Recent Articles

( ${}^{7}{Li}$ , $t$ ) on $1 f - 2 p$ shell nuclei

R. I. Cutler, K. W. Kemper, and A. Roy

Phys. Rev. C 21, 1799 (1980) - Published 1 May, 1980

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( ${}^{7}{Li}$ , $t$ ) angular distributions have been measured on the targets ${}^{40}{Ca}$ , ${}^{44}{Ca}$ , and ${}^{58}{Ni}$ at $E = 34$ MeV for the ground and first excited state transitions. The results of the exact finite-range distorted-wave Born-approximation analyses of the data show a greater $α$ spectroscopic strength for ${}^{62}{Zn}$ than for either ${}^{44}{Ti}$ or ${}^{48}{Ti}$ .

NUCLEAR REACTIONS ${}^{40}{Ca}$ , ${}^{44}{Ca}$ , ${}^{58}{Ni}$ ( ${}^{7}{Li}$ , $t$ ), $E = 34$ MeV; measured $σ (θ)$ $θ = 3 ° - 50 °$ c.m. for $0^{+}$ and $2^{+}$ states in residual nuclei. Compared data to finite-range DWBA calculations; extracted relative and absolute $α$ spectroscopic strengths.

${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ and ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{16}O$ ) ${}^{24}{Mg}$ reactions at backward angles

M. Paul, S. J. Sanders, D. F. Geesaman, W. Henning, D. G. Kovar, C. Olmer, J. P. Schiffer, J. Barrette, and M. J. LeVine

Phys. Rev. C 21, 1802 (1980) - Published 1 May, 1980

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Excitation functions of the ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ and ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{16}O$ ) ${}^{24}{Mg}$ reactions to the ground states and first-excited $2^{+}$ states in ${}^{28}{Si}$ and ${}^{24}{Mg}$ have been measured at $θ_{c . m .} = 180$ ° over the energy range $24 \leq E_{c . m .} \leq 40$ MeV, where the ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ reaction is known to exhibit a strong resonant behavior at forward angles. The four measured excitation functions show prominent structures, about 1 MeV wide, strongly correlated in the elastic and inelastic channels. Angular distributions in the range $110 ° \leq θ_{c . m .} \leq 180 °$ were measured at $E_{c . m .} = 27.8, 30, 8, and 36.2$ MeV. At 27.8 and 36.2 MeV, where prominent peaks exist in the ( ${}^{16}O$ , ${}^{12}C$ ) backward-angle excitation function, the angular distributions of the transfer to the $0^{+}$ ground state are strongly rising toward 180° and have an oscillatory shape. The partial waves $L = (20, 22) and 26$ , respectively, are predominant at these two energies. At 30.8 MeV the data indicate the interference between odd and even partial waves.

NUCLEAR REACTIONS ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ), ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{16}O$ ) $E_{c . m .} = 24 - 40$ MeV; measured $σ (E, θ)$ ; correlation analysis; DWBA and ${P_{L}}^{2}$ analyses; deduced $J$ values.

Resonant behavior of the ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ reaction

S. J. Sanders, M. Paul, J. Cseh, D. F. Geesaman, W. Henning, D. G. Kovar, R. Kozub, C. Olmer, and J. P. Schiffer

Phys. Rev. C 21, 1810 (1980) - Published 1 May, 1980

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The ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ reaction has been studied over the energy range $26.3 < E_{c . m .} < 32.4$ MeV. Angular distributions with $4.5 ° \leq θ_{c . m .} \leq 50 °$ were measured at nine different energies in this range and an excitation function was measured over a wider range at $θ_{c . m .} \approx 90 °$ . The results of the present measurements, together with previously measured excitation functions at 0° and 180°, are analyzed within the framework of two resonances, at 27.6 and 30.8 MeV, added to a direct reaction background. Probable spin assignments for the two resonances are $J = 20$ (27.6 MeV) and $J = 23$ (30.8 MeV).

NUCLEAR REACTIONS ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ (g.s.); measured $σ (E, θ)$ ; resonance analysis; deduced spins, reduced widths.

Complete fusion of ${}^{15}N$ + ${}^{27}{Al}$

F. W. Prosser, Jr., R. A. Racca, K. Daneshvar, D. F. Geesaman, W. Henning, D. G. Kovar, K. E. Rehm, and S. L. Tabor

Phys. Rev. C 21, 1819 (1980) - Published 1 May, 1980

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The total fusion cross section for the system ${}^{15}N$ + ${}^{27}{Al}$ has been measured over an energy range $27 MeV \leq E_{lab} \leq 70 MeV$ by detection of the fusion-evaporation residues. In addition elastic scattering was measured at six energies and fitted by optical model calculations. The fusion cross section for the system saturates at 1150±50 mb. The data can be well described by the model of Glas and Mosel, using a reasonable set of parameters. The model of Horn and Ferguson also describes the data well if an appropriate charge radius is used. Comparison is made between these results and the fusion cross sections for ${}^{16}O$ + ${}^{26}{Mg}$ and ${}^{18}O$ + ${}^{24}{Mg}$ , which lead to the same compound nucleus. The results for ${}^{15}N$ + ${}^{27}{Al}$ are quite similar to those for ${}^{18}O$ + ${}^{24}{Mg}$ , and the differences between the fusion cross sections for these two systems and those for ${}^{16}O$ + ${}^{26}{Mg}$ may be evidence for an entrance channel effect.

NUCLEAR REACTIONS ${}^{15}N$ + ${}^{27}{Al}$ , $E_{lab} = 27 - 70$ MeV; measured $σ_{fusion} (E)$ ; measured $\frac{d σ}{d Ω}$ elastic scattering; data fitted with Glas and Mosel model, Horn and Ferguson model.

Backward angle cross sections for ${}^{27}{Al}$ + ${}^{16}O$ reaction products

D. Shapira, J. L. C. Ford, Jr., J. Gomez del Campo, and P. H. Stelson

Phys. Rev. C 21, 1824 (1980) - Published 1 May, 1980

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Reactions induced by bombarding a ${}^{16}O$ gas target with ${}^{27}{Al}$ ions were studied. Evaporation residues as well as target-like recoils were measured over a wide range of $Q$ values. The yield of particles with 6 ≤ Z ≤ 9 was found to be forward peaked in the laboratory frame. These target-like particles emerge with center-of-mass kinetic energies that, on the average, are independent of the reaction angle. Their combined cross section has a $\frac{1}{{sin θ}_{c . m .}}$ angular dependence. If this cross section is assumed to be symmetric about 90° (c.m.) the integrated cross section is about 10% of the measured evaporation residue cross section at a center-of-mass energy of 54 MeV.

NUCLEAR REACTIONS ${}^{27}{Al}$ + ${}^{16}O$ , $E_{{}^{27}{Al}} = 105, 145$ MeV; measured $\frac{d σ}{d Ω}$ for reaction products with $6 <~ Z <~ 9$ and $Z > 13$ for $2.5 ° <~ θ_{L} <~ 15 °$ . Extracted $σ$ for evaporation residues and damped events.

Velocity dependence of the dynamic magnetic field acting on swift O and Sm ions

N. K. B. Shu, D. Melnik, J. M. Brennan, W. Semmler, and N. Benczer-Koller

Phys. Rev. C 21, 1828 (1980) - Published 1 May, 1980

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The hyperfine dynamic field acting on fast ions traversing polarized iron foils has been measured as a function of the ion velocity in the region $0.03 < \frac{v}{Z v_{0}} < 0.06$ for Sm ions. The dynamic field increases with velocity but not linearly. The same conclusions were obtained from measurements on oxygen ions traversing thin iron foils or stopping in thick iron foils. All available data on dynamic-field measurements at ions with $8 < Z < 62$ traversing thin foils were examined and fitted to a single general form for the dynamic field. The region of validity of this parametrization of the dynamic field, as well as possible explanations of its origin, are discussed.

NUCLEAR REACTIONS ${}^{150, 152}{Sm}$ ( ${}^{16}O$ , ${}^{16}O$ ′) ${}^{150, 152}{Sm}$ ( $2_{1}^{+}$ ), ${}^{150, 152}{Sm}$ ( ${}^{32}S$ , ${}^{32}S$ ′) ${}^{150, 152}{Sm}$ ( $2_{1}^{+}$ ), and ${}^{16}O$ ( $α$ , $α^{'}$ ) ${}^{16}O$ ( $3_{1}^{-}$ ): $E_{0} \sim 40$ MeV, $E_{s} \sim 70 - 80$ MeV, $E_{α} = 17.55$ MeV; measured $W (θ, B, \infty)$ through polarized iron; deduced ${B_{DYNAMIC}}^{(v)}$ ; compiled existing data to obtain general parametrization for $B_{DYNAMIC} (v, Z)$ .

Spectroscopy of ${}^{213}{At}$ , ${}^{212}{Po}$ , and ${}^{210}{Pb}$ following ${}^{208}{Pb}$ + ${}^{7}{Li}$

T. P. Sjoreen, U. Garg, and D. B. Fossan

Phys. Rev. C 21, 1838 (1980) - Published 1 May, 1980

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The bombardment of ${}^{208}{Pb}$ by ${}^{7}{Li}$ ions has been used to study the properties of excited states in ${}^{213}{At}$ , ${}^{212}{Po}$ , and ${}^{210}{Pb}$ . In-beam measurements with Ge(Li), intrinsic Ge, and Si surface barrier detectors of $α$ -decay excitation functions, $α - γ$ coincidences, $γ - γ$ coincidences, $γ$ -ray angular distributions, and pulsedbeam- $γ$ timing were made to establish decay schemes, level energies, $γ$ -ray multipolarities, spin-parity assignments, and isomeric lifetimes. Excited states with spins up to $\frac{19}{2} ℏ$ in ${}^{213}{At}$ and $6 ℏ$ in ${}^{212}{Po}$ were identified. The mean lifetimes of the 1272-keV $8^{+}$ and 1193-keV $6^{+}$ states in ${}^{210}{Pb}$ were measured to be 225(22) and 30(10) nsec, respectively. These lifetimes imply $B (E 2)$ values of $51 (12) e^{2}$ ${fm}^{4}$ for the $8^{+}$ state and $308 (115) e^{2}$ ${fm}^{4}$ for the $6^{+}$ state. The ${}^{213}{At}$ decay scheme and the ${}^{210}{Pb}$ $B (E 2)$ values are compared with shell model calculations.

NUCLEAR REACTIONS ${}^{208}{Pb}$ ( ${}^{7}{Li}$ , $2 n$ ) ${}^{213}{At}$ , ${}^{208}{Pb}$ ( ${}^{7}{Li}$ , $t$ ) ${}^{212}{Po}$ , ${}^{208}{Pb}$ ( ${}^{7}{Li}$ , $α p$ ) ${}^{210}{Pb}$ , $E_{Li} = 30 - 34$ MeV; measured $α$ -decay excitations, $α - γ$ coincidences, $γ - γ$ coincidences, $γ_{-} W (θ)$ , pulsed-beam- $γ$ timing; deduced level schemes, $γ$ multipolarities, $J^{π}$ , $T_{\frac{1}{2}}$ , $B (E 2)$ .

Exactly central heavy-ion collisions by nuclear hydrodynamics

Henry H. K. Tang and Cheuk-Yin Wong

Phys. Rev. C 21, 1846 (1980) - Published 1 May, 1980

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We study the dynamics of heavy-ion collisions using the hydrodynamical description and focus our attention on the head-on collisions which provide the most favorable case for such a description. Angular distributions and energy distributions were obtained for various combinations of projectiles and targets of equal and unequal masses in the energy range from 50 to 400 MeV per projectile nucleon. It is found that regions of high density (the shock regions) are formed during the collisions and that the angular and energy distributions for many of these collisions have prominent features. In the collision of a small projectile with a heavy target, there is the forward angular peak of slow dissociated particles which represent much of the projectile nuclear matter stopped in the larger target nucleus, in addition to the nucleons from the expansions of the shock region. There is the side angular peak corresponding to the sidesplash of the target nuclear matter due to the impact of the projectile. There is also the backward angular peak due to the expansion of the shock region into the backward direction. In the collision of two equal nuclei, there are only the forward angular peak and the side angular peak. The effects of viscosity and thermal conductivity are investigated and found to affect the angular and energy distributions of the reaction products.

NUCLEAR REACTIONS Heavy-ion reactions, nuclear hydrodynamics, ${}^{20}{Ne}$ + ${}^{197}{Au}$ and ${}^{208}{Pb}$ + ${}^{208}{Pb}$ at 50, 100, 250, and 400 MeV per projectile nucleon. Nuclear viscosity and thermal conductivity.

Complete fusion of ${}^{12}C$ with ${}^{20}{Ne}$

I. Tserruya, J. Barrette, S. Kubono, P. Braun-Munzinger, M. Gai, and C. D. Uhlhorn

Phys. Rev. C 21, 1864 (1980) - Published 1 May, 1980

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Total fusion cross sections $σ_{F}$ have been measured for ${}^{12}C$ + ${}^{20}{Ne}$ in the energy range $24 < E_{c . m .} < 42$ MeV using the $Δ E - E$ technique. The excitation function of $σ_{F}$ shows only two structures at $E_{c . m .} = 29 and 38$ MeV which seem of different origin than those observed in the ${}^{16}O$ + ${}^{16}O$ system. The saturation value of the measured fusion cross section agrees with that obtained for other systems with nucleons in the $s - d$ shell.

NUCLEAR REACTIONS ${}^{12}C$ + ${}^{20}{Ne}$ , $24 < E_{c . m .} < 42$ MeV; measured fusion excitation function.

Closed-form description of heavy-ion transfer reactions based on distorted-waves theory

W. E. Frahn

Phys. Rev. C 21, 1870 (1980) - Published 1 May, 1980

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The transition amplitude for quasielastic transfer reactions between heavy ions, given by distorted-waves theory, is evaluated in closed form. By means of suitable approximations the transfer partial-wave amplitude is expressed in terms of the elastic $S$ matrix elements in the initial and final channels and of known functions defined by the Coulomb radial integrals of the transfer form factor. The partial-wave summation is performed by using the Poisson sum formula in conjunction with Fourier-Bessel transform techniques for evaluating integrals over localized functions in $l$ space. The resulting expressions cover uniformly the whole angular range including forward and backward directions. The general structure of the excitation functions at 0° and 180° is discussed, including possible backward-angle enhancements of the transfer cross section. A crucial step in the derivation is the introduction of a mean elastic $S$ -matrix, whose dependence on the initial and final angular momenta allows the display in detail of the magnetic quantum number and $Q$ -value dependences of the smooth and oscillatory parts of the cross section. Applications and extensions of the present formalism will be given in subsequent papers.

NUCLEAR REACTIONS Closed-form $S$ -matrix theory of heavy-ion transfer reactions based on DWBA. Uniform approximation for transfer angular distributions, 0° and 180° excitation functions. Explicit form of magnetic quantum number and $Q$ -value dependences.

Imaginary part of the ion-ion interaction potential

B. Behera, K. C. Panda, and R. K. Satpathy

Phys. Rev. C 21, 1883 (1980) - Published 1 May, 1980

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The energy density formalism of Brueckner is extended to the complex domain with the use of a complex two-body effective interaction, so as to generate simultaneously the real and imaginary part of the ion-ion interaction potential. A simple effective interaction consisting of a density dependent delta function repulsion and a Gaussian attraction is chosen for the real part of the complex effective interaction, whereas the imaginary component is derived by using the forward scattering amplitude approximation. In using this approximation, emphasis has been given to use the complex two-body matrix $T$ , where the propagator has the nuclear many-body Hamiltonian rather than the free two-body matrix $t$ . For the average nucleon-nucleon cross section $〈 σ 〉$ , required in constructing the complex effective interaction, a modified version of the relation suggested by Bohr and Mottelson is used which compares quite well with that of Clemental and Villi. The real part of the ion-ion interaction potential calculated in this model has already been reported in an earlier work and the present work deals with the calculation of the imaginary part of the potential for five pairs of spherical nuclei. The region of the potential beyond the surface is parametrized into a Woods-Saxon shape. The calculated imaginary potential for the system ${}^{40}{Ca}$ - ${}^{16}O$ is compared with the phenomenological one of Becchetti et al. and the agreement between the two sets of potentials is found to be quite good in the region beyond the strong absorption radius.

NUCLEAR REACTIONS Complex two-body effective interaction, forward scattering amplitude approximation, imaginary part of ion-ion interaction potential.

Parametrization of exact-finite-range distorted-wave Born approximation overlap integral for reactions induced by heavy ions

T. Udagawa, T. Tamura, and D. Price

Phys. Rev. C 21, 1891 (1980) - Published 1 May, 1980

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In a few recent publications, which utilized exact-finite-range distorted-wave Born approximation, we successfully fitted continuum spectra observed in a variety of heavy-ion reactions. In making it feasible to carry out the numerical calculations involved, we found the use of properly parametrized transition amplitudes was very powerful and almost indispensable. In the present article, methods used for this parametrization are explained in detail.

NUCLEAR REACTIONS Distorted-wave Born approximation; exact-finite-range form factors; parametrization of overlap integrals; recoil effects; heavy-ion reactions; continuum spectra.

Diffraction structure in back angle $p$ - ${}^{4}{He}$ elastic scattering

L. G. Arnold, B. C. Clark, and R. L. Mercer

Phys. Rev. C 21, 1899 (1980) - Published 1 May, 1980

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A Dirac equation optical model calculation with a relativistic Majorana exchange potential is used to represent the large angle diffraction structure observed in the 788 MeV $p$ - ${}^{4}{He}$ cross section data.

NUCLEAR REACTIONS ${}^{4}{He}$ ( $p$ , $p$ ), $E = 788$ MeV; calculated $σ (θ)$ , $A (θ)$ , and $Q (θ)$ from relativistic optical model. Relativistic Majorana exchange potential, large angle scattering.

Systematic features of the pion-nucleus interaction

R. S. Bhalerao, L. C. Liu, and C. M. Shakin

Phys. Rev. C 21, 1903 (1980) - Published 1 May, 1980

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We analyze pion elastic-scattering data for ${}^{40}{Ca}$ and ${}^{48}{Ca}$ using a covariant theory of the optical potential developed previously. Combining these results with the information obtained from the analysis of pion scattering from ${}^{12}C$ and ${}^{16}O$ reported earlier, we are able to discuss the systematics of the pion-nucleus optical potential. Our model contains a first-order optical potential which is obtained from a parameter-free calculation. The parameters of a second-order potential are determined by requiring that the sum of the first-and second-order potentials provides a fit to the elastic-scattering data. The parameters of the second-order potential exhibit a smooth dependence on energy and target mass number. These parameters have a marked resonance behavior. We find that the maximum value of the magnitude of the imaginary part of the second-order potential occurs at about 150 MeV while the first-order potential has a maximum for the magnitude of the imaginary part at about 240 MeV. The imaginary part of the first-order potential has a width at half maximum of about 200 MeV. This corresponds to a kinematic broadening of the (3,3) resonance due to the effects of the Fermi motion of the target nucleons. (This increased width is unrelated to the effects of the true absorption process or of collision broadening.) We also find a significant isospin violation in the second-order potential. For example, the imaginary part of the second-order potential for $π^{-}$ scattering is found to be systematically larger than that for $π^{+}$ scattering for nuclei with $N = Z$ . An explanation for this feature of the optical potential is presented.

NUCLEAR REACTIONS Elastic scattering of pions from ${}^{40}{Ca}$ (40-241 MeV) and ${}^{48}{Ca}$ (130 MeV). Systematics of first- and second-order optical potentials.

Probing inclusive production mechanisms with the ( $p$ , $2 p$ ) reaction

David H. Boal

Phys. Rev. C 21, 1913 (1980) - Published 1 May, 1980

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Several models for the inclusive production of protons at backward angles are reviewed. From the model amplitudes, predictions for the ( $p$ , $2 p$ ) differential cross section in which one of the protons is emitted in the backward direction are calculated. It is found that the magnitudes and angle dependence of the predicted cross sections vary significantly from one model to the next.

NUCLEAR REACTIONS Inclusive production mechanisms at intermediate energies, effective momentum distributions, predictions for ( $p$ , $2 p$ ) reaction.

Consistency between pion exchange currents and $N - N$ potential in doubly radiative $n - p$ capture

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

Phys. Rev. C 21, 1921 (1980) - Published 1 May, 1980

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The consistency between the exchange currents in the pionic range and the Reid soft-core potential, which has an asymptotic beahvior like $V_{OPE}$ , is studied in the doubly radiative $n - p$ capture process. The cross section is evaluated using the interaction Hamiltonian expressed by means of the nuclear current, that includes the two-body terms deriving from one-pion exchange. The gauge invariance is preserved by the generalized contact term. This cross section is compared to that obtained with the Siegert form of the interaction Hamiltonian. The difference between the values of the cross section, which is of the order of 24%, constitutes a quantitative estimate of the lack of consistency between pion exchange currents and the nuclear potential considered. The use of purely phenomenological wave functions leads to a great disagreement. Finally, the existence of an exchange effect of the order of 30% is pointed out in the process under examination, which occurs via the emission of two $E 1$ photons.

NUCLEAR REACTIONS Meson exchange currents, Reid soft-core potential and Siegert's theorem; ${}^{1}H$ ( $n$ , $γ γ$ ), thermal $n$ , calculated $σ_{2 γ}$ .

Proton- ${}^{4}{He}$ elastic scattering at intermediate energies

G. A. Moss, L. G. Greeniaus, J. M. Cameron, D. A. Hutcheon, R. L. Liljestrand, C. A. Miller, G. Roy, B. K. S. Koene, W. T. H. van Oers, A. W. Stetz, A. Willis, and N. Willis

Phys. Rev. C 21, 1932 (1980) - Published 1 May, 1980

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The differential cross section and analyzing power for $p$ - ${}^{4}{He}$ elastic scattering at 200, 350, and 500 MeV incident proton energy in the laboratory angle range from 4° to 168° are presented. Comparisons to theoretical calculations at 200 and 350 MeV have been made.

NUCLEAR REACTIONS Proton- ${}^{4}{He}$ elastic scattering 200, 350, 500 MeV measured differential cross section and analyzing power, $4 ° ≲ θ_{lab} ≲ 168 °$ .

Extraction of the $π NN$ form factor from charged pion photoproduction

C. A. Dominguez and Robert Beck Clark

Phys. Rev. C 21, 1944 (1980) - Published 1 May, 1980

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The $π NN$ form factor $F_{π NN} (t)$ , at small values of the momentum transfer, $0 < | t | \overset{∽}{<} 0.3$ ( ${G e V / c)}^{2}$ , has been determined from an analysis of the experimental data on $γ p \to π^{+} n$ for incident photon energies in the range 3.4-18 GeV. A total of 104 unpolarized differential cross sections and 22 asymmetries have been fitted with a Reggeized one-pion-exchange model. The best fits give for a monopole vertex function a range $Λ \approx 1000$ MeV and for a dual model type of form factor, an asymptotic rate parameter $β \approx 2.3 - 2.5$ . These results are consistent with those of a recent analysis of $NN$ charge exchange scattering data at high energy and the same range of momentum transfers. The contribution of non-one-pion exchanges to the photoproduction amplitudes has been found to be negligible and does not affect the $χ^{2}$ , thus leading to an essentially model independent extraction of $F_{π NN} (t)$ . The implications of these results for the construction of one-pion-exchange potentials in nuclear physics is briefly discussed.

NUCLEAR REACTIONS Pion photoproduction on nucleons at high energies; extraction of the $π NN$ form factor at small momentum transfers; the one-pion-exchange potential.

Relativistic calculation of radiative muon capture in hydrogen and ${}^{3}{He}$

Harold W. Fearing

Phys. Rev. C 21, 1951 (1980) - Published 1 May, 1980

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In view of the fundamental importance of radiative muon capture, particularly in light nuclei, and of the somewhat confused theoretical situation, a new calculation of radiative muon capture on the proton and on ${}^{3}{He}$ has been made. This calculation is based on the standard set of diagrams but, unlike previous calculations, has been performed without making nonrelativistic approximations. Results are given for the rate and photon spectrum for both ${}^{1}H$ and ${}^{3}{He}$ . A detailed comparison of this calculation is made with the approach developed by Hwang and Primakoff which is based on general constraints of conserved vector current, partially conserved axial vector current, and gauge invariance and on a special linearity hypothesis to try to understand why the Hwang-Primakoff results differ markedly from all previous results. It is shown that this calculation, as well as other standard ones, satisfy the general constraints of Hwang and Primakoff and that the differences arise because of their linearity hypothesis and other approximations. These differences are examined in detail, and it is shown that the numerically most important one arises because the linearity hypothesis has been used in such a way that it leads to a Hwang-Primakoff amplitude which violates the Low soft photon theorem.

RADIOACTIVITY $μ^{-} p \to ν n γ$ and $μ^{-} {}^{3}{He} \to ν {}^{3}H γ$ ; relativistic calculations of rate and photon spectrum.

Relativistic description of $π d$ elastic scattering in the (3,3) resonance region

N. Giraud, C. Fayard, and G. H. Lamot

Phys. Rev. C 21, 1959 (1980) - Published 1 May, 1980

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The $π d$ elastic scattering observables are calculated in the 142 to 256 MeV energy range within a relativistic three-body theory without $π$ absorption. The nonresonant $π N$ partial waves are included perturbatively to an excellent degree of accuracy. Various $NN$ tensor forces are elaborated at different levels of quality. The sensitivity of elastic differential cross sections and polarization parameters to the description of the $NN$ and $π N$ channels is investigated. The importance of using a realistic deuteron wave function is demonstrated.

NUCLEAR REACTIONS $π d$ elastic scattering, $T_{π} = 140 - 260$ MeV, $\frac{d σ}{d Ω}$ , total cross section, vector and tensor polarizations, Faddeev calculation, relativistic $NN$ tensor force.

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( ${}^{7}{Li}$ , $t$ ) on $1 f - 2 p$ shell nuclei

${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ and ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{16}O$ ) ${}^{24}{Mg}$ reactions at backward angles

Resonant behavior of the ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{28}{Si}$ reaction

Complete fusion of ${}^{15}N$ + ${}^{27}{Al}$

Backward angle cross sections for ${}^{27}{Al}$ + ${}^{16}O$ reaction products

Velocity dependence of the dynamic magnetic field acting on swift O and Sm ions

Spectroscopy of ${}^{213}{At}$ , ${}^{212}{Po}$ , and ${}^{210}{Pb}$ following ${}^{208}{Pb}$ + ${}^{7}{Li}$

Exactly central heavy-ion collisions by nuclear hydrodynamics

Complete fusion of ${}^{12}C$ with ${}^{20}{Ne}$

Closed-form description of heavy-ion transfer reactions based on distorted-waves theory

Imaginary part of the ion-ion interaction potential

Parametrization of exact-finite-range distorted-wave Born approximation overlap integral for reactions induced by heavy ions

Diffraction structure in back angle $p$ - ${}^{4}{He}$ elastic scattering

Systematic features of the pion-nucleus interaction

Probing inclusive production mechanisms with the ( $p$ , $2 p$ ) reaction

Consistency between pion exchange currents and $N - N$ potential in doubly radiative $n - p$ capture

Proton- ${}^{4}{He}$ elastic scattering at intermediate energies

Extraction of the $π NN$ form factor from charged pion photoproduction

Relativistic calculation of radiative muon capture in hydrogen and ${}^{3}{He}$

Relativistic description of $π d$ elastic scattering in the (3,3) resonance region

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