Recent Articles

Meson dynamics and the nuclear many-body problem. II. Finite density Hartree-Fock

L. Wilets, R. D. Puff, D. Chiang, and William T. Nutt

Phys. Rev. C 14, 2269 (1976) - Published 1 December, 1976

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The field-theoretic many-nucleon problem is formulated, and an analysis which sums all "uncrossed meson line" diagrams is investigated in detail. The calculation of energy per nucleon, after proper identification of infinite mass renormalization terms, exhibits effects of nuclear recoil, relativistic kinematics, and retardation. Numerical results are presented for $π$ and $ω$ mesons, and the nucleon interaction energies obtained are compared with the traditional static limit of infinite nucleon mass.

NUCLEAR STRUCTURE Nuclear matter, mesons and nucleons, relativistic Hartree-Fock, finite density.

Exact solution of the quadrupole surface vibration Hamiltonian in body-fixed coordinates

T. M. Corrigan, F. J. Margetan, and S. A. Williams

Phys. Rev. C 14, 2279 (1976) - Published 1 December, 1976

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Exact, closed-form eigenfunctions for the harmonic, quadrupole surface vibration model of Bohr are developed. These angular momentum labeled, multiplicity-resolved functions of $β$ , $γ$ , and the Euler angles are valid for an arbitrary number of phonons.

NUCLEAR STRUCTURE Exact $γ$ -vibration solutions, multiplicity resolved; theory.

Collective and two-quasiparticle excitations in ${}^{102, 104, 106}{Pd}$ following ( ${}^{13}C, 3 n γ$ ) reactions

J. A. Grau, L. E. Samuelson, F. A. Rickey, P. C. Simms, and G. J. Smith

Phys. Rev. C 14, 2297 (1976) - Published 1 December, 1976

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Even- $A$ Pd nuclei were studied using the reactions ${}^{92, 94, 96}{Zr} ({}^{13}C, 3 n γ) {}^{102, 104, 106}{Pd}$ . The experiments included $γ$ -ray yield as a function of energy, $γ$ -ray angular distributions, $γ$ -ray linear polarizations, and $γ - γ$ coincidence measurements. A new treatment of $γ - γ$ directional correlation from oriented nuclei, which combines data from all appropriate coincidence pairs to reduce uncertainties, has aided in determining multipolarities for 49 contaminated transitions. Extensive decay schemes are presented which include many high-angular-momentum, positive- and negative-parity states. In addition to the ground-state band, there appear to be three collective bands built on excited two-quasiparticle states. The measurements favor a slightly deformed rotor description of these nuclei over an interpretation in terms of a vibrational (interacting boson) model.

NUCLEAR STRUCTURE ${}^{92, 94, 96}{Zr} ({}^{13}C, 3 n γ)$ $E = 45 - 56$ MeV; measured $I_{γ} (E ({}^{13}C))$ , $I_{γ} (θ)$ , $γ γ$ coin, $γ γ$ DCO, $P_{γ}$ . ${}^{102, 104, 106}{Pd}$ deduced levels, $J$ , $π$ , $γ$ multipolarity.

Comment on "New methods for solving the Bethe-Goldstone equation"

S. F. Tsai and T. T. S. Kuo

Phys. Rev. C 14, 2319 (1976) - Published 1 December, 1976

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With an ( $ω - Q T Q$ ) type energy denominator in the propagator of the Bethe-Goldstone equation, Znojil's recent exact solution for the defect wave function is shown to follow from Tsai and Kuo's earlier exact solution for the $G$ matrix.

NUCLEAR STRUCTURE Accurate methods for calculating nuclear reaction matrix.

Reply to "Comment on `New methods for solving the Bethe-Goldstone equation' "

M. Znojil

Phys. Rev. C 14, 2321 (1976) - Published 1 December, 1976

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Comment on elastic proton scattering from ${}^{56}{Fe}$ in the giant resonance region of ${}^{57}{Co}$

W. Haeberli

Phys. Rev. C 14, 2322 (1976) - Published 1 December, 1976

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In a recent publication, the rapid variation of the real part $δ$ of the $J^{π} = {\frac{5}{2}}^{+}$ phase shift for proton scattering from ${}^{56}{Fe}$ has been interpreted as the effect of the giant dipole resonance in ${}^{57}{Co}$ It is shown that the rapid variation of $δ$ does not correspond to a rapid variation of the scattering amplitude of the $J^{π} = {\frac{5}{2}}^{+}$ partial wave and thus does not indicate a resonance.

NUCLEAR REACTIONS ${}^{56}{Fe} (p, p)$ phase shifts reanalyzed. No evidence for resonance.

Reply to "Comment on elastic proton scattering from ${}^{56}{Fe}$ in the giant resonance region of ${}^{57}{Co}$ "

H. R. Weller

Phys. Rev. C 14, 2324 (1976) - Published 1 December, 1976

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Critique of explanations of the anomalous large-angle scattering of alpha particles

N. S. Wall

Phys. Rev. C 14, 2326(R) (1976) - Published 1 December, 1976

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Several alternative analyses of anomalous large-angle scattering data for elastic scattering of $α$ particles from nuclei are illustrated. Statistically equivalent fits to the data are achieved by various parametrizations of the optical potential. These fits though statistically insignificant in the sense that $\frac{χ^{2}}{N} ≫ 1$ are comparable to or better than those produced by different representations of the potential. We therefore question the ability to reach detailed conclusions about any microscopic model of the processes giving rise to anomalous large-angle scattering.

NUCLEAR REACTION Anomalous large-angle elastic scattering, $α$ particles $E = 15 - 30$ Mev. Optical model analyses.

RAPID COMMUNICATION

Systematics in back-angle alpha-particle scattering: Sc, Ti, V, and Cr isotopes

K. A. Eberhard, M. Wit, J. Schiele, W. Trombik, W. Zipper, and J. P. Schiffer

Phys. Rev. C 14, 2332(R) (1976) - Published 1 December, 1976

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Elastic $α$ -scattering cross sections from ${}^{45}{Sc}$ , ${}^{49, 50}{Ti}$ , ${}^{50, 52, 53}{Cr}$ , and ${}^{50, 51}V$ have been measured between 140° and 180° at a bombarding energy of $E_{α} (lab) = 25$ MeV. All angular distributions are similar and show no evidence of an anomalous backward enhancement. No evidence for a spin dependence of the cross section, within experimental uncertainties, is found for these nuclei, where the spins range from $I = 0 ({}^{50}{Ti}, {}^{50}{Cr}) to I = 6 ({}^{50}V)$ . Back-angle integrated cross sections (140°-180°) are compared with neighboring target nuclei between $A \approx 40$ and $A \approx 60$ .

NUCLEAR REACTIONS ${}^{45}{Sc} (α, α_{0})$ , ${}^{49, 50}{Ti} (α, α_{0})$ , ${}^{50, 52, 53}{Cr}$ , ${}^{50, 51}V (α, α_{0})$ , $E = 25$ MeV; measured $σ (E, θ)$ . Enriched targets; $θ = 141 ° - 176 °$ ; calculated $σ (θ)$ .

RAPID COMMUNICATION

Measurement of the magnetic dipole moment of $β$ -emitting ${}^{31}S$ by use of a polarized proton beam and nuclear magnetic resonance detection

T. Minamisono, J. W. Hugg, J. R. Hall, D. G. Mavis, D. L. Clark, and S. S. Hanna

Phys. Rev. C 14, 2335(R) (1976) - Published 1 December, 1976

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Polarized $β$ -emitting ${}^{31}S$ nuclei ( $I^{π} = {\frac{1}{2}}^{+}$ , $T_{\frac{1}{2}} = 2.6$ s) were produced in the reaction ${}^{31}P (\vec{p}, n) {}^{31}S$ $E_{p} = 7.9$ MeV, in a thick target of red phosphorous which served also as host for the implanted ${}^{31}S$ nuclei. The net polarization transferred to the ${}^{31}S$ nuclei, observed by measuring the $β$ -decay asymmetry, was antiparallel to the proton polarization for direct ground-state production and parallel for production through the first excited state. The magnetic dipole moment of ${}^{31}S$ , measured by nuclear-magnetic-resonance destruction of the polarization, is $| μ | = [0.487 93 (8)] μ_{N}$ , including the diamagnetic correction.

RADIOACTIVITY Polarized ${}^{31}S$ from ${}^{31}P (\vec{p}, n)$ ; measured $β$ asymmetry, polarization transfer; relaxation time $T_{1}$ , NMR; ${}^{31}S$ deduced magnetic moment $μ$ . Natural thick target, magnetic fields, plastic scintillators.

RAPID COMMUNICATION

Mass of ${}^{57}{Ni}$

H. Nann, E. Kashy, D. Mueller, A. Saha, and S. Raman

Phys. Rev. C 14, 2338(R) (1976) - Published 1 December, 1976

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A measurement of the $Q$ values of the ${}^{59}{Ni} (p, t) {}^{57}{Ni}$ and the ${}^{58}{Ni} ({}^{3}{He}, α) {}^{57}{Ni}$ reactions shows a significant discrepancy with the current tabulated mass values. We find -127 38.2 ± 3.3 keV and +8360.3 ± 4.0 keV, respectively, leading to a new improved mass excess for ${}^{57}{Ni}$ of -560 78.4 ± 3.0 keV.

NUCLEAR REACTIONS ${}^{59}{Ni} (p, t)$ ; ${}^{58}{Ni} ({}^{3}{He}, α)$ ; measured $Q$ values, deduced mass excess for ${}^{57}{Ni}$ .

RAPID COMMUNICATION

Three-hump potential barrier in the ${}^{234}{Th}$ nucleus

R. C. Sharma and J. N. Leboeuf

Phys. Rev. C 14, 2340(R) (1976) - Published 1 December, 1976

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Fission penetrability is calculated for the ${}^{234}{Th}$ nucleus by extending Cramer and Nix's method to a three-hump potential barrier where a second intermediate well is present. The computed results compare favorably with experimental results.

NUCLEAR REACTIONS, FISSION Fission penetrability computed through three-hump potential barrier in ${}^{234}{Th}$ . Results compare favorably with experiments.

RAPID COMMUNICATION

Behavior of the $Λ (1405)$ resonance in nuclear matter

J. M. Eisenberg

Phys. Rev. C 14, 2343(R) (1976) - Published 1 December, 1976

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Strong interaction effects in kaonic atoms are heavily influenced by the properties of the subthreshold $Λ (1405)$ resonance, which are here shown to be sizably modified by dynamic effects in nuclear matter. The present approach provides a simple view of an effect which is implicitly present in calculations which couple $K N$ and $Σ π$ channels and incorporate a pion optical potential.

NUCLEAR STRUCTURE Kaonic atoms, baryon resonances in nuclear matter.

Erratum: $α$ decay of ${}^{186}{TI}$

M. A. Ijaz, J. Lin, E. L. Robinson, and K. S. Toth

Phys. Rev. C 14, 2346 (1976) - Published 1 December, 1976

Erratum: Hypertriton as a test of theoretical hyperon-nucleon potentials

B. F. Gibson and D. R. Lehman

Phys. Rev. C 14, 2346 (1976) - Published 1 December, 1976

Erratum: Mechanisms contributing to $K$ electron ejection in nuclear $β$ decay

J. Law and J. L. Campbell

Phys. Rev. C 14, 2347 (1976) - Published 1 December, 1976

On the use of $α + α$ scattering to study the nucleon-nucleon interaction

Ronald E. Brown and Y. C. Tang

Phys. Rev. C 14, 1675 (1976) - Published 1 November, 1976

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An analysis of $δ_{4}$ for $α + α$ scattering below 15 MeV (c.m.) has been made to study whether or not useful information about the direct part $V_{d}$ of the nucleon-nucleon interaction can be obtained. It was expected that the peripheral nature of the $l = 4$ interaction would allow a relatively simple analysis to be made. However, it was found that such an analysis does not exclude any of the commonly used nucleon-nucleon potentials as being inconsistent with $α + α$ scattering, but that proper handling of the short-range part of $V_{d}$ might well result in such an exclusion.

NUCLEAR REACTIONS Analysis of $α + α$ scattering to study direct part of nucleon-nucleon potential; $E_{c . m .} < 15$ MeV.

Padé approximation for distorted waves

B. Giraud, A. B. Khalil, and P. Moussa

Phys. Rev. C 14, 1679 (1976) - Published 1 November, 1976

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The distorted wave formalism generates a residual $K$ matrix which is well adapted to the definition of Padé approximants. A method for calculating the phase shifts for the singular changing sign potential is introduced. An explicit numerical example dealing with the hard core problem is provided. Some indications are given for applying similar methods for complex optical potentials.

NUCLEAR REACTIONS Distorted wave approximations, strongly repulsive potential, Padé approximation, regularization of divergent expansion, hard-core interaction.

Polarized triton experiments on the five-nucleon system

G. G. Ohlsen, R. A. Hardekopf, Nelson Jarmie, R. V. Poore, R. L. Walter, and P. W. Lisowski

Phys. Rev. C 14, 1688 (1976) - Published 1 November, 1976

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Angular distributions of the analyzing power, polarization function, and polarization transfer coefficient $K_{y}^{y^{'}}$ at $E_{t} = 10.5$ MeV for the ${}^{2}H (t, n) {}^{4}{He}$ reaction have been measured. In addition, $K_{y}^{y^{'}} (0 °)$ data for energies between 6 and 14 MeV have been obtained. Both neutron and charged particle detection were used in these measurements. Also, an angular distribution of the analyzing power for the elastic scattering process ${}^{2}H (t, t) {}^{2}H$ at 10.5 MeV is presented. Comparisons with predictions of an $R$ -matrix analysis of the five-nucleon system are included.

NUCLEAR REACTIONS ${}^{2}H (t, n)$ , $E_{t} = 10.5$ MeV, measured analyzing $A_{y} (θ)$ at $θ_{c . m .} = 39 - 148 °$ ; polarization function $P^{y^{'}} (θ)$ and polarization transfer coefficient $K_{y}^{y^{'}} (θ)$ at $θ_{c . m .} = 0 °$ to $θ_{c . m .} = 115 °$ ; $K_{y}^{y^{'}} (0 °)$ at $E_{t} = 5.4 to 15.7$ MeV. Also, nuclear reaction ${}^{2}H (t, t)$ , $E_{t} = 10.5$ MeV, measured $A_{y} (θ)$ , $θ_{c . m .} = 48 - 138 °$ .

${}^{22}{Ne} (d, α) {}^{20}F$ reaction

H. T. Fortune and J. D. Garrett

Phys. Rev. C 14, 1695 (1976) - Published 1 November, 1976

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The reaction ${}^{22}{Ne} (d, α) {}^{20}F$ has been studied at a bombarding energy of 10.0 MeV, and excitation energies 0-7 MeV. Within the resolution of 24 KeV, the reaction populates all known states below 6 MeV in excitation and four new states at 4.372, 4.518, 5.131, and 5.574 MeV. Angular distributions from 15° to 152.5° (lab) have been extracted for all states below 4.4 MeV, and integrated to get total cross sections. A large compound-nucleus component is present for all states. In addition, states expected to have a large direct-pickup cross section are observed to have a measurable direct component.

NUCLEAR REACTIONS ${}^{22}{Ne} (d, α)$ , $E = 10$ MeV; measured $σ (θ)$ , integrated $σ$ ${}^{20}F$ levels, 0-7 MeV. Enriched target, DWBA analysis of integrated $σ$ , resolution 24 keV; $θ = 15 - 152.5 °$ , $Δ θ = 7.5 °$ .

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Recent Issues

Meson dynamics and the nuclear many-body problem. II. Finite density Hartree-Fock

Exact solution of the quadrupole surface vibration Hamiltonian in body-fixed coordinates

Collective and two-quasiparticle excitations in ${}^{102, 104, 106}{Pd}$ following ( ${}^{13}C, 3 n γ$ ) reactions

Comment on "New methods for solving the Bethe-Goldstone equation"

Reply to "Comment on `New methods for solving the Bethe-Goldstone equation' "

Comment on elastic proton scattering from ${}^{56}{Fe}$ in the giant resonance region of ${}^{57}{Co}$

Reply to "Comment on elastic proton scattering from ${}^{56}{Fe}$ in the giant resonance region of ${}^{57}{Co}$ "

Critique of explanations of the anomalous large-angle scattering of alpha particles

Systematics in back-angle alpha-particle scattering: Sc, Ti, V, and Cr isotopes

Measurement of the magnetic dipole moment of $β$ -emitting ${}^{31}S$ by use of a polarized proton beam and nuclear magnetic resonance detection

Mass of ${}^{57}{Ni}$

Three-hump potential barrier in the ${}^{234}{Th}$ nucleus

Behavior of the $Λ (1405)$ resonance in nuclear matter

Erratum: $α$ decay of ${}^{186}{TI}$

Erratum: Hypertriton as a test of theoretical hyperon-nucleon potentials

Erratum: Mechanisms contributing to $K$ electron ejection in nuclear $β$ decay

On the use of $α + α$ scattering to study the nucleon-nucleon interaction

Padé approximation for distorted waves

Polarized triton experiments on the five-nucleon system

${}^{22}{Ne} (d, α) {}^{20}F$ reaction

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