Spin-polarized Deuterium Research Articles

Depolarization of spin-polarized hydrogen via collisions with chlorine atoms at ultrahigh density

Recently, the production of ultrahigh-density (∼1019cm−3) spin-polarized deuterium (SPD) atoms was demonstrated, from the photodissociation of deuterium iodide, but the upper density limit was not determined. Here, we present studies of spin-polarized hydrogen (SPH) densities up to 1020cm−3, by photodissociating 5 bar of hydrogen chloride with a focused 213 nm, 150 ps laser pulse. We extract the depolarization cross-section of hydrogen and chlorine atom collisions, which is the main depolarization mechanism at this high-density regime, to be σH-Cl=7(2)×10−17cm2. We discuss the conditions under which the ultrahigh SPH and SPD densities can be reached, and the potential applications to ultrafast magnetometry, laser-ion acceleration, and tests of polarized nuclear fusion.

Spin-Polarized Hydrogen Depolarization Rates at High Hydrogen Halide Pressures: Hyperfine Depolarization via the HY-H Complex.

We measure the magnetization quantum beats of spin-polarized hydrogen (SPH) and spin-polarized deuterium (SPD) with a pickup coil, from the UV photodissociation of HCl, HBr, and DI, in the 5-5000 mbar pressure range. The pressure-dependent depolarization rate is linear at low pressures and reaches a plateau at higher pressures. The high-pressure depolarization rate is observed to be proportional to the halogen nuclear electric quadrupole coupling constant. We also investigate how the presence of an inert gas, SF6 or N2, affects the depolarization rate. The results are explained using a model in which depolarization occurs predominantly through an HY-H intermediate species (Y = Cl, Br, I).

An Experimental Setup for Production of Polarized H2 and D2 Molecules

The setup is designed to produce spin-polarized hydrogen and deuterium molecules. Superconducting sextupole magnets with a magnetic induction of 3.4 T near the poles and a field gradient of 320 T/m were used for the spatial separation of molecules with different magnetic moments by spin filtration in an inhomogeneous magnetic field. The choice of the location of the polarized-molecule source elements is justified. Cryogenic pumps are used in the molecular-beam detection chamber in order to obtain an ultrahigh vacuum. At a nozzle temperature of 7 K, the measured flux of spin-polarized hydrogen molecules is 3 × 1012 molecules/s. For deuterium, the measured flux is lower by more than seven times due to the small magnetic moments.

Highly Nuclear-Spin-Polarized Deuterium Atoms from the UV Photodissociation of Deuterium Iodide

We report a novel highly spin-polarized deuterium (SPD) source, via the photodissociation of deuterium iodide at 270nm. I(^{2}P_{3/2}) photofragments are ionized with m-state selectivity, and their velocity distribution measured via velocity-map slice imaging, from which the D polarization is determined. The process produces ∼100% electronically polarized D at the time of dissociation, which is then converted to ∼60% nuclear D polarization after ∼1.6 ns. These production times for SPD allow collision-limited densities of ∼10^{18} cm^{-3} and at production rates of ∼10^{21} s^{-1} which are 10^{6} and 10^{4} times higher than conventional (Stern-Gerlach separation) methods, respectively. We discuss the production of SPD beams, and combining high-density SPD with laser fusion, to investigate polarized D-T, D-^{3}He, and D-D fusion.

Quantum Monte Carlo study of spin-polarized deuterium

The ground state properties of spin-polarized deuterium (D$\downarrow$) at zero temperature are obtained by means of the diffusion Monte Carlo calculations within the fixed-node approximation. Three D$\downarrow$ species have been investigated (D$\downarrow_1$, D$\downarrow_2$, D$\downarrow_3$), corresponding respectively to one, two and three equally occupied nuclear spin states. Influence of the backflow correlations on the ground state energy of the systems is explored. The equilibrium densities for D$\downarrow_2$ and D$\downarrow_3$ liquids are obtained and compared with ones obtained in previous approximate prediction. The density and the pressure at which the gas-liquid phase transition occurs at $T$=0 is obtained for D$\downarrow_1$.

Influence of the Interaction Potential on the D↓1 Equation of State

The ground-state properties of spin-polarized deuterium with only one occupied nuclear spin state (D↓1) at zero temperature are studied by means of the variational Monte Carlo (VMC) method. Influence of the backflow correlations on the ground-state energy of this Fermi system under investigation is also explored. The calculations have been performed using several interatomic potentials and the quantum phase of the D↓1 system is discussed. Our results are compared with other previously reported variational results.

T-matrix and effective scattering in spin-polarized atomic deuterium (↓D)

Abstract The Galitskii–Migdal–Feynman (GMF) formalism is applied to spin-polarized atomic deuterium (↓D). The effective scattering length is calculated from the GMF T-matrix, which is essentially the effective scattering amplitude dependent on the medium. It is found that the S-wave effective scattering length for ↓D2 and ↓D3 varies discontinuously from negative to positive values at some critical density. This indicates a crossover from a dimer-less regime to a regime with dimers. In addition, it is confirmed that ↓D1 remains a gas down to zero Kelvin. Finally, the binding energy of the weakly bound dimers in both species ↓D2 and ↓D3 is computed. For completeness as well as for comparison purposes, the scattering length in the free-scattering limit is also calculated and it is found to be in a good agreement with previous calculations.

Stability limits of mixed spin-polarised tritium clusters

We present variational and diffusion Monte Carlo studies of pure and mixed spin-polarised tritium clusters. Our results for pure clusters, consisting of only tritium atoms T↓, are in good agreement with previous calculations. We show that mixed clusters, consisting of up to 60 T↓ atoms and one spin-polarized deuterium D↓ atom are stable. On the other hand, we verified that tritium clusters of up to N = 60 atoms do not bind even one H↓ atom; the ground-state energy of the considered mixed T↓-H↓ clusters is within the errorbars equal to or higher than the energy of the pure tritium cluster. In addition to the energy, we present results of the structure of the clusters, which has been determined using unbiased estimators. For larger N, a D↓ atom forms an Andreev state on the surface of a tritium cluster core. The H↓ atoms stay further away from the center of the cluster than the D↓ atoms and slowly increase their separation as the simulation proceeds, indicating instability.

Quantum Monte Carlo study of small pure and mixed spin-polarized tritium clusters

We have investigated the stability limits of small spin-polarized clusters consisting of up to ten spin-polarized tritium T downward arrow atoms and the mixtures of T downward arrow with spin-polarized deuterium D downward arrow and hydrogen H downward arrow atoms. All of our calculations have been performed using the variational and diffusion Monte Carlo methods. For clusters with D downward arrow atoms, the released node procedure is used in cases where the wave function has nodes. In addition to the energy, we have also calculated the structure of small clusters using unbiased estimators. Results obtained for pure T downward arrow clusters are in good accordance with previous calculations, confirming that the trimer is the smallest spin-polarized tritium cluster. Our results show that mixed T downward arrow-H downward arrow clusters having up to ten atoms are unstable and that it takes at least three tritium atoms to bind one, two, or three D downward arrow atoms. Among all the considered clusters, we have found no other Borromean states except the ground state of the T downward arrow trimer.

SPIN-POLARIZED ATOMIC DEUTERIUM (↓D) IN THE STATIC FLUCTUATION APPROXIMATION (SFA)

Spin-polarized atomic deuterium (↓D) is investigated in the static fluctuation approximation with a Morse-type potential. The thermodynamic properties of the system are computed as functions of temperature. In addition, the ground-state energy per atom is calculated for the three species of ↓D : ↓D 1, ↓D 2, and ↓D 3. This is then compared to the corresponding ground-state energy per atom for the ideal gas, and to that obtained by the perturbation theory of the hard sphere model. It is deduced that ↓D is nearly ideal.

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target.

Spin diffusion in doubly spin polarized atomic deuterium

Using an extension of the Boltzmann equation for the Wigner distribution appropriate for dilute spin 1 systems, spin diffusion equations are derived in the limit of large nuclear polarization in the non-degenerate regime. As an example of a system to which this work may be applied, the domain of validity of the Boltzmann equation for doubly spin-polarized deuterium, D↓↓, is studied. The effect of a finite field gradient is discussed. A calculated spin wave spectrum for a model one-dimensional system in the presence of a gradient is presented. Analogous effects in spin 1/2 systems are compared and contrasted.

Spin-exchange optical pumping as a source of spin-polarized atomic deuterium.

Optical pumping of potassium atoms followed by spin-exchange scattering with deuterium atoms in a high magnetic field was found to produce an intense, highly spin-polarized beam of atomic deuterium. In particular, the atomic polarization of deuterium was determined to be (73\ifmmode\pm\else\textpm\fi{}3)% at an intensity of 2.1\ifmmode\times\else\texttimes\fi{}${10}^{17}$ atoms/s.

Spin-polarized hydrogen, deuterium, and tritium: II. Pressure and compressibility calculated by a lowest order constrained-variation method

The pressure and the compressibility of spin-polarized H↓, D↓, and T↓ are obtained from ground-state energies calculated by means of a modified variational lowest order constrained-variation method. The pressure and the compressibility are calculated or estimated from the dependence of the ground-state energy on density or molar volume, generally in a density region from 0 to 1.5σ−3 corresponding to a molar volume of more than 20 cm3/mol, where σ = 3.69 Å (1Å = 10−10 m); the calculations are done for five different two-body potentials. Theoretical results for the pressure are 54.1–57.9 atm for spin-polarized H↓ 18.4–23.4 atm for spin-plolarized D↓, and 5.6–12.9 atm for spin-polarized T↓ at a particle density of 0.50σ−3 or a molar volume of 60 cm3/mol (1 atm = 101 kPa). Theoretical results for the compressibility are 51 × 10−4 −54 × 10−4 atm−1 for spin-polarized H↓, 108 × 10−4 −120 × 10−4 atm−1 for spin-polarized D↓, and 162 × 10−4 −224 × 10−4 atm−1 for spin-polarized T↓ at a particle density of 0.50σ−3 for a molar volume of 60 cm3/mol. The relative agreement between results for different potentials is somewhat better for higher densities.

Spin-polarized hydrogen, deuterium, and tritium: I. Ground-state energy calculated by a lowest order constrained-variation method

The ground-state energy of spin-polarized hydrogen, deuterium, and tritium is calculated by means of a modified variational lowest order constrained-variation method, and the calculations are done for five different two-body potentials. Spin-polarized H↓ is not self-bound according to our theoretical results for the ground-state binding energy. For spin-polarized D↓, however, we obtain theoretical results for the ground-state binding energy per particle from −0.42 K at an equilibrium particle density of 0.25 σ−3 or a molar volume of 121 cm3/mol to + 0.32 K at an equilibrium particle density of 0.21 σ−3 or a molar volume of 142 cm3/mol, where σ = 3.69 Å (1 Å = 10−10 m). It is, therefore, not clear whether spin-polarized deuterium should be self-bound or not. For spin-polarized T↓, we obtain theoretical results for the ground-state binding energy per particle from −4.73 K at an equilibrium particle density of 0.41 σ−3 or a molar volume of 74 cm3/mol to −1.21 K at an equilibrium particle density of 0.28 σ−3 or a molar volume of 109 cm3/mol.

Spin-polarized deuterium in magnetic traps.

We have calculated the spin-exchange two-body rate constants associated with the population dynamics of the hyperfine levels of atomic deuterium as a function of magnetic field in the Boltzmann zero-temperature limit. Results indicate that a gas of low-field--seeking deuterium atoms trapped in a static magnetic field minimum decays rapidly into an ultrastable gas of doubly spin-polarized deuterium. We also discuss the temperature dependence of various effects.

Spin-Polarized Deuterium: Stabilization in Magnetic Traps

We report on a calculation of the spin-exchange two-body rate constants associated with the population dynamics of the hyperfine levels of atomic deuterium as a function of magnetic field in the Boltzmann zero temperature limit. We find that a gas of low field seeking deuterium atoms trapped in a static magnetic field minimum decays rapidly into an ultra stable gas of doubly spin-polarized deuterium.

Measurements on Mixtures of Doubly Spin-Polarized Hydrogen and Doubly Spin-Polarized Deuterium

We have been able to prepare a mixture of doubly spin-polarized hydrogen H↓↓ and doubly spin-pola-rized deuterium D↓↓ in a closed cell at temperatures of the order of 0.7 K. The time dependence of the densities of the two species, measured by ESR in a 40 kG field, show unusual and interesting properties both for the natural decay and for the decay under conditions where the microwave field perturbs the level populations. We find that at 0.68 K the intrinsic two-body surface recombination rate between D↓- and H↓-atoms is approximately 6x larger than the rates between D↓-atoms.

Observation of doubly spin-polarized deuterium by electron-spin resonance.

We have studied spin-polarized deuterium, ${\mathrm{D}}_{\ensuremath{\downarrow}}$, in the temperature range 0.3 to 0.7 K in a field of 40 kG using electron-spin resonance at 114 GHz. The intrinsic rates for recombination of two D atoms to form ${\mathrm{D}}_{2}$ on the surface of $l\ensuremath{-}^{4}\mathrm{He}$ have been measured for both the ortho and para channels. The two rates are approximately equal and when extrapolated to zero field are 1600 times greater than the rates for ${\mathrm{H}}_{2}$ formation. Doubly spin-polarized deuterium, ${\mathrm{D}}_{\ensuremath{\downarrow},↡}$, has been observed for the first time, with nuclear-spin purities > 0.98 and sample lifetimes as long as 1 h.

The quantal collision integrals and transport coefficients of dilute gaseous spin-polarized deuterium with spin-polarized hydrogen and the isotopes of helium

The collision integrals and transport coefficients of spin-polarized deuterium D↑ and its admixtures with spin-polarized hydrogen H↑ and the isotopes of helium are calculated with representative Lennard-Jones interatomic potentials at temperatures below 2 K. Diffractive features previously predicted to be significant in H↑ are absent here in D↑ and its admixtures.