Time-of-flight spectra

In this section, we shall discuss our time-of-flight spectrum (TOFS) measurements. Table 8.14 summarizes the runs for TOF time spectra measurements. In all of these runs, we had a 14 T$\cdot l$D₂ layer US to slow down the $\mu t$ beam emitted from the emission layer. Recall that the RT minimum is around 10-15 eV in lab $\mu t$energy, which is too high for the resonant molecular formation energies that we are interested in. While Series A had a 500 T$\cdot l$ H₂substrate under the D₂ reaction layer DS, in Series B the deuterium was deposited directly on the Au foil. The H₂ substrate was initially used with the intention of reducing a background (especially in the neutron detectors) from muon capture on Au, which comes from $\mu t$ passing through the thin reaction layer and reaching the Au foil, hence having the time structure similar to that of a real signal. But as we saw in the yield measurements, the H₂ causes significant background due to muon decay, and as far as the background with the characteristic time-of-flight is concerned, it is dominated by the $\mu t$ directly hitting the Si detectors. Furthermore, it was learned in the course of the analysis that the H₂ substrate creates some ambiguity in the interpretation of the data due to possible $\mu t$ re-emission.

 

Table 8.14: Summary of the runs for the TOF time measurements. See Tables 8.7, 8.8 for the background subtraction methods.

TOF spect.	ID	US	DS	DS	Energy cut	BG
		(T$\cdot l$)	substrate	(T$\cdot l$)	(MeV)	Run	Method
Series A	II-9	14	H2	3	3.1; 3.7	6+7+8	2
($c_t=0.1\%$)	II-10		(500 T$\cdot l$)	6	2.7 ;3.7	6	standard
	II-11			20	2.0 ;3.7	6	standard
Series B	II-14	14	Au foil	3	3.1;3.7	7	3-nr
($c_t=0.2\%$)	II-15		(50 $\mu$m)	23	2.0 ;3.7	7	standard

 

  

Figure 8.15: The TOF run with 3 T$\cdot l$ DS for Series A ($c_t=0.1\%$) in filled circles, together with background run BG6 in open circles, both with an energy cut of 3101<E<3700 ch (top). Background subtracted time-of-flight fusion spectrum (bottom).

  

Figure 8.16: The TOF run with 3 T$\cdot l$ DS for Series B ($c_t=0.2\%$) in filled circles, together with background run BG7 in open circles, both with an energy cut of 3101<E<3700 ch (top). Background subtracted time-of-flight fusion spectrum (bottom).

Much of the details about background and various other corrections were already given in the previous sections. It should be recalled that the background includes events from muon decay electrons, muon capture on Si, delayed dt fusion from US, and dd fusion protons (if the energy window extends lower than 3 MeV). The complexity in the background processes makes it virtually impossible to predict the time structure, and makes it unreliable to use a simple analytical function, hence we rely on bin-by-bin subtraction, which at the cost of statistical precision allows us better control of the systematics.

We show some examples of the fusion time-of-flight spectra in Figs. 8.15 and 8.16. Figure 8.15 shows the TOF spectrum for Series A ($c_t=0.1\%$) 3 T$\cdot l$ measurement, together with the background data from BG6, both with the energy cut of 3.1<E<3.7 (see Table 8.2 for the background run information), while Figure 8.16 is for the 3 T$\cdot l$ measurement in Series B ($c_t=0.2\%$). In the top figures, the non-exponential peak in the fusion time spectra is noticeable at around 2-4 $\mu$s, which, together with the lack of such a peak in the runs without DS reaction layers, indicate the fusion is indeed taking placing in the DS layer after a traversing the drift space. The fact that for the thin DS layer measurement, the energy width of these delayed events was so narrow in Fig. 8.9-8.12 in the previous section, corroborates that fusion is occurring at the downstream layer in which the $\alpha$ particle suffers less energy loss.