A Measurement of the K0 charge radius and a CP violating asymmetry together with a search for CP violating e1 direct photon emission in the rare decay K(L) ---> pi+ pi- e+ e-

: Using the complete KTeV data set of 5,241 candidate K(L)--> pi(+) pi(-) e(+) e(-) decays (including an estimated background of 204 +/- 14 events), we have measured the coupling g(CR)= 0.163 +/- 0.0149(stat) +/- 0.023(syst) of the CP conserving charge radius process and from it determined a K(0) charge radius of = [-0.077 +/- 0.007(stat) +/- 0.011(syst)]fm(2). We have determined a first experimental upper limit of 0.04 (90% C.L.) /g(e1)/ / /g(M1)/ of the couplings for the E1 and M1 direct photon emission processes. We also report the measurement of /g(M1)/ including a vector form factor /g(M1)/(1 + (a(1)/a(2))/((M(2)(p)-(M(2)(k))= 2M(K)E(gamma*)), where vector /g(M1)/= 1.11+/- 0.12(stat) +/- 0.08(syst) and a(1)/a(2) = [-0.744 +/- 0.027(stat) +/- 0.032(syst)] GeV(2)/c(2). Finally, a CP-violating asymmetry of [13.6 +/- 1.4(stat) +/- 1.5(syst)]% in the CP and T odd angle phi between the decay planes of the e(+) e(-) and pi(+) pi(-) pairs in the K(L) center of mass is reported.