Recent Articles

Absolute cross sections for the ${}^{12}C$ ( $π^{\pm}$ , $π N$ ) ${}^{11}C$ reactions between 40 and 600 MeV

B. J. Dropesky, G. W. Butler, C. J. Orth, R. A. Williams, M. A. Yates-Williams, G. Friedlander, and S. B. Kaufman

Phys. Rev. C 20, 1844 (1979) - Published 1 November, 1979

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The excitation functions for the ${}^{12}C$ ( $π^{\pm}$ , $π N$ ) ${}^{11}C$ reactions have been established for 40- to 600-MeV $π^{-}$ and 50- to 520-MeV $π^{+}$ . These excitation functions are dominated by the (3,3) pion-nucleon resonance but show an upward energy shift in the resonance peak for $π^{-}$ (to about 190 MeV) and a downward shift for $π^{+}$ (to about 160 MeV). The $\frac{σ (π^{-})}{σ (π^{+})}$ ratio at 180 MeV is 1.59±0.07. The results are compared with theoretical calculations based on a semiclassical transport model including nucleon charge exchange and an intranuclear cascade model.

NUCLEAR REACTIONS ${}^{12}C$ ( $π^{\pm}$ , $π N$ ) ${}^{11}C$ , excitation functions, $E π^{+} = 50 - 520$ MeV, $E π^{-} = 40 - 600$ MeV. Plastic scintillator targets, measured ${}^{11}C$ by $β^{+} - γ$ coincidences. Compared with semiclassical transport and intranuclear cascade calculations.

Proton-nucleus total cross sections in the intermediate energy range

L. Ray

Phys. Rev. C 20, 1857 (1979) - Published 1 November, 1979

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Proton-nucleus total and reaction cross sections are computed for a number of target nuclei at energies ranging from 100 to 2200 MeV using the Kerman, McManus, and Thaler optical potential formalism and the impulse approximation. Corrections due to Pauli, short-range dynamical, and center-of-mass correlations are included in the calculations. In addition, the electric form factor of the neutron and the nucleon magnetic moments are included in deriving the necessary proton densities from available empirical charge distributions. The proton-nucleon scattering amplitudes are obtained from phase shift solutions or directly from the published $N - N$ data. The proton and neutron point densities are deduced where possible from analyses of electron and proton scattering or from Hartree-Fock predictions if the appropriate elastic angular distribution data are unavailable. An estimate of the uncertainty in the calculated total cross sections is given. The total and reaction cross sections computed in this way are shown to be in very good agreement with the data above 400 MeV but overestimate the data by 15-25% at lower energies, indicating that the approximate multiple scattering calculations generally performed near 1 GeV are inadequate when applied at energies below 400 MeV. Several theoretical improvements are suggested for this lower energy range and some numerical estimates are given. Analysis of total cross section data is also shown to be an unsuitable method for obtaining accurate measurements of neutron matter densities.

NUCLEAR REACTIONS proton-nucleus scattering; total and reaction cross sections; $E_{p} = 100 to 2200$ MeV; targets ${}^{12}C$ , ${}^{16}O$ , ${}^{27}{A 1}$ , ${}^{56}{Fe}$ , ${}^{63, 65}{Cu}$ , ${}^{72, 74}{Ge}$ , ${}^{127}I$ , and ${}^{208}{Pb}$ ; Kerman, McManus, and Thaler optical potential; target nucleon correlations.

Energetic charged-particle spectrum following $μ^{-}$ capture by nuclei

K. S. Krane, T. C. Sharma, L. W. Swenson, D. K. McDaniels, P. Varghese, B. E. Wood, R. R. Silbar, H. D. Wohlfahrt, and C. A. Goulding

Phys. Rev. C 20, 1873 (1979) - Published 1 November, 1979

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The energy spectra of charged particles (mainly protons) emitted following muon capture have been measured for targets of Al, Cu, and Pb. The intensity of the energetic (40-70 MeV) emitted particles falls exponentially with increasing energy, $I = I_{0} \exp (- \frac{E}{E_{0}})$ , with exponential constant $E_{0}$ 7.5±0.4 MeV (Al), 8.3±0.5 MeV (Cu), 9.9±1.1 MeV (Pb). The integrated yield for particles above 40 MeV was found to be (1.38±0.09)× $10^{- 3}$ per capture for Al, (1.96±0.12) × $10^{- 3}$ per capture for Cu, and (0.171±0.028)× $10^{- 3}$ per capture for Pb.

NUCLEAR REACTIONS Al, Cu, Pb ( $μ^{-}$ , $x$ ), $E = 0$ , measured charged particle spectrum, $σ (E)$ .

Direct knockout model for nuclear fragmentation

David H. Boal and R. M. Woloshyn

Phys. Rev. C 20, 1878 (1979) - Published 1 November, 1979

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A direct knockout model is developed for intermediate energy inclusive nuclear reactions involving the emission of light fragments in the backward hemisphere. In particular, the model is applied to the $A (p, α) X$ reactions where $A = {}^{9}{Be}, {}^{27}{Al}, and Ag$ . Predictions are made for the ( $p$ , $p α$ ) reaction with the α particle scattered into the backward hemisphere.

NUCLEAR REACTIONS Direct knockout model; ( $p$ , $α$ ) inclusive reactions at intermediate energy; ( $p$ , $p α$ ) predictions.

Positive pion-nucleus elastic scattering at 40 MeV

M. Blecher, K. Gotow, D. Jenkins, F. Milder, F. E. Bertrand, T. P. Cleary, E. E. Gross, C. A. Ludemann, M. A. Moinester, R. L. Burman, M. Hamm, R. P. Redwine, M. Yates-Williams, S. Dam, C. W. Darden, III, R. D. Edge, D. J. Malbrough, T. Marks, and B. M. Preedom

Phys. Rev. C 20, 1884 (1979) - Published 1 November, 1979

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Differential cross sections for elastic scattering of 40 MeV positive pions from ${}^{12}C$ , ${}^{16}O$ , ${}^{40}{Ca}$ , ${}^{90}{Zr}$ , and ${}^{208}{Pb}$ were measured at 18 angles in the angular range 25°-160°. Relative uncertainties of 2.5% to 7% and overall normalization uncertainties of 4% to 7% were obtained. An optical potential fit of the data indicates that while the magnitudes of the strength parameters, except for $Re b_{1}$ , are different from values obtained from free $π N$ scattering amplitudes, the variation of these magnitudes with target mass is roughly as predicted by the impulse approximation. Coulomb effects, especially in the cases of ${}^{90}{Zr}$ and ${}^{208}{Pb}$ , are extremely important, but impossible to unambiguously separate from the strong interaction in the optical model.

NUCLEAR REACTIONS Elastic scattering of 40 MeV $π^{+}$ from ${}^{12}C$ , ${}^{16}O$ , ${}^{40}{Ca}$ , ${}^{90}{Zr}$ , ${}^{208}{Pb}$ . Angular distributions: $25 ° < θ_{L} < 160 °$ . Optical model and partialwave analysis of cross-section data.

Beta decay of ${}^{15}C$

D. E. Alburger and D. J. Millener

Phys. Rev. C 20, 1891 (1979) - Published 1 November, 1979

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The spectrum of $γ$ rays following the $β$ decay of ${}^{15}C$ , produced in the ${}^{13}C$ ( $t$ , $p$ ) ${}^{15}C$ reaction, has been studied with a 50- ${cm}^{3}$ Ge(Li) detector. Allowed $β$ -ray branches to all available ${}^{15}N$ excited states known to have $J^{π} = \frac{1}{2^{+}} or \frac{3}{2^{+}}$ were measured including a branch to the 8571-keV state not reported previously. A value of 2.449±0.005 sec was obtained for the ${}^{15}C$ half-life by multiscaling $β$ rays detected in a plastic scintillator. The experimental ${}^{15}C$ $β$ -ray transition rates are compared with theoretical calculations.

RADIOACTIVITY ${}^{15}C$ ; measured $E_{γ}$ , $I_{γ}$ , $t_{\frac{1}{2}}$ ; deduced decay scheme and experimental $log ft$ values; calculated $log ft$ values from theory; compared experiment with theory.

Decay of ${}^{172}{Hf}$ to levels in ${}^{172}{Lu}$

K. S. Toth, Y. A. Ellis, D. C. Sousa, H. K. Carter, D. Sen, and E. F. Zganjar

Phys. Rev. C 20, 1902 (1979) - Published 1 November, 1979

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The electron-capture decay of ${}^{172}{Hf}$ was investigated. Single and coincidence measurements were made by using germanium x-ray detectors. In addition, a Si(Li) detector was used to study the low-energy portion, ≲ 60 keV, of the $γ$ -ray spectrum. These results were then combined with available conversion-electron data which had been obtained with a magnetic spectrometer. From this information, a decay scheme for ${}^{172}{Hf}$ was constructed. It incorporates 17 transitions into 11 excited levels in ${}^{172}{Lu}$ and differs from previously proposed decay schemes. Several transitions previously attributed to ${}^{172}{Hf}$ decay were not observed in the present study. The electron-capture decay energy was deduced from measured $K$ x-ray intensities and the level scheme to be 350±50 keV.

RADIOACTIVITY ${}^{172}{Hf}$ , measured $E_{γ}$ , $I_{γ}$ , $I_{x}$ , $γ γ$ coin; deduced $Q_{EC}$ . ${}^{172}{Lu}$ deduced levels $J^{π}$ .

Realistic effective interactions for the $sd$ shell: Global and discrete nuclear properties

B. J. Dalton, W. J. Baldridge, and J. P. Vary

Phys. Rev. C 20, 1908 (1979) - Published 1 November, 1979

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Comparisons of the Kuo and Vary-Yang $sd$ shell realistic effective shell-model interactions are presented through studies of the resulting global and discrete nuclear properties. The methods of spectral distributions are used to obtain energy moments for ${}^{21}{Ne}$ and spin cutoff factors for ${}^{28}{Si}$ for each interaction. Shell-model spectra are presented for some mass $A = 18$ to $A = 21$ $sd$ shell nuclei. In each case we show for comparison the results using the Chung-Wildenthal empirical interaction. In addition to demonstrating the role of various approximations through resulting global and discrete properties, we show that certain conclusions drawn from global properties are consistent with those based upon discrete properties.

NUCLEAR STRUCTURE Realistic effective interactions for $sd$ shell, spectral distribution theory, level densities, and spin cutoff factors.

Lowest negative parity state of ${}^{8}{Be}$

L. G. Arnold and R. G. Seyler

Phys. Rev. C 20, 1917 (1979) - Published 1 November, 1979

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Shell model and multichannel cluster model calculations yield different predictions for the lowest negative parity state of ${}^{8}{Be}$ . Several shell model calculations predict a $1^{-}$ state below about 18.5 MeV which has the same quantum numbers as an $α - α^{*}$ cluster state near 22 MeV. The experimental situation pertaining to this problem is examined.

NUCLEAR STRUCTURE ${}^{8}{Be}$ structure, ${}^{7}{Li}$ ( $p$ , $p$ ) ${}^{7}{Li}$ phase shifts.

Microscopic versus empirical effective interactions in a single $j$ shell

Bruce R. Barrett

Phys. Rev. C 20, 1926 (1979) - Published 1 November, 1979

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Effective-interaction matrix elements within a single $j$ shell can be determined directly from experimental data. Such matrix elements have been found to be much different from those calculated microscopically within a complete major shell. The recent work of Moszkowski et al. showed that this difference is at least partially due to the severe truncation to a single $j$ shell. We have constructed the microscopic effective interaction for a single $j$ shell using two different methods: (1) simple perturbation theory and (2) explicit projection from the full major shell to a single $j$ shell. We conclude that the empirical matrix elements and the full major-shell matrix elements should not agree, since the model spaces are different. On top of this the empirical values and the microscopic results for a single $j$ shell would be expected to be similar only when the configurations $| (j^{2}) J T 〉$ are very pure.

NUCLEAR STRUCTURE Effective interactions, empirical and microscopic, in a single $j$ shell; importance of model space size and of configuration purity.

Level densities for odd mass nuclei in the $1 f_{\frac{7}{2}}$ shell

A. M. Bastawros and K. I. Grais

Phys. Rev. C 20, 1930 (1979) - Published 1 November, 1979

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From the spacings of levels populated by a single nucleon transfer reactions to bound states, the parameters of the Bethe formula have been determined. Employing the same parameters, level spacings in the bound and resonance energy regions are estimated. A fair agreement with the experimental spacings is found. This is in accordance with the level density dependence $ρ (U, J) \propto U^{- 2} \exp [2 {(aU)}^{\frac{1}{2}} - \frac{{(J + \frac{1}{2})}^{2}}{2 σ^{2}}]$ used in the analysis of nuclear reactions.

NUCLEAR STRUCTURE Odd mass nuclei in the $1 f_{\frac{7}{2}}$ shell; deduced level density parameters, estimated level spacings.

Muonic resonance excitation of ${}^{188}{Os}$ and ${}^{172}{Yb}$

M. V. Hoehn and E. B. Shera

Phys. Rev. C 20, 1934 (1979) - Published 1 November, 1979

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"Anomalous" lines of significant intensity have been observed in the muonic spectra of ${}^{188}{Os}$ and ${}^{172}{Yb}$ . These anomalous lines are interpreted as $3 d - 2 p$ muonic-nuclear resonances involving $1^{-}$ and $3^{-}$ nuclear states at about 2-MeV excitation energy. Electric multipole moments and isomer shifts of the resonant nuclear states have been determined. Such accidental resonances, which presumably occur in other heavy muonic atoms, can provide an opportunity to obtain otherwise unavailable nuclear structure information.

NUCLEAR STRUCTURE ${}^{188}{Os}$ , ${}^{172}{Yb}$ ; measured muonic x-ray spectra; observed $3 d - 2 p$ muonic-nuclear resonances; derived electric moments and isomer shifts of resonant nuclear states.

RAPID COMMUNICATION

Laser-induced resonant absorption of $γ$ radiation

C. B. Collins, S. Olariu, M. Petrascu, and Iovitzu Popescu

Phys. Rev. C 20, 1942(R) (1979) - Published 1 November, 1979

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This paper reports an analytic estimate developed from a multiphoton model of the cross section for the absorption of a $γ$ -ray photon when the nuclear recoil is compensated by the simultaneous absorption of an optical photon from the radiation field of a high power laser. Tabulated data show 22 experimentally accessible nuclear transitions which might be expected to demonstrate this effect.

NUCLEAR REACTIONS Calculated $B (E 1)$ for multiphoton absorption; $γ$ +optical photon from laser.

RAPID COMMUNICATION

Pion double charge exchange reactions in ${}^{12}C$ and ${}^{40, 44, 48}{Ca}$

J. Davis, J. Källne, J. S. McCarthy, R. C. Minehart, C. L. Morris, H. A. Thiessen, G. Blanpied, G. R. Burleson, K. Boyer, W. Cottingame, C. F. Moore, and C. A. Goulding

Phys. Rev. C 20, 1946(R) (1979) - Published 1 November, 1979

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Cross sections, $\frac{d^{2} σ}{d Ω dT}$ , on ${}^{12}C$ , ${}^{40, 44, 48}{Ca}$ are presented for inclusive ( $π^{+}$ , $π^{-}$ ) and ( $π^{-}$ , $π^{+}$ ) reactions at an incident energy of $T_{π} = 290$ MeV with the exit pions detected over an energy range of $T_{π} = 175 - 255$ MeV at an angle of 60°. These cross sections are found to vary systematically with reported proton-neutron differences in nuclear radial distributions.

NUCLEAR REACTIONS ${}^{12}C$ , ${}^{40, 44, 48}{Ca}$ ( $π^{\pm}$ , $π^{\mp}$ ); measured $\frac{d^{2} σ}{d Ω dT}$ , $T = 290$ MeV, $θ = 60 °$ , nondiscrete final states; discussed the sensitivity to proton-neutron differences.

RAPID COMMUNICATION

Breakup processes in heavy-ion induced reactions

T. Udagawa, T. Tamura, T. Shimoda, H. Fröhlich, M. Ishihara, and K. Nagatani

Phys. Rev. C 20, 1949(R) (1979) - Published 1 November, 1979

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Cross sections for breakup of ${}^{20}{Ne}$ into ${}^{16}O$ and $α$ during scattering from ${}^{40}{Ca}$ were calculated in terms of the distorted wave Born approximation. The inclusive ${}^{16}O$ cross section observed in the ${}^{40}{Ca}$ ( ${}^{20}{Ne}$ , ${}^{16}O$ ) reaction was then found to be fitted very well by the sum of this breakup contribution and that of the $α$ -transfer reaction calculated in our previous work.

NUCLEAR REACTIONS ${}^{40}{Ca}$ ( ${}^{20}{Ne}$ , ${}^{16}O$ ) breakup reactions, calculated $\frac{d^{2} σ}{d Ω dE}$ ; $E ({}^{20}{Ne}) = 149 - 262$ MeV, direct reaction mechanism for heavy-ion reaction.

RAPID COMMUNICATION

Treatment of charged three-body problems

T. Sasakawa and T. Sawada

Phys. Rev. C 20, 1954(R) (1979) - Published 1 November, 1979

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The Faddeev equation is generalized to accommodate the Coulomb potentials. This equation may be used even if there are no (short range) nuclear interactions. In the coordinate space, this equation can be solved by the existing computer code for a non-Coulomb problem after a minor modification. This equation may be used also for attractive Coulomb potentials with some care.

NUCLEAR REACTIONS Three-body equation with Coulomb potentials.

RAPID COMMUNICATION

Validity of the Pauli exclusion principle for nucleons

B. A. Logan and A. Ljubičić

Phys. Rev. C 20, 1957(R) (1979) - Published 1 November, 1979

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The validity of the Pauli exclusion principle for nucleons has been investigated. The mean life against $p$ -shell nucleons in ${}^{12}C$ falling into the fully occupied $1 s_{\frac{1}{2}}$ shell has been shown to be > 6 × $10^{27}$ sec (99.7% confidence limit). A limit has also been obtained for the relative amplitude of symmetric components in the wave functions of nucleons.

RADIOACTIVITY ${}^{12}C$ , measured $T_{\frac{1}{2}}$ against violation of Pauli exclusion principle; NaI(Tl) detector.

RAPID COMMUNICATION

Parity violation in neutron scattering at threshold

G. Karl and D. Tadić

Phys. Rev. C 20, 1959(R) (1979) - Published 1 November, 1979

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We discuss the threshold enhancement of parity violation in neutron scattering in two simple models. We check that the Born approximation is reliable by comparing with an exact amplitude and also find that the original estimate of Forte for the enhancement in ${}^{124}{Sn}$ is probably realistic.

NUCLEAR REACTIONS Scattering theory, parity violation.

RAPID COMMUNICATION

Application of the diffractional model to quasi-elastic transfer reactions to continuum states

M. C. Mermaz

Phys. Rev. C 20, 1962(R) (1979) - Published 1 November, 1979

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A parametrization based on the distorted-wave Born-approximation (DWBA) formalism, using the diffractional model is given in order to fit angular distributions and continuum energy spectra of direct transfer reactions induced by heavy ions populating continuum states at incident energy well above the Coulomb barrier.

NUCLEAR REACTIONS DWBA and diffractional model applied to direct reactions induced by heavy ions—continuum states.

RAPID COMMUNICATION

Spin current contributions to the photonuclear sum rule

H. Arenhövel and D. Drechsel

Phys. Rev. C 20, 1965(R) (1979) - Published 1 November, 1979

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The photonuclear sum rule of Gerasimov is revisited and found to be violated for both a Dirac particle and spin current contributions. For a relativistic particle a modified sum rule is derived which is consistent with the Gell-Mann, Goldberger, and Thirring sum rule. In the case of nonrelativistic spin currents, violation of causality leads to a strong violation of dispersion sum rules.

NUCLEAR REACTIONS Photonuclear sum rule, spin current contributions, dispersion relations.

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Absolute cross sections for the ${}^{12}C$ ( $π^{\pm}$ , $π N$ ) ${}^{11}C$ reactions between 40 and 600 MeV

Proton-nucleus total cross sections in the intermediate energy range

Energetic charged-particle spectrum following $μ^{-}$ capture by nuclei

Direct knockout model for nuclear fragmentation

Positive pion-nucleus elastic scattering at 40 MeV

Beta decay of ${}^{15}C$

Decay of ${}^{172}{Hf}$ to levels in ${}^{172}{Lu}$

Realistic effective interactions for the $sd$ shell: Global and discrete nuclear properties

Lowest negative parity state of ${}^{8}{Be}$

Microscopic versus empirical effective interactions in a single $j$ shell

Level densities for odd mass nuclei in the $1 f_{\frac{7}{2}}$ shell

Muonic resonance excitation of ${}^{188}{Os}$ and ${}^{172}{Yb}$

Laser-induced resonant absorption of $γ$ radiation

Pion double charge exchange reactions in ${}^{12}C$ and ${}^{40, 44, 48}{Ca}$

Breakup processes in heavy-ion induced reactions

Treatment of charged three-body problems

Validity of the Pauli exclusion principle for nucleons

Parity violation in neutron scattering at threshold

Application of the diffractional model to quasi-elastic transfer reactions to continuum states

Spin current contributions to the photonuclear sum rule

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