Jackson Model Research Articles

Kinetic analysis of the annealing period in the formation of the Poly (A)-2Poly (U) triple helix.

AbstractThe slow kinetics of annealing processes in multistranded nucleic acids is spectrophotometrically investigated using poly(A)·2poly(U) as a model system. The absorbance changes at specific wavelengths show that double‐helical (A·U) base pairs appear as transient intermediates. The annealing process is identified by the enlargement of triple‐helical sequences at the cost of (A·U) base pairs and unpaired (U) residues. A large time range in the reorganization of mismatched chain configurations is characterized by a logarithmic dependence on time. This observation is quantitatively described by a kinetic model developed by Jackson. In Jackson's model the rate‐limiting process in the slow annealing phase of maximizing triple‐helical sequences, is the removal of strand entanglements, knots, and hairpin loops by complete unwinding of those helical stretches which stabilize the mismatched configurations. The results of the present study are briefly discussed in terms of optimum conditions for hybridization experiments and for the preparation of polynucleotide complexes commonly used to produce interferons.

Absolute (p, xn) cross-section measurements on 232Th

Excitation functions have been measured for both the (p, 6n) and (p, 7n) reactions on 232Th at incident energies up to 100 MeV using the external beam of the McGill synchrocyclotron. The natural activity of the target material is used to determine the target thickness, making it unnecessary to use monitor foils, or to carry out chemical separations following bombardment. The shape of both excitation functions is consistent with the prediction of the Jackson model. If fission competition is taken into account the observed cross sections are in reasonable quantitative agreement with the theoretical predictions. The (p, 6n) excitation function is found to be in disagreement with a number of earlier measurements.

Physical properties of aromatic hydrocarbons: V. The solidification behavior of 1:2 diphenylbenzene

The crystallization behavior of purified 1:2 diphenylbenzene has been studied over approximately six orders of magnitude in growth rate and 75°C of undercooling. Crystallization rates range from 1.81 × 10 -6 cm sec -1 at 55.1°C to 3.60 × 10 -3 cm sec -1 at 39°C (where the rate passes through a maximum value), down to 3.40 × 10 -9 cm sec -1 at -19.1°C, the lowest temperature studied. The growth rate varies smoothly with temperature, but cannot be adequately described by the classical Fisher-Turnbull model for crystallization kinetics. The logarithm of the product of the growth rate and the viscosity varies non-linearly with the undercooling cooling expressed as ( TΔ T) -1. When self-diffusion data are used in the analysis in place of the viscosity results, an almost linear dependence was noted. However, it was also necessary to modify the transport term of the rate equation since the classical Arrhenius form overestimates the contribution of the interfacial transport term to the growth rate. A kinetic limit at small undercooling, in excess of 1°C, and other morphological and kinetic evidence support a surface nucleation growth mechanism. The crystalline phase exhibits a faceted interface at all temperatures in keeping with Jackson's model for materials possessing large entropies of fusion. Parameters pertinent to the crystalline and glassy condition of 1:2 DPB are discussed and compared with other materials. Factors responsible for the disagreement between theory and experiment are discussed.

Spallation products produced by bombardment of dysprosium with protons of energies 9–87 MeV

Natural dysprosium, and dysprosium enriched in various isotopes were bombarded with protons of energies between 9 and 87 MeV. Mass assignments of holmium and dysprosium activities were verified, as well as half-lives and γ-ray assignments. An α-emitter with half-life 27 min has been assigned to 153Ho. Cross-sections of natural dysprosium for production of various spallation products have been determined. Formation cross-sections from some individual dysprosium isotopes were obtained by comparison of enriched isotopic and natural dysprosium bombardments. These cross sections showed reasonable agreement with those predicted by the Jackson model.

THE SPALLATION OF IRIDIUM WITH PROTONS OF ENERGIES 9–87 MEV

Iridium metal has been bombarded with protons varying in energy from 8 to 87 Mev. The spallation products were radiochemically separated and decay characteristics and formation cross sections were determined. It was confirmed that both Pt187 and Pt186 have half-lives of about 3 hr, and a half-life of 13.3 ± 0.2 days was found for Ir189. An isomeric state of Ir186 with half-life 2.0 ± 0.5 hr has been found. Fair agreement was obtained between excitation functions for (p,xn) reactions determined experimentally and those predicted by the Jackson model. The (p,pn) yield at 84 Mev has been compared with that calculated from Monte Carlo cascade data combined with evaporation theory and found to be too high by a factor of 4.

REACTIONS PRODUCED ON ERBIUM BY PROTONS OF ENERGIES BETWEEN 6 AND 87 MEV

Erbium was bombarded with protons of energies varying between 6 and 87 Mev. Nuclear characteristics and excitation functions were studied for isotopes of Tm, Er, Ho, and Dy, formed by various (p,xn) and (p,xpxn) reactions. Bombardment of enriched Er isotopes helped elucidate some of the excitation functions. A comparison has been made of the experimental (p,xn) cross sections with those predicted by the Jackson model and reasonable agreement has been found. Holmium was bombarded with α-particles to produce the compound nucleus Tm169* and the ratios σ (p,n): σ (p,2n) = σ (α,n): σ(α,2n) were found to hold.

NUCLEAR REACTIONS INDUCED IN TANTALUM BY PROTONS OF ENERGY UP TO 84 MEV

Nuclear reactions induced in tantalum by protons of energy up to 84 Mev have been studied and excitation functions obtained for products formed by (p,xn), (p,pxn), (p,2pxn), and (p,3pxn) reactions. Radiation characteristics of the products were redetermined. Previously unreported γ-rays with energies 90 to 1050 kev have been found for W176, and 113 kev for W177. A new half-life of 2.7 ± 0.1 hr for W176 is reported. The cross sections for the (p,xn) reactions were compared with the values predicted by Jackson's schematic model and found to be in reasonable agreement. More complex reactions are discussed in the light of current nuclear theories.

Excitation Functions ofU235andU238Bombarded with Helium and Deuterium Ions

Cross sections were determined for the reactions ${\mathrm{U}}^{238}({\mathrm{He}}^{4}, n){\mathrm{Pu}}^{241}$ [including ${\mathrm{U}}^{238}({\mathrm{He}}^{4}, p){\mathrm{Np}}^{241}\ensuremath{-}{\ensuremath{\beta}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{Pu}}^{241}$], ${\mathrm{U}}^{238}({\mathrm{He}}^{4}, 2n){\mathrm{Pu}}^{240}$, ${\mathrm{U}}^{238}({\mathrm{He}}^{4}, 3n){\mathrm{Pu}}^{239}$, ${\mathrm{U}}^{238}({\mathrm{He}}^{4}, 4n){\mathrm{Pu}}^{238}$, ${\mathrm{U}}^{238}$(${\mathrm{He}}^{4}$, fission), ${\mathrm{U}}^{235}({\mathrm{He}}^{4}, n){\mathrm{Pu}}^{238}$, and ${\mathrm{U}}^{235}({\mathrm{He}}^{4}, 3n){\mathrm{Pu}}^{236}$ induced by helium ions of energies from 18.0 to 43.0 Mev. The yields of ${\mathrm{Pu}}^{239}$, ${\mathrm{Pu}}^{240}$, and ${\mathrm{Pu}}^{241}$ were determined by a mass spectrometric technique. Cross sections were measured for the reactions ${\mathrm{U}}^{238}(d, p){\mathrm{U}}^{239}$, ${\mathrm{U}}^{238}(d, 2n){\mathrm{Np}}^{238}$, ${\mathrm{U}}^{238}(d, 4n){\mathrm{Np}}^{236}(22 \mathrm{hr})$, ${\mathrm{U}}^{238}(d, t; d, p2n){\mathrm{U}}^{237}$, ${\mathrm{U}}^{235}(d, n){\mathrm{Np}}^{236}(22 \mathrm{hr})$, ${\mathrm{U}}^{235}(d, 2n){\mathrm{Np}}^{235}$, and ${\mathrm{U}}^{235}(d, 3n){\mathrm{Np}}^{234}$ induced by deuterons of energies from 5.8 to 21.5 Mev. The above excitation functions are compared with similar excitation functions of nonfissile nuclei to show the effect of fissionability on spallation cross sections. Mean values of $\frac{{\ensuremath{\Gamma}}_{n}}{{\ensuremath{\Gamma}}_{f}}$ are derived for several heavy nuclides by fitting the experimental excitation functions with theoretical cross sections calculated from the Jackson model modified for fission. In addition to the discussion on the compound-nucleus formation mechanism, some discussion of the experimental evidence for direct interactions is given.

Excitation Functions of Bismuth and Lead

Cross sections for the reactions ${\mathrm{Bi}}^{209}({\mathrm{He}}^{4}, 2n){\mathrm{At}}^{211}$, ${\mathrm{Bi}}^{209}({\mathrm{He}}^{4}, 3n){\mathrm{At}}^{210}$, and ${\mathrm{Bi}}^{209}({\mathrm{He}}^{4}, 4n){\mathrm{At}}^{209}$ were measured with helium ions of energies from 20.6 to 43.3 Mev. Cross sections for the reactions ${\mathrm{Bi}}^{209}(d, p)\mathrm{RaE}$, ${\mathrm{Bi}}^{209}(d, n){\mathrm{Po}}^{210}$, ${\mathrm{Bi}}^{209}(d, 2n){\mathrm{Po}}^{209}$, ${\mathrm{Bi}}^{209}(d, 3n){\mathrm{Po}}^{208}$, and ${\mathrm{Pb}}^{208}(d, p){\mathrm{Pb}}^{209}$ were measured with deuterons of energies from 6.3 to 21.5 Mev. Some information is presented on the ${\mathrm{Bi}}^{209}({\mathrm{He}}^{4}, t){\mathrm{Po}}^{210}$ reaction. A half-life of 7.23\ifmmode\pm\else\textpm\fi{}0.04 hr was measured for ${\mathrm{At}}^{211}$. The ${\mathrm{Bi}}^{209}(d, 3n){\mathrm{Po}}^{208}$ threshold energy is 12.0\ifmmode\pm\else\textpm\fi{}0.3 Mev (center-of-mass system). The compound nucleus reaction cross sections are compared with the predictions of the Jackson model, and good agreement is obtained. The ($d, n$) and ($d, p$) stripping cross sections are discussed briefly.