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The decay by protons and $α$ 's of ${}^{24}{Mg}$ and ${}^{40}{Ca}$ excited to an energy region from about 10 to 30 MeV has been studied in an ( $α$ , $α^{'} \bar{c}$ ) experiment at $E_{α} = 120$ MeV. A strong increase of forward-backward asymmetry as a function of $E_{x}$ starting at $E_{x} = Q$ value + Coulomb barrier has been found for almost all decay channels studied indicating that this asymmetry is due to interference between the decay of the giant resonance structures and direct knockout processes.

NUCLEAR REACTIONS ${}^{24}{Mg}$ , ${}^{40}{Ca}$ ( $α$ , $α p$ ), ( $α$ , $2 α$ ), $E_{α} = 120$ MeV; measured $α - p$ , $α - α$ angular correlations giant resonances decay; deduced decay properties giant resonances.

RAPID COMMUNICATION

Pion double charge exchange on Ca isotopes

H. T. Fortune, S. J. Greene, C. F. Moore, and C. L. Morris

Phys. Rev. C 25, 2142(R) (1982) - Published 1 April, 1982

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A simple two-amplitude model introduced to relate pion double charge exchange on ${}^{16}O$ and ${}^{18}O$ is used to predict cross sections for ${}^{42 - 48}{Ca}$ , based solely on experimental data for ${}^{40}{Ca}$ and simple predictions for double isobaric analog transitions. The presence of the "forbidden" core component increases the expected ${}^{42}{Ca}$ cross sections by a factor of 6 above the double isobaric analog transition prediction and changes the expected ${}^{48}{Ca}$ / ${}^{42}{Ca}$ ratio by a factor of 4.5.

NUCLEAR REACTIONS ${}^{40 - 48}{Ca}$ ( $π^{+}$ , $π^{-}$ ) ${}^{40 - 48}{Ti}$ ; $θ = 5 °$ , $E_{π} = 164, 292$ MeV, two-amplitude model of cross sections.

RAPID COMMUNICATION

Predominance of the sequential pickup mechanism in the ${}^{208}{Pb}$ ( $p$ , $t$ ) ${}^{206}{Pb}$ $3^{+}$ transition

Masamichi Igarashi and Ken-ichi Kubo

Phys. Rev. C 25, 2144(R) (1982) - Published 1 April, 1982

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The roles of simultaneous (one-step) and sequential (two-step) transfer processes in the reaction ${}^{208}{Pb}$ ( $p$ , $t$ ) ${}^{206}{Pb}$ ( $3^{+}$ ,1.34 MeV) are investigated. Both processes are accurately evaluated employing realistic wave functions and finite-range interactions. The sequential transfer process is found to be dominant in this reaction, contrary to the conclusion of Nagarajan et al. The comparison of the polarization asymmetry calculation with the data confirms this result.

NUCLEAR REACTIONS ${}^{208}{Pb}$ ( $p$ , $t$ ) $3^{+}$ , $E_{p} = 22, 35$ MeV; first and second order DWBA analysis, calculated $σ (θ)$ , $A (θ)$ . Reaction mechanism.

RAPID COMMUNICATION

Role of isobar-hole excitations in the quenching of the ${}^{40}K$ ( $β^{-}$ ) ${}^{40}{Ca}$ transition

B. Castel, H. Toki, and P. Blunden

Phys. Rev. C 25, 2148(R) (1982) - Published 1 April, 1982

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The quenching effects of nuclear and $Δ$ excitations on the $β$ decay of ${}^{40}K$ are examined. It is found that although configuration mixing still provides the largest retardation, the inclusion of isobar-hole excitation is necessary to bring the calculation within calling distance of the experimental decay rate.

RADIOACTIVITY ${}^{40}K$ ( $β^{-}$ ) ${}^{40}{Ca}$ . Shell model calculation including isobar-hole excitations.

Failure of the distorted-wave Born approximation in analysis of the ${}^{24}{Mg}$ ( $\vec{p}$ , $d$ ) ${}^{23}{Mg}$ reaction at $T_{p} = 94$ MeV

J. R. Shepard, E. Rost, and P. D. Kunz

Phys. Rev. C 25, 1127 (1982) - Published 1 March, 1982

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We describe a detailed analysis for the $l = 0$ transition to the 2.36 MeV $½^{+}$ level in ${}^{23}{Mg}$ where the analyzing powers are large and oscillatory at $T_{p} = 94$ MeV. Distorted-wave Born approximation calculations completely fail to reproduce this behavior. Qualitative agreement is obtained only by introducing a great deal of absorption artifically, e.g., by using a large radial cutoff.

NUCLEAR REACTIONS ${}^{24}{Mg}$ ( $\vec{p}$ , $d$ ) ${}^{23}{Mg}$ , $E = 94$ MeV; calculated analyzing powers including exact finite-range effects, deuteron-tensor interaction in optical potential, explicit treatment of deuteron breakup and multistep processes; calculations also performed with radial cutoffs. Compared with data.

$NN$ interaction from bag-model quark interchange

B. L. G. Bakker, M. Bozoian, J. N. Maslow, and H. J. Weber

Phys. Rev. C 25, 1134 (1982) - Published 1 March, 1982

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A partial-wave helicity-state analysis of elastic nucleon-nuclon scattering is carried out in momentum space. Its basis is a one- and two-boson exchange amplitude from a bag-model quark interchange mechanism. The resulting phase shifts and bound-state parameters of the deuteron are compared with other meson theoretic potentials and data up to laboratory energies of ∼350 MeV.

NUCLEAR REACTIONS $NN$ elastic scattering, $E_{lab} \leq 350$ MeV. Coupling constants, form factors of renormalized OBE calculated from bag-model quark interchange. Phase shifts, deuteron parameters calculated from covariant partial-wave analysis.

Triton form factor from 0.29 to 1.00 ${fm}^{- 2}$

D. H. Beck, J. Asai, and D. M. Skopik

Phys. Rev. C 25, 1152 (1982) - Published 1 March, 1982

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Recoil tritons were detected from the elastic electron scattering reaction ${}^{3}H$ $(e, t) e^{'}$ . From these data charge form factors were determined in the range $0.29 \leq {q_{μ}}^{2} \leq 1.0$ ${fm}^{- 2}$ . No significant change in the previously reported charge radius for ${}^{3}H$ was found.

NUCLEAR REACTIONS ${}^{3}H$ ( $e$ , $t$ ), $E = 77 - 147$ MeV, measured $σ (E, E_{r}, θ_{r})$ deduced charge form factor, rms charge radius.

Elastic magnetic form factor of ${}^{6}{Li}$

J. C. Bergstrom, S. B. Kowalski, and R. Neuhausen

Phys. Rev. C 25, 1156 (1982) - Published 1 March, 1982

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The magnetic form factor for the ground state of ${}^{6}{Li}$ has been measured for momentum transfers $q = 0.8 - 2.8$ ${fm}^{- 1}$ . The diffraction minimum has been located at $q = 1.41$ ${fm}^{- 1}$ , and the results extend over the second maximum. All available longitudinal and transverse form factors of ${}^{6}{Li}$ are shown to be consistent with the $α - d$ cluster model providing the $d$ cluster is deformed and aligned. Comparison is made between the elastic and 3.56 MeV $M 1$ form factors, and the effects of exchange currents are considered. The ground-state current density is deduced by a Fourier-Bessel analysis of the elastic $M 1$ data.

NUCLEAR REACTIONS ${}^{6}{Li}$ ( $e$ , $e^{'}$ ), $E = 80 - 300$ MeV; $σ (E; E_{e^{'}}, θ)$ . ${}^{6}{Li}$ deduced elastic $M 1$ form factor. Cluster model. Exchange currents. Current density.

Test of the polarization-analyzing power equality in two ( $\vec{p}$ , $d$ ) reactions and their inverses

B. L. Burks, R. E. Anderson, T. B. Clegg, H. Paetz gen Schieck, E. J. Ludwig, R. L. Varner, and J. F. Wilkerson

Phys. Rev. C 25, 1168 (1982) - Published 1 March, 1982

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Angular distributions of vector analyzing power, $A_{y}$ , were measured for the ${}^{11}B$ ( $\vec{p}$ , $d$ ) ${}^{10}B$ and ${}^{13}C$ ( $\vec{p}$ , $d$ ) ${}^{12}C$ reactions. These analyzing powers were measured for each reaction at seven energies, 100 keV apart, which spanned the same excitation-energy range in the compound nuclei, ${}^{12}C$ and ${}^{14}N$ , as existing measurements of the outgoing proton polarization, $P_{y}$ , in the inverse reactions, ${}^{10}B$ ( $d$ , $\vec{p}$ ) ${}^{11}B$ and ${}^{12}C$ ( $d$ , $\vec{p}$ ) ${}^{13}C$ . We find general agreement between $P_{y}$ and $A_{y}$ except in a region where the $P_{y}$ measurements are known to be difficult to make. We are not yet convinced that this difference constitutes evidence for a violation of time-reversal invariance.

NUCLEAR REACTIONS ${}^{11}B$ ( $\vec{p}$ , $d$ ) ${}^{10}B$ measured $A_{y} (θ, E)$ for $E = 11.34 to 11.94$ MeV. ${}^{13}C$ ( $\vec{p}$ , $d$ ) ${}^{12}C$ measured $A_{y} (θ, E)$ for $E = 13.79 to 14.39$ MeV.

Functional approach to statistical theories of nuclear reactions

Mauricio Fortes and Laurence Jacobs

Phys. Rev. C 25, 1174 (1982) - Published 1 March, 1982

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Nuclear reactions for equivalent channels are considered in the framework of the entropy approach. We show that in the limit of many open channels, the resulting partition function may be expressed in terms of a functional integral whose trajectories are labeled by the eigenvalue density of the $S$ matrix. A saddle-point method is used to establish a linear integral equation for the eigenvalue density function of largest probability. This function can then be used to express all averages of physical interest. As an example, a particular partition function which has no transition points is used to determined cross sections and the enhancement factor. We find good agreement with other theories.

NUCLEAR REACTIONS Equivalent channels; functional methods.

High-lying $0^{+}$ and $3^{-}$ levels in ${}^{12}C$

S. S. Hanna, W. Feldman, M. Suffert, and D. Kurath

Phys. Rev. C 25, 1179 (1982) - Published 1 March, 1982

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The $γ$ decays of the levels at 17.77 and 18.36 MeV in ${}^{12}C$ are studied by proton capture and the assignments of ( $0^{+}$ ,1) and ( $3^{-}$ ,1), respectively, are confirmed. The very great strength of the decay of the ( $0^{+}$ ,1) level to the lower ( $1^{+}$ ,0) level at 12.71 MeV is consistent with a spin- and isospin-flip deuteronlike transition. The strong decay of the ( $3^{-}$ ,1) level to the lower ( $3^{-}$ ,0) level at 9.64 MeV is fairly typical of an analog to antianalog transition. The $γ$ -decay widths of these levels are compared with shell-model calculations.

NUCLEAR REACTIONS ${}^{11}B$ ( $p$ , $γ$ ) ${}^{12}C$ , $E_{p} = 0.82 - 2.83$ MeV. Measured excitation functions and angular distributions of resonances at 17.77 and 18.36 MeV; deduced spins, parities, and transition strengths to levels at 12.71 and 9.64 MeV, respectively. Enriched targets.

Determination of the neutron-nucleus optical potential from the angular dependence of the scattering amplitude

M. A. Hooshyar, R. Nadeau, and M. Razavy

Phys. Rev. C 25, 1187 (1982) - Published 1 March, 1982

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If the neutron-nucleus scattering amplitudes for no spin change, $f (θ)$ , and for spin flip, $g (θ)$ , are given at a fixed energy, then by replacing the Schrödinger equation in the interior of the potential by a difference equation it is possible to construct the optical potential including the spin-orbit force. The method has been applied to obtain local interactions for $n$ - ${}^{16}O$ and $n$ - ${}^{40}{Ca}$ .

NUCLEAR REACTIONS Construction of neutron-nucleus optical potential; $n$ - ${}^{16}O$ and $n$ - ${}^{40}{Ca}$ scattering at low energies.

Implications of anomalous isospin violation for the low energy nucleon-nucleon interaction

Paul Langacker and D. A. Sparrow

Phys. Rev. C 25, 1194 (1982) - Published 1 March, 1982

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Quark mass differences are used to derive an anomalous (i.e., due to the strong interactions) isospin violating potential. The potential includes the effects of pseudoscalar ( $π - η - η^{'}$ ) and vector meson ( $ρ - ω$ ) mixing. The finite $ρ$ width is included. Low energy $nn$ , $pp$ , and $np$ phase shift differences are calculated in terms of the fundamental coupling constants. Despite considerable uncertainty in the coupling constants, it is possible to understand the very small $nn$ and $pp$ scattering length differences. Furthermore, it appears that effects in the $l > 0$ partial waves at finite energies are large enough to be observable in the next few years. Estimates of effects in bound nuclei are presented. These include calculations of the contributions to mirror nuclei binding energy differences and to isospin mixing for a few characteristic cases. In most of those cases the anomalous isospin breaking contributions are of roughly the same size as observed discrepancies. However, inclusion of short range correlations substantially reduces the calculated effects in these cases.

NUCLEAR REACTIONS $pp$ , $pn$ , and $nn$ elastic scattering, $E = 0 - 350$ MeV, calculated phase shift differences due to anomalous isospin breaking. Effects in finite nuclei estimated.

Microscopic distorted wave theory of inelastic scattering

A. Picklesimer, P. C. Tandy, and R. M. Thaler

Phys. Rev. C 25, 1215 (1982) - Published 1 March, 1982

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An exact microscopic distorted wave theory of inelastic scattering is formulated which contains the physical picture usually associated with distorted wave approximations without the usual redundancy. This formulation encompasses the inelastic scattering of two fragments, elementary or composite (both with or without the full complexity of interfragment Pauli symmetries). The fact that these considerations need not be based upon elementary potential interactions is an indication of the generality of the approach and supports its applicability to inelastic meson scattering. The theory also maintains a description of inelastic scattering which is a natural extension of the description of elastic scattering and it provides a general basis for obtaining truncation models with an explicit distorted wave structure. The distorted wave impulse approximation is presented as an example of a particular truncation/approximation encompassed by this theory and the nature of the distorted waves is explicated.

NUCLEAR REACTIONS Distorted wave theory, inelastic scattering, multiple scattering, spectator expansion, Pauli exclusion principle, composite particles, unitarity structure.

Use of distorted waves in the theory of inelastic scattering

A. Picklesimer, P. C. Tandy, and R. M. Thaler

Phys. Rev. C 25, 1233 (1982) - Published 1 March, 1982

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A distorted wave description of inelastic scattering of nucleons from nuclei is formulated so that the microscopic content of the various ingredients can be made explicit. Special care is taken to ensure that physical processes are not overcounted as a consequence of the use of distorted waves in both the initial and final channels. Two attitudes to applications of the theory are taken. In the first, it is assumed that phenomenological distorted waves are employed and attention is focused upon the microscopic transition potential and the final distorted wave. Theoretically based recommendations for practical calculations of both these quantities are given. Secondly, we present a completely microscopic treatment wherein the truncations of the microscopic distorting potentials and the transition potential, at the single scattering level, are consistent with the underlying theoretical framework which links them. Our approach is designed to embody the distorted wave impulse approximation as a suitable lowest order result. Again, recommendations for practical calculations are given.

NUCLEAR REACTIONS Inelastic scattering, distorted wave Born approximation, distorted wave impulse approximation, multiple scattering.

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Erratum: Charge and transition densities for the samarium isotopes by electron scattering

Erratum: Decay of 13.9-min ${}^{241}{Np}$

Erratum: Back-angle differential cross section measurements for ( $d$ , $p$ ) reactions on light nuclei at low bombarding energies

Erratum: Radiochemical study of the combined ( $p$ , $π^{0}$ ) and ( $p$ , $γ$ ) reactions on bismuth with protons from 62 to 480 MeV

Erratum: Nuclear magnetic moment of 2.8 d ${}^{111}{In}$

Origin of the forward-backward asymmetry in the decay of the giant resonance structures of ${}^{24}{Mg}$ and ${}^{40}{Ca}$

Pion double charge exchange on Ca isotopes

Predominance of the sequential pickup mechanism in the ${}^{208}{Pb}$ ( $p$ , $t$ ) ${}^{206}{Pb}$ $3^{+}$ transition

Role of isobar-hole excitations in the quenching of the ${}^{40}K$ ( $β^{-}$ ) ${}^{40}{Ca}$ transition

Failure of the distorted-wave Born approximation in analysis of the ${}^{24}{Mg}$ ( $\vec{p}$ , $d$ ) ${}^{23}{Mg}$ reaction at $T_{p} = 94$ MeV

$NN$ interaction from bag-model quark interchange

Triton form factor from 0.29 to 1.00 ${fm}^{- 2}$

Elastic magnetic form factor of ${}^{6}{Li}$

Test of the polarization-analyzing power equality in two ( $\vec{p}$ , $d$ ) reactions and their inverses

Functional approach to statistical theories of nuclear reactions

High-lying $0^{+}$ and $3^{-}$ levels in ${}^{12}C$

Determination of the neutron-nucleus optical potential from the angular dependence of the scattering amplitude

Implications of anomalous isospin violation for the low energy nucleon-nucleon interaction

Microscopic distorted wave theory of inelastic scattering

Use of distorted waves in the theory of inelastic scattering

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