Nuclear resonant scattering of synchrotron radiation

The principal ideas of the theory and the main results of the experimental studies of the coherent resonant scattering of-radiation by nuclear ensembles in matter are briefly over-viewed. An analysis of transmission of the Mössbauer-radiation and of synchrotron radiation through a nuclear resonant medium is suggested using an approach based on the optical theory. The feasibilities of the nuclear resonant scattering of synchrotron radiation as a new technique for studying the hyperfine interactions and some other phenomena of the physics of condensed matter are considered.     

Spinning Q-Balls for the Klein-Gordon-Maxwell Equations

The nonlinear Klein-Gordon-Maxwell equations provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term W is positive and W(0) = 0. This fact makes the theory more suitable for physical models (for example models in supersymmetry theory and in cosmology; see e.g. [16, 22, 28] and their references).     

Dark energy and gravity

I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding the nature of gravity. Section 1 briefly overviews the currently popular “concordance cosmology” and summarizes the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant. Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction—described in terms of a metric on a smooth spacetime—is an emergent, long wavelength phenomenon, and can be described in terms of an effective theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the shift of the matter energy momentum tensor T _ab → T _ab + Λ _gab and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein’s theory at the lowest order with Lanczos–Lovelock type corrections. In this approach, the observed value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary of a spacetime region.     

Viscoelasticity of a Fermi liquid

Infinite homogeneous Fermi systems in the degenerate regime are described by the Uehling-Uhlenbeck equation. The eigenvalue problem associated with the linearized collision operator is solved analytically. Initial value problems are studied with the help of the spectral representation of the time evolution operator. The dynamic transport coefficients of the system can then be calculated in the framework of linear response theory. As an example the viscoelastic behaviour of the Fermi liquid is related to the relaxation of a quadrupole deformation in momentum space. In this connection also the coupling of the driving field to 2p-2h excitations will be discussed. The theory is applied to normal liquid³He and to nuclear matter.     

Neutron-proton mass difference in isospin-asymmetric nuclear matter

Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s - and p -wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter.     

On quantization of free fields in stationary space-times

In Section 1 we analyse the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections; we give an existence and uniqueness theorem for the Lichnerowicz distribution kernelG ₁ together with its proper Fourier expansion, and we construct the Hilbert spaces of frequency-part solutions defined by means ofG ₁.In Section 2 an analysis, a theorem and a construction similar to the above are formulated for thefree real field spin 1, massm>0, in one kind of static space-times.In this letter, only results are given. For detailed proofs and further results, see reference [9], [10] and [11].     

Properties of nuclear matter andN=Z closed-shell nuclei

A simple three-parameter density dependent effective interaction is used to study the properties of nuclear matter, neutron matter and some bulk properties such as ground state energies and rms charge radii of three double-closed shell nuclei⁴He,¹⁶O and⁴⁰Ca. The three parameters of the effective interaction are determined by requiring to fit the binding energy and density of infinite nuclear matter at saturation density as well as ground state energy of¹⁶O in the first order perturbation theory. This interaction gives correct saturation in nuclear matter with a value of 283 MeV for compressibility. The symmetry coefficienta _T atk _F=1·36 fm^–1 is 28·58 MeV. The energy per particle in neutron matter is calculated in the range of nuclear matter densities and it compares well with those ofNemeth andSprung. Groundstate energies and rms charge radii of⁴He,¹⁶O and⁴⁰Ca are calculated using oscillator eigen functions as single particle wave functions. Results for ground state energies are in good agreement with empirical values and rms charge radii are slightly better than those obtained byMoszkowski with the MDI.The authors are thankful to the Computer Centre, Utkal University, Bhubaneswar for providing computational facilities for this work.     

Loop Homotopy Algebras in Closed String Field Theory

Barton Zwiebach constructed [20] “string products” on the Hilbert space of a combined conformal field theory of matter and ghosts, satisfying the “main identity”. It has been well known that the “tree level” of the theory gives an example of a strongly homotopy Lie algebra (though, as we will see later, this is not the whole truth). Strongly homotopy Lie algebras are now well-understood objects. On the one hand, strongly homotopy Lie algebra is given by a square zero coderivation on the cofree cocommutative connected coalgebra [13, 14]; on the other hand, strongly homotopy Lie algebras are algebras over the cobar dual of the operad &?om for commutative algebras [9]. As far as we know, no such characterization of the structure of string products for arbitrary genera has been available, though there are two series of papers directly pointing towards the requisite characterization. As far as the characterization in terms of (co)derivations is concerned, we need the concept of higher order (co)derivations, which has been developed, for example, in[2, 3]. These higher order derivations were used in the analysis of the ”master identity“. For our characterization we need to understand the behavior of these higher (co)derivations on (co)free (co)algebras. The necessary machinery for the operadic approach is that of modular operads, anticipated in [5] and introduced in [8]. We believe that the modular operad structure on the compactified moduli space of Riemann surfaces of arbitrary genera implies the existence of the structure we are interested in the same manner as was explained for the tree level in [11]. We also indicate how to adapt the loop homotopy structure to the case of open string field theory [19]. Received: 10 November 1999 / Accepted: 29 March 2001     

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation betwee...     

Selection of optimal combinations of inputs in a partial least squares model for prediction of soil organic matter

Abstract

Partial least squares model is widely used in estimation of soil physical and chemical parameters such as soil organic matter and moisture content, due to its advantages in dealing with collinearity of variables like hyperspectral reflectance. However, it is hard to determine optimal combination of partial least squares model input for soil organic matter prediction since there are lots of possibilities such as, different mathematical transformation of spectral reflectance, wavelength ranges, and spectral resolution. Laboratory hyperspectral reflectance of soils in Songnen plain were analyzed in this study, and the orthogonal experimental design method for deriving optimal combination of input variables for soil organic matter prediction models was introduced. For intercalating orthogonal experimental design table, five different levels which commonly used by researchers were assigned to factors. Results show that the optimal combination input for single black soil is using the derivative logarithmic reciprocal reflectance in the wavelength range selected by multiple stepwise regression at a spectral resolution of 5?nm (R²=?0.95, RMSE?=?0.21, and RPD?=?4.49), and different soils is using continuum removed in the wavelength range selected by MSR at a spectral resolution of 5?nm (R²?=?0.77, RMSE?=?0.74, and RPD?=?2.08). With optimal combination input, the partial least squares model prediction ability was evaluated as excellent for single black soil, possible for different soils. This study illustrates the orthogonal experimental design method can be an effective way to identify the optimal input variables of a partial least squares model for soil organic matter prediction, and multiple stepwise regression can be a preprocessing step to reduce hyperspectral data redundancy before using partial least squares to predict soil organic matter. Overall, this study provides a new approach for determining optimal input of partial least squares predicting model.     

More is the Same; Phase Transitions and Mean Field Theories

This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of “singularity”, “order parameter”, “mean field theory”, “variational method”, “correlation length”, “universality class”, “scale changes”, and “renormalization”. The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and Sciences in 2006. It has appeared in draft form on the authors’ web site (http://jfi.uchicago.edu/~leop/) since then. The title of this article is a hommage to Philip Anderson and his essay “More is Different” (Sci. New Ser. 177(4047):393–396, 1972; N.-P. Ong and R. Bhatt (eds.) More is Different: Fifty Years of Condensed Matter Physics, Princeton Series in Physics, Princeton University Press, 2001) which describes how new concepts, not applicable in ordinary classical or quantum mechanics, can arise from the consideration of aggregates of large numbers of particles. Since phase transitions only occur in systems with an infinite number of degrees of freedom, such transitions are a prime example of Anderson’s thesis.     

Saturation of nuclear matter and realistic interactions

In this communication we study symmetric nuclear matter for the Brueckner-Hartree-Fock approach, using two realistic nucleon-nucleon interactions (CD-Bonn and Bonn C). The single-particle energy is calculated self-consistently from the real on-shell self-energy. The relation between different expressions for the pressure is studied in cold nuclear matter. For best calculations the self-energy is calculated with the inclusion of hole-hole (hh) propagation. The effects of hh contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Using two different methods, namely, G-matrix and bare potential, the hh term is calculated. We found that using G-matrix brought about non-negligible contribution to the self-energy, but this difference is very small and can be ignored if compared with the large contribution coming from particle-particle term. The contribution of the hh term leads to a repulsive contribution to the Fermi energy which increases with density. For extended Brueckner-Hartree-Fock approach the Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove relation.     

A semimicroscopic model of nuclear vibrations with separable forces and the giant dipole resonance of 12C

In the generalized ph basis generated for the realistic nuclear ground state, the nuclear hamiltonian is approximated by an expression containing the separable effective forces and terms which can be estimated from the spectroscopic data. The model hamiltonian obtained is used to describe normal nuclear vibrations. The application of this approach in the shell-model theory of nuclear reactions is discussed. The S-matrix for nucleon-nucleus scattering is calculated explicitly. The ¹²C photodisintegration calculation is made as a test example.     

Greensche Funktionen in der Theorie der Kernmaterie

The aim of this article is the representation of the theory of nuclear matter with the technique of many-body Green functions. We have treated the theory of Green functions thoroughly in the first chapters taking support of the functional method, which offers a convenient approach to the construction of the theory. After treatment of the properties of the exact two-point function and of the effective single-particle potential, preconditions and properties of the approximate solutions are discussed. Results achieved todate are treated in chapter 6. Brueckner theory and allied methods are not further discussed, since these are sufficiently known. The theory of linear response, being important for the semi-phenomenological treatment of real atomic nuclei, is presented in appendix A.     

A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner-crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously, the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R _c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.     

Nucleon sigma term and quark condensate in nuclear matter

We study the bound-nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar σ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear-matter density.