Level densities of silicon-28, titanium-46, chromium-52 and nickel-60 from Ericson fluctuations

Ericson fluctuations in the differential cross sections are investigated for the compound reactions 27Al(p , n₀)27Si, 45Sc(p, n ₄)45_Ti,45Sc( p, n₅)45Ti, 51V(p, n₀ )51Cr and 53 Ni(p, n₀)59 Co. The excitation functions vary rapidly and irregularly with energy in a form that depends on the mass number A; for low A the fluctuations are stretched in energy while the opposite is observed for medium A nuclei.; Level widths in the compound nuclei 28Si, 46Ti, 52Cr and 60Ni are extracted from the analysis of the differential cross sections by the Fourier method and a nonlinear fit to the ln < $A2k+B2k$ > distribution. The neutron spectra for each reaction were measured at least at three backward angles but the coherence width < Γ > does not show a strong angular dependence. The results then were weighted obtaining: < Γ > = (33 ± 5) keV for 28Si at U = 18.9 MeV; < Γ > = (5.9 ± 4) keV for 46 Ti at U = 15.5 MeV; < Γ > = (9.6 ± 4) keV for 52Cr at U = 13.5 MeV and < Γ > = (6.9 ± 4) keV for 60Ni at U = 12.9 MeV.; Nuclear level densities for the above nuclei were extracted by relating the average level spacing DJπ to the average level width ΓJ π using the fluctuation theory. The level density equation obtained by this procedure depends in general on the transmission coefficients, the density of levels in the residual nuclei and the spin cutoff parameter on the compound nucleus. Local optical model parameters (OMP) were preferred to global ones in order to find the transmission coefficients, this was the case in general for (p,p) reactions and in some cases for (α,α) reactions, however given the lack of OMP for neutrons we resorted to global systematics. For the present analysis the density of levels in the residual nuclei are model independent except for (p,p) reactions in 27 Al and 45Sc. This is due to the low excitations in the residual nuclei for the kinetic energy of the projectiles involved in the experiment and also because in the range of analysis $Tnl>Tpl>Tal$. For the spin cutoff we assumed a 100% solid sphere dependency on the excitation energy. Level density parameters of Al-Quraishi were employed to evaluate level densities in other ranges of energies for widths obtained by fluctuation measurements from database compilations.; Reasonable agreements are found with level density compilations based in the Fermi gas formalism of Al-Quraishi and Huang for 28 Si, 46Ti and 52 Cr but the comparison diverges for 60Ni for which additional measurements are required in order to clarify the observed discrepancies. The level density parameters that best describe the data are a = 3.57...