Technical Note Yukawa-Enhanced Diosi--Penrose Timescale for MAQRO-Like Superpositions

This note evaluates Diósi–Penrose gravitational self-energy decoherence for a MAQRO-like superposition using a rigid homogeneous-sphere mass model. For (M=10^{10},\mathrm{amu}) and (s=100,\mathrm{nm}), the Newtonian DP timescale spans (\sim 9)–(100) minutes across representative densities. A Yukawa correction (V(r)=-(Gm_1m_2/r)[1+\alpha e^{-r/\lambda}]) is included by modifying the DP kernel; for (\lambda \gg {R,s}), the timescale reduces approximately by (1+\alpha). For the benchmark ((\alpha,\lambda)=(612.5,20.4,\mu\mathrm{m})), the predicted timescale is (\sim 0.9)–(9.7) seconds.