Exclusive measurements of the quasi-free $np to nppi^0pi^0$ reaction have been performed by means of $dp$ collisions at $T_d$ = 2.27 GeV using the WASA detector setup at COSY. Total and differential cross sections have been obtained covering the energy region $sqrt s$ = (2.35 - 2.46) GeV, which includes the region of the ABC effect and its associated $d^*(2380)$ resonance. Adding the $d^*$ resonance amplitude to that for the conventional processes leads to a reasonable description of the data. The observed resonance effect in the total cross section is in agreement with the predictions of Faldt and Wilkin as well Albadajedo and Oset. The ABC effect, {it i.e.} the low-mass enhancement in the $pi^0pi^0$-invariant mass spectrum, is found to be very modest - if present at all, which might pose a problem to some of its interpretations.
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