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Rhodium-103 Self-Powered Neutron Detectors (SPNDs) are used in typical Pressurized Water Reactors (PWRs) for flux measurement. They are slow responding neutron detectors. The slow response of Rhodium-103 SPND restricts its direct use for monitoring, control and determination of parameters like neutron flux distribution, local flux peaking. These reactor parameters are indirectly calculated in terms of Departure from Nucleate Boiling Ratio (DNBR) & Linear Heat Generation Rate (LHGR), so that the extracted power limits from Fuel Assembly do not exceed the design limit. Whereas benefits offered by Rhodium-103 SPNDs like simple response, ease in handling and replacement from core etc., make them suitable candidates for this applications. In this paper, the goal is to develop a Discrete-Time Kalman Filter (DTKF) based delay compensator to improve the response time of Rhodium-103 SPNDs. The simulation results of delay compensation algorithm of Rhodium-103 SPND are compared with the collected data from 1000 MWe VVER units-1&2, Kudankulam, India. It is established that the simulation output is in very good agreement with the prompt responding Ex-core (Ion chamber) detectors. This puts the possibility of using Rhodium-103 detectors for fuel health monitoring inside reactor core.

A preliminary, and perhaps the first, study of astrophysical applications of Delbruck scattering in a gamma-ray emitting celestial object like a gamma-ray burst ( GRB ) has been made. At energies≥100 MeV the elastic scattering of gamma-ray photons off the molecular dust surrounding the GRB site is dominated by Delbruck scattering. Expressions for Delbruck-scattered gamma-ray flux as a function of time has been obtained for a few selected energies by assuming a simple model of GRB . These are compared with Compton-scattered flux. At certain situations, interestingly, the former is found to exceed the latter for the first few milliseconds of the burst. The issue of detectability of Delbruck-scattered gamma-ray echo from the cloud of a GRB is discussed. Although it is observed that the detection of such an echo is not within the capability of the presently operating gamma-ray missions such as Fermi LAT, a rough estimate shows that one can be optimistic that future generation gamma-ray telescopes might be able to see such photons' contribution to the total flux.

The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in predictions of elastic photon-atom scattering is assessed with the aid of the state-of-the-art numerical calculation of Rayleigh scattering obtained using the second-order S-matrix theory, in the photon energy range from 100 eV to 1 MeV. A comparison is made with predictions from S-matrix theory in the same atomic model for representative low-Z (carbon, Z = 6) and high-Z (lead, Z = 82) elements to get a general idea of the validity of these simpler more approximate methods. The importance of bound–bound contributions and the angle dependence of the anomalous scattering factors is discussed. A prescription is suggested, with the assumption of angle independence, that uses simpler approaches to obtain the elastic scattering cross sections in the soft-X-ray regime at the level of accuracy of the S-matrix calculation, failing at large momentum transfers for high-Z elements. Predictions from this prescription are compared with experiment. With starting point the many-body elastic scattering amplitude, a detailed discussion is presented of the partition of the elastic scattering amplitude into Rayleigh and Delbruck scattering components. This partition of the optical theorem reveals contributions from bound–bound atomic transitions, bound pair annihilation and bound pair production that are not usually associated with elastic scattering. In the partitioned optical theorem for Rayleigh scattering, as in the many-body optical theorem for scattering from excited states, subtracted cross sections naturally appear. These terms are needed, in addition to the familiar terms for photoionization, to relate the real and imaginary parts of the scattering amplitude.

The conventional perception is that the amplitudes of Delbr\"uck scattering calculated to all orders in the charge number $Z$ of the target nucleus should exhibit a scaling behavior at high energies. To examine this hypothesis the available experimental data of differential cross sections of elastic scattering in the energy range between 140 MeV and $7.11$ GeV are analyzed. It is found that the experimental data do not show scaling characteristics. Such a finding, though apparently against the standard notion, is not unexpected because at high energies Delbr\"uck scattering is in very forward direction and the theoretical arguments demand that to observe scaling, not only the energy itself but the product of scattering angles and energy also should be very large.

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S -matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [42] ; Vrinceanu et al. (2000) [24] ; Sokolovski and Msezane (2004) [23] ). The algorithm involves iterative ‘preconditioning’ of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select ‘true’ physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [45] ) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H 2 → HF + H, F + HD → HF + D, Cl + HCl → ClH + Cl and H + D 2 → HD + D reactions. Some detailed examples are given in the text. Program summary Program title: PADE II Catalogue identifier: AEHO_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 959 No. of bytes in distributed program, including test data, etc.: 158 380 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Any computer equipped with a FORTRAN 90 compiler Operating system: UNIX, LINUX RAM: 256 Mb Classification: 16.8 External routines: NAG Program Library ( http://www.nag.co.uk/numeric/fl/FLdescription.asp ) Nature of problem: The package extracts the positions and residues of resonance poles from numerical scattering data supplied by the user. The data can then be used for quantitative analysis of interference patterns observed in elastic, inelastic and reactive integral and differential cross sections. Solution method: The S -matrix element is analytically continued in the complex plane of either energy or angular momentum with the help of Pade approximation of type II. Resonance (complex energy or Regge) poles are identified and their residues evaluated. Unusual features: Use of multiple precision MPFUN package (Bailey (1993) [45] ). (Distributed with the PADE II code.) Running time: From several seconds to several minutes depending on the precision level chosen and the number of iterations performed.

Photon attenuation cross sections have been measured from time to time using radioactive isotopes as photon sources in various geometries. There are, however, inconsistencies between the measured values and the available tabulated values of attenuation coefficients based on different theoretical models. The measured values are particularly deficient for photon energies in the neighbourhood of the K-shell binding energies of attenuator elements. With the objective of filling such gaps in the experimental data as well as improving the data of earlier measurements, we have undertaken the present measurements in the energy region 43–1330 KeV. The measurements are made with the transmission technique using a NaI detector in the "good geometry," in which no gamma-ray photon scattered from the absorber at an angle greater than 0.3° can reach the detector. Results covering the elements from Z = 6–92 are presented and compared with the tabulated values of Hubbell et al. and Schaupp et al.

We study the effect of overlapping resonances on the angular distributions of the reaction F+H2(v=0,j=0)--HF(v=2,j=0)+H in the collision energy range from 5 to 65 meV, i.e., under the reaction barrier. Reactive scattering calculations were performed using the hyperquantization algorithm on the potential energy surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. The positions of the Regge and complex energy poles are obtained by Pade reconstruction of the scattering matrix element. The Sturmian theory is invoked to relate the Regge and complex energy terms. For two interacting resonances, a two-sheet Riemann surface is contracted and inverted. The semiclassical complex angular momentum analysis is used to decompose the scattering amplitude into the direct and resonance contributions.

Elastic photon scattering from the ground state and various excited states of carbon atoms and ions has been investigated, using the S-matrix formalism, for incident photon energies ranging from 100 eV to 10 keV, contrasting the results obtained for different configurations. The excited states considered include hollow-atom states, where one or more inner shells are completely vacated. Ionic cases are considered as a limit of excitation. Results demonstrate how cross sections for different excited states group together according to shared properties of the configurations, such as the number of K electrons. Cross sections may exhibit deep dips below the K edge, depending on the occupation of the subshells corresponding to the strongest transitions. Scattering from excited states can have significantly larger cross sections than scattering from the ground state, particularly just below the K resonance region, and therefore it needs to be considered in situations where there is a large population of these excited states. Results are interpreted in terms of form-factor arguments and the qualitative behavior of individual subshell amplitudes. The angular dependence of cross sections can be understood in terms of angle-dependent form factors and anomalous scattering factors, taken to be angle independent. Cases are identified for whichmore » excited-state total integrated cross sections are much larger than the corresponding cross sections for scattering from the ground state. Our main results use an averaging over magnetic substates at the level of the amplitude, exact only for fully filled subshells, but generally appropriate for the carbon case considered, which simplifies the discussion and explains most of the general features. We also present results for a hollow lithium atom with and without this approximation to illustrate the differences that can arise in certain circumstances. (c) 2000 The American Physical Society.« less

The angular distribution of K x rays emitted following K conversion has been investigated theoretically. It is shown that the static nuclear quadrupole moment may sufficiently perturb the innermost electron shell to cause anisotropy in the angular distribution between the K x rays and the coincident ..gamma.. rays, as suggested by Sen and subsequently confirmed experimentally by Sen, Salie, and Tomchuk. (AIP)

Theoretical studies of Rayleigh scattering of photons from neon atoms with different degrees of ionization, for energies both below and above the K-edges of the ions, are presented. Some unexpected structures both in Rayleigh scattering and in photoionization from neutral and weakly ionized atoms, very close to threshold, have been reported. It has recently been realized that some of the predicted structures may have a nonphysical origin and are due to the limitation of the independent-particle model and also to the use of a Coulombic Latter tail. Use of a K-shell vacancy potential — in which an electron is assumed to be removed from the K-shell — in calculating K-shell Rayleigh scattering amplitudes removes some of the structure effects near threshold. We present in this work a discussion of scattering angular distributions and total cross sections, obtained utilizing vacancy potentials, and compare these predictions with those previously obtained in other potential models.

New results of relatively high-precision measurements to study atomic pair production by photons in the threshold region together with some other previous measurements are presented for a critical evaluation of the new calculations with corrections of Coulomb effect and atomic-electron screening effect in the low-energy pair production. This evaluation reveals the degree in which the theory is in greater agreement with measurements in the threshold region and indicates the trend of cross sections as a function of atomic number and photon energy.

A detailed comparison is carried out between consistency contributions to the nuclear quadrupole antishielding factor for the ${\mathrm{Fe}}^{+3}$ ion obtained by the linked-cluster many-body perturbation procedure, as well as a procedure employing perturbed wave functions used in conventional differential-equation procedures for studying antishielding factors. The agreement between results by the two procedures is found to be good, indicating that the procedure using perturbed wave functions is a viable one for studying consistency effects, at least for positive ions.

New measurements of coherent (Rayleigh) scattering of photons of energies in the vicinity of K-absorption edges of gold and lead atoms together with other recent measurements with a coverage in the momentum transfer region up to 1.0 mc are presented for a critical evaluation of (i) the latest relativistic calculation of coherent scattering factors, (ii) the anomalous dispersion correction to the scattering factors and (iii) the exact numerical Rayleigh scattering amplitudes of inner electron shells. This evaluation reveals the ranges of applicability of these calculations and indicates the trend of behaviour due to the proximity of K-absorption edges of scatter atoms.

Coherent and incoherent photon scattering by bound electrons in low, medium and high Z atoms, over energies of 0.145-1.33 MeV and scattering angles below 15 degrees (momentum-transfer range 0-0.4 mc) and from 15 degrees to 150 degrees (0.1-4.0 mc), have been investigated experimentally. The results of the authors' relatively high precision measurements have also been compared with the predictions of new theoretical calculations for bound-electron incoherent and coherent scattering in the incoherent scattering-factor and form-factor approximations and for the Rayleigh and Delbruck scattering amplitudes over a high momentum-transfer range, to give a critical verification of the theory. It was found that for 0.145 MeV photons scattered with low momentum transfer, the F(q,Z) formalism is valid for low and medium Z atoms but not for the high Z (Z=82) atom. At all energies and in the low momentum-transfer range studied in the present work, the S(q,Z) formalism was found to be adequate for bound-electron incoherent scattering for all the atoms.

The multiplet splittings of core $p$-vacancy levels have recently been observed in various transition-metal complexes and in some rare-earth as well as actinide complexes. This paper presents the calculation of the multiplet structure of core $p$-vacancy levels in the Hartree-Fock free-ion approximation. The spin-orbit and crystal-field effects have been included. The cases studied are ${\mathrm{Mn}}^{2+}$ in Mn${\mathrm{F}}_{2}$ and the free ion ${\mathrm{Fe}}^{3+}$. For $3p$ vacancies these effects appear to be unimportant from the point of view of photoelectron spectroscopy owing to the limited resolution of the technique. For $2p$ vacancies the spin-orbit interaction is comparable to the electrostatic interaction between the electrons and both the interactions must be considered simultaneously. The conclusion is that the x-ray photoelectron spectra of inner-core electrons are more suitable for chemical analysis than those of outer electrons which, in addition, contain large correlation and many-body effects.

The band energy of silver has been calculated by the composite wave variational method at the symmetry points Γ X and L of the Brilloun zone, using the quantum defect method to find out the logarithmic derivatives of the radial wave functions inside the atomic cell. The results show that the p states at the zone faces are below the s states, and the band gap obtained at the zone face L is not sufficient for the Fermi surface to make a contact with the zone face L.

The band energy of silver in the metallic state has been calculated by the orthogonalized plane wave method at the symmetry points T, X and L of the Brillouin zone. The p states are seen to be below the s states at the zone faces. The value of Es - Ep along with the distortion parameter d (Cohen and Heine) has been discussed to investigate the possible contact of the Fermi surface with the nearest Brillouin zone face L. The results show that the Fermi surface is in contact with the zone face L. A value of the neck radius has been calculated and is compared with that obtained from recent experiments.

A knowledge of the energy spectrum of the neutron beam from the 156-inch cyclotron was required for cross section measurements. The spectrum of the recoil protons produced in n-p collisions was measured with a counter telescope containing a copper absorber of variable thickness. A calibration run was made in the external proton beam to measure the transmission of the absorber as a function of proton energy. It was found that the shape of the spectrum was consistent with the assumption that the neutrons are produced in `elastic' proton-neutron collisions in the beryllium target. The shape is then determined by the amplitude of radial oscillations in the cyclotron and the energy lost by the protons in their multiple traversals of the target.

The absoluteK-conversion coefficients of the 496 keV-124 keV cascadeγ-rays in131Cs have been determined from angular correlation experiments using a new approach. The value ofαK=0.0100±0.0007 obtained for the 496 keV transition is in excellent agreement with the theory whereas a strong case is presented for the existence of an anomalous nuclear-structure-dependent conversion coefficient for the 124 keV transition. TheK-conversion coefficient for this transition has been measured to be 0.742±0.077 giving a value of 1.25±0.13 for the ratioαK(expet)/αK(theory). The result is interpreted as being due to the presence of electric monopole,E0, electron transition. A value of 0.26±0.14 has been obtained for theE0/E2 electron conversion ratio and the absolute value of the electric monopole matrix element has been determined to be 0.07±0.02.

A new phase-lock system which remarkably reduces the VCO phase-noise with respect to the clean reference is described. Unlike the conventional system it allows much wider loop-bandwidth together with low-settling time. The superiority of this over the existing design is corroborated by the experimental data presented here.

Observations on the Faraday rotation of a transionospheric VHF signal obtained from a network of four stations near the path of totality during the total solar eclipse of 16 February 1980 are reported. A small decrease of 3–4% in the total ionization has been obtained around the time of totality. Absence of any periodic structure following the eclipse indicates that the TIDs are not of significant amplitude in the present case to be detected by the Faraday rotation technique.

The new results of measurements of coherent scattering of photons by bound atomic electrons over a momentum transfer $q$ range $0\ensuremath{-}4mc$ together with those from other recent measurements with a coverage in the momentum transfer up to $10mc$ are presented for a critical evaluation of the previous and new calculations on Rayleigh scattering. This evaluation reveals the ranges of applicability of the form-factor formalism in the nonrelativistic and relativistic domain and demonstrates the trend of behavior of the exact theoretical predictions as a function of $\frac{q}{\ensuremath{\alpha}\mathrm{Zm}}$.

Simple analytic parametrizations of the inner shell photoelectron angular distribution and total cross-section for photon scattering by atomic electrons are presented.

Rayleigh scattering amplitudes and elastic photon-atom scattering cross sections have been calculated for ${\mathrm{C}}^{0}$, ${\mathrm{C}}^{1+}$, ${\mathrm{C}}^{2+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{Ne}}^{0}$, ${\mathrm{Ne}}^{1+}$, ${\mathrm{Ne}}^{2+}$, ${\mathrm{Ne}}^{4+}$, ${\mathrm{Ne}}^{6+}$, ${\mathrm{Ne}}^{8+}$, and ${\mathrm{Ne}}^{9+}$ atoms and ions in their ground state. Some data were also obtained for oxygen. X-ray energies considered are in the regions above and below the threshold energy for K-shell photoionization. Except in the immediate neighborhood of this threshold energy, the primary effect of ionization on the atomic cross section is to reduce the number of electrons from which scattering occurs. The resonance region near threshold widens with increasing ionization, as with vacancies in deeper-lying states transitions to intermediate states further below threshold are allowed. Above the threshold energy, K-shell amplitudes in an isonuclear sequence, except for hydrogenlike-ion cases, share a common curve differing only in the position of the threshold. Further, when the photon energy is expressed in units of the K-shell threshold energy, both carbon and neon imaginary amplitudes share a common curve. Well above the threshold, the real part of amplitudes approach form-factor predictions.

The study of the energy levels of ions in solids is complicated because of the electric potential due to the rest of the ions. Crystal field theory is a simplified approach for dealing with the complexity. We make the assumption that the ions (ligands) surrounding a given ion (metal ion) are fixed, nonoverlapping, hard spherical charge distributions with a definite arrangement (crystal structure). We then calculate the electrostatic potential in the neighbourhood of the given ion in terms of certain parameters (crystal field parameters) representative of the arrangement and charge of the surrounding ions, and allow the potential to interact with the ion assumed to possess free space Hamiltonian. The energy level structure and the energy separation between the different levels are thus obtained in terms of the crystal potential parameters. The experimental information on the energy levels of the metal ion is then used to calculate the crystal potential parameters. Although a priori calculation of the crystal potential parameters is possible in principle, various simplifying assumptions have to be made even in most elaborate calculations. As a result the theoretical values of the parameters are rarely anywhere near to the experimental values. However, the true symmetry of the ligands surrounding the metal ion is not seriously affected by our simplified assumptions and the description of its energy levels remains valid in terms of unknown crystal potential parameters, as long as ‘covalence’ effects between the metal ions and the ligands are small. In the covalent compounds such as IrCl6, MnF 2, CoF 2 the observed energy levels are not correlated to the free-ion; they are easier to interpret as belonging to Molecular orbitals obtained by combining the atomicorbitals. The ligand field theory is a hybridization of the pure crystal field theory and the molecular orbital theory and we shall not consider it here.

Using the implicit summation technique, the parameters of two-photon ionization of rubidium by the second harmonic of ruby laser are reported. The Hartree-Fock and Hartree-Fock-Slater wavefunctions have been used and the spin-orbit perturbation has been included.