Recent Articles

Channel cross correlation of the ${}^{31}P (d, α) {}^{29}{Si}$ and ${}^{31}P (d, p) {}^{32}P$ reactions

S. C. Yeh, C. C. Hsu, V. K. C. Cheng, C. S. Lin, P. S. Song, and H. H. Lin

Phys. Rev. C 27, 57 (1983) - Published 1 January, 1983

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The excitation functions for the $α$ particles and protons from the reactions ${}^{31}P (d, α) {}^{29}{Si}$ and ${}^{31}P (d, p) {}^{32}P$ were measured and analyzed by the channel cross correlation function, the autocorrelation function, and the statistical compound nuclear theory of Feshbach to determine the number of correlating channels $n_{d}$ , the average total level width $〈 Γ_{μ} 〉$ , and the ratio $\frac{〈 Γ_{μ} 〉}{D}$ . With these values, the theoretical intermediate width $〈 Γ_{d} ↑ 〉$ was calculated to be 158±25 keV, which was consistent with the experimental result 198±34 keV within the errors. The ratio $\frac{n_{d} (n_{d} - 1)}{n^{2}}$ was determined to be 0.27, which was also in agreement with the theoretical prediction ${(\frac{2 D}{π 〈 Γ_{μ} 〉})}^{\frac{1}{2}} = 0.28 \pm 0.04$ .

NUCLEAR REACTIONS ${}^{31}P (d, α)$ , ${}^{31}P (d, p)$ , $E = 3.5 - 6.2$ MeV; measured $σ (E, θ)$ ; ${}^{33}S$ ; deduced $n_{d}$ , $〈 Γ_{μ} 〉$ , $\frac{〈 Γ_{μ} 〉}{D}$ , $〈 Γ_{d} ↑ 〉$ , natural target.

Low-energy ${}^{7}{Li} (t, α) {}^{6}{He}$ cross sections

F. E. Cecil, R. F. Fahlsing, Nelson Jarmie, R. A. Hardekopf, and R. Martinez

Phys. Rev. C 27, 6 (1983) - Published 1 January, 1983

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The thick target yield of the reaction ${}^{7}{Li} (t, α)$ has been measured to the ground and first excited states of ${}^{6}{He}$ for bombarding energies between 70 and 110 keV. These yields are used to deduce the reaction cross sections and astrophysical $S$ factors at intermediate values of energy. The zero energy $S$ factor $S (0)$ for ${}^{7}{Li} (t, α) {}^{6}{He}^{*} (1.81)$ is 14±2.5 MeVb. Applications of the measured values of the cross section for this reaction to the diagnostics of high temperature tritium plasmas are discussed. Efforts to detect alphas from induced reactions on other light targets ${}^{6}{Li}$ , ${}^{9}{Be}$ , ${}^{10}B$ , and ${}^{11}B$ are discussed.

NUCLEAR REACTIONS ${}^{7}{Li} (t, α) {}^{6}{He}$ , ${}^{9}{Be} (t, α) {}^{8}{Li}$ , ${}^{11}B (t, α) {}^{10}{Be}$ ; $E_{t} = 70 - 110$ keV, $θ = 150 °$ . Measured thick target yields. Deduced $σ (θ, E)$ , $S (θ, E)$ .

Separable approximations of two-body interactions

J. Haidenbauer and W. Plessas

Phys. Rev. C 27, 63 (1983) - Published 1 January, 1983

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We perform a critical discussion of the efficiency of the Ernst-Shakin-Thaler method for a separable approximation of arbitrary two-body interactions by a careful examination of separable ${}^{3}S_{1} - {}^{3}D_{1}$ $N - N$ potentials that were constructed via this method by Pieper. Not only the on-shell properties of these potentials are considered, but also a comparison is made of their off-shell characteristics relative to the Reid soft-core potential. We point out a peculiarity in Pieper's application of the Ernst-Shakin-Thaler method, which leads to a resonant-like behavior of his potential 3SD1D. It is indicated where care has to be taken in order to circumvent drawbacks inherent in the Ernst-Shakin-Thaler separable approximation scheme.

NUCLEAR REACTIONS Critical discussion of the Ernst-Shakin-Thaler separable approximation method. Pieper's separable $N - N$ potentials examined on shell and off shell.

${}^{3}{He}$ magnetic form factor

P. C. Dunn, S. B. Kowalski, F. N. Rad, C. P. Sargent, W. E. Turchinetz, R. Goloskie, and D. P. Saylor

Phys. Rev. C 27, 71 (1983) - Published 1 January, 1983

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The ${}^{3}{He}$ magnetic form factor has been measured for momentum transfers between 0.7 and 11 ${fm}^{- 2}$ with improved precision over previous measurements. The charge form factor has been measured for momentum transfers less than 1 ${fm}^{- 2}$ . The charge radius was determined to be 1.935±0.03 fm, and the magnetic radius 1.935±0.04 fm. Comparisons are made with calculations which include meson exchange corrections and reasonable agreement is found.

NUCLEAR REACTIONS $d (e, e^{'}) d$ , $q^{2} = 0.7 to 11$ ${fm}^{- 2}$ , $θ = 160 °$ , measured magnetic form factor; $q^{2} < 1$ ${fm}^{- 2}$ , $θ = 60 °$ , measured charge radius.

Generalized three-body Alt-Grassberger-Sandhas equations including three-body forces

W. Glöckle and R. Brandenburg

Phys. Rev. C 27, 83 (1983) - Published 1 January, 1983

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Derivation of the Lippmann-Schwinger $N$ -body equations from the time-independent Schrödinger equation

W. Tobocman

Phys. Rev. C 27, 88 (1983) - Published 1 January, 1983

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The Lippmann-Schwinger $N$ -body equations are ordinarily derived from time dependent scattering theory. Derivations from time independent scattering theory by means of Green's theorem have also been given. Both derivations are based on unproven assumptions. We present a new derivation based on different assumptions which we believe to be more plausible. Our derivation is particularly simple and provides a new insight into the nature of the Lippmann identity.

NUCLEAR REACTIONS Derivation of the Lippmann-Schwinger $N$ -body equations; properties of the Lippmann identity operator.

Charge exchange reactions and solar neutrino detection in ${}^{81}{Br}$

K. F. Liu and F. Gabbard

Phys. Rev. C 27, 93 (1983) - Published 1 January, 1983

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The feasibility of ${}^{81}{Br}$ as the detector of the solar neutrino flux hinges upon the knowledge of the Gamow-Teller matrix element from the ground state of ${}^{81}{Br}$ to the ${\frac{5}{2}}^{-}$ state at 0.457 MeV in ${}^{81}{Kr}$ . The possibility of obtaining this matrix element is discussed in terms of the ( $p, n$ ) and ( ${}^{3}{He}$ , $t$ ) charge exchange reactions.

NUCLEAR REACTIONS ${}^{81}{Br} (p, n) {}^{81}{Kr}$ and ${}^{81}{Br} ({}^{3}{He}, t) {}^{81}{Kr}$ ; Gamow-Teller transitions; solar neutrino detection.

Band structure in ${}^{180}{Ta}$ studied with transfer reactions

E. Warde, G. J. Costa, D. Magnac, R. Seltz, C. Gerardin, M. Buenerd, Ph. Martin, W. Saathoff, and C. A. Wiedner

Phys. Rev. C 27, 98 (1983) - Published 1 January, 1983

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The differential cross sections of emitted particles have been measured in the reactions ${}^{181}{Ta} (p, d) {}^{180}{Ta}$ at 19 MeV, ${}^{179}{Hf} ({}^{3}{He}, d) {}^{180}{Ta}$ at 36 MeV, and ${}^{179}{Hf} (α, t) {}^{180}{Ta}$ at 62.2 MeV. The energy resolution was 15 to 40 keV depending on the reaction. Differential cross sections were fitted using a distorted wave program and level characteristics of ${}^{180}{Ta}$ were deduced in the framework of the Nilsson model for odd-odd deformed nuclei including Coriolis coupling. Members of rotational bands have been identified up to 1 MeV excitation energy. The short-lived isomer in ${}^{180}{Ta}$ with spin $1^{+}$ was found to be the ground state whereas the long-lived isomer at 82±20 keV excitation energy has spin $9^{-}$ .

NUCLEAR REACTIONS ${}^{181}{Ta} (p, d) {}^{180}{Ta}$ , $E = 19$ MeV; ${}^{179}{Hf} ({}^{3}{He}, d) {}^{180}{Ta}$ , $E = 36$ MeV; ${}^{179}{Hf} (α, t) {}^{180}{Ta}$ , $E = 62.2$ MeV; measured $σ (θ)$ . DWBA and Nilsson model analysis, deduced level characteristics, neutron separation energies of isomeric states.

Virtual photons and electrodisintegration of the deuteron

L. E. Wright and L. Tiator

Phys. Rev. C 26, 2349 (1982) - Published 1 December, 1982

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The validity of the virtual photon concept in the analysis of deuteron electrodisintegration for equivalent photon energies up to 300 MeV is investigated. The deuteron and the final state interaction are described by the consistent nonrelativistic calculation of Fabian and Arenhövel neglecting the effects of meson exchange currents and isobar configurations. We find that in well defined kinematic domains the use of the virtual photon concept is justified in extracting photodisintegration cross sections.

NUCLEAR REACTIONS $d (e, p) n$ ; virtual photon theory.

Cross section and polarization in deuteron photodisintegration: General formulas

A. Cambi, B. Mosconi, and P. Ricci

Phys. Rev. C 26, 2358 (1982) - Published 1 December, 1982

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Influence of 1p- 1h-excited $α$ particles on elastic $α - α$ scattering

H. R. Fiebig and W. Timm

Phys. Rev. C 26, 2367 (1982) - Published 1 December, 1982

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The influence of channels with 1p- 1h-excited $α$ particles with $S = T = 0$ on elastic $α - α$ scattering is studied in the framework of the Feshbach projection operator formalism. Calculated phase shifts and transmission coefficients for $α - α$ scattering are compared to experimental data for c.m. energies between 15 and 35 MeV. The effect of positive parity $α - α^{*}$ rotational states is discussed.

NUCLEAR REACTIONS Excited $α$ particles in elastic $α - α$ scattering microscopic absorptive potential. Feshbach projection operator formalism. Phase shifts and transmission coefficients.

Effects of nuclear parity violation in deuterium atoms and elastic electron-deuteron scattering

E. M. Henley and W -Y. P. Hwang

Phys. Rev. C 26, 2376 (1982) - Published 1 December, 1982

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We confirm a suggestion made by Desplanques that the nuclear induced parity violation caused by the magnetization current is numerically more important than that due to the convection current. The resulting deuteron parity-violating electromagnetic form factor $G_{V} (q^{2})$ remains sensitive mainly to the ${}^{3}{\tilde{P}}_{1}$ abnormal-parity admixture in the deuteron wave function and is determined primarily by the parity-violating pion-nucleon coupling. We also argue that the nucleon-only impulse approximation constrained by gauge invariance is a good first approximation.

NUCLEAR REACTIONS ${}^{2}H (e, e^{'}) {}^{2}H$ ; parity-violating electromagnetic form factor, magnetization current versus convection current, validity of the NOIA/GI.

Formulas for the $δ$ -shell-plus-Coulomb potential for all partial waves

L. P. Kok, J. W. de Maag, H. H. Brouwer, and H. van Haeringen

Phys. Rev. C 26, 2381 (1982) - Published 1 December, 1982

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Closed forms are given for a large number of quantities occurring in the theory of potential scattering in an arbitrary partial-wave state $l$ for the cases (i) the $δ$ -shell potential $V (r) = - λ R^{- 2} δ (r - R)$ , and (ii) the $δ$ -shell plus Coulomb potential. Furthermore, the trajectories of the poles of the total $T$ operator in the complex $k$ plane, with varying complex $λ$ , are investigated in detail for zero, repulsive, and attractive Coulomb force, respectively. Expressions are given for the effective-range parameters, and the Coulomb-modified effective-range parameters, for all $l$ , with application to the $NN$ system, and the $N α$ system, respectively. The connection between Coulomb-level shifts and effective-range parameters is considered. Improvements on the standard small-shift approximation, which is relatively poor, are suggested.

NUCLEAR REACTIONS Charged-particle scattering. $δ$ -shell plus Coulomb potential. Effective-range parameters for all $l$ . Application to $NN$ and $N α$ . Coulomb-level shifts.

Meson wave functions in the meson-nucleon shell model

M. Bolsterli

Phys. Rev. C 26, 2397 (1982) - Published 1 December, 1982

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When the meson wave functions in the meson-nucleon shell model are chosen by analogy with the nucleon static model, direct effects of external mesons on the ground-state energy are minimized, and the Hartree approximation is realized in a particularly simple way.

NUCLEAR STRUCTURE Pion wave functions.

Two-pion exchange contributions to charge asymmetric and charge dependent nuclear forces

S. A. Coon and M. D. Scadron

Phys. Rev. C 26, 2402 (1982) - Published 1 December, 1982

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We develop a simple but systematic approach to the $2 π$ exchange contributions to $NN$ scattering graphs. When applied to $s$ -wave $NN$ scattering lengths, this scheme predicts a $2 π$ contribution of magnitude ${| a_{nn} |}_{2 π} - {| a_{pp} |}_{2 π} \approx \frac{1}{3}$ fm and ${| a_{pn} |}_{2 π} - {| a_{nn} |}_{2 π} \approx - \frac{1}{6}$ fm. If we then combine this effect with simple $π^{\pm}$ , $π^{0}$ and $ρ^{\pm}$ , $ρ^{0}$ pole graphs, the net charge asymmetric scattering length is $| a_{nn} | - | a_{pp} | \approx 1.2$ fm while the net charge dependent result is $| a_{pn} | - | a_{nn} | \approx 2.7$ fm. This compares favorably with the respective experimental values of approximately 1.5 and 5 fm.

NUCLEAR REACTIONS Charge asymmetric and charge dependent nuclear forces, nucleon mass differences in two-pion exchange graphs, effects on low energy nucleon scattering.

$N$ + ${}^{6}{Li}$ system with flexible cluster wave function

D. J. Stubeda, Y. Fujiwara, and Y. C. Tang

Phys. Rev. C 26, 2410 (1982) - Published 1 December, 1982

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The $n$ + ${}^{6}{Li}$ and $p$ + ${}^{6}{Li}$ systems are studied with the single-channel resonating-group method. The ${}^{6}{Li}$ internal wave function used is either a single translationally-invariant harmonic-oscillator shell-model function or a superposition of two such functions. The result shows that the main features of this system do not depend sensitively on which of these functions is employed, although significant differences in cross-section values do appear at backward angles. The fit to experimental data is only fair, indicating that the present calculation should be refined by including the $N$ + ${}^{6}{Li}$ *( $3^{+}$ ) inelastic channel, by taking into better account $d + α$ clustering in ${}^{6}{Li}$ , by carefully considering the effect of specific distortion, and by, perhaps, also adopting a noncentral nucleon-nucleon potential in the formulation.

NUCLEAR REACTIONS ${}^{6}{Li} (p, p)$ , ${}^{6}{Li} (n, n)$ ; calculated phase shifts and $σ (θ)$ . Resonating-group method with complex-generator-coordinate technique.

Analyzing powers in the ${}^{58}{Ni} (\vec{p}, p^{'})$ reaction calculated with the statistical multistep direct emission theory

R. Bonetti, L. Colli Milazzo, I. Doda, and P. E. Hodgson

Phys. Rev. C 26, 2417 (1982) - Published 1 December, 1982

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The fully quantum mechanical statistical multistep direct theory of Feshbach, Kerman, and Koonin is used to calculate the analyzing powers of the ${}^{58}{Ni} (\vec{p}, p^{'})$ reaction at 65 MeV to the continuum. The overall behavior of the analyzing powers and differential cross sections as a function of energy and angle is reasonably described by the theory and the relative contributions of the single and multistep processes are evaluated.

NUCLEAR REACTIONS ${}^{58}{Ni} (\vec{p}, p^{'})$ , $E_{p} = 65$ MeV. Statistical multistep direct emission. Calculated differential cross sections and analyzing powers.

Inclusive proton reactions at 164 MeV

R. E. Segel, T. Chen, L. L. Rutledge, Jr., J. V. Maher, John Wiggins, P. P. Singh, and P. T. Debevec

Phys. Rev. C 26, 2424 (1982) - Published 1 December, 1982

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Singles proton, deuteron, triton, ${}^{3}{He}$ , and alpha spectra resulting from the bombardment of ${}^{27}{Al}$ , ${}^{58}{Ni}$ , ${}^{62}{Ni}$ , and ${}^{208}{Pb}$ targets were measured. Data were taken over the angular range 25°-150°. Most of the data were taken at a bombarding energy of 164 MeV; some data were taken at 100 MeV. The ratios of fast (>30 MeV) particle yields are $p : d : t : {}^{3}{He} : α \approx 100 : 10 : 1 : 1 : 1$ . The deuteron spectra fall off more sharply with exit particle energy than do the proton spectra while tritons fall still more sharply, and the fast ${}^{3}{He}$ and $α$ spectra are similar in shape to the triton spectra. Fast particle angular distributions are all forward peaked with the forward peaking increasing with increasing outgoing particle energy. Angular distributions for the different particle species are quite similar and shapes of both spectral and angular distributions are rather independent of target. Proton and alpha evaporation peaks are prominent, deuterons less so, and evaporation peaks are not apparent in the triton and ${}^{3}{He}$ spectra.

NUCLEAR REACTIONS 164, 100 MeV $p$ on ${}^{27}{Al}$ , ${}^{58}{Ni}$ , ${}^{62}{Ni}$ , ${}^{208}{Pb}$ ; measured outgoing $p$ , $d$ , $t$ , ${}^{3}{He}$ , $α$ spectra $25 ° \leq θ \leq 150 °$ .

Fast-neutron total and scattering cross sections of ${}^{182}W$ , ${}^{184}W$ , and ${}^{186}W$

Peter T. Guenther, Alan B. Smith, and James F. Whalen

Phys. Rev. C 26, 2433 (1982) - Published 1 December, 1982

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Neutron total cross sections of ${}^{182}W$ , ${}^{184}W$ , and ${}^{186}W$ were measured from 0.3 to 5.0 MeV at intervals of ≲50 keV to accuracies of 1 to 3%. Differential elastic- and inelastic-scattering cross sections of the same three isotopes were measured from 1.5 to 4.0 MeV at incident-energy intervals of ≲200 keV over the angular range 20 to 160 deg. Approximately thirty scattered-neutron groups were observed for each isotope. Prominent among these are excitations attributed to rotational and vibrational bands. The experimental results are interpreted in terms of the statistical and the coupled-channels models with particular attention to the ground-state-rotational and the beta- and gamma-vibrational bands.

NUCLEAR REACTIONS Measured $σ_{n}$ (total) of ${}^{182}W$ , ${}^{184}W$ , ${}^{186}W$ , 0.3-5.0 MeV; measured $\frac{d σ}{d Ω_{n}}$ (elastic and inelastic) 1.5-4.0 MeV, 20-160 deg; statistical and coupled-channels model interpretations.

Independent cross sections of Na, K, Rb, Cs, and Fr isotopes produced in Ta and U targets bombarded by ${}^{12}C$ ions up to 77 MeV/nucleon

M. de Saint Simon, S. Haan, G. Audi, A. Coc, M. Epherre, P. Guimbal, A. C. Mueller, C. Thibault, F. Touchard, and M. Langevin

Phys. Rev. C 26, 2447 (1982) - Published 1 December, 1982

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Isotopic distribution measurements for Na, K, Rb, Cs, and Fr in the reactions ${}^{181}{Ta} ({}^{12}C, X) Na$ ,K,Rb,Cs and ${}^{238}U ({}^{12}C, X) Na$ ,K,Rb,Cs,Fr at different energies $E = 13, 27, and 77$ MeV/nucleon are reported. The independently observed yields of Rb and Cs show an important contribution for neutron-deficient nuclei. The U target shows very broad isotopic distributions which may be understood as a sum of two components. The results are compared to those obtained by nuclear reactions induced by protons over a wide energy range.

NUCLEAR REACTIONS ${}^{181}{Ta} ({}^{12}C, X) Na$ ,K,Rb,Cs; ${}^{238}U ({}^{12}C, X) Na$ ,K,Rb,Cs,Fr; $E = 13, 27, 77$ MeV/nucleon; measured Na, K, Rb, Cs, Fr isotopic distributions, heavy ion induced fission, spallation, on-line mass spectrometry.

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Channel cross correlation of the ${}^{31}P (d, α) {}^{29}{Si}$ and ${}^{31}P (d, p) {}^{32}P$ reactions

Low-energy ${}^{7}{Li} (t, α) {}^{6}{He}$ cross sections

Separable approximations of two-body interactions

${}^{3}{He}$ magnetic form factor

Generalized three-body Alt-Grassberger-Sandhas equations including three-body forces

Derivation of the Lippmann-Schwinger $N$ -body equations from the time-independent Schrödinger equation

Charge exchange reactions and solar neutrino detection in ${}^{81}{Br}$

Band structure in ${}^{180}{Ta}$ studied with transfer reactions

Virtual photons and electrodisintegration of the deuteron

Cross section and polarization in deuteron photodisintegration: General formulas

Influence of 1p- 1h-excited $α$ particles on elastic $α - α$ scattering

Effects of nuclear parity violation in deuterium atoms and elastic electron-deuteron scattering

Formulas for the $δ$ -shell-plus-Coulomb potential for all partial waves

Meson wave functions in the meson-nucleon shell model

Two-pion exchange contributions to charge asymmetric and charge dependent nuclear forces

$N$ + ${}^{6}{Li}$ system with flexible cluster wave function

Analyzing powers in the ${}^{58}{Ni} (\vec{p}, p^{'})$ reaction calculated with the statistical multistep direct emission theory

Inclusive proton reactions at 164 MeV

Fast-neutron total and scattering cross sections of ${}^{182}W$ , ${}^{184}W$ , and ${}^{186}W$

Independent cross sections of Na, K, Rb, Cs, and Fr isotopes produced in Ta and U targets bombarded by ${}^{12}C$ ions up to 77 MeV/nucleon

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