simple formula.In the last few years many measurements of the fusion cross section for heavy ions have been reported. Refs. [1][2][3][4][5][6] are some examples. At low energies the behavior of Ofus(E ) is thought to be dominated by the interaction barrier V(RB). A simple parametrization, based on semiclassical or classical ideas, yields the relation [ 1 ] :E being the center-of-mass energy. This expression is considered by Glas and Mosel [7] a limiting case of a more elaborated theory in which the critical distance or "point of no return" becomes smaller at higher energies. Expression of of us(E), as a function of the mass A and charge Z of the colliding nuclei, have been obtained from the proximity potential [8] or from empirical potentials fitted to the data [9]. Recent experiments, nevertheless, point to a Ofus(E ) dependence on the nuclear structure of the particular colliding nuclei [3,6] : an oscillatory behavior of Ofus(E) around the maximum is found in some cases (12C + 12C, 12C + 160, 160 + 160). Also a clear enhancement of the maximum value of the fusion cross section, ofumaXs, is noticed when one or two nucleons are first added to a new major shell. Horn and Ferguson [10] have introduced into their very simple empirical formula some information on the target and projectile structure by means of a "contact distance", b, which is taken to be the sum of the radii at 1.35% of the central charge density. Eq. (1) is changed into:where D = Z1Z2e2/E is the minimum distance in a head-on collision between point-like particles, only the Coulomb potential has been explicitly considered, and a varying parameter 0 has been introduced instead ofR B in order to simulate the effects of the nuclear interaction. Over a range of energies from 1.2 times the Coulomb barrier up to beyond the energy E 1 for which Bass [9] predicts the onset of tangential friction, good agreement with empirical data is found if the parameter 0 differs from the above-mentioned contact distance by a term proportional to E:The coefficient m = do/dE depends on the compound nucleus mass and is given [10] by the equation m -1 = 1812.23 -(A 1 +A2) 1/3] MeV/fm. In this letter we modify Horn and Ferguson's prescription and relate the contact distance b to the nuclear mass density rather than to the charge density. We do so because the former should be of greater significance, and particularly because in some similar problems we have succeeded in reproducing small departures from a mere A 1/3 -behavior by usin~ reformation on the nuclear matter density at far out distances. So the critical radii for alpha-particle elastic scattering, as analyzed by Badawy et al. [11 ], have been related to the distance where the density is 0.002 nucleon fm -3 [12]. In the latter work we used the nuclear density distribution calculated as the sum of singlepartic...

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