Using the DIANA data on the charge-exchange reaction $K^+n rightarrow pK^0$ on a bound neutron, in which the s-channel formation of the pentaquark baryon $Theta^+(1538)$ has been observed, we analyze the dependence of the background-subtracted $Theta
^+ rightarrow pK^0$ signal on the $K^0$ emission angle in the $pK^0$ rest frame. In order to describe the observed $cosTheta_K^mathrm{cms}$ distribution, invoking the interference between the nonresonant s-wave and the $Theta^+$-mediated higher-wave contributions to the amplitude of the charge-exchange reaction is required at a 2.8$sigma$ level. The spin--parity assignment of 1/2$^-$ for the $Theta^+$ baryon is ruled out at a statistical level of 2.9 standard deviations. A physically-meaningful selection in $cosTheta_K^mathrm{cms}$ based on the observed angular dependence of the $Theta^+ rightarrow pK^0$ signal allows to boost the statistical significance of the signal up to 7.1 standard deviations. This is far in excess of previously reported signals and renders the $Theta^+$ existence more credible.
The charge-exchange reaction K^+ Xe --> K^0 p Xe is investigated using the data of the DIANA experiment. The distribution of the pK^0 effective mass shows a prominent enhancement near 1538 MeV formed by sim 80 events above the background, whose width
is consistent with being entirely due to the experimental resolution. Under the selections based on a simulation of K^+Xe collisions, the statistical significance of the signal reaches 5.5sigma. We interpret this observation as strong evidence for formation of a pentaquark baryon with positive strangeness, Theta^+(uuddbar{s}), in the charge-exchange reaction K^+ n --> K^0 p on a bound neutron. The mass of the Theta^+ baryon is measured as m(Theta^+) = 1538+-2 MeV. Using the ratio between the numbers of resonant and non-resonant charge-exchange events in the peak region, the intrinsic width of this baryon resonance is determined as Gamma(Theta^+) = 0.34+-0.10 MeV.
The data on the reactions K^+Xe --> K^0 gamma X and K^+Xe --> K^+ gamma X, obtained with the bubble chamber DIANA, have been analyzed for possible radiative decays of the Theta^+(1540) baryon: Theta^+ --> K^0 p gamma and Theta^+ --> K^+ n gamma. No s
ignals have been observed, and we derive the upper limits Gamma(Theta^+ --> K^0 p gamma) / Gamma(Theta^+ --> K^0 p) < 0.032 and Gamma(Theta^+ --> K^+ n gamma) / Gamma(Theta^+ --> K^+ n) < 0.041 which, using our previous measurement of Gamma(Theta^+ --> KN) = (0.39+-0.10) MeV, translate to Gamma(Theta^+ --> K^0 p gamma) < 8 keV and Gamma(Theta^+ --> K^+ n gamma) < 11 keV at 90% confidence level. We have also measured the cross sections of K^+ -induced reactions involving emission of a neutral pion: sigma(K^+n --> K^0 p pi^0) = (68+-18) mub and sigma(K^+N --> K^+ N pi^0) = (30+-8) mub for incident K^+ momentum of 640 MeV.
