Continuous spontaneous localization reduction rate for rigid bodies

In the context of spontaneous wave function collapse models, we investigate the properties of the continuous spontaneous localization (CSL) collapse rate for rigid bodies in a superposition of two states located at different places. By exploiting the Euler-Maclaurin formula, we show that for standard matter the rate for a continuous mass distribution accurately reproduces the exact rate (i.e., the one for a discrete distribution). We compare the exact rate with previous estimates in the literature and we asses their validity. We find that the reduction rate displays a peculiar mass density difference effect, which we investigate and describe in detail. We show that the recently proposed layering effect is a consequence of the mass density difference effect.