Critical velocity of continuous vortex formation in rotating<Superscript>3</Superscript>He-A

Vortex lines with continuous (singularity-free) core structure are usually formed when superfluid³He-A is accelerated to rotation. The critical counterflow velocityv _c (T), at which vortex formation starts, has been measured with cw NMR. The onset of vortex formation is found to depend on the order parameter texture and differs from that of singular core vortices in⁴He-II or³He-B due to much larger length scale.     

Vortex sheet in superfluid<Superscript>3</Superscript>He-A

The vortex sheet (VS) is the most unexpected discovery in rotating superfluids during the last ten years. Usually superfluids respond to rotation by creating an array of vortex lines, which are parallel to the rotation axis, and the circulation around them is quantized. In the VS the vorticity is located on a 2 dimensional sheet that folds to equidistant layers in a rotating container. The VS is one out of five stable vortex structures in³He-A. The stability of the VS in³He-A arises from a special structure, which consists of a nonsingular vorticity bound to a topologically stable domain wall. The vortex sheet forms the equilibrium state of³He-A at rotation velocities larger than ～3 rad/s, but it is also created as metastable state at lower velocities. Experimentally the vortex sheet is distinguished from its NMR response.     

Aerogel: Impurities in superfluid<Superscript>3</Superscript>He?

We present results of torsional oscillator experiments that are in progress or completed at Cornell. Taken together, these experiments suggest that the properties of superfluid³He in aerogel are substantially different from those exhibited by bulk superfluid³He. Featured are the differences between bulk and superfluid³He in aerogel with temperature and pressure. Comparisons to proposed models of³He in aerogel are also made.     

Vortex mutual friction in rotating superfluid<Superscript>3</Superscript>He

The Manchester rotating cryostat has been used to measure the longitudinal and transverse coefficients of vortex mutual friction in the A and B phases of superfluid³He. In the B phase the dominant contribution to the mutual friction is scattering of excitations off occupied bound states in the vortex core. The A phase results are explained quantitatively by assuming that doubly quantised continuous vortices are created with a dynamics determined by the equation of motion of the orbital vectorI; the measurements enable us to put an upper limit on the orbital inertia of less than 0.01h per Cooper pair. History-dependent textural effects which had to be overcome in order to make meaningful measurements in the A phase are explained by noting that for a given rotation direction the most stable vortices can be formed more easily from one direction of uniformI texture than the other.     

Spin dynamics of superfluid<Superscript>3</Superscript>He in non-hydrodynamic regime

We review recent results of experimental and theoretical studies of superfluid³He spin dynamics at ultra low temperature, where density of the normal component is virtually zero. We describe a number of new phenomena: catastrophic relaxation, NMR in the Landau field, surface instability of homogeneous precession, persistent NMR signal etc. We propose that superfluid³He in the ultralow temperature limit may provide a system for the experimental modelling of nonequilibrium quantum field theories.     

Simulated cosmic strings in a “big bang” in superfluid<Superscript>3</Superscript>He at 100 μK

During studies of the impact of single neutrons on superfluid³He at around 100μK we have measured the thermal energy released in the superfluid following the nuclear reaction, n+³He→p+³H+764keV. However, we find that the measured energy deposited in the quasiparticle system shortly after this reaction is substantially less than what we expect. We believe that this energy deficit represents that energy which has gone into the creation of vortices, in analogy to the creation of cosmic strings in the early universe via the Kibble mechanism. Furthermore, from the magnitude of the deficit, we can infer the vortex density which compares favorably with that predicted in Zurek’s scenairo.     

Equilibrium number of quantized vortex lines in rotating<Superscript>3</Superscript>He-B

A slow cool-down at constant rotation velocity Ω from the normal to the superfluid state is expected to give the equilibrium state of vortex lines. We have checked this by counting the number of vortex lines in³He-B using cw NMR. Our measurements with 0≤Ω≤0.28 rad/s confirm the expectation.     

Helicity theorem and vortex lines in superfluid4He

The helicity conservation theorem is demonstrated in the case of superfluid⁴He. As in the case of a classical barotropic fluid, the helicity integral expresses some topological properties of vortex lines.     

Magnetic relaxation in superfluid<Superscript>3</Superscript>He-B at very low temperatures

Main properties of the spin supercurrents and coherent precession of magnetization in the superfluid³He-B in hydrodynamic regime seem to be very well understood now. But recently surprisingly new unpredicted phenomena such as, for example, “catastrophic” relaxation, persistent spin precession, very strong magnetic relaxation, etc., have been observed in³He-B at ultralow temperatures in so-called non-hydrodynamic regime using both pulse and cw-NMR techniques. This paper deals with some of these new phenomena (a “linear term” in magnetic relaxation and a reduction of magnetization of coherent precession with magnetic field gradient) observed by cw-NMR technique, compares these results with new effects found by pulse NMR and speculates about the nature of these new phenomena.     

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.     

Dirac monopoles on quantized vortices in superfluid3He

Quantized vortices in superfluid³He display a variety of novel structures that have previously not been observed in any other quantum fluids; their basic experimental manifestations and theoretical features have been reviewed by Hakonen, Lounasmaa and Simola [Physica B160 (1989) 1] and by Salomaa and Volovik [Rev. Mod. Phys.59 (1987) 533]. In order not to repeat these reviews in this paper, here we choose to discuss the theme of the possible pointlike orderparameter singularities, monopoles, that can occur on the quantized³He vortices. Such monopoles, mathematical analogues of the magnetic Dirac monopole, may exist in superfluid³He due to the complicated order-parameter structure, which makes it possible to have several different types of quantized vortex lines and phase boundaries between the superfluid states. Analogs of Dirac monopoles, and also monopoles with 1/2 and 1/4 of the magnetic charge of the Dirac monopole, may exist at the points of intersections of quantized vortex lines and phase boundaries — or along vortices if they change their quantum state; several examples are discussed.Invited talk at the International Conference on Macroscopic Quantum Phenomena, Smolenice Castle, Czechoslovakia, September 18–22, 1989.I want to thank G. E. Volovik for a useful discussion and O. V. Lounasmaa for encouragement. This research has been supported through the Award for the Advancement of European Science by the Körber-Stiftung (Hamburg, FRG) and by the Academy of Finland.     

Metastability and hysteresis of the vortex states in rotating superfluid<Superscript>3</Superscript>He-B

We have investigated the vortex core transition in³He-B by measuring the associated changes in mutual fricition dissipation within the superfluid. If rotation is continuously stopped and restarted while cooling or warming then the transition occurs at a clearly defined temperature, but temperature sweeps during continuous rotation show substantial supercooling and superheating. Moreover, the high temperature vortex shows a continuum of metastable states when supercooled to a constant, arbitrary low temperature, the mutual friction dissipaton depending on the temperature at which rotation was started. Our current interpretation is that the high temperature vortex state is a temperature-dependent mixture of two vortex types.     

Extreme-ultraviolet emissivity from Xe<Superscript>8+</Superscript> to Xe<Superscript>12+</Superscript> by using a detailed line-by-line method

A theoretical model has been developed to calculate the emissivity of low densityxenon plasmas (from Xe⁸⁺ to Xe¹²⁺) by employing a detailed lineaccounting formalism. A complete set of atomic datasuch as transition probabilities for electric (magnetic) dipoleand quadruple E1, E2, M1 and M2 and electron impact excitationcollision strength, which is accurate to fine-structure level,was calculated using a full configuration interaction formalismand was used to solve the rate equation which determines thepopulation of different levels. Detailed results are given forpure Xe¹⁰⁺ ion, which is essential for extreme-ultravioletemission at 13.5 nm, and for low density plasmas (the electron densitywas taken to be 10¹² cm^-3) at temperatures of 30, 45, 55, 65and 75 eV. The fraction of different ionization stages was obtained by acompletely coupled rate equation from neutral atom to Xe²⁰⁺ by usinga detailed configuration accounting method. The results show that theemissivity of the dipole forbidden lines of transition array4s ²4p ⁶4d ⁷5s \(\rightarrow\) 4s ²4p ⁶4d ⁸ of Xe¹⁰⁺is very sensitive to the temperature, which should be a useful tool todiagnose the temperature in EBIT plasmas.     

Nucleation of vortices in superfluid<Superscript>3</Superscript>He-B

In a smooth-walled rotating container vortices nucleate spontaneously in³He-B at a critical velocityv _c (T, P) which is related to the bulk superflow instability velocityv _cb (T, P). This process takes place at the wall of the container. Vortices are also observed to nucleate at lower velocities in the bulk liquid in ionizing radiation. For this thermal neutrons are most practical since for them the absorption cross section is large in³He. An absorption event creates local overheating, a hot bubble in the cold superflow. An increasing number of vortex rings is observed to emerge from the bubble as a function of the superflow velocity.     

A miniature tunable TEA CO<Subscript>2</Subscript> laser using isotope <Superscript>13</Superscript>C<Superscript>16</Superscript>O<Subscript>2</Subscript> and <Superscript>12</Superscript>C<Superscript>16</Superscript>O<Subscript>2</Subscript>

A miniature tunable TEA CO₂ laser using isotope ¹³C¹⁶O₂ as the active medium is developed to extend the spectral range of CO₂ lasers for further application. The optimization of the energy parameters of the tunable TEA ¹³C¹⁶O₂ laser and the same laser using ¹²C¹⁶O₂ are studied. When a gas mixture (¹³C¹⁶O₂: N₂: He = 1: 1: 3) at a total pressure of 6.4 × 10⁴ Pa is used, the TEA ¹³C¹⁶O₂ laser of a 45-cm³ active volume obtains 51 emission lines in the [00⁰1–10⁰0] and [00⁰1–02⁰0] bands. The maximum pulse energy of the TEA ¹³C¹⁶O₂ laser is about 357 mJ. The same laser using the conventional gas mixture (¹²C¹⁶O₂: N₂: He = 1: 1: 3) at a pressure of 6.66 × 10⁴ Pa is measured to obtain 69 laser emission lines and the maximum pulse energy of laser radiation is about 409 mJ.     

Spectrum of bound fermion states on vortices in <Superscript>3</Superscript>He-B

We study subgap spectra of fermions localized within vortex cores in ³He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular o and u vortices the anomalous branches are similar to the standard Caroli-de Gennes-Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the ν, w and uvw vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.     

Estimation of rotational temperature of<Superscript>121</Superscript>Sb<Superscript>16</Superscript>O molecule

The (0,1), (0,0), (1,0) and (2,0) bands ofB →X system of antimony monoxide have been excited in rf discharge tube source and photographed in the 9th order of a two metre plane grating spectrograph (PGS-2). Intensity records of the rotational lines have been obtained. The intensity measurements ofQ andP branch lines of the above four bands andJ numberings are used to estimate the effective rotational temperature of the source emitting the spectrum of¹²¹Sb¹⁶O molecule. It is concluded that¹²¹Sb{ su16}O may be present inK type stars.     

Absorption line strengths of <Superscript>15</Superscript>NH<Subscript>3</Subscript> in the near infrared spectral region

We present initial results of an investigation of the near infrared absorption spectrum of ¹⁵NH₃ between 6468 and 6692 cm⁻¹. A widely tunable external cavity diode laser is used in a direct absorption setup to determine the line positions and line strengths of several lines in that spectral range. Line data measurements on a ¹⁴NH₃ sample are used for validation of the setup by comparison of the results with available literature data. The presented overview measurements on absorption lines of ¹⁵NH₃ have been performed to serve as a starting point for candidate line selection for prospective isotopic ratio measurements of ¹⁴NH₃ and ¹⁵NH₃.     

Cohesive energy of zincblende (A<Superscript>III</Superscript>B<Superscript>V</Superscript> and A<Superscript>II</Superscript>B<Superscript>VI</Superscript>) structured solids

In this paper we present an expression relating the cohesive energy (E _coh in kcal/mol) of A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z ₁ Z ₂) and nearest-neighbour distance d (Å). The cohesive energy values of these solids exhibit a linear relationship when plotted on a log-log scale against the nearest-neighbour distance d (Å), but fall on different straight lines according to the ionic charge product of the solids. A good agreement has been found between the experimental and calculated values of the cohesive energy of A^IIIB^V and A^IIB^VI semiconductors.     

Density matrix for3He/He II mixture

The hydrodynamic equations of a mixture of superfluid⁴He with normal fluid³He are derived by an extension of statistical mechanic techniques previously applied to pure superfluid⁴He.