famu.tex

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\title{FAMU: optimizing the conditions to measure the HFS in the $\mu$p-p ground state}

\author{Emiliano Mocchiutti on behalf of the FAMU Collaboration}

\address{National Institute for Nuclear Physics (INFN), Sezione di Trieste, via A. Valerio 2, 34127 Trieste, Italy}

\ead{Emiliano.Mocchiutti@ts.infn.it}

\begin{abstract}
The FAMU experiment main goal is the measurement of the proton Zemach
radius using muonic hydrogen. In order to extract the Zemach radius,
preliminary measurements of the muon transfer rate from hydrogen to
higher Z gas are needed. In 2017 the FAMU collaboration had
one data taking sessions at the Rutherford Appleton Laboratory (UK)
aimed at studying the muon beam characteristics and at extending the
measurement of the temperature dependence of the transfer rate from muonic hydrogen to oxygen.
\end{abstract}

\section{FAMU goals} 
 Preliminary experimental studies have been performed in preparation
 of the measurement of the hyperfine splitting (hfs) in the 1S state
 of muonic hydrogen $\Delta E_{hfs}(\mu p)1S$, to allow the choice of the final
 lay-out and confirm the details of the foreseen methodology~\cite{adam1,baka1,baka2,adam2,mocchi,vacchi1}. We
 report the results of the experimental phase performed at the Port 1
 of RIKEN RAL facility during 2017. By measuring the transition
 $\Delta E_{hfs}(\mu p)1S$ in $\mu$p with $\delta \lambda/\lambda<10^{-5}$, the experiment will provide the
 Zemach radius of the proton $r_Z$ with high precision, disentangling in
 this way among discordant theoretical values. The level of
 discrepancy between values of $r_Z$ as extracted from normal and muonic
 hydrogen atoms will be quantified, a result important also for the
 not yet explained anomalies on the charge rch radius of the
 proton. The physical process behind this experiment is the following:
 $\mu$p are formed in a mixture of hydrogen and a higher-Z gas. When
 absorbing a photon at resonance-energy $\Delta E_{hfs}\approx$0.182 eV, in subsequent
 collisions with the surrounding $H_2$ molecules, the $\mu$p is quickly
 de-excited and and accelerated by ~2/3 of the excitation energy. The
 observable is the time distribution of the K-lines X-rays emitted
 from the $\mu$Z formed by muon transfer $(\mu p)+Z\rightarrow (\mu Z)^*+p$, a reaction whose
 rate depends on the μp kinetic energy. The maximal response, to the
 tuned laser wavelength, of the time distribution of X-ray from
 K-lines of the $(\mu Z)^*$ cascade indicate the resonance. 

\section{Muon beam tuning} 
 During 2017, using the beam-hodoscopes set~\cite{bone} developed on
 purpose, it has been possible to verify the adaptability of the beam
 to our experimental lay-out. 

 \begin{figure}[!hbt]
   \centering
   \includegraphics[width=0.6\textwidth]{fig1.eps}
   \caption{Hodoscope beam profile (inset) and total charge collected.}
   \label{hodo}       
 \end{figure}
 Figure~\ref{hodo} shows the beam profile (inset, 1 mm per strip) and the total
 charge detected by the hodoscope before (dashed line) and after (solid
 line) magnets tuning. As can be seen from Fig.~\ref{hodo} a gain of about 10\%
 in the muon beam intensity was obtained. 

\section{Measurement of the transfer rate}
 As an addition to the
 previously performed measurements in 2016 of the muon transfer rate
 to oxygen at different temperatures, the same FAMU cryogenic gas
 target~\cite{vacchi2} has been used to perform a detailed study of the shape of
 the background underneath the peaks of the x-rays characterizing the
 delayed transition of the muon from $\mu$p
 to oxygen. The target loaded with high purity hydrogen has been
 exposed to the 57 MeV/c muon beam, the x-ray spectra was detected
 with LaBr fast detectors~\cite{baldaz}. During a subsequent phase dedicated to
 extend the temperature range of the 2016 transfer rate measurements
 it was discovered with great disappointment that the custom delivered
 gas mixture was badly polluted with nitrogen.

 Since it was impossible
 to obtain timely a new delivery, to make virtue of necessity and
 obtain useful data we investigated the condensation temperature
 limits of the heavy elements in the available mixture. Under the
 assumption of perfect gases and the Dalton law, we can calculate that
 the gas condensation on the internal vessel surface occur at 54~K for
 oxygen and 46~K for nitrogen but in our experimental conditions of
 pressurized gas mixture this needs to be experimentally verified.  
 \begin{figure}[!hbt]
   \centering
   \includegraphics[width=0.6\textwidth]{fig2.eps}
   \caption{X-rays energy spectrum at 47 and 42~K, the nitrogen lines disappear.}
   \label{xray}       
 \end{figure}
 Figure~\ref{xray}, 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. It can be noticed that the nitrogen lines
 disappears due to its condensation on the target walls and a pure hydrogen background signal remain visible.

 In 2017 the system performed as expected. Data collected allow to
 verify the beam shape and position for the gas target and optical
 cavity of the final experiment.

\section{FAMU computing during CNAF shutdown} 
Due to the major accident at CNAF site in late 2017, most of the data
analysis has been moved by the FAMU collaboration to the computing
farm at Trieste INFN site. Most of the data were recovered using
external disk backups.

\section{Conclusions} 
CNAF continues to play a major role in the computing of the FAMU
experiment. Most of the computing resources and all the storage
capabilities are provided by this facility. The CNAF shutdown caused
some delays to the data analysis. However, 2017 data set was used to
better determine the experimental conditions of the final experiment.

\ack
The research activity presented in this paper has been carried out in the framework of the FAMU
experiment funded by Istituto Nazionale di Fisica Nucleare (INFN). The use of the low energy muons
beam has been allowed by the RIKEN RAL Muon Facility. We thank the RAL
staff (cooling, gas, and radioactive sources sections) and especially Mr. Chris Goodway,
Pressure and Furnace section Leader, for their help, suggestions,
professionality and precious collaboration in the set up of the
experiment at RIKEN-RAL port 4 and port 1.
We gratefully recognize the help of T. Schneider, CERN EP division,
for his help in the optical
cutting of the scintillating fibers of the hodoscope detector and the
linked issues and N. Serra from Advansid srl for useful discussions on SiPM problematics.
We thank our colleagues Chiara Boschi and Ilaria Baneschi (IGG, CNR
Pisa) for their help in the measurement of the gas isotopic composition.
A. Adamczak and D. Bakalov acknowledge the support within the
bilateral agreement between the Bulgarian Academy of Sciences and the Polish Academy of Sciences.
D. Bakalov, P. Danev and M. Stroilov acknowledge the support of Grant 08-17 of the Bulgarian Science Fund.
The collaboration gratefully acknowledge the International Society for
Optics and Photonics (SPIE) for the the crucial support in the
development of the laser source of the FAMU experiment.
\vspace{10mm}

\begin{thebibliography}{}
\bibitem{adam1} 
Adamczak A et al 2012 {\it NIM Section B} {\bf 281}

\bibitem{baka1}
Bakalov D et al 2015 {\it Hyp. Int.} {\bf 233}

\bibitem{baka2}
Bakalov D et al 2015 {\it Phys. Lett. A} {\bf 379}

\bibitem{adam2}
Adamczak A et al 2016 {\it J. of Inst.} {\bf 11}

\bibitem{mocchi}
Mocchiutti E et al 2018 {\it J. of Inst.} {\bf 13}

\bibitem{vacchi1}
Vacchi A et al 2016 {\it RIKEN Accel. Prog. Rep.} {\bf 49}

\bibitem{bone}
Bonesini M et al 2017 {\it J. of Inst.} {\bf 12}

\bibitem{vacchi2}
Vacchi A et al 2017 {\it RIKEN Accel. Prog. Rep.} {\bf 50}

\bibitem{baldaz}
Baldazzi G et al 2017 {\it J. of Inst.} {\bf 12}

\end{thebibliography}
\end{document}