Calculation Of Response Functions Research Articles

Variations in the electrical conductivity of the upper mantle beneath North America and the Pacific Ocean

Variations in the electrical conductivity of the mantle beneath Carty Lake in the Canadian Shield, Tucson in the southwest United States, and Honolulu and Midway in the north central Pacific were determined through the inversion of long‐period magnetotelluric and geomagnetic depth sounding data. Inversion of computed response functions is carried out using a minimum structure, regularized approach. The upper mantle beneath Carty Lake is approximately an order of magnitude more resistive than the upper mantle beneath Tucson and nearly 1.5 orders of magnitude more resistive than Honolulu and Midway Island. Inversions were also carried out where the minimum structure constraint was removed at known upper mantle discontinuities. These models show a jump in conductivity of ∼1.5 orders of magnitude across the 660 km discontinuity, a result that is consistent with laboratory experiments on realistic mantle assemblages. Mantle conductivity profiles at Carty Lake are significantly more resistive than those at Tucson, Honolulu, and Midway to depths of ∼300–400 km. These observations likely reflect differing thermal states, the presence (or absence) of partial melt and volatiles, and may also be related to chemical differences between depleted and undepleted upper mantle. The observed conductivity variations may be interpreted as lateral variations in temperature, partial melt, and/or dissolved hydrogen in olivine.

Calculating response functions in time domain with nonorthonormal basis sets

We extend the recently proposed order-N algorithms for calculating linear- and nonlinear-response functions in time domain to the systems described by nonorthonormal basis sets.

Fast Algorithm for Calculating Two-Photon Absorption Spectra by Real-Time Real-Space Higher-Order Finite-Difference Method

The newly developed fast algorithm for the calculation of nonlinear response functions is applied to the calculation of the two-photon absorption spectra of crystalline silicon. The algorithm combines the real-time real-space higher-order finite-difference method with the use of random vectors for intermediate states. Despite the radical difference in methodology, the result is in fair agreement with that of the conventional method.

Fast algorithm for calculating two-photon absorption spectra

We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows a reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multidimensional time integration is greater for the calculation of nonlinear response functions of higher order at higher energy resolution.

A development of NRESPG Monte Carlo code for the calculation of neutron response function for gas counters

A Monte Carlo code Neutron RESPonse function for Gas counters (NRESPG) has been developed for the calculation of neutron response functions and efficiencies for neutron energies up to 20 MeV, which can be applied for 3He, H 2, or BF 3 gas proportional counters with or without moderator. This code can simulate the neutron behavior in a two-dimensional detector configuration and treat the thermal motion of a moderator atom which becomes important as the neutron energy becomes sufficiently low. Further, a more precise measured data was taken to simulate the position-dependent gas multiplication in the sensitive and insensitive gas region of a proportional counter. The NRESPG code has been applied for the calculation of response functions of 3He cylindrical proportional counters to determine neutron energy and neutron fluence in a monoenergetic calibration field. Thus, a remarkable discrepancy in the lower portion of the full-energy peak produced by the 3He(n,p)T reaction can be removed which results in a good agreement between simulations and experiments. The code has been also used for the simulation of the response of a McTaggart-type long counter consisting of a central cylindrical BF 3 counter surrounded by a polyethylene moderator. The results of the NRESPG simulations were compared with those obtained from MCNP calculations.

A 14 MeV neutron spectrometer for the Joint European Torus deuterium-tritium experiments

A 14 MeV neutron spectrometer, based on the principle of the proton recoil telescope, has been installed as a deuterium–tritium (DT) plasma diagnostic at the Joint European Torus. The device comprises three identical telescope modules arranged one behind the other, to increase efficiency without worsening resolution. It views the plasma along a horizontal line of sight. The total efficiency is 7.05×10−5 counts per (neutron per cm2), and the calculated response function has a full width at half maximum of 2.2% at an incident neutron energy of 14.1 MeV. The spectrometer was operational throughout the recent DT experiment No. 1, and selected neutron spectra have been analyzed in terms of the contributions from the various neutron production mechanisms.

First-Principles Calculations of Nonlinear Optical Response Functions in Semiconductors

ABSTRACTWe present our implementation of the length-gauge formalism of Sipe and coworkers (Phys. Rev. B 48, 11705 (1993); ibid 52, 14636 (1995)) using the linearized muffin-tin orbital (LMTO) method and discuss its application to the calculation of second order response functions. The importance of gap corrections beyond LDA is discussed. As primary application, we discuss the second harmonic generation (SHG) coefficients of the SiC polytypes and of the chalcopyrites of both the II-IV-V2 and I-III-VI2 families. These examples illustrate the relation of the second order response function to the modification of the crystal structure and chemical substitutions.

On the absolute efficiency of large neutron detectors for μCF

The absolute efficiency for a large organic scintillator neutron detector has been calculated via Monte Carlo simulation for neutrons of 14 MeV. The influence of the environmental geometry (source scattering, etc.) has been taken into account. Full differential cross-sections, including resonances, have been used. The calculated response function compares well with the measured one.

Special absorber neutron detector moderator assembly: A new detector system for flux measurements of collimated 2.5 MeV neutrons

A new detector system has been developed for time resolved flux measurements of collimated D-D neutrons in large magnetic confinement fusion experiments. The novel detection concept, called the special absorber neutron detector moderator assembly, is to place a scatterer behind a collimator and to detect the scattered neutrons in a small Bonner sphere. The system has been optimized by means of the Monte Carlo neutron photon transport code (MCNP) simulations and is capable to be extended for a neutron profile camera. First tests and calibration measurements of a system using a 3 in. Bonner sphere have been carried out in the 2.5 MeV neutron field at the accelerator facility of the Physikalisch-Technische Bundesanstalt in Braunschweig. The numerical and experimental results are presented. The measurements differ from the calculated values by a factor of about 1.09. It is questionable if these discrepancies can be explained by differences in the shielding, moderator and detector characteristics employed in the experiment and those assumed in the calculation. This is highlighting the importance of experimentally validating numerical MCNP response function calculations wherever possible.

Calculation of neutron response functions in complex geometries with the MCNP code

For the analysis of (e,én) coincidence experiments at the superconducting Darmstadt electron linear accelerator S-DALINAC, neutron response functions of NE 213 liquid scintillation detectors had to be calculated. We report, for the first time, on calculations of neutron response functions with a modification of the MCNP code taking into consideration nonlinear light output functions for secondary charged particles. The code was tested for a simple detector geometry against the widely used NRESP code. Excellent agreement between results of NRESP and MCNP calculations was achieved for neutron energies up to 8 MeV when the same detector model, light output functions and neutron cross sections were used. With this modification of the MCNP code, the response functions can now be determined for arbitrary complex detector arrangements, e.g. including massive shieldings.

Generalized integral-screening for efficient calculations of nonlinear optical properties of large molecules

We describe the implementation of integral screening in the integral-direct SCF calculation of cubic response functions. The screening is applied to all computational steps that involve the construction of Fock matrices or one-index transformed Fock matrices. We apply this implementation to study the length dependence of the polarizability and second hyperpolarizability of diphenylpolyenes. It is demonstrated that calculations of the second hyperpolarizability of molecules containing more than 140 atoms are now accessible by ab initio methods on a time scale that makes it of interest in real applications.

Antisymmetrized random phase approximation for quasi-elastic scattering in nuclear matter: Non-relativistic potentials

Many-body techniques for the calculation of quasi-elastic nuclear matter response functions in the fully antisymmetrized random phase approximation on a Hartree-Fock basis are discussed in detail. The methods presented here allow for an accurate evaluation of the response functions with little numerical effort. Formulae are given for a generic non-relativistic potential parameterized in terms of meson exchanges; on the other hand, relativistic kinematical effects have been accounted for.

Relativistic effects in the electromagnetic current at GeV energies

We employ a recent approach to the nonrelativistic reduction of the electromagnetic current operator in calculations of electronuclear reactions. In contrast to the traditional scheme, where approximations are made for the transferred momentum, transferred energy, and initial momentum of the struck nucleon in obtaining an on-shell inspired form for the current, we treat the problem exactly for the transferred energy and transferred momentum. We calculate response functions for the reaction ${}^{2}\mathrm{H}{(e,e}^{\ensuremath{'}}p)n$ at CEBAF (TJNAF) energies and find large relativistic corrections. We also show that in plane wave impulse approximation, it is always possible to use the full operator, and we present a comparison of such a limiting case with the results incorporating relativistic effects to the first order in the initial momentum of the struck nucleon.

Use of 4He-filled proportional counters as neutron spectrometers

Neutron response functions of two commercially available cylindrical 4He-filled proportional counters (filling pressure about 2 MPa) have been measured in the neutron energy range 144–14 000 keV. Measurements were carried out using optimal settings for the detector high voltage and amplifier shaping time which were determined within the scope of this study. The experimental results have been analyzed and compared to calculated response functions using empirically determined energy and resolution calibration functions. The theoretically determined response functions show good agreement with the measured response except for energies above 10 MeV. The discrepancies are attributed to unsatisfactory electronics. The Monte-Carlo code Gas-filled neutron spectrometer response (GNSR) which has been developed for the calculation of response functions and efficiencies of gas-filled neutron detectors, is briefly described.

Single determinant calculations of excited state polarizabilities

We apply response theory to simulate excited state polarizabilities emphasizing the possibility to do so by means of optimization of a ground state single determinant only. The excited state polarizabilities are given by the double residues of the cubic response functions. A set of molecules with varying ground state configurations and properties have been considered: water, ozone, formaldehyde, ethylene, butadiene, cyclobutadiene, pyridine, pyrazine and s-tetrazine. The results have been compared to excited state experiments where available and with linear response calculations of the multi-determinant optimized excited state. It is shown that calculations of excited state polarizabilities based on a ground state optimized single determinant work well for most of the cases investigated. This contention is exemplified by the fact the gas phase value from an electrochromism experiment for the polarizability of the 1 1 B 2 excited state of formaldehyde is better reproduced by ground state cubic response theory than by the corresponding separate state linear response function calculation, and by that the calculations call for an experimental reinvestigation of the excited state polarizabilities of s-tetrazine. A few prerequisites are given: The excited state should be isolated in energy, the ordering of the main contributing states should be reproduced, and the geometric conformation of the excited state in question should not be very different from the ground state geometry. The computational and formal advantages of the approach are discussed.

Crossover between High and Low Energy-States in Two-Coupled Chains of Tomonaga Model

By applying the renormalization group method to two-coupled chains in the Tomonaga model, the role of interchain hopping has been studied in the entire energy region. The energy for a crossover from the perturbational regime to the relevant regime becomes smaller than that of the interchain hopping due to one-dimensional fluctuations of the mutual interaction. From the calculation of response functions for charge density waves and superconducting states, the phase diagram of dominant and subdominant states has been obtained in the plane of mutual interactions with fixed energy.

Measurement of the stray field emanating from magnetic force microscope tips by Hall effect microsensors

We describe the use of micronic Hall sensors as magnetic-field profilometers with submicron resolution. The procedure involves the deconvolution of Hall voltage maps produced by scanning the field source over the sensor, with a scanning probe microscope. The response function of an infinite Hall cross is calculated analytically in the two-dimensional case, using conformal mapping techniques. Various methods of deconvolution of the Hall voltage maps are presented and compared. The calculated response function is used for the deconvolutions, and different effective sensor sizes are tried. It is shown that the remaining main uncertainties come from the ignorance of the true response function of the sensor, ascribed to the charge depletion phenomenon that is known to occur at the sensor edges. The method is applied to thin-film magnetic force microscope tips for which a precise knowledge of the tips field at sample location proves crucial to image interpretation. Maximum fields in the range 10–100 Oe are found at a distance known to be about 100 nm from the tip contact surface, depending on the tip coating thickness and magnetization direction.

Ab initiostudy of the ferroelectric transition in cubicPb3GeTe4

In the substitutionally disordered narrow-gap semiconductor Pb_{1-x}Ge_xTe, a finite-temperature cubic-rhombohedral transition appears above a critical concentration $x \approx 0.005$. As a first step towards a first-principles investigation of this transition in the disordered system, a (hypothetical) ordered cubic Pb_3GeTe_4 supercell is studied. First principles density-functional calculations of total energies and linear response functions are performed using the conjugate-gradients method with ab initio pseudopotentials and a plane-wave basis set. Unstable modes in Pb_3GeTe_4 are found, dominated by off-centering of the Ge ions coupled with displacements of their neighboring Te ions. A model Hamiltonian for this system is constructed using the lattice Wannier function formalism. The parameters for this Hamiltonian are determined from first principles. The equilibrium thermodynamics of the model system is studied via Metropolis Monte Carlo simulations. The calculated transition temperature, T_c, is approximately 620K for the cubic Pb_3GeTe_4 model, compared to the experimental value of T_c \approx 350K for disordered Pb_{0.75}Ge_{0.25}Te. Generalization of this analysis to the disordered Pb_{1-x}Ge_xTe system is discussed.

PC/FRAM: a code for the nondestructive measurement of the isotopic composition of actinides for safeguards applications

The Nuclear Safeguards Program at the Los Alamos National Laboratory has developed and fielded techniques for the gamma-ray spectrometry measurement of the isotopic composition of plutonium and other actinides for over 20 years, ever since Parker and Reilly first proposed a practical method for the measurement of the arbitrary sample. Their procedures, incorporating internal (to the measured gamma-ray spectrum) or ‘intrinsic’ self-determination of the relative efficiency function of the sample-detector measurement system, are widely applied today. The PC/FRAM code is the most recent and most highly developed Los Alamos code developed specifically for the nuclear safeguards applications of this technique. We will describe the measurement principles that allow accurate measurements to be taken on samples of arbitrary size, shape, and measurement geometry—and of arbitrary physical and chemical composition—through the use of known nuclear decay data (half-lives and branching intensities). Subsequently, we will describe the analysis methodology, which is driven by an easily edited parameter file that frees the user from dependence on a dedicated programmer for analyses of special cases. This methodology relies on internal gamma-ray peaks from the spectrum under analysis to self-calibrate the unknown spectrum for energy and peak shape (energy dependence of full width at half maximum (FWHM) and tailing parameters). The program uses these parameters to calculate response functions that are fit to the analysis peaks requested in the parameter file. The structure of the code and its Windows 3.1 user interface allows use with equal ease by the experienced spectroscopist or operator-level personnel in a working facility. The code has been applied primarily to the analysis of gamma-ray spectra from plutonium with the isotopic results used to calculate the parameters 240Pu eff for interpretation of neutron coincidence counting assays and P eff (W/g Pu) for the interpretation of calorimetry measurements. These measurement combinations form the backbone of nondestructive assay measurements for materials control and accountability both domestically and internationally. We will present examples of the results of measurements of these parameters with PC/FRAM and discuss the wide range of materials measured, including uranium samples and samples with lead shielding.

Calculation of linear and second-order optical response in wurtzite GaN and AlN

We calculate the linear and nonlinear optical response of GaN and AlN in the wurtzite structure. The dielectric function \ensuremath{\epsilon}(\ensuremath{\omega}), the second harmonic generation susceptibility ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega}), and the linear electro-optic susceptibility ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-\ensuremath{\omega};\ensuremath{\omega},0) are all evaluated over a broad frequency range. These results are based on a first principles electronic structure calculation using the full-potential linearized augmented plane-wave method within the local density approximation. Corrections to the underestimation of the band gaps are included at the level of the scissors approximation, which is carefully incorporated within our susceptibility formalism. All independent components for the response functions are calculated; the results for GaN and AlN are very different, and those of AlN are in strong disagreement with predictions of the bond charge model. Results for all response functions at zero frequency are underestimated with respect to the available experimental values. A comparison of the calculated response functions for nonzero frequencies is made with the limited experimental data. We confirm both analytically and numerically that the calculated second-order susceptibilities obey various symmetry constraints below the band gap.