Using polarized neutrons, we have determined phases as well as interference amplitudes for noncyclic spinor evolutions in static magnetic fields. Both these quantities depend on the angle subtended by the neutron spin with the field. This experiment elucidates the subtle, and widely misunderstood, concepts involved. [S0031-9007(98)

The structural changes of protein bovine serum albumin (BSA) during its unfolding on the addition of anionic surfactant sodium dodecyl sulfate (SDS) have been studied using small-angle neutron scattering (SANS) and dynamic light scattering (DLS). It is observed that at small surfactant concentrations, individual surfactant molecules bind to the protein, increasing the size of the protein. On the other hand, surfactant molecules at higher concentrations aggregate to form micelle-like clusters along the unfolded polypeptide chains of the protein. SANS data indicates the formation of a fractal structure representing a necklace model of micelle-like clusters randomly distributed along the polypeptide chain. The overall size of the complex increases and the fractal dimension decreases on increasing the surfactant concentration. The size of the micelle-like clusters does not show any change, while the number of such micelle-like clusters in protein-surfactant complexes increases with the surfactant concentration. The conformation of the unfolded protein has been determined directly using contrast variation SANS measurements by contrast matching the surfactant to the medium. It is found that the protein acquires a random coil Gaussian conformation on unfolding, with its radius of gyration increasing with an increase in surfactant concentration. The results of DLS measurements are found to be in good agreement with those obtained using SANS.

We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of p radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry. [S0031-9007(96)02278-8] PACS numbers: 03.65. Bz, 42.25.Hz, 42.25.Ja In general, a quantal system evolving under a timedependent Hamiltonian H͑t͒ acquires, apart from the dynamical phase 2Re R ͗H͑t͒͘dt͞", a nonintegrable and Hamiltonian-independent phase component called geometric phase, which depends only on the geometry of the curve traced in the ray space. Pancharatnam was the first to explicitly recognize geometric phase during his studies [1] of interference between optical beams of distinct polarizations. However, geometric phase attracted little further attention until Berry provided a general quantal framework [2] for geometric phase in the context of adiabatic evolutions, triggering an intense activity in this field. Geometric phase, already included in the standard formulation of quantum mechanics, can arise in any general evolution, be it nonadiabatic [3], noncyclic [4], or even nonunitary [4]. A completely general ray-space expression [5,6], in terms of just the pure state density operator, has been provided for geometric phase. Geometric phase has since been observed in a broad spectrum [7-15] of physical phenomena.In the first quantal prescription [2] of geometric phase an adiabatic evolution was considered. The early neutron experiments [10,11] therefore observed geometric phase for an eigenstate of a slowly rotating magnetic field. However, an adiabatic evolution generates a dynamical phase background which is much larger than the geometric phase signal. An ideal geometric phase experiment should therefore effect not an adiabatic evolution, but a parallel transportation [16], an intrinsically nonadiabatic evolution, that eliminates dynamical phase and yields a pure geometric phase. In an evolution which does not parallel transport the state, it is still possible to generate a pure geometric phase by arranging for a null dynamical phase [16][17][18] at the end of the evolution.The wave function of a spin 1 2 particle changes sign [19,20] when the spin precesses through 2p radians. This 4p spinor symmetry has been directly verified in neutron interference experiments [21][22][23]. The spinor phase also depends on the orientation [17] of the precession axis. While elucidating this dependence, Wagh and Rakhecha proposed the first experiment effecting a clear separation [18] of geometric and dynamical phases. Here a jz͘-polarized neutron beam incident on an interferometer (Fig. 1) permeated by a uniform guide field B 0ẑ splits into subbeams I and II. The subbeams pass through identical spin flippers F 1 and F 2 w...

Coacervation is a dense liquid-liquid phase separation and herein we report coacervation of protein bovine serum albumin (BSA) in the presence of polyelectrolyte sodium polystyrene sulfonate (NaPSS) under varying solution conditions. Small-angle neutron scattering (SANS) measurements have been performed on above protein-polyelectrolyte complexes to study the structural evolution of the process that leads to coacervation and the phase separated coacervate as a function of solution pH , protein-polyelectrolyte ratio and ionic strength. SANS study prior to phase separation on the BSA-NaPSS complex shows a fractal structure representing a necklace model of protein macromolecules randomly distributed along the polystyrene sulfonate chain. The fractal dimension of the complex decreases as pH is shifted away from the isoelectric point ( approximately 4.7) of BSA protein, which indicates the decrease in the compactness of the complex structure due to increase in the charge repulsion between the protein macromolecules bound to the polyelectrolyte. Concentration-dependence studies of the polyelectrolyte in the complex suggest coexistence of two populations of polyelectrolytes, first one fully saturated with proteins and another one free from proteins. Coacervation phase has been obtained through the turbidity measurement by varying pH of the aqueous solution containing protein and polyelectrolyte from neutral to acidic regime to get them to where the two components are oppositely charged. The spontaneous formation of coacervates is observed for pH values less than 4. SANS study on coacervates shows two length scales related to complex aggregations (mesh size and overall extent of the complex) hierarchically branched to form a larger network. The mesh size represents the distance between cross-linked points in the primary complex, which decreases with increase in ionic strength and remains the same on varying the protein-polyelectrolyte ratio. On the other hand, the overall extent of the complex shows a similar structure irrespective of varying ionic strength and protein-polyelectrolyte ratio. A large fraction ( approximately 50%) of protein-polyelectrolyte complexes is also found to be free in the supernatant after the coacervation.

The liquid-liquid phase transition (LLPT) in aqueous salt solutions of lysozyme protein has been studied by small-angle neutron scattering. Measurements have been carried out on fixed protein concentration with varying salt concentration approaching LLPT. The data are fitted considering protein interaction by the two Yukawa (2Y) potential which combines short-range attraction and long-range repulsion. We show that LLPT arises because of enhancement of non-DLVO (Derjaguin-Landau-Verwey-Overbeek) short-range attraction without any conformational structural change of the protein. The salt concentration required for LLPT as well as corresponding short-range attraction decreases significantly with increase in protein concentration.