Muon Capture on the Proton and Deuteron

By measuring the lifetime of the negative muon in pure protium (hydrogen-1), the MuCap experiment determines the rate of muon capture on the proton, from which the proton's pseudoscalar coupling g_p may be inferred. A precision of 15% for g_p has been published; this is a step along the way to a goal of 7%. This coupling can be calculated precisely from heavy baryon chiral perturbation theory and therefore permits a test of QCD's chiral symmetry. Meanwhile, the MuSun experiment is in its final design stage; it will measure the rate of muon capture on the deuteron using a similar technique. This process can be related through pionless effective field theory and chiral perturbation theory to other two-nucleon reactions of astrophysical interest, including proton-proton fusion and deuteron breakup.Comment: Submitted to the proceedings of the 2007 Advanced Studies Institute on Symmetries and Spin (SPIN-Praha-2007

Vectorial Ribaucour Transformations for the Lame Equations

The vectorial extension of the Ribaucour transformation for the Lame equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an example we apply the vectorial Ribaucour transformation to the Cartesian background.Comment: 12 pages. LaTeX2e with AMSLaTeX package

A high-pressure hydrogen time projection chamber for the MuCap experiment

The MuCap experiment at the Paul Scherrer Institute performed a high-precision measurement of the rate of the basic electroweak process of nuclear muon capture by the proton, $\mu^- + p \rightarrow n + \nu_\mu$. The experimental approach was based on the use of a time projection chamber (TPC) that operated in pure hydrogen gas at a pressure of 10 bar and functioned as an active muon stopping target. The TPC detected the tracks of individual muon arrivals in three dimensions, while the trajectories of outgoing decay (Michel) electrons were measured by two surrounding wire chambers and a plastic scintillation hodoscope. The muon and electron detectors together enabled a precise measurement of the $\mu p$ atom's lifetime, from which the nuclear muon capture rate was deduced. The TPC was also used to monitor the purity of the hydrogen gas by detecting the nuclear recoils that follow muon capture by elemental impurities. This paper describes the TPC design and performance in detail.Comment: 15 pages, 13 figures, to be submitted to Eur. Phys. J. A; clarified section 3.1.2 and made minor stylistic corrections for Eur. Phys. J. A requirement

Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar Coupling g_P

The MuCap experiment at the Paul Scherrer Institute has measured the rate L_S of muon capture from the singlet state of the muonic hydrogen atom to a precision of 1%. A muon beam was stopped in a time projection chamber filled with 10-bar, ultra-pure hydrogen gas. Cylindrical wire chambers and a segmented scintillator barrel detected electrons from muon decay. L_S is determined from the difference between the mu- disappearance rate in hydrogen and the free muon decay rate. The result is based on the analysis of 1.2 10^10 mu- decays, from which we extract the capture rate L_S = (714.9 +- 5.4(stat) +- 5.1(syst)) s^-1 and derive the proton's pseudoscalar coupling g_P(q^2_0 = -0.88 m^2_mu) = 8.06 +- 0.55.Comment: Updated figure 1 and small changes in wording to match published versio

Measurement of the Rate of Muon Capture in Hydrogen Gas and Determination of the Proton's Pseudoscalar Coupling gPg_P

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 target's 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.Comment: submitted to Phys.Rev.Let

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

A Circulating Hydrogen Ultra-High Purification System for the MuCap Experiment

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 with 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.Comment: submitted to Nucl. Instr. Methods Phys. Res.