Classical Computation of NeutraCHAMP Energy Loss due to Polarization by 14 N

Recently, several theoretical and experimental studies have been completed concerning the existence of a charged massive particle (CHAMP) as the missing matter of the universe. In particular, if a negatively charged CHAMP, X , is neutralized by a proton, then the neutraCHAMP can remain unobserved, except to the most astute observer. In order to observe better, researchers need a better estimate of the neutraCHAMP energy loss . In the classical approximation, we calculate the polarization energy loss of the neutraCHAMP, X p, in 14 N , as a function of velocity. We can approximate quite well the attractive ( 14 N;X p) potential, by neglecting electronic and protonic screening of the X from the 14 N nucleus, and retaining only the r 4 term. Therefore, due to the power-law form of the potential, the scattering angle equation can be integrated exactly, giving us analytical results for the variation of scattering angle, (b), and energy transfer, T (b), with impact parameter, b. We show that the energy loss in 14 N is proportional to velocity: dE= dx = 0:84 v=v 0 MeV cm 2 =g, where v 0 = 300km=s is the velocity dispersion of the hypothetical galactic X p ensemble. We also include protonic screening, by introducing a cuto to the r 4 potential, as (r 2 + a 2 ) 2 , where the cuto parameter is given by a = p 1:5a p , where a p = 28:8fm is the Bohr radius of the neutraCHAMP. For the velocities of interest, v 1000km=s, the energy loss is still proportional to velocity: dE= dx = 0:14 v=v 0 MeV cm 2 =g. We discuss the impact parameter limitations on our classical calculation of energy loss. This calculation of the neutraCHAMP energy loss resides within the rough lower and upper limits set by previous authors, and gives a more de nitive estimate of the detectability of X p in cosmic ray experiments. De R ujula, Glashow and Sarid [?] speculate that charged massive particles, euphemistically called CHAMPs, close the universe, and comprise dark galactic haloes. CHAMPs come in two forms, X , with a possible mass range of M x 2 [10 4 GeV; 10 6 GeV ]. If we assume that CHAMPs are the only dark matter component, then we can calculate a local number density for X's: n x 9m p n p =m x , where n p 0:24 cm 3 . With this number density and assuming a Maxwellian