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Interior probing capability in kaon-nucleus inelastic scattering

Stephen R. Cotanch

Phys. Rev. C 21, 2115(R) (1980) - Published 1 May, 1980

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Results from a nuclear structure form factor study are presented to investigate the extent of surface localization and volume sensitivity in $K^{+}$ -nucleus inelastic scattering. Using wave functions from a macroscopic collective model and the microscopic particle-hole model of Gillet and Vinh Mau, form factors (transition densities) and cross sections are independently calculated and then compared for low-lying excited states in ${}^{12}C$ . Unlike strongly absorbed projectiles (including the pion), which have dominant surface localized reaction mechanisms, the interior differences between model form factors are clearly reflected (measurably distinct) at all scattering angles.

NUCLEAR REACTIONS kaon-nucleus inelastic scattering. DWIA, KMT, and RPA. Calculated $σ (θ, E)$ for ${}^{12}C$ . Comparative form factor study.

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Pion electroproduction from the nucleon near threshold

E. T. Dressler, N. Freed, and H. B. Miska

Phys. Rev. C 21, 2119(R) (1980) - Published 1 May, 1980

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We investigate the dependence on production amplitude of the low energy scattering cross section for positive pion electroproduction from the nucleon. Calculations based on the threshold approximation to the full amplitudes of Dombey and Read are illustrated and compared to results for the full amplitudes. Inclusion of the momentum-dependent terms yields differential cross sections in the near-threshold region differing from those given by the threshold approximation by no more than 15% at any angle.

NUCLEAR REACTIONS Dependence of $σ (θ)$ for electron scattering on nucleon upon production amplitudes.

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Truncated pion-nucleon amplitudes and pion-nucleus interactions

K. L. Kowalski

Phys. Rev. C 21, 2122(R) (1980) - Published 1 May, 1980

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It is pointed out that there are considerable structural differences among the various types of truncated pion-nucleon amplitudes which have been proposed in order to avoid overcounting ambiguities in pionnucleus interactions. A previously proposed prescription is shown to yield truncated amplitudes which are free of the usual problems involved with the proper representation of the nucleon-pole term. It is shown that these truncated amplitudes can also possess ghost pole singularities arising from the $π NN$ vertex function. Some problems caused by the appearance of such ghost poles in approximations to pion-nucleus amplitudes are discussed.

NUCLEAR REACTIONS Pion-nucleon amplitudes without nucleon propagator terms. Overcounting in pion-nucleus interactions. Pion-nucleon vertex function ghost poles in approximate pion-nucleus amplitudes.

RAPID COMMUNICATION

Projection operator method for heavy ion reactions and application to ${}^{12}C$ + ${}^{12}C$

Thomas L. Larry and William P. Beres

Phys. Rev. C 21, 2126(R) (1980) - Published 1 May, 1980

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A projection operator formalism based on the Feshbach doorway approach is developed for low energy heavy ion scattering. An application to ${}^{12}C$ + ${}^{12}C$ is made with doorways taken as quasibound or virtual states of the reduced mass coupled to $2^{+}$ and $3^{-}$ vibrations. The elastic differential cross section at 90° is calculated and agrees rather well with experiment by producing both the gross and intermediate molecular structure.

NUCLEAR REACTIONS ${}^{12}C$ + ${}^{12}C$ elastic scattering, $E = 10 - 30$ MeV c.m., projection operator intermediate structure theory, calculated $σ (90 °)$ .

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Existence of strongly bound states of pions in nuclei

Javier Sesma

Phys. Rev. C 21, 2130(R) (1980) - Published 1 May, 1980

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References are given to mostly unknown work on velocity-dependent potentials of the kind used in optical pion-nucleus models for which the possibility of an infinity of strongly bound states has been recently suggested.

NUCLEAR REACTIONS Pion-nucleus optical potential; nuclear bound states of pions in nuclei; complex velocity-dependent potential.

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Bremsstrahlung from ${}^{12}C$ + $p$ near the 1.7-MeV resonance

C. C. Trail, P. M. S. Lesser, A. H. Bond, Jr., M. K. Liou, and C. K. Liu

Phys. Rev. C 21, 2131(R) (1980) - Published 1 May, 1980

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The spectrum of bremsstrahlung radiation emitted by the scattering of protons by ${}^{12}C$ near the 1.7-MeV resonance has been studied at bombarding energies 76 and 146 keV above the resonance and 140 keV below the resonance. The spectra are in very good agreement with a complete calculation using the Feshbach-Yennie approximation which includes both the principal term and correction term.

NUCLEAR REACTION Measurement of bremsstrahlung spectrum from $p$ + ${}^{12}C$ near $E_{p} = 1.7$ MeV.

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Levels in ${}^{44}K$ via the ${}^{48}{Ca}$ ( $p$ , $α n$ ) reaction

P. A. Mandò, G. Poggi, G. Lo Bianco, and N. Molho

Phys. Rev. C 21, 2135(R) (1980) - Published 1 May, 1980

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Excited levels in ${}^{44}K$ have been populated via the ${}^{48}{Ca}$ ( $p$ , $α n$ ) reaction. From $γ - γ$ coincidence measurements, the level and decay schemes have been obtained for ${}^{44}K$ , up to $E_{x} = 1368$ keV, including several so far unobserved levels and transitions. No lifetime > ∼ 1 ns has been detected for any of these levels. A comparison is done with the neighboring even- $A$ ${}^{46}K$ isotope and with a simple shell model calculation to give a set of possible $J^{π}$ assignments.

NUCLEAR REACTIONS ${}^{48}{Ca}$ ( $p$ , $α n$ ) ${}^{44}K$ , $E = 18 - 45$ MeV; measured $E_{γ}$ , $σ (E, E_{γ})$ , $γ - γ$ coin, pulsed beam electronic timing; deduced ${}^{44}K$ levels and transitions, lifetime limits. Enriched target, Ge(Li) coax. and HP Ge.

Erratum: Neutron capture cross sections on ${}^{138}{Ba}$ , ${}^{140, 142}{Ce}$ , ${}^{175, 176}{Lu}$ , and ${}^{181}{Ta}$ at 30 keV: Prerequisite for investigation of the ${}^{176}{Lu}$ cosmic clock

H. Beer and F. Käppeler

Phys. Rev. C 21, 2139 (1980) - Published 1 May, 1980

Erratum: Intranuclear cascade calculation of high-energy heavy-ion interactions

Y. Yariv and Z. Fraenkel

Phys. Rev. C 21, 2139 (1980) - Published 1 May, 1980

${}^{14}N$ ( $p$ , $p^{'}$ ) ${}^{14}N$ reaction between 25 and 40 MeV and the tensor part of the effective interaction

S. H. Fox and Sam M. Austin

Phys. Rev. C 21, 1133 (1980) - Published 1 April, 1980

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Differential cross sections for the scattering of protons from ${}^{14}N$ , leaving this nucleus in its ground, 2.31- or 3.95-MeV states, were measured at bombarding energies of 29.8, 36.6, and 40.0 MeV. In addition, cross sections for the next ten excited states with $E_{x} < 8.7$ MeV were obtained at 29.8 MeV. Emphasis was placed on obtaining reliable results for the transition to the weakly excited $J^{π} = 0^{+}$ , $T = 1$ state at 2.31 MeV, which is unusually favorable for studies of the tensor part of the effective interaction. The present data for the 2.31-MeV state, together with results from the literature at $E_{p} = 24.8$ MeV, were analyzed using a microscopic model distorted-wave approximation; contributions from the knock-on exchange amplitude and from central, tensor, and spin-orbit two-body forces were included. The fits obtained were satisfactory at 24.8 and 29.8 MeV, but failed to reproduce a peak in the cross section which appeared near 80° at the higher bombarding energies. Strengths of the tensor force were extracted and were found to be 20-75% larger than estimates based on the one-pion-exchange potential. Available evidence on the strength of the tensor force is summarized. Of the other observed states, those whose structure is dominated by $1 p$ -shell orbitals [at 3.95 MeV ( $1^{+}$ , $T = 0$ ) and at 7.03 MeV ( $2^{+}$ , $T = 0$ )] were compared with microscopic distorted-wave approximation calculations using an empirically derived central force. Cross section enhancement factors were calculated in an effective charge approximation. The resulting cross sections have roughly the correct magnitude, but the shapes are only qualitatively correct. A systematic optical model analysis was carried out to provide optical model parameters for use in the distorted-wave approximation calculations. The rate of change of the real potential with bombarding energy was found to be $\frac{d V_{R}}{d E_{p}} = - 0.50$ .

NUCLEAR REACTIONS ${}^{14}N$ ( $p$ , $p^{'}$ ) $E = 29.8, 36.6, 40.0$ MeV; measured $σ (θ)$ . Deduced optical model parameters. Microscopic distorted-wave analysis, deduced tensor effective interaction.

Neutron-proton analyzing power at 50 MeV

R. Garrett, J. W. Watson, F. P. Brady, D. H. Fitzgerald, J. L. Romero, J. L. Ullmann, and C. Zanelli

Phys. Rev. C 21, 1149 (1980) - Published 1 April, 1980

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The analyzing power in neutron-proton elastic scattering has been measured at 50 MeV. A neutron beam with a polarization of 0.476±0.017, found by an absolute method, was used to determine the analyzing power at seven angles in the range 60° to 120° center of mass by detecting scattered neutrons. These measurements are complementary to a previous set made at this laboratory in which only recoil protons were observed. The two sets of data agree well in the overlap region and are compared with the only other data measured much earlier by a different method. Absolute statistical errors in the analyzing powers range from ±0.019 to ±0.023 in addition to a scale uncertainty of about 4% arising from the beam polarization. The results are compared with a phase shift analysis of Signell.

NUCLEAR REACTIONS ${}^{1}H (\vec{n}, n) p$ , $E = 50.0$ MeV; measured $A_{y} (θ)$ for $60.6 <~ θ_{c . m .} <~ 120.6$ , about every 10° c.m.

( $p$ , $p^{'} γ$ ) spin-flip measurement for $1^{+}$ states in ${}^{12}C$ at $E_{p} = 23.5 - 27$ MeV

R. H. Howell, F. S. Dietrich, D. W. Heikkinen, and F. Petrovich

Phys. Rev. C 21, 1153 (1980) - Published 1 April, 1980

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An out-of-plane ( $p$ , $p^{'} γ$ ) angular correlation measurement has been made to determine the spin-flip contribution to the ( $p$ , $p^{'}$ ) cross sections for the $1^{+}$ , $T = 0$ ( $Q = - 12.71$ MeV) and $1^{+}$ , $T = 1$ ( $Q = - 15.11$ MeV) excitations in ${}^{12}C$ at proton energies near 27 MeV. A definite isospin dependence is observed in the experimental spin-flip angular distributions for the two states. Microscopic distorted wave calculations based on a realistic $G$ matrix interaction give a rough account of the trends in the spin-flip data, but underestimate the experimental differential cross sections. It is concluded that reaction contributions calculated in the distorted wave approximation are insufficient to gain a complete understanding of the data.

NUCLEAR REACTIONS ${}^{12}C$ ( $p$ , $p^{'} γ$ ) $E_{p} = 22 to 27$ MeV; measured spin-flip $M 1$ states, DWBA analysis.

Effect of the tensor force on gamma-ray de-excitation angular distributions from dipole states populated in the ${}^{12}C$ ( $p$ , $p^{'}$ ) reaction

R. H. Howell, F. S. Dietrich, and F. Petrovich

Phys. Rev. C 21, 1158 (1980) - Published 1 April, 1980

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Angular distributions have been measured for the de-excitation gamma rays from the isoscalar and isovector $1^{+}$ states populated in the ${}^{12}C$ ( $p$ , $p^{'}$ ) reaction at $E_{p} (lab) = 22 - 27$ MeV. Fluctuations in the $A_{0}$ coefficients, which measure the total excitation cross sections, are observed to decrease with energy toward the high end of the region investigated. The $a_{2}$ coefficients are still fluctuating at 27 MeV, but exhibit reasonably well-defined average values of about -0.40 and 0.15 for the $T = 0$ and $T = 1$ levels, respectively. Microscopic distorted-wave calculations based on a realistic $G$ matrix interaction, while not sufficient to completely describe the present data, suggest that the isospin dependence of the $a_{2}$ coefficients is associated with the tensor force. The theoretical calculations have been extended to 50 MeV and this effect of the tensor force persists.

NUCLEAR REACTIONS ${}^{12}C$ ( $p$ , $p^{'} γ$ ) $E_{p} = 22 - 27$ MeV; measured gamma-ray angular distribution; $M 1$ states miscroscopic DWBA analysis.

Magnetic electron scattering from deuterium at low-momentum transfer

E. C. Jones, Jr., W. L. Bendel, L. W. Fagg, and R. A. Lindgren

Phys. Rev. C 21, 1162 (1980) - Published 1 April, 1980

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The elastic and inelastic cross sections of deuterium for 56.4 MeV electrons scattered at 180°, have been measured up to an excitation energy of 19 MeV. The experimental cross sections are compared with those calculated by Miller, by Durand, and by Arenhövel and Fabian, and also with the sum rules of O'Connell. The results indicate that the contribution of meson exchange currents at this low-momentum transfer is significant.

NUCLEAR REACTIONS ${}^{2}H$ ( $e$ , $e^{'}$ ); $θ = 180 °$ , $E = 56.4$ MeV; measured $σ$ for $E_{x} = 0 to 19$ MeV. Deduced elastic magnetic form factor.

Photoreaction mechanism of ${}^{6}{Li}$

M. Kusuhara

Phys. Rev. C 21, 1165 (1980) - Published 1 April, 1980

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Photoreaction mechanisms of ${}^{6}{Li}$ were studied using bremsstrahlung below the ( $γ$ , ${}^{3}H$ ) threshold. It was confirmed by the present work that only the ${}^{6}{Li}$ ( $γ$ , $p$ ) ${}^{5}{He}$ and ${}^{6}{Li}$ ( $γ$ , $n$ ) ${}^{5}{Li}$ reactions actually occur in the energy range of incident $γ$ ray lower than the ( $γ$ , ${}^{3}H$ ) threshold, and the ${}^{6}{Li}$ ( $γ$ , $np$ ) ${}^{4}{He}$ reaction in various types does not occur in practice although this reaction is energetically possible. The assignment of the reactions ${}^{6}{Li}$ ( $γ$ , $p$ ) ${}^{5}{He}$ and ${}^{6}{Li}$ ( $γ$ , $n$ ) ${}^{5}{Li}$ to the measured photoproton spectrum for 15.4 MeV irradiation is presented.

NUCLEAR REACTIONS ${}^{6}{Li}$ , checked photoreaction mechanisms, breamsstrahlung E=15.4 and 10.2 MeV, measured proton spectra, peak energies and widths, $σ (θ)$ , confirmed only ${}^{6}{Li}$ ( $γ$ , $p$ ) ${}^{5}{He}$ and ${}^{6}{Li}$ ( $γ$ , $n$ ) ${}^{5}{Li}$ actually occur below the ${}^{6}{Li}$ ( $γ$ , ${}^{3}H$ ) ${}^{3}{He}$ threshold.

Resonating-group study and odd-even features in the ${}^{3}{He}$ + ${}^{6}{Li}$ system

M. LeMere and Y. C. Tang

Phys. Rev. C 21, 1170 (1980) - Published 1 April, 1980

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The resonating-group method in the single-channel approximation is used to investigate the ${}^{3}{He}$ + ${}^{6}{Li}$ system. The result shows that there exist a number of bound and sharp resonance levels in the energy region below about 10 MeV. In addition, it is found that, with the introduction of a phenomenological imaginary potential to take reaction effects into account, the calculation can yield differential cross sections in satisfactory agreement with experimental data. The effect of the Pauli principle is also examined. Here one finds that the odd-even feature is rather prominent and, similar to the $d$ + ${}^{3}{He}$ case, has distinctly different behavior in the two channel-spin states.

NUCLEAR REACTIONS ${}^{6}{Li}$ ( ${}^{3}{He}$ , ${}^{3}{He}$ ); calculated phase shifts and $σ (θ)$ . Resonating-group method and effects of Pauli principle.

Elastic and inelastic charge form factors for ${}_{3}^{6}{Li}$ from electron scattering

Gerald L. Payne and B. P. Nigam

Phys. Rev. C 21, 1177 (1980) - Published 1 April, 1980

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A harmonic oscillator hard core plus residual two-body potential has been used to obtain the independent-particle shell-model wave functions for ${}_{3}^{6}{Li}$ . These wave functions have been utilized to calculate the theoretical elastic and inelastic electron scattering charge form factors. These are then compared with the experimental data.

NUCLEAR REACTIONS Elastic and inelastic charge form factors for ${}_{3}^{6}{Li}$ from electron scattering using harmonic hard core plus residual two-body potential.

Neutron-proton scattering. I. Differential cross section at 63.1 MeV

N. S. P. King, J. D. Reber, J. L. Romero, D. H. Fitzgerald, J. L. Ullmann, T. S. Subramanian, and F. P. Brady

Phys. Rev. C 21, 1185 (1980) - Published 1 April, 1980

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The neutron-proton differential cross section has been measured at 63.1 MeV. The data span an angular range from $θ_{c . m .} = 40 ° to 165 °$ with a relative precision of ≳ 3.0%. A different angular behavior is observed in the present results as compared to that in the data between 55 and 65 MeV currently used in phase parameter analyses.

NUCLEAR REACTIONS ${}^{1}H (n, p) n$ , $E_{n} = 63.1$ MeV; measured $σ (θ)$ from 39.4 to 165.8 c.m.

Neutron-proton scattering. II. Spin correlation parameter $A_{yy} (θ)$ at 50 MeV

D. H. Fitzgerald, F. P. Brady, R. Garrett, S. W. Johnsen, J. L. Romero, T. S. Subramanian, J. L. Ullmann, and J. W. Watson

Phys. Rev. C 21, 1190 (1980) - Published 1 April, 1980

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We report on our remeasurement of the $n - p$ scattering observable $A_{yy} (θ)$ , in which 50 MeV (lab) polarized neutrons were scattered from a polarized proton target. Several improvements to the target system have enabled us to greatly reduce the normalization uncertainty in $A_{yy}$ , compared to our earlier measurement. Incorporating these results in a phase shift analysis yields the results $\bar{δ} ({}^{1}P_{1}) = - 6.4 ° \pm 1.1 °$ and $\bar{ε} = 3.6 ° \pm 1.0 °$ , where ${\bar{ε}}_{1}$ is the ${}^{3}S_{1} - {}^{3}D_{1}$ mixing parameter.

NUCLEAR REACTIONS ${}^{1}H (n, p) n$ , $E_{n} = 50.0$ MeV; measured $A_{yy} (θ)$ from 108° to 174° c.m.

Analog $E 2$ transitions in the $A = 30$ nuclei; lifetime and branching ratio measurements of levels in ${}^{30}P$

A. Anttila and J. Keinonen

Phys. Rev. C 21, 1196 (1980) - Published 1 April, 1980

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The $γ$ -ray decays of the first two $J^{π} = 2^{+}$ , $T = 1$ states in ${}^{30}P$ ( $T_{z} = 0$ ) at $E_{x} = 2.938 and 4.183$ MeV have been studied through the ${}^{29}{Si}$ ( $p$ , $γ$ ) ${}^{30}P$ reaction. One new branch from the 2.938 MeV state and three new branches from the 4.183 MeV state were found. The recently reported isoscalar $E 2$ transition 4.183( $2^{+}$ ,1) →0.677( $0^{+}$ ,1) MeV was confirmed and the relative intensity of (1.3±0.3)% was determined. Employing the Doppler-shift attenuation (DSA) method, the lifetime $τ_{m} = (90 \pm 11)$ fs was determined for the 2.938 MeV state and in the present, exceptionally advantageous conditions the lifetime (3.1±0.9) fs for the 4.183 MeV state was determined for the first time. In the analysis, the Monte-Carlo method was employed. The $E 2$ branches 2.938( $2^{+}$ ,1)→0.677( $0^{+}$ ,1) and 4.183( $2^{+}$ ,1)→0.677( $0^{+}$ ,1) MeV are compared with the analog transitions in ${}^{30}{Si}$ ( $T_{z} = + 1$ ) and ${}^{30}S$ ( $T_{z} = - 1$ ) as well as with shell-model calculations.

NUCLEAR REACTION ${}^{29}{Si}$ ( $p$ , $γ$ ), $E = 0.73, 1.75$ MeV, measured $σ (E; E_{γ}, θ)$ , Doppler-shift attenuation. ${}^{30}P$ levels, deduced $γ$ -ray branching ratios, $τ_{m}$ . Implanted, enriched ${}^{29}{Si}$ targets.

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Physical Review C

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Recent Issues

Interior probing capability in kaon-nucleus inelastic scattering

Pion electroproduction from the nucleon near threshold

Truncated pion-nucleon amplitudes and pion-nucleus interactions

Projection operator method for heavy ion reactions and application to ${}^{12}C$ + ${}^{12}C$

Existence of strongly bound states of pions in nuclei

Bremsstrahlung from ${}^{12}C$ + $p$ near the 1.7-MeV resonance

Levels in ${}^{44}K$ via the ${}^{48}{Ca}$ ( $p$ , $α n$ ) reaction

Erratum: Neutron capture cross sections on ${}^{138}{Ba}$ , ${}^{140, 142}{Ce}$ , ${}^{175, 176}{Lu}$ , and ${}^{181}{Ta}$ at 30 keV: Prerequisite for investigation of the ${}^{176}{Lu}$ cosmic clock

Erratum: Intranuclear cascade calculation of high-energy heavy-ion interactions

${}^{14}N$ ( $p$ , $p^{'}$ ) ${}^{14}N$ reaction between 25 and 40 MeV and the tensor part of the effective interaction

Neutron-proton analyzing power at 50 MeV

( $p$ , $p^{'} γ$ ) spin-flip measurement for $1^{+}$ states in ${}^{12}C$ at $E_{p} = 23.5 - 27$ MeV

Effect of the tensor force on gamma-ray de-excitation angular distributions from dipole states populated in the ${}^{12}C$ ( $p$ , $p^{'}$ ) reaction

Magnetic electron scattering from deuterium at low-momentum transfer

Photoreaction mechanism of ${}^{6}{Li}$

Resonating-group study and odd-even features in the ${}^{3}{He}$ + ${}^{6}{Li}$ system

Elastic and inelastic charge form factors for ${}_{3}^{6}{Li}$ from electron scattering

Neutron-proton scattering. I. Differential cross section at 63.1 MeV

Neutron-proton scattering. II. Spin correlation parameter $A_{yy} (θ)$ at 50 MeV

Analog $E 2$ transitions in the $A = 30$ nuclei; lifetime and branching ratio measurements of levels in ${}^{30}P$

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