Test of the Linearity of Quantum Mechanics Using ARGON-37 Polarized by Spin-Exchange Optical Pumping.

Recently, Steven Weinberg has formulated a general framework for introducing nonlinear corrections to quantum mechanics. This thesis describes the use of polarized ^{37}Ar nuclei in a search for evidence of such nonlinear terms in the Schrodinger equation. The ^{37}Ar nuclei are polarized by the method of spin exchange with optically -pumped potassium atoms. This is the first application of this method to an argon isotope, so we have made measurements of nuclear polarization relaxation rates and nuclear magnetic resonance frequency shifts due to the K-^ {37}Ar interaction. From these data we determine that, at 62 torr nitrogen pressure, 59 +/- 21% of the spin-exchange rate is due to spin exchange in van der Waals molecules with the remainder due to binary collisions. The polarization of the ^{37}Ar nuclei is determined by measuring the parity-violating asymmetry in the angular distribution of the internal bremsstrahlung that accompanies the electron capture decay of ^{37 }Ar. Our maximum observed nuclear polarization is 56%. The nonlinear quantum mechanics test is performed by doing a transient nuclear magnetic resonance experiment on the polarized ^{37}Ar. The nuclei interact with the magnetic field and electric field gradients at the cell wall. This leads to a signal that is the superposition of three exponentially decaying sinusoids with a transverse relaxation time of 1 hour, allowing for very precise frequency measurements. We search for a dependence of the precession frequencies on the initial projection of the nuclear spins along the magnetic field axis. In this way we set a 1sigma confidence level upper limit of {|varepsilon |over h}<3.9 mu{rm Hz} on Weinberg's nonlinearity parameter varepsilon. This limit implies that the fraction of the binding energy per ^ {37}Ar nucleon that could be due to nonlinear corrections to quantum mechanics is <2.0 times 10^{-27 }.. We also measure the magnetic moment of ^{37}Ar to be 1.146(1) mu_{N}, a factor of 200 more precise than the previous measurement. This new value is included in an analysis of the magnetic moments and Gamow-Teller strengths of isospin-mirror ground state nuclear pairs.