Recent data on backward pion production in 0.8-4.89-GeV proton-nucleus collisions are analyzed within the scope of models where target nucleons react collectively. It is shown that the nuclear-size dependence in data is a sensitive probe of the effective target mass. The experimental results hint at a synthesis of the cluster ("fluctuon") model and the collective tube model. PACS numbers: 13.85. Kf, 12.40.Cc, 25.40.Rb, 24.10.Dp In a recent Lawrence Berkeley Laboratory experiment Schroeder etal. 1 measured the backward yield of pions inp +A-^(180°) +X at kinetic energies 7^ = 0.8-4.89 GeV and with nuclear targets having A = 12-207. Special attention was given to the so-called cumulative production discovered by Baldin etal. in 1971. 2 This occurrence of pions with T^>T^{NN^NNn) has inspired a vast amount of theoretical work. Many theories for high-energy collisions with nuclei are built on intuitive pictures of the space-time development of a hadronic collision. 3 Most, of these are expected to work only when the nucleus is Lorentz contracted to a thickness of less than around 1 fm in the projectile rest system, or alternatively, when a typical reaction time exceeds the time which the projectile needs to pass the whole nucleus. As this happens only at T P <;A 1/3 GeV, the data of Ref. 1 cover an interesting transition region in T p .The data demonstrate three clear energy dependences from 0.8 to 4.89 GeV. First, the ratio 7r"/7r + of produced pions grows from 0.3 to 1. Second, the pion spectrum obeys E da/d 3 p ~ exp(-T ff / T 0 ) with T 0 growing from 30 to 60 MeV. Third, the A dependence changes. One finds that Edo/ d 3 p ~A n {T v ) at fixed T\. At ^ = 0.8 GeV the exponent n~ 0.8 for all T v . At T p = 4.89 GeV there is, however, an increase in n{T^) with T".. For T\ «2.5T ff max one finds n* 1.2, which is a considerable enhancement compared to the 0.8-GeV data. All these trends indicate that there is a limiting situation at infinite energies which seems to be reached already in the 8.4-GeV data of Baldin et al. 4 and perhaps even in the 4.89-GeV data.The aim of this Letter is to show that the A dependence serves as a sensitive test of theoretical models of the nuclear response in high-energy collisions with nuclei. The slope parameter T 0 and the ratio 7r"Ar + , taken on a fixed nucleus, do not play this role. They instead probe the nature of the quark reaction responsible for cumulative production.There are two different ways of explaining the existence of cumulative pions: Either the effective target is not stationary or it is more massive than a single nucleon.The conclusion from models where nucleonic Fermi motion is held responsible for cumulative production is that "too many" fast nucleons are needed. I will not analyze these models, because any data can naturally be fitted with some Fermi motion. Data show that such a distribution would have to be strongly A dependent at 4.89 GeV but virtually A independent at 0.8 GeV. This is hard to understand since the Fermi motion depends only on the nuclear d...