We propose to measure the rate Rd for muon capture on the deuteron to better than 1.5% precision. This process is the simplest weak interaction process on a nucleus that can both be calculated and measured to a high degree of precision. The measureme
nt will provide a benchmark result, far more precise than any current experimental information on weak interaction processes in the two-nucleon system. Moreover, it can impact our understanding of fundamental reactions of astrophysical interest, like solar pp fusion and the $ u+d$ reactions observed by the Sudbury Neutrino Observatory. Recent effective field theory calculations have demonstrated, that all these reactions are related by one axial two-body current term, parameterized by a single low-energy constant. Muon capture on the deuteron is a clean and accurate way to determine this constant. Once it is known, the above mentioned astrophysical, as well as other important two-nucleon reactions, will be determined in a model independent way at the same precision as the measured muon capture reaction.
The singlet capture rate $Lambda_S$ for the semileptonic weak process $mu+p to n+ u_mu$ has been measured in the MuCap experiment. The novel experimental technique is based on stopping muons in an active target, consisting of a time projection chambe
r operating with ultra-pure hydrogen. This allows the unambiguous determination of the pseudoscalar form factor $g_P$ of the charged electroweak current of the nucleon. Our first result $g_P(q^2=-0.88 m^2_mu) = 7.3 pm 1.1 $ is consistent with accurate theoretical predictions and constitutes an important test of QCD symmetries. Additional data are being collected with the aim of a three-fold reduction of the experimental uncertainties. Building on the developed advanced techniques, the new MuSun experiment is being planned to measure the muon capture rate on the deuteron to 1.5% precision. This would provide the by far most accurate experimental information on the axial current interacting with the two-nucleon system and determine the low energy constant $L_{1A}$ relevant for solar neutrino reactions. Muon induced atomic and molecular processes represent challenges as well as opportunities for this science program, and their interplay with the main nuclear and weak-interaction physics aspects will be discussed.
The MuCap experiment is a high-precision measurement of the rate for the basic electroweak process of muon capture, mu- + p -> n + nu . The experimental approach is based on an active target consisting of a time projection chamber (TPC) operating wit
h pure hydrogen gas. The hydrogen has to be kept extremely pure and at a stable pressure. A Circulating Hydrogen Ultrahigh Purification System was designed at the Petersburg Nuclear Physics Institute (PNPI) to continuously clean the hydrogen from impurities. The system is based on an adsorption cryopump to stimulate the hydrogen flow and on a cold adsorbent for the hydrogen cleaning. It was installed at the Paul Scherrer Institute (PSI) in 2004 and performed reliably during three experiment runs. During several months long operating periods the system maintained the hydrogen purity in the detector on the level of 20 ppb for moisture, which is the main contaminant, and of better than 7 ppb and 5 ppb for nitrogen and oxygen, respectively. The pressure inside the TPC was stabilized to within 0.024% of 10 bar at a hydrogen flow rate of 3 standard liters per minute.
The rate of nuclear muon capture by the proton has been measured using a new experimental technique based on a time projection chamber operating in ultra-clean, deuterium-depleted hydrogen gas at 1 MPa pressure. The capture rate was obtained from the
difference between the measured $mu^-$ disappearance rate in hydrogen and the world average for the $mu^+$ decay rate. The targets low gas density of 1% compared to liquid hydrogen is key to avoiding uncertainties that arise from the formation of muonic molecules. The capture rate from the hyperfine singlet ground state of the $mu p$ atom is measured to be $Lambda_S=725.0 pm 17.4 s^{-1}$, from which the induced pseudoscalar coupling of the nucleon, $g_P(q^2=-0.88 m_mu^2)=7.3 pm 1.1$, is extracted. This result is consistent with theoretical predictions for $g_P$ that are based on the approximate chiral symmetry of QCD.
