The study of neutron spectra in water bath from Pb target irradiated by 250MeV/u protons

The spallation neutrons were produced by the irradiation of Pb with 250 MeV protons. The Pb target was surrounded by water which was used to slow down the emitted neutrons. The moderated neutrons in the water bath were measured by using the resonance detectors of Au, Mn and In with Cd cover. According to the measured activities of the foils, the neutron flux at different resonance energy were deduced and the epithermal neutron spectra were proposed. Corresponding results calculated with the Monte Carlo code MCNPX were compared with the experimental data to check the validity of the code.

Multi-bump solutions of $-Delta u=K(x)u^{frac{n+2}{n-2}}$ on lattices in $R^n$

We consider critical exponent semi-linear elliptic equation with coefficient K(x) periodic in its first k variables, with 2k smaller than n-2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in Rk, including infinite lattices. We also show that for 2k greater than or equal to n-2, no such solutions exist.