Cryogenic masers

Various factors affecting the frequency stability of hydrogen masers are described and related to maser design parameters. The long-term frequency stability of a hydrogen maser is limited by the mechanical stability of the cavity, and the magnitudes of the wall relaxation, spin exchange, and recombination rates which affect the Q of the line. Magnetic resonance studies of hydrogen atoms at temperatures below 1 K and in containers coated with liquid helium films demonstrated that cryogenic masers may allow substantial improvements in all of these parameters. In particular the thermal expansion coefficients of most materials are negligible at 1 K. Spin exchange broadening is three orders of magnitude smaller at 1 K than at room temperature, and the recombination and wall relaxation rates are negligible at 0.52 K where the frequency shift due to the 4 He-coated walls of the container has a broad minimum as a function of temperature. Other advantages of the helium-cooled maser result from the high purity, homogeneity, and resilence of helium-film-coated walls and the natural compatibility of the apparatus with helium-cooled amplifiers

Impurity scattering and localization in dd-wave superconductors

Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of non-magnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to $50\times 50$ sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite size dependence of inverse participation ratios.Comment: 4 pages REVTeX with 2 embedded .ps figures; submitted to PRB as Rapid Communicatio

Theoretical Analysis of Inelastic Neutron Scattering in Solid Hydrogen

The inelastic-neutron-scattering cross section of (J=1) solid hydrogen is studied and the experimental data of Stein and co-workers analyzed. The rms displacement ⟨u2⟩1/2 is deduced from the data via different methods and mutually consistent values of order 0.65 Å are obtained. The enhancement of the cross section at the libron energy due to libron-phonon interactions is found to be the same, about 40% each for both one-and two-libron processes, in agreement with the neutron scattering data. The rms splitting at the libron-phonon crossovers is found to be about 1 cm−1, somewhat smaller than found by Mertens and Biem. A sum rule for the J=1 to J=0 cross section is given which relates the average energy of this transition to the orientational internal energy. Using high-temperature expansions and experimental data for the specific heat, we obtain a qualitative fit to the neutron scattering data in the orientationally disordered phase. In the ordered phase both the sum rule and a direct calculation indicate the existence of a libron sideband above the main J=1 to J=0 line having an intensity of 10% of the main line. The energy of the main line at zero temperature is calculated including (a) tipping corrections, (b) virtual excitations with J not conserved, and (c) modified zero-point energy. The value of the electrostatic quadrupole-quadrupole coupling constant deduced from the data of Stein and co-workers using this calculation is in agreement with that obtained from other experiments