Remarks on the mixed Ramond-Ramond, open string scattering amplitudes of BPS, non-BPS and brane-anti-brane

From the world-sheet point of view we compute three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these mixed S-matrix elements including a Ramond-Ramond closed string (RR) in the bulk and a scalar/gauge or tachyons with all different pictures (including an RR in asymmetric and symmetric pictures) have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on the upper half plane, it is realised that some of the equations (which must be true) for BPS branes cannot be necessarily applied to non-BPS amplitudes. We also derive the S-matrix elements of <(VC-2V phi VAVT0)-V-0-V-0 > and clarify the fact that in the presence of the scalar field and an RR, the terms carrying momentum of an RR in the transverse directions play an important role in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix elements of type IIA (IIB) superstring theory.