Theory of muon spin depolarization in crystalline phases of 3He

As is obvious from the energetic point of view, positive muons must form the molecular ion ( He_2μ)⁺ in condensed phases of helium. A theory of positive muon spin depolarization in crystalline phase of ³He in this model is devised. The theory explains experimental results. It is shown that the abrupt temperature dependence of the muon spin depolarization rate at T < 2 K which is observed in experiments is explained by spin–phonon interaction. This interaction mechanism arises due to a modulation of the exchange interaction between host atoms of the ³He‐lattice. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear spin dynamics of nuclear-ordered solid<Superscript>3</Superscript>He in the low field phase

Pulsed NMR was used to investigate nuclear spin dynamics of nuclear-ordered solid³He in the low field phase. The nuclear spin motion became unstable under certain conditions. Under stable conditions the spin motion can be described by the OCF equations. The tipping-angle-dependent frequency shift and multiple spin echoes were observed, which are similar to the case of superfluid³He. The onset of the instability of spin motion is attributed to the stimulated emission mechanism through the three-magnon relaxation process, which is similar to the Suhl instability in electronic magnetism. We derived the magnon life time from the analysis of the instability. During the instability, a largenegative frequency shift was observed. This negative shift is explained by the extension of Fomin-Ohmi's theory to include the state of decayed magnon and this explanation is consistent with the instability model.     

Appearance of anomalous phase in <Superscript>4</Superscript>He crystal in the presence of small <Superscript>3</Superscript>He impurity

The kinetics of formation of an anomalous phase from a solution with a small ³He impurity was studied in the temperature range 0.2–0.7 K up to a supersaturation of ～30 mbar. The phase diagram was determined for normal and anomalous growths. It is found that, in the presence of impurities, the formation of a fast-growing state is retarded. This experimental fact indicates that the dissipative processes in fluids have an appreciable effect on the phase formation kinetics. The retardation is, possibly, caused by the direct interaction of an impurity with the crystal surface.     

Low-temperature instability of uniform spin precession in the <Emphasis Type="Italic">B</Emphasis> phase of pure <Superscript>3</Superscript>He and <Superscript>3</Superscript>He in an aerogel

The magnetic-field dependences of the threshold temperature of the low-temperature instability of uniform spin precession in pure ³He-B and ³He-B in an aerogel have been determined for the bulk mechanism. These dependences appear to be different. The theoretical dependence of the threshold temperature for the pure case has been compared with the experimental dependence. The threshold temperature of the instability for ³He in the aerogel has been estimated for typical experimental conditions.     

Microscopic description of diffractive deuteron breakup by <Superscript>3</Superscript>He nuclei

A microscopic formalism for describing observed cross sections for deuteron breakup by threenucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction ²H(³He, ³Hep)n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by ³He nuclei at the projectile energy of 89.4MeV. The importance of employing, in calculations, a deuteron wave function that has a correct asymptotic behavior at large nucleon–nucleon distances was demonstrated.     

Semiclassical description of the <Superscript>6</Superscript>He+<Superscript>12</Superscript>C elastic scattering

The results of the elastic scattering of ⁶He+¹²C systemat E _Lab = 18 MeV by using the barrier and internal wave decomposition of the S-matrix element within the framework of the WKB method are presented. This is the first detailed study for the interaction of the exotic ⁶He nucleus on different stable nuclei by using a semiclassicalmethod. In this paper, we show that in order to obtain the elastic scattering cross section of the ⁶He+¹²C systemat energies close to the Coulomb barrier, it is vitally important to take into account the inner complex turning points in the calculations and the tunneling effects play a crucial role to explain the experimental data. The semiclassical results are compared with the experimental data as well as the quantum-mechanical one.     

Different formulations of <Superscript>3</Superscript>He and <Superscript>3</Superscript>H photodisintegration

Different momentum space Faddeev-like equations and their solutions for the radiative pd-capture and the three-nucleon photodisintegration of ³He are presented. Applications are based on the AV18 nucleon-nucleon and the Urbana IX three-nucleon forces. Meson exchange currents are included using the Siegert theorem. A very good agreement has been found in all cases indicating the reliability of the used numerical methods. Predictions for cross-sections and polarization observables in the pd-capture and the complete three-nucleon breakup of ³He at different incoming-deuteron/photon energies are presented.     

Kinetics of the sorption of <Superscript>3</Superscript>He by C<Subscript>60</Subscript> fullerite. The quantum diffusion of <Superscript>3</Superscript>He and <Superscript>4</Superscript>He in fullerite

The kinetics of the sorption and subsequent desorption of gaseous ³He in a C₆₀ fullerite powder has been studied in the temperature range of 2–292 K. The temperature dependences of the diffusion coefficients of ³He and ⁴He impurities in fullerite have been plotted using the measured characteristic times of filling of octahedral and tetrahedral interstices, as well as previous data. These temperature dependences of the diffusion coefficients of ³He and ⁴He impurities in fullerite are qualitatively similar. A decrease in the temperature from 292 to 79 K is accompanied by a decrease in the diffusion coefficients, which corresponds to the dominance of the thermally activated diffusion of helium isotopes in fullerite. A further decrease in the temperature to 8–10 K leads to an increase in the diffusion coefficients by more than an order of magnitude. The diffusion coefficients of ³He and ⁴He are independent of the temperature below 8 K, indicating the tunnel character of the diffusion of helium in C₆₀ fullerite. The isotope effect is manifested in the difference between the absolute values of the diffusion coefficients of ³He and ⁴He atoms at the same temperatures.     

Recent results on hyperpolarized<Superscript>3</Superscript>He−<Superscript>4</Superscript>He liquid mixtures

Laser optical pumping in low magnetic field provides very high nuclear polarizations in gaseous helium mixtures, and is used to prepare polarized liquid. Wall relaxation in glass cells is effiently reduced using cesium coatings, and bulk longitudinal relaxation times are measured. In highly magnetized samples, dipolar fields control the spin dynamics in anisotropic volumes and weak external magnetic field inhomogeneities. Long lived magnetostatic modes are observed by pulsed NMR. Detailed analysis of their frequency and damping gives information on magnetization density and spin diffusion coefficient in polarized mixtures. Experiments are performed above 0.2 K on mixtures with³He concentrations of order a few percents or larger. When phase separation occurs, the³He-rich phase retains a high polarization.     

Nonlinear NMR in a superfluid B phase of <Superscript>3</Superscript>He in aerogel

The properties of liquid ³He in a low-density aerogel preliminarily covered with a few monolayers of ⁴He were studied by pulsed and nonlinear CW NMR techniques. It was found that an NMR frequency shift from the Larmor value exhibits a sharp increase at a magnetization tilting angle exceeding 104°. Nonlinear CW NMR signals related to the formation of a macroscopic region featuring homogeneous precession of the magnetization (homogeneous precession domain) were observed. The experimental results confirm that the low-temperature superfluid ³He phase in the aerogel is analogous to the B-phase in bulk ³He and indicate that the spin supercurrents play an important role in the spin dynamics of superfluid ³He in aerogel.     

Magnetization studies of the nuclear spin ordered phases of solid <Superscript>3</Superscript>He in silver sinters

Solid ³He, in the bcc lattice between 34 and 100 bar, exhibits two nuclear magnetic ordered phases in the sub-mK temperature range, the so called U2D2 low (magnetic) field phase and the “high field phase” above 0.4 T. To determine the exact spin structure of these phases we started a project of neutron scattering from the ordered solid in collaboration with the Hahn-Meitner Institute, Berlin, and other European and US groups. For this experiment it is crucial to grow a single crystal within the sinter needed for cooling the solid to temperatures of the order of 500 μK (or even twenty times lower in the case of the hcp lattice which is formed above 100 bar) and to keep it there long enough to measure a magnetic neutron reflection. We studied the growth of crystals in Ag sinters of different pore size and with different growth speeds to find an optimal way to obtain single crystalline samples. As a first diagnostic step we performed pulsed NMR measurements in the ordered phases of solid ³He in a sinter of 2700 Å particle size down to temperatures of 450 μK at various molar volumes. We could keep the samples in the ordered state for as long as 140 h. The second method we used was SQUID magnetometry. For the low field phase T_N was indicated by a drop of the intensity, both in the NMR signal and in the dc magnetization, whereas in the high field phase an increase of about 30% was observed below the ordering temperature. For the fabrication of the sinters a packing fraction of 50% and subsequent annealing proved to be very favorable to obtain cold ordered solid. Furthermore, we find that a paramagnetic surface contribution from a few monolayers of ³He exists down to 500 μK in addition to the bulk magnetization.     

Applications of <Superscript>3</Superscript>He neutron detectors

Neutron detectors with ³He-filled proportional counters are described. The use of these detectors in measuring the probability of neutron emission (in particular, multiparticle neutron emission) after the β decay of neutron-rich nuclei and in studying rare events of spontaneous fission of superheavy nuclei is considered.     

Fermi points and the Nambu sum rule in the polar phase of <Superscript>3</Superscript>He

We discuss the polar phase of ³He, which is realized in the anisotropic aerogel. We consider it in the framework of the BCS model. In the absence of the spin–orbit interaction, this model predicts the appearance of the Fermi line. However, it is topologically unstable. We demonstrate that the spin–orbit interaction gives rise to the appearance of the two Fermi points instead of the Fermi line. In addition to the gapless Nambu–Goldstone bosons in this system the collective gapped bosonic states exist. Their gaps are calculated, and the corresponding Nambu sum rule is established.     

Observation of magnetic coupling between the nuclei of liquid <Superscript>3</Superscript>He and the <Superscript>141</Superscript>Pr nuclei of PrF<Subscript>3</Subscript> crystalline powder

The resonance magnetic coupling between the nuclei of liquid ³He and the ¹⁴¹Pr nuclei of a fine-dispersed powder of PrF₃ Van Vleck paramagnet with the grain size below 45 μm has been discovered at a temperature of 1.5 K with the use of a pulsed NMR technique. The magnetic specific heat of the corresponding spin systems is estimated theoretically.     

Interaction of two magnetic resonance modes in the polar phase of superfluid <Superscript>3</Superscript>He

We report results of low frequency nuclear magnetic resonance (NMR) experiments in the superfluid polar phase of ³He, which is stabilized by a new type of “nematic” aerogel—nafen. We have found that an interaction between transverse and longitudinal NMR modes may essentially influence the spin dynamics. Theoretical formulas for NMR resonant frequencies are derived and applied for interpretation of the experimental results.     

Momentum distributions of <Superscript>4</Superscript>He nuclei from the <Superscript>6</Superscript>He and <Superscript>6</Superscript>Li breakup

Experimental data on the momentum distributions of ⁴He nuclei originating from ⁶He and ⁶Li breakup on various targets are presented over a wide beam energy range. The experiment with ⁶He was performed at the DRIBs accelerator complex for radioactive beams at the Joint Institute for Nuclear Research (JINR, Dubna). The intensity of the ⁶He beam used was 5 × 10⁶ particles per second and its energy was 10 MeV per nucleon. The momentum distributions of breakup products were measured by means of the MSP-144 magnetic spectrometer. The distribution width was shown to be virtually independent of the target mass. A small value of this width, σ ～ 28 MeV/c, confirms the presence of a halo in ⁶He. The measurements performed with ⁶Li beams of energy 18 and 46 MeV per nucleon at the U-400M accelerator yielded a width value of σ ～ 50 MeV/c for the momentum distributions of ⁴He nuclei, which is intermediate between that for ⁶He and those for stable nuclei. A compilation of the widths of the momentum distributions of fragments originating from the breakup of various nuclei is presented versus the binding energy of one or two neutrons in these nuclei, the target mass and the projectile energy.     

<Superscript>6</Superscript>He + <Superscript>6</Superscript>He Clustering of <Superscript>12</Superscript>Be in a Microscopic Algebraic Approach

The norm kernel of the A=12 system composed of two ⁶He clusters, and the L=0 basis functions (in the SU(3) and angular momentum-coupled schemes) are analytically obtained in the Fock-Bargmann space. The norm kernel has a diagonal form in the former basis, but the asymptotic conditions are naturally defined in the latter one. The system is a good illustration for the method of projection of the norm kernel to the basis functions in the presence of SU(3) degeneracy that was proposed by the authors. The coupled-channel problem is considered in the algebraic version of the resonating-group method, with the multiple decay thresholds being properly accounted for. The structure of the ground state of ¹²Be obtained in the approximation of zero-range nuclear force is compared with the shell-model predictions. In the continuum part of the spectrum, the S-matrix is constructed, the asymptotic normalization coefficients are deduced and their energy dependence is analyzed.