Spin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« lessSpin polarized hydrogen and helium are being studied extensively because they are expected to exhibit quantum effects on a macroscopic scale. Here, low density properties of spin polarized hydrogen gas in two and three dimensions are studied using a quantum virial expansion. These properties include heat capacities, chemical potentials, and estimates of critical temperatures and densities for Bose-Einstein condensation in three dimensions and for a possible superfluid transition in two dimensions. The classical virial expansion and the validity of effective-range theory is also discussed. The heat capacity of adsorbed helium films of 3He, 4He and spin polarized 3He is also studied. Virial calculations with a structureless substrate approximation but with substrate mediated corrections to the Lennard-Jones potential are performed as a function of applied magnetic field and magnetization. Effects of substrate potential and geometry on the thermodynamics, low density submonolayer helium films physisorbed on rare gas plated graphite substrates are investigated using a tight-binding formalism and a lattice version of potential scattering theory. A generalization of the formalism to lattices with a basis is made and applied to the honeycomb lattice. The calculations with this theory exhibit systematic trends in the specific heat that are in qualitative agreement with presentlymore » available experimental data.« less

Jan 1, 19830 citations

Chapter 3: Spin-Polarized Atomic Hydrogen

Isaac F. Silvera, Jook T. M. Walraven

Progress in low temperature physicsJan 1, 198675 citations

Frequency Shifts in Spin-Exchange Optical Pumping Experiments

L. C. Balling, R. J. Hanson, F. M. Pipkin

A theory is derived to predict the density matrices describing two atoms after a spin-exchange collision from the density matrices before the collision and the scattering amplitude for binary collisions. This theory is then applied to a system of quasifree electrons interacting with optically pumped rubidium atoms. For calculating the change in the electron density matrix, the ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ are replaced by a fictitious rubidium isotope with no nuclear spin. Expressions are derived for the change in the light transmission when a radiofrequency field is present at the electron frequency. In addition to the linewidth for the electron signal, the spin-exchange theory predicts a frequency shift the magnitude of which depends upon the two-body scattering amplitude, the rubidium polarization and the rubidium density. Experiments performed to test various aspects of the theory are then reported. The measurements were made on a system of quasifree electrons interacting with rubidium atoms. Measurements of the electron linewidth as a function of temperature indicated that spin-exchange collisions dominated the electron relaxation. The predicted frequency shift was measured by observing the electron resonance frequency first with left circularly polarized light and then with right circularly polarized light. For electrons colliding with rubidium atoms the shift is negative when the rubidium polarization is positive and the ratio of the shift to the linewidth is $\frac{\ensuremath{\delta}{\ensuremath{\nu}}_{0}}{\ensuremath{\Delta}\ensuremath{\nu}}=\ensuremath{-}0.025\ifmmode\pm\else\textpm\fi{}0.005$. From the measured values of the shift and the linewidth, a value is derived for the electron-rubidium spin-flip cross section. In one Appendix the replacement of the ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ by the fictitious rubidium isotope with no nuclear spin is justified. In a second Appendix the calculations for the simple electron-rubidium system are generalized and applied to more complicated systems. Results are reported for the change in the density matrix of hydrogen atoms when they collide with polarized electrons, the change in the density matrix of ${\mathrm{Rb}}^{87}$ atoms when they collide with polarized electrons, and the change in the density matrix of hydrogen atoms when they collide with hydrogen atoms.A theory is derived to predict the density matrices describing two atoms after a spin-exchange collision from the density matrices before the collision and the scattering amplitude for binary collisions. This theory is then applied to a system of quasifree electrons interacting with optically pumped rubidium atoms. For calculating the change in the electron density matrix, the ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ are replaced by a fictitious rubidium isotope with no nuclear spin. Expressions are derived for the change in the light transmission when a radiofrequency field is present at the electron frequency. In addition to the linewidth for the electron signal, the spin-exchange theory predicts a frequency shift the magnitude of which depends upon the two-body scattering amplitude, the rubidium polarization and the rubidium density. Experiments performed to test various aspects of the theory are then reported. The measurements were made on a system of quasifree electrons interacting with rubidium atoms. Measurements of the electron linewidth as a function of temperature indicated that spin-exchange collisions dominated the electron relaxation. The predicted frequency shift was measured by observing the electron resonance frequency first with left circularly polarized light and then with right circularly polarized light. For electrons colliding with rubidium atoms the shift is negative when the rubidium polarization is positive and the ratio of the shift to the linewidth is $\frac{\ensuremath{\delta}{\ensuremath{\nu}}_{0}}{\ensuremath{\Delta}\ensuremath{\nu}}=\ensuremath{-}0.025\ifmmode\pm\else\textpm\fi{}0.005$. From the measured values of the shift and the linewidth, a value is derived for the electron-rubidium spin-flip cross section. In one Appendix the replacement of the ${\mathrm{Rb}}^{85}$ and ${\mathrm{Rb}}^{87}$ by the fictitious rubidium isotope with no nuclear spin is justified. In a second Appendix the calculations for the simple electron-rubidium system are generalized and applied to more complicated systems. Results are reported for the change in the density matrix of hydrogen atoms when they collide with polarized electrons, the change in the density matrix of ${\mathrm{Rb}}^{87}$ atoms when they collide with polarized electrons, and the change in the density matrix of hydrogen atoms when they collide with hydrogen atoms.

Physical ReviewFeb 3, 1964131 citations

{\mathrm{Rb}}^{85}

and

{\mathrm{Rb}}^{87}

are replaced by a fictitious rubidium isotope with no nuclear spin. Expressions are derived for the change in the light transmission when a radiofrequency field is present at the electron frequency. In addition to the linewidth for the electron signal, the spin-exchange theory predicts a frequency shift the magnitude of which depends upon the two-body scattering amplitude, the rubidium polarization and the rubidium density. Experiments performed to test various aspects of the theory are then reported. The measurements were made on a system of quasifree electrons interacting with rubidium atoms. Measurements of the electron linewidth as a function of temperature indicated that spin-exchange collisions dominated the electron relaxation. The predicted frequency shift was measured by observing the electron resonance frequency first with left circularly polarized light and then with right circularly polarized light. For electrons colliding with rubidium atoms the shift is negative when the rubidium polarization is positive and the ratio of the shift to the linewidth is $\frac{\ensuremath{\delta}{\ensuremath{\nu}}_{0}}{\ensuremath{\Delta}\ensuremath{\nu}}=\ensuremath{-}0.025\ifmmode\pm\else\textpm\fi{}0.005$. From the measured values of the shift and the linewidth, a value is derived for the electron-rubidium spin-flip cross section. In one Appendix the replacement of the

{\mathrm{Rb}}^{85}

and

{\mathrm{Rb}}^{87}

by the fictitious rubidium isotope with no nuclear spin is justified. In a second Appendix the calculations for the simple electron-rubidium system are generalized and applied to more complicated systems. Results are reported for the change in the density matrix of hydrogen atoms when they collide with polarized electrons, the change in the density matrix of

{\mathrm{Rb}}^{87}

atoms when they collide with polarized electrons, and the change in the density matrix of hydrogen atoms when they collide with hydrogen atoms.