Henry R. Glyde

Excitations in Liquid and Solid Helium

Introduction 1. Dynamic response functions 2. Physics of solid helium 3. Dynamic structure factor of solid helium 4. Self consistent phonon theory 5. Neutron studies of solid helium 6. Introduction to liquid 4He 7. Microscopic picture 8. Historical development of ideas 9. Observed properties of liquid 4He 10. Theory of liquid 4He 11. Nature of excitations in liquid 4He 12. Excitations in liquid 3He 13. Dynamic susceptibility of liquid 3He 14. Approximations to the dynamic susceptibility 15. Models of S(Q,omega) in liquid 3He 16. Mori and kinetic theories of liquid 3He 17. The impulse approximation 18. Final state contributions 19. Intermediate and high momentum transfer 20. Recent monographs and conference proceedings References Appendices A-C

Relation of vacancy formation and migration energies to the Debye temperature in solids

Abstract A derivation of the relation between the vacancy formation energy E f , the migration energy E m and the Debye temperature θ D is presented. In the Debye model, the relation between E m and θ D follows directly from the “dynamical” form of diffusion theories. The relation between E f and θ D is obtained for solids obeying a corresponding states law. The Debye temperature appearing in the derived expressions is θ D (Debye-Waller factor) rather than θ D ( C v ).

Dynamics of liquid 4He in vycor

Using inelastic neutron scattering, we have observed well-defined phonon-roton ( p-r) excitations in superfluid 4He in Vycor over a wide wave-vector range, 0.3</=Q</=2.15 A(-1). The p-r energies and lifetimes at all temperatures are the same as in bulk liquid 4He. However, the weight of the single p-r component does not scale with the superfluid fraction rho(S)(T)/rho as it does in the bulk. In particular, we observe a p-r excitation above T(c) = 1.952 K, where rho(s)(T) = 0 in Vycor. This suggests, if the p-r excitation intensity scales with the Bose condensate, that there is a separation of the Bose-Einstein condensation temperature and the superfluid transition temperature T(c) of 4He in Vycor.

VACANCIES IN SOLID ARGON

Abstract The enthalpy and entropy of vacancy creation in solid argon are re-evaluated using the two-body force approximation. At the triple point, the resulting vacancy free energy is g v = 1900 −4.0 RT cal mole vac. This does not agree well with previous calculations of g v , but agrees well with experimental values of g v obtained from the argon specific heat(8) C p (but not with the questionable values obtained from C v ) and with direct measurements (13) of ( n N ) = exp( −g v RT ) . If the present value of g v is correct, the agreement with experiment suggests that many-body effects contribute little to the binding of argon atoms around a vacancy.

Bose-Einstein condensation in trapped bosons: A variational Monte Carlo analysis

Several properties of trapped hard-sphere bosons are evaluated using variational Monte Carlo techniques. A trial wave function composed of a renormalized single-particle Gaussian and a hard-sphere Jastrow function for pair correlations is used to study the sensitivity of condensate and noncondensate properties to the hard-sphere radius and the number of particles. Special attention is given to diagonalizing the one-body density matrix and obtaining the corresponding single-particle natural orbitals and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single-particle orbital with the highest occupation. The effect of interaction on other quantities such as the ground-state energy, the mean radial displacement, and the momentum distribution is calculated as well. Results are compared with mean-field theory in the dilute limit.

Helium diffusion in aluminium

Abstract The diffusion in Al of reaction product He was measured by observing its rate of release from Al sheet on a mass spectrometer. Trapping of the He in Al was observed but prior to the trapping the diffusion coefficient was measured as: The average distance the He atoms must migrate in the Al to be trapped (obtained from the anneal curve shapes) depended on the anneal temperature and was ∼ 1 to 3 × 10−4 cm. This distance and its temperature dependence are best explained if He is trapped by diffusing to irradiation created vacancy clusters.

Helium and argon diffusion in magnesium

Abstract The diffusion coefficients of He and A in Mg, obtained by measuring the rate of release of artificially introduced atoms from Mg sheet annealed at constant temperatures, are found to be: The coefficients (a) and (b) were obtained from Mg samples in which the He concentration was f He ∼ 1×10−6 and f He∼3–6×10−9 (atomic fraction) respectively and D 40A from samples in which fA∼2×10−5. Both D He and D A appeared to be concentration dependent. The isotope measurements require He and A diffusion by a mechanism involving vacancies; the vacancy or interstitialcy of the accepted mechanisms. There was no evidence of He or A gas bubble formation in Mg.

Long-time mean-square displacements in proteins.

We propose a method for obtaining the intrinsic, long-time mean square displacement (MSD) of atoms and molecules in proteins from finite-time molecular dynamics (MD) simulations. Typical data from simulations are limited to times of 1 to 10 ns, and over this time period the calculated MSD continues to increase without a clear limiting value. The proposed method consists of fitting a model to MD simulation-derived values of the incoherent intermediate neutron scattering function, I(inc)(Q,t), for finite times. The infinite-time MSD, , appears as a parameter in the model and is determined by fits of the model to the finite-time I(inc)(Q,t). Specifically, the is defined in the usual way in terms of the Debye-Waller factor as I(Q,t=∞)=exp(-Q(2)/3). The method is illustrated by obtaining the intrinsic MSD of hydrated lysozyme powder (h=0.4 g water/g protein) over a wide temperature range. The intrinsic obtained from data out to 1 and to 10 ns is found to be the same. The intrinsic is approximately twice the value of the MSD that is reached in simulations after times of 1 ns which correspond to those observed using neutron instruments that have an energy resolution width of 1 μeV.

Intrinsic Mean Square Displacements in Proteins

The thermal mean-square displacement (MSD) of hydrogen in proteins and its associated hydration water is measured by neutron scattering experiments and used an indicator of protein function. The observed MSD as currently determined depends on the energy resolution width of the neutron scattering instrument employed. We propose a method for obtaining the intrinsic MSD of H in the proteins, one that is independent of the instrument resolution width. The intrinsic MSD is defined as the infinite time value of (r(2)) that appears in the Debye-Waller factor. The method consists of fitting a model to the resolution broadened elastic incoherent structure factor or to the resolution dependent MSD. The model contains the intrinsic MSD, the instrument resolution width, and a rate constant characterizing the motions of H in the protein. The method is illustrated by obtaining the intrinsic MSD (r(2)) of heparan sulphate (HS-0.4), ribonuclease A, and staphysloccal nuclase (SNase) from data in the literature.

Bose-Einstein condensation in solid 4He.

We present neutron scattering measurements of the atomic momentum distribution n(k) in solid helium under a pressure p=41 bar (molar volume Vm=20.01+/-0.02 cm3/mol) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200 mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0 state below Tc, we find a condensate fraction of n0=(-0.10+/-1.20)% at T=80 mK and n0=(0.08+/-0.78)% at T=120 mK, consistent with zero. The shape of n(k) also does not change on crossing Tc within measurement precision.