Proton elastic scattering from the chromium isotopes

Piecewise constant potentials and discrete ambiguities

“…Indeed discrete ambiguities are often observed for nucleus-nucleus scattering with a heavy target, for instance for α − 208 Pb scattering (not so for α − 58 Ni), whereas few attempts have been made for nucleon-nucleus scattering. Note that for proton scattering on Cr isotopes at 10 MeV, discrete ambiguities have been reported by Andrews et al [20]. The difference in the potential depth is about 100 per cent.…”

“…In the Table 1 are shown the different values of r 1 < R = 10 obtained from Eqs. (20). Only the first two zeros of the spherical Bessel function j 1 (z) = u 1 (z)/z namely x 1,1 = 4.493409, x 1,2 = 7.725252, are displayed in Table 1.…”

“…For this very reason, the model is quoted as simply soluble. With this value of K 2 1 , equation (20) allows us to determine r 1 . In this case, the first source of ambiguities come from the choice of the value of r 1 among the zeros of ψ 1 smaller than R. The next step consists in determining v 0 .…”

“…We recall that K 2 1 is recovered from equation ( 21), and is therefore identical to the starting value. In the table 1 different values of r 1 < R = 10 obtained from equations (20) are shown. Only the first two zeros of the spherical Bessel function j 1 (z) = u 1 (z)/z, namely x 1,1 = 4.493 409, x 1,2 = 7.725 252 are displayed in table 1.…”

Neutron scattering and models: chromium

“…The prominent 52Cr isotope is magic in neutron number (N = 28) and is holes in the well represented by a proton core with four & closed shell [Joh+85,MBZ641. The spectroscopy of 52Cr has been extensively studied theoretically primarily using shell-model concepts, and experimentally using a wide variety of nucleon-transfer and knock-out reactions.…”