Ⅱ-9. Instrumentation

RIKEN Accel. Prog. Rep. 51 (2018)

Optimizing the conditions to measure the hyperfine splittingin the µp ground state
A. Vacchi,∗1,∗2,∗3 K. Ishida,∗1 E. Mocchiutti,∗3 and E. Furlanetto∗2,∗3 on behalf of the FAMU collaboration
Experimental studies were performed during 2017 at
Port 1 of the RIKEN RAL facility, in preparation forthe measurement of the hyperﬁne splitting in the 1S
state of muonic hydrogen ∆Ehfs (µ − p)1S , to allow thechoice of the ﬁnal layout and conﬁrm the details of theforeseen methodology.1–6) By measuring the transition∆Ehfs (µ − p)1S in µp with a precision of < 10−5 , the experiment will provide the Zemach radius of the proton rZ
with high precision, allowing diesntanglement of the discordant theoretical values. The level of discrepancy between the values of rZ as extracted from the normal andmuonic hydrogen atoms will be quantiﬁed, a result thatis also important for the not yet explained anomalies on
the charge rch radius of the proton. The physical process
behind this experiment is as follows: µp are formed in amixture of hydrogen and a higher-Z gas. When a photon
is absorbed at resonance-energy ∆Ehfs ≈ 0.182 eV, in subsequent collisions with the surrounding H2 molecules, theµp is quickly de-excited and and accelerated by ∼2/3 ofthe excitation energy. The observable is the time distribution of the K X-rays emitted from the µZ formed by muontransfer (µp) + Z → (µZ)∗ + p, a reaction whose rate depends on the µp kinetic energy. The maximal response,to the tuned laser wavelength, of the time distribution ofK X-ray from the (µZ)∗ cascade indicates the resonance.
During 2017, using the set of beam-hodoscopes7) developed for this purpose, it has been possible to show
the adaptability of the beam to our layout and to verify
its shape and position. Figure 1 shows the total charge
deposited in the hodoscope, an increase of about 10% indicates that by tuning the beam optics a muon beam intensity increase was obtained.
Subsequently, as an addition to the previously performed measurements (in 2016) of the muon transfer rateto oxygen at diﬀerent temperatures, the same FAMU
cryogenic gas target8) was used to perform a detailed
study of the shape of the background underneath thepeaks of the x-rays characterizing the delayed transition

Fig. 2. Upper panel, shows the delayed nitrogen X-rays lines
at a temperature of 47 K. In the lower panel the same
spectrum is shown at a temperature of 42 K.

of the muon from µp to oxygen. The target loaded withhigh purity hydrogen was exposed to the 57 MeV/c muon
beam, the x-ray spectra was detected with LaBr fast detectors.9)
During the following phase, dedicated to extending thetemperature range of the 2016 transfer rate measurements, it was discovered with great disappointment thatthe custom delivered gas mixture was badly polluted withnitrogen. Since it was impossible to obtain a new delivery
on time, by virtue of necessity and to obtain useful data,
we investigated the condensation temperature limits of
the heavy elements in the available mixture. Under theassumption of perfect gases and the Dalton law, we cancalculate that the gas condensation on the internal vessel
surface occur at 54 K for oxygen and 46 K for nitrogen,however in our experimental conditions of pressurized gas
mixture, this needs to be veriﬁed experimentally.
The delayed nitrogen X-rays lines, at the temperatureof 47 K, is shown in the upper panel of Fig. 2. At 42 K thenitrogen lines disappear and pure hydrogen background
distribution remains visible in the lower panel. The equipment used in the 2017 experiments performed as expected
except for the gas contamination. This has restricted ourprogram especially the possibility to extend the study oftransfer rate to oxygen at higher temperatures.
ReferencesFig. 1. Total charge detected by the hodoscope before (reddashed line) and after (black solid line) the tuning of themagnets and, in the insert, the two dimensional beam profile of 1 mm per strip.
∗1
∗2
∗3

RIKEN Nishina Center
Department Math, Info, Physics, University of Udine
INFN Trieste

1) A. Adamczak, et al., Nucl. Instrum. Methods Phys. Res B
281, 72–76 (2012).
2) D. Bakalov et al., Hyp. Int. 233, 97–101 (2015).
3) D. Bakalov et al., Phys. Lett. A 379, 151–156 (2015).
4) A. Adamczak et al., J. of Inst. 11, P05007 (2016).
5) E. Mocchiutti et al., arXiv:1708.03172 [physics] (2017).
6) A. Vacchi et al., RIKEN Accel. Prog. Rep. 49, 230 (2016).
7) M. Bonesini et al., J. of Inst. 12, C03035 (2017).
8) A. Vacchi et al., RIKEN Accel. Prog. Rep. 50, 24 (2017).
9) G. Baldazzi, et al., J. of Inst. 12, C03067 (2017).

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