## 4 The New Scattering Effect  
### Example: INS from Single H\({}_{2}\) Molecules in C-Nanotubes  
Carrying out materials science research, a striking INS finding was recently observed [28] in the quantum excitation spectrum of H\({}_{2}\) adsorbed in multi-walled nanoporous carbon. The latter have pore diameters in the range 8-20 A). These experiments were carried out with the TOF spectrometer ARCS (SNS, O.R.N.L., USA) [15]. The temperature was \(T=23\) K. The incident neutron energy was \(E_{0}=90\) meV. Consequently, the energy transfers in this experiment cannot excite H\({}_{2}\)-vibrations, but rotations and translation (which is also called recoil) only. Note that H\({}_{2}\) interacts only weakly with the substrate. Thus it holds  
\[E=E_{rot}+E_{trans}. \tag{9}\]  
The measured two-dimensional INS intensity map \(S(K,E)\) of H is presented in Figure 3, which is reproduced from the original publication of [PERSON] et al. [28]. The following features should be observed.The intensive peak centered at \(E_{rot}\approx 14.7\) meV is due to the first rotational excitation \(J=0\to 1\) of the H\({}_{2}\) molecule [11]. Furthermore, the corresponding momentum transfer of this intensity peak is \(K_{rot}\approx 2.7\) A\({}^{-1}\). Hence, the peak position in the \(K-E\) plane fulfills the relation \(E_{rot}=(\hbar K_{rot})^{2}/2M_{H}\) with the mass \(M_{H}\) of the free H atom,  
\[\text{H}_{2}\text{ rotation }(J=0\to 1):\ \ M_{eff}=M_{H}=1.0079\ \text{ a.m.u.} \tag{10}\]  
Thus the spectral position of this rotational excitation in the \(K-E\) plane is fully in line with conventional expectations, and one can say that each neutron scatters from a single H atom. Recall that an agreement with conventional theory was also observed in scattering from \({}^{4}\)He. However, the novel finding of [28] is the following. A detailed numerical analysis of the roto-recoil data (as shown in Figure 3) was presented, from which the authors extracted a strongly reduced effective mass of the recoiling H\({}_{2}\) molecule (left parabola, green):  
\[\text{H}_{2}\text{ translation (recoil):}\ \ \ M_{eff}(\text{H}_{2})\approx 0.64 \pm 0.07\ \text{ a.m.u.} \tag{11}\]  
Additionally, no significant sample-dependent variation in this value was found. This result is in blatant contrast to the conventionally expected value \(M(\text{H}_{2})=2.01\) a.m.u. for a freely recoiling H\({}_{2}\) molecule (right parabola). This striking experimental result provides strong evidence for the new \"anomalous\" effect of excess \(E\)-transfer (or equivalently, \(K\)-transfer deficit [26]) accompanying an elementary collision of a neutron with a recoiling molecule. As already pointed out, every conventional H\({}_{2}\)/substrate binding can never decrease the molecule's effective mass. Therefore these INS results contradict conventional theoretical expectations. However, as discussed below, they find a natural interpretation in the frame of QTD. Second Example--INS from Single H\({}_{2}\) Molecules in the Metal-Organic Framework Material \"HKUST-1\"  
Due to its considerable magnitude, the surprising E-excess quantum effect discussed in the preceding subsection could be suspected to be an experimental artifact (e.g., due to wrongly calibrated spectrometer, erroneous data analysis, etc.). Hence it is important to have another, fully independent confirmation of this effect. Aiming at discovering novel materials for potential use in the storage and transport of hydrogen for energy applications, also the adsorption of H\({}_{2}\) on porous metal-organic framework materials has attracted much attention over the past few years. Among the wide diversity of such suitable materials, the material known as HKUST-1 (see [29] for its chemical formula and structure) has emerged as a model system for adsorption studies. For our present purposes, it is sufficient to note that HKUST-1 constitutes a three-dimensionally connected network that has a trimodal pore structure, having pores with diameters in the range 5-12 A.