Recent Articles

Coupled-channels calculation for scattering and capture of alpha particles near the giant quadrupole resonance

D. P. Stanley and Dean Halderson

Phys. Rev. C 20, 2114 (1979) - Published 1 December, 1979

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Coupled-channels calculations were performed for ${}^{54}{Fe}$ ( $α$ , $α_{0}$ ) ${}^{54}{Fe}$ and ${}^{54}{Fe}$ ( $α$ , $α_{1}$ ) ${}^{54}{Fe}$ * in the region of the giant quadrupole resonance. Reasonable agreement with the data was obtained. The wave functions were then employed to calculate the $α$ capture cross section. This calculation suggests that the capture cross section is nonresonant. The implications for decay modes of the giant quadrupole resonance are discussed.

NUCLEAR REACTIONS Coupled-channels calculation; alpha scattering on ${}^{54}{Fe}$ ; alpha capture to ${}^{58}{Ni}$ ; giant quadrupole resonance.

Finite-range coupled reaction channel investigation of the elastic transfer process

P. J. Griffin and R. D. Koshel

Phys. Rev. C 20, 2119 (1979) - Published 1 December, 1979

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Results of calculations for the elastic transfer reaction ${}^{13}C$ ( ${}^{12}C$ , ${}^{12}C$ ) ${}^{13}C$ at laboratory energies of 15 and 87 MeV are presented. The exchange amplitude is calculated using finite-range coupled reaction channel and distorted-wave Born-approximation methods. Recoil was included in all calculations. The results of the calculations indicate that coupled reaction channel effects are important at the lower of the two energies while recoil effects are not. At the higher energy for the reaction studied the results of the calculation indicate that coupled reaction channel effects are negligible while recoil effects are important.

NUCLEAR REACTIONS ${}^{13}C$ ( ${}^{12}C$ , ${}^{12}C$ ) ${}^{13}C$ , $E = 15 and 87$ MeV; CRC and DWBA calculations of exchange elastic scattering.

Single particle transfer reactions and backward angle elastic scattering for the ${}^{15}N$ , ${}^{16}O$ + ${}^{28}{Si}$ systems

S. Kahana, B. T. Kim, and M. Mermaz

Phys. Rev. C 20, 2124 (1979) - Published 1 December, 1979

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Strongly absorbing optical potentials in a distorted-wave context are unable to describe the single neutron-stripping and single proton-pickup reactions induced by 44 MeV ${}^{15}N$ on a ${}^{28}{Si}$ target. Modifications of the imaginary potential consistent with the surface transparency requirements for backward angle ${}^{16}O$ + ${}^{28}{Si}$ elastic scattering greatly improve the transfer predictions. In addition, the altered potentials yield a reasonably qualitative picture of the backward elastic excitation function over a broad range of energy.

NUCLEAR REACTIONS ${}^{28}{Si}$ ( ${}^{15}N$ , ${}^{16}O$ ), ${}^{28}{Si}$ ( ${}^{15}N$ , ${}^{14}N$ ), excitation function and angular distribution for elastic scattering.

Multinucleon transfer reactions induced by ${}^{18}O$ on ${}^{28}{Si}$

M. C. Mermaz, A. Greiner, B. T. Kim, M. A. G. Fernandes, N. Lisbona, E. Müller, W. Chung, and B. H. Wildenthal

Phys. Rev. C 20, 2130 (1979) - Published 1 December, 1979

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The experimental angular distributions of several multinucleon transfer reactions induced by ${}^{18}O$ on ${}^{28}{Si}$ have been measured and compared with distorted-wave reaction calculations. The shape and relative intensities of the data can be reproduced by theoretical calculations which seem to open the way for this type of study of structure of nuclei in the middle of the $2 s - 1 d$ shell. On the other hand, we have not found it possible either to reproduce the shapes of the angular distributions with an optical potential derived from an elastic scattering analysis or to correctly calculate the absolute values of the cross sections. These difficulties which are similar to those encountered in other heavy-ion reaction studies will require extended improvements in the current formulations of the theory for the reaction processes.

NUCLEAR REACTIONS ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{16}O$ ), ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{20}{Ne}$ ), ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{22}{Ne}$ ), ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{15}N$ ), and ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{15}O$ ) $E_{{}^{18}O} = 56$ MeV—angular distribution measured between 5° and 35° laboratory angles—distorted wave reaction analysis; shell-model structure analysis.

Structure in the 180° scattering of ${}^{12}C$ by ${}^{27}{Al}$

A. Roy, A. D. Frawley, and K. W. Kemper

Phys. Rev. C 20, 2143 (1979) - Published 1 December, 1979

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An excitation function for elastic and inelastic scattering at $θ_{c . m .} = 180 ° \pm 2.0 °$ has been measured for ${}^{12}C$ + ${}^{27}{Al}$ in the energy range $14 ≲ E_{c . m .} ≲ 25$ MeV. The data exhibit a strong enhancement at $E_{c . m .} ≃ 19.5$ MeV with a width of ∼2 MeV. Elastic scattering angular distributions at $E_{{}^{12}C} (lab) = 30, 32, 35, and 40$ MeV show oscillatory structure in the angle range $40 ° ≲ θ_{c . m .} ≲ 110 °$ . It is not possible to describe the elastic scattering data with an energy independent optical model.

NUCLEAR REACTIONS ${}^{12}C$ + ${}^{27}{Al}$ , measured $σ (θ, E)$ elastic and inelastic scattering, $θ_{c . m .} - 180 ° \pm 2.0 °$ , $14 < E_{c . m .} < 25$ MeV. Measured $σ (θ)$ elastic, $E_{c . m .} = 20.8, 22.2, 24.2, and 27.6$ MeV $14 ° <~ θ_{c . m .} <~ 110 °$ , deduced optical model parameters.

Energy dependence of the fusion and elastic scattering of ${}^{16}O$ + ${}^{40}{Ca}$

S. E. Vigdor, D. G. Kovar, P. Sperr, J. Mahoney, A. Menchaca-Rocha, C. Olmer, and M. S. Zisman

Phys. Rev. C 20, 2147 (1979) - Published 1 December, 1979

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In a study of the system ${}^{16}O$ + ${}^{40}{Ca}$ , the total evaporation-residue cross section has been measured at nine energies, and elastic-scattering angular distributions at five energies, within the range $40 MeV \leq E_{lab} \leq 214 MeV$ . The fusion cross section is observed to saturate above $E_{lab} = 63$ MeV. Several possible mechanisms to explain this effect are considered, and the shortcomings of each are pointed out. The model based on a critical distance in the entrance channel is judged the most nearly acceptable. At the highest bombording energies the fusion residues exhibit (1) angular distributions which suggest significant emission of energetic $α$ particles (or larger clusters), and (2) total cross sections in conflict with expectations based on the vanishing of the rotating-liquid-drop model fission barrier. An optical model analysis of the elastic-scattering data is used to extract total reaction cross sections ( $σ_{reac}$ ). The nonlinear dependence of $σ_{reac}$ on $\frac{1}{E_{c . m .}}$ is noted and the implications for the extraction of "interaction barrier" and "fusion barrier" parameters are discussed. A method for unified analysis of low-energy elastic-scattering and fusion data, based on the assumption that a single potential is relevant to both, is suggested. Simultaneous fits to 56-MeV elastic-scattering and lowenergy fusion measurements for ${}^{16}O$ + ${}^{40}{Ca}$ are attained with Woods-Saxon potentials only if the real well diffuseness is constrained to the range (0.50±0.05) fm, a value not compatible with several proposed potentials based on liquid-drop model concepts. The real potentials preferred in this low-energy analysis are not capable of providing good optical model fits to the highest-energy elastic data.

NUCLEAR REACTIONS Fusion and elastic scattering of ${}^{16}O$ + ${}^{40}{Ca}$ , $40 <~ E_{lab} <~ 214$ MeV; measured $σ_{fusion} (E)$ , $σ_{elastic} (θ, E)$ ; evaluation of various mechanisms for saturation of $σ_{fusion}$ at high energies; optical model analysis of $σ_{elastic}$ ; simultaneous analyis of low-energy elastic and fusion data; deduced $s$ -wave barrier parameters, real well diffuseness of nucleus-nucleus potential.

Coulomb excitation of Yb nuclei

L. L. Riedinger, E. G. Funk, J. W. Mihelich, G. S. Schilling, A. E. Rainis, and R. N. Oehlberg

Phys. Rev. C 20, 2170 (1979) - Published 1 December, 1979

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Multiple Coulomb excitation measurements have been performed with ${}^{16}O$ projectiles on ${}^{168, 170, 172, 174, 176}{Yb}$ , Measured $γ$ -ray yields were compared to the Winther-deBoer calculations in order to extract $B (E 2)$ and $B (E 3)$ values to vibrational and rotational states. The $2^{+}$ member of the $γ$ -vibrational band was observed in all the nuclei, the $4^{+}$ member in three cases, and excited $0^{+}$ states in ${}^{168, 170, 172, 174}{Yb}$ . The $B (E 2; 0^{+'} \to 2^{+})$ values from $0^{+}$ states at 1228 keV in ${}^{170}{Yb}$ and 1154 keV in ${}^{168}{Yb}$ are in excess of one single-particle unit, the first such cases observed in Yb nuclei. $B (E 3)$ values to octupole states were deduced for ${}^{172, 174}{Yb}$ . Members of the ground state rotational band up to $I = 8$ were excited in each nucleus. The measured yield of the $8^{+}$ state relative to that of the $6^{+}$ level is compared to calculations and discussed for the five nuclei studied.

NUCLEAR REACTIONS ${}^{168, 170, 172, 174, 176}{Yb}$ ( ${}^{16}O$ , ${}^{16}O^{'} γ$ ), $E = 58 - 62$ MeV; measured $σ (E)$ , $I_{γ}$ . ${}^{168, 170, 172, 174, 176}{Yb}$ deduced levels, $J$ , $π$ , $B (E 2)$ , $B (E 3)$ . Enriched targets; Ge(Li) detector.

Generalized spectator expansion for interacting composite systems

Larry D. Ludeking and James P. Vary

Phys. Rev. C 20, 2188 (1979) - Published 1 December, 1979

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Interactions of two composite clusters are treated in a multiple scattering framework whereby many-particle operators are decomposed into a systematic and finite series such that there is an ordered sequestering according to particle rank. Thus an $N$ -body operator is written as the superposition of all distinct groupings of interactions that occur between pairs of particles, three particles, four particles, etc., such that all groupings contain at least one particle from each of the composite systems. It is shown how the transition operator, a reaction operator, and an optical potential may be described in this framework. The general nature of this decomposition is demonstrated and its connection to more standard multiple-scattering prescriptions delineated.

NUCLEAR REACTIONS scattering theory, multiple scattering, nucleus-nucleus scattering, nuclear reactions, reaction operator expansion, transition operator expansion.

High spin states in ${}^{194}{Tl}$

A. J. Kreiner, M. Fenzl, U. Heim, and W. Kutschera

Phys. Rev. C 20, 2205 (1979) - Published 1 December, 1979

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High spin states in ${}^{194}{Tl}$ , excited through the ${}^{181}{Ta}$ ( ${}^{18}O$ , $5 n)$ reaction in the energy range $E = 80 - 100$ MeV, were studied using in-beam $γ$ -ray spectroscopic techniques. Excitation functions, activity spectra, $γ$ -ray angular distributions, and $γ - γ$ coincidences were measured. The strongly Coriolis distorted $\tilde{π} h_{\frac{9}{2}} \otimes \tilde{ν} i_{\frac{13}{2}}$ two-quasiparticle band already known in ${}^{196, 198}{Tl}$ has also been found in this case. It is based on an $I^{π} = 8^{-}$ isomeric state located 292.8 keV above ${}^{194}{Tl}^{m}$ , $I^{π} = 7^{+}$ .

NUCLEAR REACTIONS ${}^{181}{Ta}$ ( ${}^{18}O$ , $5 n γ$ ), $E = 80 - 100$ MeV, measured $E_{γ}$ , $I_{γ}$ , $σ (E, E_{γ}, θ_{γ})$ , $γ - γ$ coin. ${}^{194}{Tl}$ deduced levels, $J$ , $π$ . Natural target. Ge(Li) detectors.

Low-energy pion production in high-energy nucleus-nucleus collisions

K. Nakai, J. Chiba, I. Tanihata, M. Sasao, H. Bowman, S. Nagamiya, and J. O. Rasmussen

Phys. Rev. C 20, 2210 (1979) - Published 1 December, 1979

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Doubly differential cross sections for production of pions with 400-MeV/N ${}^{20}{Ne}$ on C, NaF, Cu, and Pb have been measured for a range of $20 MeV < {T_{π}}^{LAB} < 100 MeV$ and $30 ° < {θ_{π}}^{LAB} < 150 °$ . The results are compared with previous data with 800-MeV/N ${}^{20}{Ne}$ . The broad maximum at $θ_{π}^{c . m .} = 90 °$ in the center-of-mass angular distribution of low-energy pions observed at 800 MeV/N is not seen at the present energy. Neither was such a maximum at the central-rapidity region observed in ( $p$ + nucleus) reactions at $E_{p} = 730$ MeV. The 90° maximum seems to be a phenomenon specific to nucleus-nucleus collisions around 1 GeV/N, where the multiplicity of $Δ$ formation is high and multiple $Δ$ interaction could influence the pion production. The distribution at higher bombarding energies has yet to be studied.

NUCLEAR REACTIONS C, NaF, Cu, $Pb ({}^{20}{Ne}, π^{+}) X$ , $\frac{E}{A} = 400$ MeV/nucleon; measured $σ (E_{π}, θ_{π})$ , $E_{π} = 20 - 100$ MeV, $θ_{π} = 30 ° - 150 °$ .

Fusion of ${}^{58, 60, 62}{Ni}$ with 113-170 MeV ${}^{40}{Ca}$ ions

B. Sikora, J. Bisplinghoff, W. Scobel, M. Beckerman, and M. Blann

Phys. Rev. C 20, 2219 (1979) - Published 1 December, 1979

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Results of measurements of the fusion excitation functions of ${}^{58, 60, 62}{Ni}$ targets with 113-170 MeV (lab) ${}^{40}{Ca}$ ions are reported. These results are used to extract fusion barrier heights and radii by several different methods. Subbarrier fusion cross sections are analyzed in terms of static deformations. Possible importance of dynamic deformation is discussed. Conclusions as to the role of static deformation are similar to those from the ${}^{35}{Cl}$ + ${}^{58, 60, 62}{Ni}$ fusion system; a large part of the subbarrier behavior can be attributed to this cause.

NUCLEAR REACTIONS ${}^{52, 58}{Ni}$ ( ${}^{40}{Ca}$ , fusion), $E_{Ca} = 113 - 170$ MeV lab, measured evaporation residue excitation functions.

Intranuclear cascade calculation of high-energy heavy-ion interactions

Y. Yariv and Z. Fraenkel

Phys. Rev. C 20, 2227 (1979) - Published 1 December, 1979

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We have extended the intranuclear cascade model of Chen et al. to high-energy reactions between two heavy ions. The results of the calculations are compared with experimental results for the inclusive proton and pion cross sections, two-particle correlations, particle multiplicity distributions, and spallation cross section distributions from light ( ${}^{12}C$ + ${}^{12}C$ ) to heavy ( ${}^{40}{Ar}$ + ${}^{238}U$ ) projectile-target systems in the laboratory bombarding energy range $\frac{E}{A} = 250 - 1000$ MeV. The comparison shows that the model is fairly successful in reproducing the various aspects of high-energy reactions between heavy ions. The discrepancies between the calculations and the experimental results are probably due to shortcomings of the present calculation, particularly the neglect of interactions between cascade particles, and do not provide strong evidence for cooperative phenomena in high-energy heavy-ion reactions. We also show that the assumption that high particle multiplicities are indicative of central (small impact parameter) collisions is well founded for heavy projectile-target systems.

NUCLEAR REACTIONS Compared predictions of intranuclear cascade model for high-energy heavy-ion reactions with experimental results for inclusive proton and pion cross sections, two-particle correlations, particle multiplicities, spallation cross sections. $E = 250 - 1000$ MeV/nucleon. ${}^{12}C$ + ${}^{12}C$ , ${}^{20}{Ne}$ + ${}^{20}{Ne}$ , ${}^{40}{Ar}$ + ${}^{40}{Ar}$ , ${}^{20}{Ne}$ + ${}^{238}U$ , ${}^{20}{Ne}$ + ${}^{208}{Pb}$ , ${}^{40}{Ar}$ + ${}^{208}{Pb}$ .

Independent yields of Rb and Cs isotopes from thermal-neutron induced fission of ${}^{235}U$

S. J. Balestrini, R. Decker, H. Wollnik, K. D. Wünsch, G. Jung, E. Koglin, and G. Siegert

Phys. Rev. C 20, 2244 (1979) - Published 1 December, 1979

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The relative yields of Rb and Cs isotopes from thermal-neutron fission of ${}^{235}U$ have been redetermined using the mass separator OSTIS, on-line at a neutron guide of the High-Flux Beam Reactor at the Institut Laue-Langevin, Grenoble, France. The separator ion source was a hot oven containing ${}^{235}U$ in a graphite matrix. The neutron beam was pulsed. Alkali fission products diffused out of the graphite and were ionized, thus producing a stepwise increase in the analyzed ion beam proportional to the independent fission yield. The ion beam and the fissions in the source were monitored simultaneously. The diffusion of Rb and Cs from the source was exponential in time with half-lives ranging from 2.8 to 18 sec, depending upon the element and source temperature. The independent fission yields of Rb and Cs are normalized by equating their element yields to each other and to a value computed from the charge distributions observed with the recoil separator LOHENGRIN and well established mass yields. Fractional independent yields are deduced from the independent fission yields, and these compare very well with the EOZ model described by Wahl.

NUCLEAR REACTIONS ${}^{235}U$ ( $n$ , $f$ ), $E = thermal$ ; measured relative abundances; deduced independent fission yields, fractional chain yields, charge displacement and dispersion, odd-even $Z$ effect. Mass separator, fast neutron detector.

Fragment mass and kinetic energy distributions for the photofission of ${}^{238}U$ with 12-, 15-, 20-, 30-, and 70-MeV bremsstrahlung

E. Jacobs, A. De Clercq, H. Thierens, D. De Frenne, P. D'hondt, P. De Gelder, and A. J. Deruytter

Phys. Rev. C 20, 2249 (1979) - Published 1 December, 1979

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Energy correlation measurements with semiconductor detectors were performed for the photofission of ${}^{238}U$ with 12-, 15-, 20-, 30-, and 70-MeV bremsstrahlung. The behavior of the mass distribution with changing total kinetic energy of the fragments and with changing excitation energy of the compound nucleus is deduced. The distribution of the total fragment kinetic energy as a function of the fragment mass and as a function of the average excitation energy of the ${}^{238}U$ compound nucleus is studied. The results are discussed in terms of the two mode and fragment-shell hypotheses.

NUCLEAR REACTIONS, FISSION ${}^{238}U$ ( $γ$ , $F$ ), $E γ_{max} = 12, 15, 20, 30, 70$ MeV; measured fragment energies $E_{1}$ , $E_{2}$ ; deduced $\frac{N (μ, E_{K})}{〈 E_{exc} (E_{e}) 〉}$ .

Backward production of light ions in the interaction of 400 GeV protons with nuclei

S. Frankel, W. Frati, M. Gazzaly, Y. D. Bayukov, V. I. Efremenko, G. A. Leksin, N. A. Nikiforov, V. I. Tchistilin, Y. M. Zaitsev, and C. F. Perdrisat

Phys. Rev. C 20, 2257 (1979) - Published 1 December, 1979

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Measurements of the invariant cross sections for the reaction $p (400 GeV) + ({}^{6}{Li}, B e, C, A l, C u, T a) \to (d, t, {}^{3}{He}, {}^{4}{He}) + X$ at laboratory angles of 70, 90, 118, 137, and 160° are reported. Comparisons are made using several scaling variables.

NUCLEAR REACTIONS Inclusive cross section; 400 GeV incident protons; ${}^{6}{Li}$ , Be, C, Al, Cu, Ta targets; production of $d$ , $t$ , ${}^{3}{He}$ , ${}^{4}{He}$ ; Lab angles 70°, 90°, 118°, 137°, and 160°.

Pion interferometry of nuclear collisions. I. Theory

M. Gyulassy, S. K. Kauffmann, and Lance W. Wilson

Phys. Rev. C 20, 2267 (1979) - Published 1 December, 1979

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The topic of pion interferometry (identical pion correlations) is analyzed in detail in the context of relativistic nuclear collisions. Through an exactly solvable field theoretic model specified by an ensemble of classical pion source currents, $J_{i} (x)$ , we calculate the $π^{-} π^{-}$ correlation function $R ({\tilde{k}}_{1}, {\tilde{k}}_{2})$ for chaotic, coherent, and partially coherent pion fields. We analyze how $R$ can be used to determine the degree of coherence of the produced pion field as well as the geometric structure of the source of the chaotic field component. With this model we are able to distinguish between those correlations due to Bose-Einstein symmetrization (the Hanbury-Brown and Twiss or Goldhaber effect) and those due to specific multiparticle production dynamics. In particular we show that Bose-Einstein symmetrization dominates the form of $R ({\tilde{k}}_{1}, {\tilde{k}}_{2})$ only for chaotic pion fields produced over a time scale large compared to ${m_{π}}^{- 1}$ . If, due to collective phenomena, there is some coherence of the pion field, then the intercept $R (\tilde{k}, \tilde{k}) = 2 - D^{2} (\tilde{k})$ is shown to measure mode by mode that degree of coherence $D (\tilde{k})$ . Geometric information about the source of the chaotic field component may be extracted from $R ({\tilde{k}}_{1}, {\tilde{k}}_{2})$ only after $D (\tilde{k})$ has been determined. Expressions are also derived that incorporate distortions of $R$ due to one-body and two-body final state interactions. These expressions will be numerically evaluated in a subsequent paper. Relative $π^{-} π^{-}$ interactions lead to a penetration factor $G ({\tilde{k}}_{1}, {\tilde{k}}_{2})$ that modulates the form of $R ({\tilde{k}}_{1}, {\tilde{k}}_{2})$ . An expression for $G$ is obtained to all orders in the one-body optical potential but to first order in the two-body potential. This penetration factor must be evaluated before data for $R$ can be used to determine $D (\tilde{k})$ .

NUCLEAR REACTIONS Relativistic nuclear collisions, multipion inclusive cross sections, $π^{-} π^{-}$ correlations, Hanbury-Brown-Twiss effect, partially coherent fields, final state interactions.

Spallation of gold by 100-300 MeV pions

S. B. Kaufman, E. P. Steinberg, and G. W. Butler

Phys. Rev. C 20, 2293 (1979) - Published 1 December, 1979

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Cross sections of radioactive products resulting from the interactions of 100-, 180-, and 300-MeV $π^{+}$ and $π^{-}$ mesons with gold have been determined by analysis of the $γ$ -ray spectra of bombarded target foils. More than 30 nuclides were identified between mass numbers 167 and 196. The results indicate the following. (1) The most probable charge for a given mass lies several charge units to the neutron-poor side of the betastability line. (2) The average cross-section ratios $\frac{σ (π^{-})}{σ (π^{+})}$ for all measured nuclides are 1.34, 1.23, and 1.05 at 100, 180, and 300 MeV, respectively. At a given energy there is no systematic variation of the ratio with nuclide mass number. These results are what is expected from Coulomb effects, with no indication of an isospin effect due to the large $T_{Z}$ of the target. (3) The influence of the (3,3) resonance is apparent in the total reaction cross section. (4) The average excitation energy transferred to the nucleus is similar for $π^{+}$ and $π^{-}$ induced reactions and increases with increasing pion kinetic energy. Comparisons of the data with intranuclear cascade-evaporation calculations indicate that the latter predict less pion absorption than actually occurs.

NUCLEAR REACTIONS ${}^{197}{Au}$ ( $π^{\pm}$ , spallation), $E = 100 - 300$ MeV; measured $σ$ for products $167 <~ A <~ 196$ ; estimated total reaction cross sections.

Total ( $p$ , $π^{+}$ ) cross sections on light nuclei near the pion Coulomb barrier

R. E. Marrs, R. E. Pollock, and W. W. Jacobs

Phys. Rev. C 20, 2308 (1979) - Published 1 December, 1979

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Angle-integrated ( $p$ , $π^{+}$ ) cross sections on ${}^{9}{Be}$ , ${}^{10}B$ , ${}^{11}B$ , ${}^{12}C$ , ${}^{13}C$ , ${}^{14}N$ , and ${}^{16}O$ have been measured over the energy range $0.5 ≲ T_{p} - T_{threshold} ≲ 10$ MeV by detecting $μ^{+}$ decays. By combining the present results with higher energy measurements we show that, for $1 p$ -shell targets, the energy dependence of the ( $p$ , $π^{+}$ ) reaction from $T_{π} \approx 0.5 to \approx 50$ MeV can be explained in terms of pion phase space and barrier penetration.

NUCLEAR REACTIONS ${}^{9}{Be}$ ( $p$ , $π^{+}$ ) ${}^{10}{Be}$ , ${}^{10, 11}B$ ( $p$ , $π^{+}$ ) ${}^{11, 12}B$ , ${}^{12, 13}C$ ( $p$ , $π^{+}$ ) ${}^{13, 14}C$ , ${}^{14}N$ ( $p$ , $π^{+}$ ) ${}^{15}N$ , and ${}^{16}O$ ( $p$ , $π^{+}$ ) ${}^{17}O$ , $T_{p} - T_{threshold} : 0.5 - 10$ MeV, measured angleintegrated cross sections.

Importance of the short-range correlation in proton-nucleus backward scattering

Tetsuyuki Yukawa and Sadataka Furui

Phys. Rev. C 20, 2316 (1979) - Published 1 December, 1979

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We study inclusive spectra of backward emitted protons for proton- or (other elementary particles)-nucleus reactions. With a simple quasifree model, we observe that the spectator process dominates for the backward emission. With this reaction mechanism the high-momentum part of the inclusive proton spectra can be explained by the short-range nucleon-nucleon correlation.

NUCLEAR REACTIONS $d (p, p^{'}) X$ , C, Cu, $Ta (p, p^{'}) X$ , $Ne ({\bar{ν}}_{μ}, p) X$ , $0.6 < E < 25$ GeV, proton backward emission, short-range correlation.

Eikonal scattering by complex potentials

F. W. Byron, Jr., C. J. Joachain, and E. H. Mund

Phys. Rev. C 20, 2325 (1979) - Published 1 December, 1979

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A systematic study is made of the properties of the eikonal approximation and related methods for nonrelativistic scattering by complex, central potentials. Particular attention is devoted to the "all-angles" properties of the eikonal approximation, the eikonal Born series method, and the eikonal expansion of Wallace. Our discussion is illustrated by considering various interaction potentials in weak, intermediate, and strong coupling situations. A detailed application is made to the elastic scattering of neutrons by ${}^{209}{Bi}$ nuclei, at neutron energies of 50, 100, and 200 MeV.

NUCLEAR REACTIONS Eikonal methods, complex potentials. ${}^{209}{Bi}$ ( $n$ , $n$ ), $E = 50 - 200$ MeV, calculated $σ (θ)$ .

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Coupled-channels calculation for scattering and capture of alpha particles near the giant quadrupole resonance

Finite-range coupled reaction channel investigation of the elastic transfer process

Single particle transfer reactions and backward angle elastic scattering for the ${}^{15}N$ , ${}^{16}O$ + ${}^{28}{Si}$ systems

Multinucleon transfer reactions induced by ${}^{18}O$ on ${}^{28}{Si}$

Structure in the 180° scattering of ${}^{12}C$ by ${}^{27}{Al}$

Energy dependence of the fusion and elastic scattering of ${}^{16}O$ + ${}^{40}{Ca}$

Coulomb excitation of Yb nuclei

Generalized spectator expansion for interacting composite systems

High spin states in ${}^{194}{Tl}$

Low-energy pion production in high-energy nucleus-nucleus collisions

Fusion of ${}^{58, 60, 62}{Ni}$ with 113-170 MeV ${}^{40}{Ca}$ ions

Intranuclear cascade calculation of high-energy heavy-ion interactions

Independent yields of Rb and Cs isotopes from thermal-neutron induced fission of ${}^{235}U$

Fragment mass and kinetic energy distributions for the photofission of ${}^{238}U$ with 12-, 15-, 20-, 30-, and 70-MeV bremsstrahlung

Backward production of light ions in the interaction of 400 GeV protons with nuclei

Pion interferometry of nuclear collisions. I. Theory

Spallation of gold by 100-300 MeV pions

Total ( $p$ , $π^{+}$ ) cross sections on light nuclei near the pion Coulomb barrier

Importance of the short-range correlation in proton-nucleus backward scattering

Eikonal scattering by complex potentials

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