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Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Phenomenological R -Matrix parameterization of direct, doorway, and compound nuclear reactions [Abstract]

Although formal expressions for scattering matrix accounting for direct, doorway, and compound nuclear (CN) resonant reactions have been derived several decades ago in both the transition ( T -)matrix formalism and the reactance ( K -)matrix formalism, the absence of corresponding expressions in phenomenological R -matrix formalism has limited the application of the latter to CN resonant reactions only. We remove this limitation by parameterizing direct, doorway, and CN resonant reactions in a phenomenological R -matrix scattering matrix, and provide a parameterization for a corresponding Reich-Moore approximation of eliminated capture channels. Direct reactions induce (previously neglected) mixing among the incoming or outgoing R -matrix channel wave functions, parameterized by real and orthonormal channel-rotation matrix, M , whereby the original scattering matrix U is transformed into M T UM . Any real and orthonormal matrix, M , can be equivalently expressed as e η , where η is a real and skew-symmetric 2 rotation-generating matrix that subsequently yields a more intuitive parameterization of eliminated direct capture reactions in Reich-Moore approximation. A phenomenological R -matrix parameterization of doorway reactions is inferred by equating the expression for reactance ( K -)matrix, given in terms of Brune’s alternative R -matrix parameterization, to a corresponding expression derived using Feshbach’s projection operator formalism. Assuming that all doorway states, just like CN states, are confined within spheres defined by R -matrix channel radii, a new R -matrix-like term induced by doorway states is gleaned, wherein each doorway state is parameterized by its energy, width, and the strength of its coupling to each CN state. Since a Reich-Moore approximation for retained-channel scattering matrix ought to approximate the effect of eliminated capture channels taking place via direct, doorway, or CN reactions, each of the three kinds of reactions contributing to the capture entails a corresponding Reich-Moore parameterization in a first-order approximation: direct contribution is parameterized by introducing finite diagonal elements of a retained-channel rotation-generating matrix, doorway contribution is parameterized by doorway capture widths, while CN contribution is parameterized by conventional Reich-Moore capture widths. We will present evidence of direct and doorway reactions observed in recent measurements of resolved resonance cross sections at the Gaerttner LINAC Center at Rensselaer Polytechnic Institute, and will outline a path for implementing this new R -matrix parameterization into the SAMMY nuclear data evaluation code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Interstellar/Precometary Organic Material and the Photochemical Evolution of Complex Organics

During the past two decades ground-, air-, and space-based infrared spectroscopic observations, combined with realistic laboratory simulations, have revolutionized our understanding of interstellar ice and dust, the raw materials from which planets, comets and stars form. Most interstellar material is concentrated in Large molecular clouds where simple molecules are formed by dust grain and gas phase reactions. Gaseous species striking the cold (10 K) dust will stick, forming an icy grain mantle. This accretion, coupled with energetic particle bombardment and UV photolysis, will produce a complex chemical mixture containing volatile, non-volatile, and isotopically fractionated species. Ices in molecular clouds contain the very simple molecules H2O, CH3OH, CO, CO2, H2, and perhaps some NH3 and H2CO, as well as more complex species including nitriles and ketones or esters. The evidence for these compounds as well as carbon rich materials such as polycyclic aromatic hydrocarbons (PAHs), microdiamonds, and amorphous carbon will be reviewed and the possible connections with comets and meteorites will be presented in the first part of the talk. The second part of the presentation will focus on interstellar/precometary ice photochemical evolution. The chemical composition and photochemical evolution of realistic interstellar/pre-cometary ice analogs containing methanol will be discussed. ultraviolet photolysis of these ices produces H2, H2CO, CO2, CO, CH4, HCO, and more complex molecules. Infrared spectroscopy, H-1 and C-13 nuclear magnetic resonance (NMR) spectroscopy, and gas chromatography-mass spectrometry demonstrate that when ices representative of interstellar grains and comets are exposed to UV radiation at low temperature a series of moderately complex organic molecules are formed in the ice including: CH3CH2OH (ethanol), HC(=O)NH2 (formamide), CH3C(=O)NH2 (acetamide), and R-C(integral)N (nitriles). Several of these are already known to be in the interstellar medium, and their presence indicates the importance of grain processing. After warming to room temperature what remains is an organic residue composed primarily of Hexamethylenetetramine (HMT, C6H12N4), with lesser amounts of polyoxymethylene related species (POMs), amides, and ketones. This is in sharp contrast to the organic residues produced by irradiating ices which do not contain methanol (unrealistic interstellar ice analogs) or thermally promoted polymerization-type reactions in unirradiated realistic ice mixtures. Here HMT is only a minor product in a residue dominated by a mixture of polyoxymethylene related species. The implications, for infrared astronomy and astrochemistry, of high concentrations of HMT in interstellar and cometary ices may be profound. The ultraviolet photolysis of HMT frozen in H20 ice produces the "XCN" band observed in the spectra of protostellar objects and laboratory ices, as well as carbon oxides and other nitriles. Thus, HMT may be a precursor of XCN in protostellar objects and a source of CN and CO in the tail of comets. Also, HMT is known to hydrolyze under acidic conditions to yield ammonia and formaldehyde as well as amino acids. Thus, HMT may have been a source of organic material delivered to the early earth by comets.

Allamandola, Lou J.↗