The non-linear Schrodinger equation and anomalous backward scattering

Elastic scattering of heavy ions and a modified liquid drop model

“…3. It is very close to the results of calculations with more realistic phenome-nological potentials [5,10]. The improvement in the quality of the angular distribution is quite impressive, yet the correspondence to experiment is by no means excellent.…”

“…The same problem is delt with in a more recent contribution by Fleckner and Mosel [8]. For lower energies the spatial dependence of the Pauli distortions evaluated by them is in good agreement with phenomenological substitutes (e.g., [5]) of the nonlinearity term of (1). The effect of antisymmetrization (the matrix elements themselves, the Pauli distortion of the densities and the Born-Oppenheimer approximation) is said to amount to around 70% of the effective potential without antisymmetrization.…”

“…Similarly as in the case of the NOSE, the philosophy of the ESP is such that the optical potential is presumed to provide an adequate description for the "normal" case, i.e., da/ds'-2 for forward angles, while the additional phenomenological repulsion V r is adjusted to experiment to account for the quasimolecular effects associated with ALAS (anomalous large angle scattering). In line with earlier investigations [5,6] we now focus our attention on the elastic scattering of ~ particles and heavy ions where ALAS is observed. In previous discussions we approximated the nonlinearity only by phenomenological potentials; the present note contains the last check to be performed before solving the NOSE numerically.…”

“…up to po,,=0.168 fm 3 i.e., the average nuclear density. Evaluation of the elastic energy, E~, put into this compression has been shown to yield a nonlinear Schr6dinger equation (NOSE) of the type [5] h 2…”

Elastic Scattering of Heavy Ions and the Compressibility of Nuclear Matter

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Analogies to hydrodynamics led recently to the derivation of a nonlinear Schrodinger equation for the elastic scattering of heavy ions (Delion et al 1978). In the present paper, the numerical solution of this equation is shown to yield realistic values for the nuclear compressibility modulus K = 9C, with very small uncertainties.

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