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We introduce LLMD, a large language model designed to analyze a patient's medical history based on their medical records. Along with domain knowledge, LLMD is trained on a large corpus of records collected over time and across facilities, as well as tasks and labels that make nuanced connections among them. This approach is critical to an accurate picture of patient health, and has distinctive advantages over models trained on knowledge alone, unlabeled records, structured EHR data, or records from a single health system. The recipe for LLMD continues pretraining a foundational model on both domain knowledge and the contents of millions of records. These span an average of 10 years of care and as many as 140 care sites per patient. LLMD is then instruction fine-tuned on structuring and abstraction tasks. The former jointly identify and normalize document metadata, provenance information, clinical named-entities, and ontology mappings, while the latter roll these into higher-level representations, such a continuous era of time a patient was on a medication. LLMD is deployed within a layered validation system that includes continual random audits and review by experts, e.g. based on uncertainty, disease-specific rules, or use-case. LLMD exhibits large gains over both more-powerful generalized models and domain-specific models. On medical knowledge benchmarks, LLMD-8B achieves state of the art accuracy on PubMedQA text responses, besting orders-of-magnitude larger models. On production tasks, we show that LLMD significantly outperforms all other models evaluated, and among alternatives, large general purpose LLMs like GPT-4o are more accurate than models emphasizing medical knowledge. We find strong evidence that accuracy on today's medical benchmarks is not the most significant factor when analyzing real-world patient data, an insight with implications for future medical LLMs.'

The combination of relativistic kinematics together with Coulomb or Yukawa potentials is a common place in atomic, nuclear and meson mass phenomenology. In meson spectroscopy, linear and Coulomb-like potentials are the most commonly used potentials and decays rates are also calculated using the value of the wavefunction at the origin. But, it has been known for sometime that the use of relativistic kinematics together with Coulomb or Coulomb-like potentials produces wavefunction singularity at the origin for S-wave \cite{DuranFriarPolyzou}. Therefore, there is a need to address this problem somehow. In this letter, we show how to overcome this problem without destroying the phenomenological success of the use of relativistic kinematics in meson mass spectroscopy. Our method can be easily implemented for similar problems in atomic, nuclear and particle phenomenology., Comment: 9 pages, 2 figures, 1 table

Generative artificial intelligence (GenAI) and large language models (LLMs) have simultaneously opened new avenues for enhancing human learning and increased the prevalence of poor-quality information in student response - termed Botpoop. This study introduces Professor Leodar, a custom-built, Singlish-speaking Retrieval Augmented Generation (RAG) chatbot designed to enhance educational while reducing Botpoop. Deployed at Nanyang Technological University, Singapore, Professor Leodar offers a glimpse into the future of AI-assisted learning, offering personalized guidance, 24/7 availability, and contextually relevant information. Through a mixed-methods approach, we examine the impact of Professor Leodar on learning, engagement, and exam preparedness, with 97.1% of participants reporting positive experiences. These findings help define possible roles of AI in education and highlight the potential of custom GenAI chatbots. Our combination of chatbot development, in-class deployment and outcomes study offers a benchmark for GenAI educational tools and is a stepping stone for redefining the interplay between AI and human learning., Comment: 13 pages, 5 figures, SI with Annexes A, B and C upon request

Recent advances in machine learning techniques have made it possible to use high-throughput screening to identify novel materials with specific properties. However, the large number of potential candidates produced by these techniques can make it difficult to select the most promising ones. In this study, we develop the oxidation state probability (OSP) method which evaluates ternary compounds based on the probability (the OSP metric) of each element to adopt the required oxidation states for fulfilling charge neutrality. We compare this model with Roost and the Fourier-transformed crystal properties (FTCP)-based synthesizability score. Among the top 1000 systems with the most database entries in Materials Project (MP), more than 500 systems exhibit an attested compound among the top 3 compositions when ranked by the OSP metric. We find that the OSP method shows promising results for certain classes of ternary systems, especially those containing nonmetals, s-block, or transition metals. When applied to the Cu-In-Te ternary system, an interesting system for thermoelectric applications, the OSP method predicted the synthesizability of CuIn$_3$Te$_5$ without prior knowledge, and we have successfully synthesized CuIn$_3$Te$_5$ in experiment. Our method has the potential to accelerate the discovery of novel compounds by providing a guide for experimentalists to easily select the most synthesizable candidates from an arbitrarily large set of possible chemical compositions., Comment: 11 pages, 3 figures

In this paper, we propose an access control method for object detection models. The use of encrypted images or encrypted feature maps has been demonstrated to be effective in access control of models from unauthorized access. However, the effectiveness of the approach has been confirmed in only image classification models and semantic segmentation models, but not in object detection models. In this paper, the use of encrypted feature maps is shown to be effective in access control of object detection models for the first time., Comment: To appear in 2022 IEEE 4th Global Conference on Life Sciences and Technologies (LifeTech 2022)

Software faults are commonly occurred due to interactions between one or more input parameters in complex software systems. Software test design techniques can be implemented to ensure the quality of the developed software. Exhaustive testing tests all possible test configurations; however, it is infeasible considering time and resource constraints. Pairwise t-way testing is a sampling strategy that focuses on testing every pair of parameter combination, effectively reducing the generated test size as opposed to testing exhaustively. In this paper, we propose a new pairwise t-way strategy called Pairwise Gravitational Search Algorithm Strategy (PGSAS). PGSAS utilizes Gravitational Search Algorithm (GSA) for generating optimal pairwise test suites. The performance of PGSAS is benchmarked against existing t-way strategies in terms of test suite size. Preliminary results showcase that PGSAS provides competitive results in most configurations and outshines other strategies in some cases., Comment: Accepted for publication in IEEE Xplore Subject: International Conference on Artificial Intelligence and Computer Science Technology(ICAICST 2021), 6 pages, 2 figures

Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or exceeds the sample size, we adopt a sparse framework and propose two penalized maximum likelihood estimators with either the Lasso or the smoothly clipped absolute deviation (SCAD) penalty. We show that both estimators are estimation consistent, while the SCAD estimator also selects relevant parameters with probability approaching one. A modified EM-algorithm is developed for the case of Gaussian errors and simulations show that the algorithm exhibits desirable finite sample performance. In an application to short-horizon return predictability in the US, we estimate a 15 variable 2-state MS-VAR(1) and obtain the often reported counter-cyclicality in predictability. The variable selection property of our estimators helps to identify predictors that contribute strongly to predictability during economic contractions but are otherwise irrelevant in expansions. Furthermore, out-of-sample analyses indicate that large MS-VARs can significantly outperform "hard-to-beat" predictors like the historical average.

In this paper, we propose a new nonparametric estimator of time-varying forecast combination weights. When the number of individual forecasts is small, we study the asymptotic properties of the local linear estimator. When the number of candidate forecasts exceeds or diverges with the sample size, we consider penalized local linear estimation with the group SCAD penalty. We show that the estimator exhibits the oracle property and correctly selects relevant forecasts with probability approaching one. Simulations indicate that the proposed estimators outperform existing combination schemes when structural changes exist. Two empirical studies on inflation forecasting and equity premium prediction highlight the merits of our approach relative to other popular methods.

This is a short essay about some fundamental results on scalar curvature and the two key methods that are used to establish them.

Perovskite solar cells (PSCs) with transparent electrodes can be integrated with existing solar panels in tandem configurations to increase the power conversion efficiency. A critical layer in semi-transparent PSCs is the inorganic buffer layer, which protects the PSC against damage when the transparent electrode is sputtered on top. The development of n-i-p structured semi-transparent PSCs has been hampered by the lack of suitable p-type buffer layers. In this work we develop a p-type CuOx buffer layer, which can be grown uniformly over the perovskite device without damaging the perovskite or organic charge transport layers, can be grown using industrially scalable techniques and has high hole mobility (4.3 +/- 2 cm2 V-1 s-1), high transmittance (>95%), and a suitable ionisation potential for hole extraction (5.3 +/- 0.2 eV). Semi-transparent PSCs with efficiencies up to 16.7% are achieved using the CuOx buffer layer. Our work demonstrates a new approach to integrate PSCs into tandem configurations, as well as enable the development of other devices that need high quality p-type layers.

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The most important function is arguably the Euclidean distance between data items, This can be used, for example, to solve the approximate nearest neighbor problem. We use random variables to model the inherent uncertainty in such approximations, and apply the Maximum Entropy Method to infer the underlying probability distribution. We propose using the expected values of distances between these random variables as improved estimates of the distance. We show by analysis and experimentally that in most cases results obtained by our method are more accurate than what is obtained by the classical approach. This improves the accuracy of a classical technique that have been used with little change for over 100 years.

Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three-Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations---3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations---predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame ($T_{\rm Lab}$) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which $T_{\rm Lab}>$ 220 MeV/n.

It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra of $G$. The integrability condition is the vanishing of a torsion tensor of type $(1,2)$. This is a slight improvement of an earlier result proved in [Min-Oo M., Ruh E.A., in Differential Geometry and Complex Analysis, Springer, Berlin, 1985, 205-211].

It is shown that irreducible two-state continuous-time Markov chains interacting on a network in a bilinear fashion have a unique stable steady state. The proof is elementary and uses the relative entropy function., Comment: 9 pages; minor typos corrected

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann-Schwinger equation with the first order optical potential that was employed in the calculation

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann- Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A $\le$ 16), and the momentum-space representation of the optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.

It is shown that a relativistic multiple scattering theory for hadron-nucleus scattering can be consistently formulated in four-dimensions in the context of meson exchange. We give a multiple scattering series for the optical potential and discuss the differences between the relativistic and non-relativistic versions. We develop the relativistic multiple scattering series by separating out the one boson exchange term from the rest of the Feynman series. However this particular separation is not absolutely necessary and we discuss how to include other terms. We then show how to make a three-dimensional reduction for hadron-nucleus scattering calculations and we find that the relative energy prescription used in the elastic scattering equation should be consistent with the one used in the free two-body t-matrix involved in the optical potential. We also discuss what assumptions are involved in making a Dirac Relativistic Impulse Approximation (RIA)., Comment: 20 pages, 9 figures, Accepted for publication in Journal of Physics G

Relativistic nucleus-nucleus reactions occur mainly through the Strong or Electromagnetic (EM) interactions. Transport codes often neglect the latter. This work shows the importance of including EM interactions for space radiation applications., Comment: 11 pages

This paper has been withdrawn by the authors due to some fatal errors that cannot be mended. The authors apologize for any inconvenience., Comment: This paper has been withdrawn

We consider the correspondence between solutions of non-gravitational field theories formulated in Euclidean space-time and Minkowski space-time. Infinitely many "Euclidean" spaces can be obtained from M4 via a group of transformations in which the Wick rotation is a special case. We then discuss how the solutions of gauge field theories formulated in these "Euclidean" spaces have a one-to-one correspondence with the solutions of field theories formulated in Minkowski space-time, provided we avoid the one-point compactification into S4 = E4 U infinity., Comment: This is a summary of a contributed talk presented at "Quark Confinement and the Hadron Spectrum V," Gagnano, Italy, September 2002. (4 pages, 1 figure). This paper is to be published in the proceedings of "Quark Confinement and the Hadron Spectrum V", edited by Nora Brambilla, World Scientific Publishing Co. (2003)

The instantaneous Bethe-Salpeter equation, derived from the general Bethe-Salpeter formalism by assuming that the involved interaction kernel is instantaneous, represents the most promising framework for the description of hadrons as bound states of quarks from first quantum-field-theoretic principles, that is, quantum chromodynamics. Here, by extending a previous analysis confined to the case of bound-state constituents with vanishing masses, we demonstrate that the instantaneous Bethe-Salpeter equation for bound-state constituents with (definitely) nonvanishing masses may be converted into an eigenvalue problem for an explicitly - more precisely, algebraically - known matrix, at least, for a rather wide class of interactions between these bound-state constituents. The advantages of the explicit knowledge of this matrix representation are self-evident., Comment: 12 Pages, LaTeX, 1 figure

The Bethe-Salpeter equation for bound states of a fermion-antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices., Comment: 4 pages, LaTeX, contributed to the International Conference on "Quark Confinement and the Hadron Spectrum IV," July 3 - 8, 2000, Vienna, Austria

The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field theory. In contrast to its further simplifications (like, for instance, the so-called reduced Salpeter equation), it allows also the consideration of bound states composed of "light" constituents. Every eigenvalue equation with solutions in some linear space may be (approximately) solved by conversion into an equivalent matrix eigenvalue problem. We demonstrate that the matrices arising in these representations of the instantaneous Bethe-Salpeter equation may be found, at least for a wide class of interactions, in an entirely algebraic manner. The advantages of having the involved matrices explicitly, i.e., not "contaminated" by errors induced by numerical computations, at one's disposal are obvious: problems like, for instance, questions of the stability of eigenvalues may be analyzed more rigorously; furthermore, for small matrix sizes the eigenvalues may even be calculated analytically., Comment: LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev. D

We prove that the largest first eigenvalue of the Dirac operator among all hermitian metrics on the complex projective space of odd dimension $m$, larger than the Fubini-Study metric is bounded by $(2m(m+1))^{1/2}$., Comment: 6 pages

In this paper, which is a natural continuation of our previous paper math.DG/0504557, we describe some special Lagrangians of cohomogeneity one in the resolved conifold. Our main result gives a foliation of the resolved conifold by T^2-invariant special Lagrangians, where the generic leaf is topologically T^2 X R. We also obtain a family of SO(3)-invariant special Lagrangians. These special Lagrangian families in both the deformed and the resolved conifold approach asymptotically the same special Lagrangian cones in the conifold., Comment: 11 pages

In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is topologically T^2 X R. In the limit, these special Lagrangians asymptotically approach a special Lagrangian cone on a torus in the conifold. Using moment map techniques we also recover the family of SO(n)-invariant special Lagrangian n-folds in the cotangent bundle of the n-sphere obtained by H. Anciaux., Comment: 22 pages, 2 figures

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy., Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarity

We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R^{2n}., Comment: 22 pages; for Revised Version: Minor changes, improved notation, streamlined exposition

The space radiation environment is a complex mixture of particle types and energies originating from sources inside and outside of the galaxy. These environments may be modified by the heliospheric and geomagnetic conditions as well as planetary bodies and vehicle or habitat mass shielding. In low Earth orbit (LEO), the geomagnetic field deflects a portion of the galactic cosmic rays (GCR) and all but the most intense solar particle events (SPE). There are also dynamic belts of trapped electrons and protons with low to medium energy and intense particle count rates. In deep space, the GCR exposure is more severe than in LEO and varies inversely with solar activity. Unpredictable solar storms also present an acute risk to astronauts if adequate shielding is not provided. Near planetary surfaces such as the Earth, moon or Mars, secondary particles are produced when the ambient deep space radiation environment interacts with these surfaces and/or atmospheres. These secondary particles further complicate the local radiation environment and modify the associated health risks. Characterizing the radiation fields in this vast array of scenarios and environments is a challenging task and is currently accomplished with a combination of computational models and dosimetry. The computational tools include models for the ambient space radiation environment, mass shielding geometry, and atomic and nuclear interaction parameters. These models are then coupled to a radiation transport code to describe the radiation field at the location of interest within a vehicle or habitat. Many new advances in these models have been made in the last decade, and the present review article focuses on the progress and contributions made by workers and collaborators at NASA in the same time frame. Although great progress has been made, and models continue to improve, significant gaps remain and are discussed in the context of planned future missions. Of particular interest is the juxtaposition of various review committee findings regarding the accuracy and gaps of combined space radiation environment, physics, and transport models with the progress achieved over the past decade. While current models are now fully capable of characterizing radiation environments in the broad range of forecasted mission scenarios, it should be remembered that uncertainties still remain and need to be addressed.

Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world’s best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three- Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scatter- ing Theory (MST) that uses 5 parameterizations—3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations—predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame (TLab) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which TLab > 220 MeV/n.

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A = 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability for both non-relativistic and relativistic kinematics.

The space radiation environment is composed of energetic particles which can deliver harmful doses of radiation that may lead to acute radiation sickness, cancer, and even death for insufficiently shielded crew members. Spacecraft shielding must provide structural integrity and minimize the risk associated with radiation exposure. The risk of radiation exposure induced death (REID) is a measure of the risk of dying from cancer induced by radiation exposure. Uncertainties in the risk projection model, quality factor, and spectral fluence are folded into the calculation of the REID by sampling from probability distribution functions. Consequently, determining optimal shielding materials that reduce the REID in a statistically significant manner has been found to be difficult. In this work, the difference of the REID distributions for different materials is used to study the effect of composition on shielding effectiveness. It is shown that the use of correlated uncertainties allows for the determination of statistically significant differences between materials despite the large uncertainties in the quality factor. This is in contrast to previous methods where uncertainties have been generally treated as uncorrelated. It is concluded that the use of correlated quality factor uncertainties greatly reduces the uncertainty in the assessment of shielding effectiveness for the mitigation of radiation exposure.

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A less than or equal to 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon- nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.

Reliable estimates of exposures due to ionizing radiations are of paramount importance in achieving human exploration and development of space, and in several technologically important and scientifically significant areas impacting on industrial and public health. For proper assessment of radiation exposures reliable transport codes are needed. An essential input to the transport codes is the information about the interaction of ions and neutrons with the matter. Most of the information about this interaction is put in by nuclear cross section data. In order to obtain an accurate parameterization of cross sections data, theoretical input is indispensable especially for the processes where there is little or no experimental data available. In the grant period reliable data base was developed and a phenomenological model was developed for the total absorption cross sections valid for any charged/uncharged light, medium and heavy collision pairs valid for the entire energy range. It is gratifying to note the success of the model. The cross sections model has been adopted and is in use in NASA cosmic ray detector development projects, the radiation protection and shielding programs and several DoE laboratories and institutions. A list of the publications based on the work done during the grant period is given below and a sample copy of one of the papers is enclosed with this report.

Transportation of ions and neutrons in matter is of direct interest in several technologically important and scientific areas, including space radiation, cosmic ray propagation studies in galactic medium, nuclear power plants and radiological effects that impact industrial and public health. For the proper assessment of radiation exposure, both reliable transport codes and accurate data are needed. Nuclear cross section data is one of the essential inputs into the transport codes. In order to obtain an accurate parametrization of cross section data, theoretical input is indispensable especially for processes where there is little or no experimental data available. In this grant period work has been done on the studies of the use of relativistic equations and their one-body limits. The results will be useful in choosing appropriate effective one-body equation for reaction calculations. Work has also been done to improve upon the data base needed for the transport codes used in the studies of radiation transport and shielding for space exploration and high speed flight transportation. A phenomenological model was developed for the total absorption cross sections valid for any system of charged and/or uncharged collision pairs for the entire energy range. The success of the model is gratifying. It is being used by other federal agencies, national labs and universities. A list of publications based on the work during the grant period is given below and copies are enclosed with this report.

A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.

Relativistic p-(Ca-40) elastic scattering observables are calculated using four sets of relativistic NN amplitudes obtained from different one-boson-exchange (OBE) models. The first two sets are based upon a relativistic equation in which one particle is on mass shell and the other two sets are obtained from a quasipotential reduction of the Bethe-Salpeter equation. Results at 200, 300, and 500 MeV are presented for these amplitudes. Differences between the predictions of these models provide a study of the uncertainty in constructing Dirac optical potentials from OBE-based NN amplitudes.

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

A method has been developed for solving two body relativistic bound state equations in momentum space with a confining interaction. A total of six different three dimensional reductions of the Bethe-Salpeter equations are studied with particular emphasis placed on the competing roles of relativistic kinematics and retardation. The results indicate that these two effects counteract each other and this sheds some light on why nonrelativistic models of meson spectroscopy have been quite successful.

Most of the research work performed under this grant were concerned with strong interaction processes ranging from kaon-nucleon interaction to proton-nucleus scattering calculations. Research performed under this grant can be categorized into three groups: (1) parametrization of fundamental interactions, (2) development of formal theory, and (3) calculations based upon the first two. Parametrizations of certain fundamental interactions, such as kaon-nucleon interaction, for example, were necessary because kaon-nucleon scattering amplitude was needed to perform kaon-nucleus scattering calculations. It was possible to calculate kaon-nucleon amplitudes from the first principle, but it was unnecessary for the purpose of the project. Similar work was also done for example for anti-protons and anti-nuclei. Formal developments to some extent were also pursued so that consistent calculations can be done.

A comprehensive summary of a many-body, microscopic, particle-hole formalism is presented that describes coherent, subthreshold, pion production in peripheral, heavy-ion collisions. The formalism uses a new separable model transition interaction that produces Delta-hole states in either the projectile or target nucleus. Shell-model states described by harmonic oscillator functions are used in the calculation of Delta formation and decay and Lorentz-contraction effects of the nucleus not at rest are included. An analytical expression to lowest multipole order for the differential cross section is examined. The sensitivity of the theoretical results to the shell-model states is determined with preliminary shape results compared with data. The effects of higher multipoles are examined with attention paid to the second-order multipole value.

The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

Relativistic p-Ca-40 elastic scattering observables are calculated using relativistic NN amplitudes obtained from the solution of a two-body relativistic equation in which one particle is kept on its mass-shell. Results at 200 MeV are presented for two sets of NN amplitudes, one with pure pseudo-vector coupling for the pion and another with a 25 percent admixture of pseudo-scaling coupling. Both give a very good fit to the positive energy on-shell NN data. Differences between the predictions of these two models (which are shown to be due only to the differences in their corresponding negative energy amplitudes) provide a measure of the uncertainty in contructing Dirac optical potentials from NN amplitudes.

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.

Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.

We calculate total cross sections for coherent pion production using localized plane-wave approximations for the shell-structure of valence nucleons that are excited to delta particles in the intermediate state in the (12C, 12B) and (12C, 12N) charge-exchange, heavy-ion reactions. We find comparable agreement to projectile downshift data for 12C(12C, 12B)12N. Then we improve the formalism by replacing the localized plane wave bound states with harmonic oscillator states which are imbedded in a multipole expansion approach and calculate pion differential cross sections to test for the sensitivity of the spectra to the single-particle mass parameter.

We calculate the coherent production of pions from subthreshold to relativistic energies in heavy-ion collisions using a quantum, microscopic, many-body model. For the first time, in this approach, we use harmonic oscillator wave functions to describe shell-model information. The theoretical quantum mechanical results obtained for the pion spectra represent an important improvement over our previous microscopic, many-body calculations.