Fig. 7

The left y-axis denotes the number of α-particles in the decay chain of ²²⁵Ac that are emitted from inside a nanoparticle with radius r measured in units of the recoil range R of the decay products of ²²⁵Ac (i.e., of ²²¹Fr, ²¹⁷At and ²¹³Bi), which is very similar for a given material. It is assumed that the ²²⁵Ac is located in the centre of the nanoparticle at r = 0. The step function refers to the worst case that all recoils are lined up in the same direction. Setting the similar recoil ranges of ²²¹Fr, ²¹⁷At and ²¹³Bi to R, these daughters of ²²⁵Ac are fully retained in nanoparticles with a radius R, 2R and 3R, respectively. The more realistic model considering the sequence of recoils as random steps in arbitrary directions in the three-dimensional space yields a higher recoil retention for nanoparticles larger than R. The right y-axis translates recoil retention into the fraction of α-particles that are emitted from the inside of the nanoparticle