Recent Articles

RAPID COMMUNICATION

Determination of the half-life of the 56.5-keV level in ${}^{74}{Ga}$ by delayed coincident summing

J. van Klinken and L. M. Taff

Phys. Rev. C 15, 431(R) (1977) - Published 1 January, 1977

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RAPID COMMUNICATION

Beta radiations from ${}^{59}{Fe}$ and ${}^{60}{Co}$ nuclei polarized in iron foils cooled by dilution refrigeration

Kevin P. Barr and Richard C. Sapp

Phys. Rev. C 15, 434(R) (1977) - Published 1 January, 1977

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Apparatus for observing the $β$ emissions from radioactive nuclides diffused into iron foils cooled to 25 mK by a simple dilution refrigerator is briefly described. Tests using ${}^{60}{Co}$ gave a $β$ asymmetry coefficient $A = - 0.80 \pm 0.04$ , compared with the theoretical value - 1, indicating the effect of scattering. For the ${}^{59}{Fe}$ 467-keV $β$ transition the asymmetry was very small, (0.8 ± 0.5)% at 30 mK; no convincing asymmetry could be observed for the 273-keV $β$ rays. This is ascribed to the recently determined small value of the magnetic moment of ${}^{59}{Fe}$ ; the results are consistent with previous measurements of the $β - γ$ circular polarization correlations. An earlier experiment with ${}^{59}{Fe}$ in rare earth double nitrate crystals is reevaluated. The magnitudes of the $β$ matrix elements are briefly compared with single-particle shell model estimates including configuration mixing. Various model estimates of the magnetic moment are also presented.

RADIOACTIVITY ${}^{59}{Fe}$ , ${}^{60}{Co}$ ; measured $I_{β} (θ)$ , deduced $μ A (y)$ , $μ < 0$ . Calculated experimental and single particle ${| M_{GT} |}^{2}$ , also model estimates of $μ$ .

RAPID COMMUNICATION

Resonances in ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$

H. T. Fortune, L. R. Greenwood, R. E. Segel, and J. R. Erskine

Phys. Rev. C 15, 439(R) (1977) - Published 1 January, 1977

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Excitation functions for ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ show a number of strongly correlated resonances in the c.m. bombarding-energy range 17-20 MeV, all with widths of ∼ 300-400 keV.

NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, α)$ , $E = 34 - 51$ MeV, measured $σ (E)$ , $θ = 5 °$ (lab). Five correlated resonances in energy range 34-40 MeV.

RAPID COMMUNICATION

Reexamination of the $β^{-}$ decay of ${}^{130}{Sn}$

L. L. Nunnelley and W. D. Loveland

Phys. Rev. C 15, 444(R) (1977) - Published 1 January, 1977

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$β - γ$ coincidence measurements of the decay of ${}^{130}{Sn}$ allow one to deduce a $Q_{β}^{-}$ for this decay of 2040 ± 50 keV. The lack of higher energy emitted $β^{-}$ particles in this decay compels one to reevaluate published decay schemes for ${}^{130}{Sn}$ .

RADIOACTIVITY ${}^{130}{Sn}$ , measured $I_{γ}$ , $E_{γ}$ , $E_{β}$ , $β - γ$ coin, $γ - γ$ coin, $x - y$ coin; deduced $log ft$ , $Q$ , ${}^{130}{Sb}$ deduced levels, $J$ , $π$ , ICC. Chemically separated ${}^{235}U$ fission products.

RAPID COMMUNICATION

Sensitivity of the reaction ${}^{40}{Ca}$ ( ${}^{13}C$ , ${}^{14}N$ ) ${}^{39}K$ to the ${}^{39}K$ + $p$ form factor

J. J. Bevelacqua, D. Stanley, and D. Robson

Phys. Rev. C 15, 447(R) (1977) - Published 1 January, 1977

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Angular distributions for the reaction ${}^{40}{Ca}$ ( ${}^{13}C$ , ${}^{14}N$ ) ${}^{39}K$ (2.53 MeV, $½^{+}$ ) (transfered $L = 1$ ) at 68 MeV bombarding energy which are known to oscillate out of phase with exact finiterange distorted-wave Born approximation calculations are shown to be insensitive to the details of the ${}^{39}K$ + $p$ form factor.

NUCLEAR REACTIONS ${}^{40}{Ca}$ ( ${}^{13}C$ , ${}^{14}N$ ) ${}^{39}K$ , calculated sensitivity of phasing of DWBA angular distribution to ${}^{39}K$ + $p$ form factor peak location.

RAPID COMMUNICATION

Structure in gamma-ray yields from the ${}^{12}C$ + ${}^{16}O$ reaction above the Coulomb barrier

Z. E. Switkowski, H. Winkler, and P. R. Christensen

Phys. Rev. C 15, 449(R) (1977) - Published 1 January, 1977

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The $γ$ -ray yields from low-lying transitions in heavy residual nuclei produced in the ${}^{12}C$ + ${}^{16}O$ reaction have been measured from $E_{c . m .} = 10.85 to 27.36$ MeV in steps of ∼200 keV. In addition to the broad (∼1 MeV) structures recently reported by Sperr et al., further resonancelike structure is observed at $E_{c . m .} \approx 22.5$ MeV and probably also at $E_{c . m .} \approx 11$ MeV. Structure is observed most clearly in the $α$ -particle channel.

NUCLEAR REACTIONS ${}^{12}C$ + ${}^{16}O$ , $E_{c . m .} = 10.85 - 27.36$ MeV. Measured $σ (E)$ for $γ$ -ray yields.

RAPID COMMUNICATION

Nuclear model-independent matter density from 1.04 GeV proton elastic scattering

I. Brissaud and M. K. Brussel

Phys. Rev. C 15, 452(R) (1977) - Published 1 January, 1977

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A nearly model-independent matter density is derived from 1 GeV proton elastic scattering on ${}^{40}{Ca}$ using the Sick method. The different moments of these densities are calculated with their corresponding uncertainties.

NUCLEAR REACTIONS ${}^{40}{Ca} (p, p)$ , $E = 1.04$ GeV, matter density and corresponding uncertainties calculated.

RAPID COMMUNICATION

Isotope shifts of $1 f_{\frac{7}{2}}$ radii from nucleon-transfer reactions

E. Friedman, A. Moalem, D. Suraqui, and S. Mordechai

Phys. Rev. C 15, 456(R) (1977) - Published 1 January, 1977

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Cross sections for $1 f_{\frac{7}{2}}$ neutron- and proton-transfer reactions on ${}^{48}{Ca}$ have been measured. A distorted-wave Born approximation analysis of these and other similar results for a ${}^{40}{Ca}$ target reveals isotope shifts of the $1 f_{\frac{7}{2}}$ rms radii which are about 0.2 fm in magnitude and have opposite signs for neutrons and protons. These shifts are in a reasonably good agreement with calculations based on average isospin dependent single-particle potentials.

NUCLEAR REACTIONS ${}^{48}{Ca} ({}^{3}{He}, d_{0})$ , $E_{3_{He}} = 8 - 10$ MeV, ${}^{48}{Ca} (d, t_{0})$ , $E_{d} = 8.5$ MeV. Measured $σ (E, θ)$ . DWBA analysis, comparisons with ${}^{40}{Ca} (t, d_{0})$ and ${}^{40}{Ca} ({}^{3}{He}, d_{0})$ . Deduced isotope shifts of rms radii of $1 f_{\frac{7}{2}}$ neutrons and protons.

RAPID COMMUNICATION

Interpretation of fission fragment anisotropies in the fission of ${}^{238}U$ induced by intermediate energy ${}^{4}{He}$ ions

S. S. Kapoor and R. K. Choudhury

Phys. Rev. C 15, 459(R) (1977) - Published 1 January, 1977

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The fragment anisotropy data in the fission of ${}^{238}U$ induced by 23-115 MeV ${}^{4}{He}$ ions are analyzed taking into consideration the expected differences in the fragment anisotropies of the fissions following compound nucleus and direct interactions. The present analysis supports the theoretical prediction made earlier that the transition state seen by the fissioning nucleus shifts from the second barrier at low energies to the liquid drop model saddle point at higher excitation energies. However, the determination of the excitation energy where the liquid drop model transition state is encountered depends on the assumption regarding the reaction mechanism and the anisotropy for the direct interaction fission component. The need for experimental measurements of the fragment anisotropies of both the direct interaction fission and compound nucleus fission components is pointed out.

NUCLEAR REACTIONS FISSION Interpretation of fragment angular distributions; ${}^{4}{He} ({}^{238}U, f)$ ; $E_{α} = 23 - 115$ MeV.

Erratum: New alternative to the resonating group method

R. Raphael, P. C. Tandy, and W. Tobocman

Phys. Rev. C 15, 463 (1977) - Published 1 January, 1977

Systematic dependence of the slowing-down environment on nuclear lifetime measurements by the Doppler-shift attenuation method

M. Toulemonde and F. Haas

Phys. Rev. C 15, 49 (1977) - Published 1 January, 1977

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The mean life of the ${}^{22}{Ne}$ 3.34 MeV level measured by Doppler-shift attenuation method at an average recoil velocity of $0.009 c$ , shows large fluctuations with different slowing-down materials ranging from Li to Pb. These fluctuations are correlated with a linear dependence of the "apparent" mean life $τ$ on the electronic slowing-down time $α$ .

NUCLEAR REACTIONS ${}^{19}F (α, p)$ , $E = 5.31$ MeV; measured Doppler-shift attenuation. ${}^{22}{Ne}$ level deduced $T_{\frac{1}{2}}$ as a function of $Z_{2}$ .

Normalization of the ( $d$ , ${}^{3}{He}$ ) reaction

N. S. Chant, N. S. Wall, C. F. Clement, S. M. Perez, and J. N. Craig

Phys. Rev. C 15, 53 (1977) - Published 1 January, 1977

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The normalization constant ${D_{0}}^{2}$ for distorted-wave Born approximation calculations for ( $d$ , ${}^{3}{He}$ ) reactions is estimated using a $J$ -dependent sum rule analysis of relative spectroscopic factors. Discrepencies in absolute spectroscopic factors for ${}^{51}V (d, {}^{3}{He}) {}^{50}{Ti}$ and ${}^{12}C (d, {}^{3}{He}) {}^{11}B$ reactions at 80 MeV are resolved. A comparison of these reactions suggests that the Coulomb part of the $d - p$ interaction should not be included in the calculations. Our analysis yields ${D_{0}}^{2} = (1.65 \pm 0.15) \times 10^{4}$ Me $V^{2}$ ${fm}^{3}$ . Together with other analyses, a value of ${D_{0}}^{2} = (2 \pm 0.4) \times 10^{4}$ Me $V^{2}$ ${fm}^{3}$ appears to be appropriate.

NUCLEAR REACTIONS ${}^{12}C (d, {}^{3}{He})$ , ${}^{51}V (d, {}^{3}{He})$ , $E = 30 - 80$ MeV; $J$ -dependent sum rule analysis; deduced normalization constant ${D_{0}}^{2}$ .

Distorted-wave impulse-approximation calculations for quasifree cluster knockout reactions

N. S. Chant and P. G. Roos

Phys. Rev. C 15, 57 (1977) - Published 1 January, 1977

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A formalism for distorted-wave impulse-approximation calculations of quasifree cluster knockout reactions is described. Results are presented for ( $p, p α$ ) and ( $α, 2 α$ ) reactions. In both cases distortion effects are large. It is concluded that incident energies between ∼ 100 and ∼ 200 MeV are most suitable for ( $p, p α$ ) studies of nuclear structure, whereas somewhat higher energies are more appropriate for ( $α, 2 α$ ) studies.

NUCLEAR REACTIONS DWIA reaction theory of cluster knockout.

Absolute spectroscopic factors from the ( $p, p α$ ) reaction at 100 MeV on $1 p$ -shell nuclei

P. G. Roos, N. S. Chant, A. A. Cowley, D. A. Goldberg, H. D. Holmgren, and R. Woody, III

Phys. Rev. C 15, 69 (1977) - Published 1 January, 1977

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The ( $p, p α$ ) reaction on ${}^{6}{Li}$ , ${}^{7}{Li}$ , ${}^{9}{Be}$ , and ${}^{12}C$ has been investigated experimentally at a bombarding energy of 100 MeV. Data were obtained at a large number of angle pairs in order to study the reaction mechanism. The data are in good agreement with distorted-wave impulse-approximation calculations; unlike most analyses of transfer reactions we obtain absolute $α$ -particle spectroscopic factors. These are in good agreement with $1 p$ shell model predictions. Thus we find no evidence for additional $α$ -particle-like correlations.

NUCLEAR REACTIONS ${}^{6}{Li}$ , ${}^{7}{Li}$ , ${}^{9}{Be}$ , ${}^{12}C (p, p α)$ , $E_{0} = 100$ MeV; measured $\frac{d^{3} σ}{d Ω_{p} d Ω_{α} d E_{p}} (θ_{p}, θ_{α}, E_{p}, E_{α})$ ; coplanar geometry; DWIA analysis; deduced $α$ -particle spectroscopic factors.

Cluster spectroscopic factors for the $p$ -shell nuclei

Yu. F. Smirnov and Yu. M. Tchuvil'sky

Phys. Rev. C 15, 84 (1977) - Published 1 January, 1977

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A convenient method of calculation has been developed to determine the cluster spectroscopic factors for the ejection of excited and complex fragments ( ${}^{4}{He}$ , ${}^{6}{Li}$ , ${}^{7}{Li}$ , ${}^{8}{Be}$ , etc.) from the low-lying levels of the $p$ -shell nuclei followed by transition both to the states of the lowest shell configuration of the daughter nucleus and to its hole states. The method can be used to analyze the cluster knock-out, transfer reactions induced by heavy ions, etc.

NUCLEAR STRUCTURE $p$ -shell nuclei; calculated cluster spectroscopic factors. Harmonic oscillator shell model.

High-spin levels in ${}^{191}{Pt}$ and ${}^{193}{Pt}$ and the triaxial rotor model

S. K. Saha, M. Piiparinen, J. C. Cunnane, P. J. Daly, C. L. Dors, T. L. Khoo, and F. M. Bernthal

Phys. Rev. C 15, 94 (1977) - Published 1 January, 1977

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The high-spin level structures of the transitional nuclei ${}^{191}{Pt}$ and ${}^{193}{Pt}$ have been studied by ( $α, 3 n γ$ ) reactions on enriched Os targets. The measurements included $γ$ -ray singles, comprehensive $γ - γ$ coincidences, half-life determinations, and $γ$ -ray angular distributions. The extensive ${}^{191}{Pt}$ and ${}^{193}{Pt}$ level schemes established are reported here. In both nuclei, decoupled $ν {i_{\frac{13}{2}}}^{- 1}$ bands, strongly resembling the ground bands of the adjacent core nuclei, and many other high-spin positive parity states have been located. Low-lying $\frac{21}{2^{-}}$ bands have also been observed in both nuclei and they are described as semidecoupled bands with microscopic structures dominated by three-quasiparticle components of the type ( $ν {i_{\frac{13}{2}}}^{- 2}, ν j^{- 1}$ ). The abundant information about $ν i_{\frac{13}{2}}$ level families obtained in these experiments and in a complementary ${}^{191}{Au}$ decay study is discussed, and it is shown that these complex level spectra can be accounted for rather well in terms of the coupling of an $i_{\frac{13}{2}}$ neutron hole to a triaxially deformed core.

NUCLEAR REACTIONS ${}^{190}{Os}$ , ${}^{192}{Os} (α, 3 n γ)$ , $E = 31 - 46$ MeV; measured $E_{γ}$ , $I_{γ} (θ)$ , $γ - γ$ coin, $T_{\frac{1}{2}}$ ; ${}^{191, 193}{Pt}$ deduced level schemes, $J$ , $π$ .

Finite-range distorted-wave Born-approximation study of the ( ${}^{4}{He}$ , ${}^{6}{Li}$ ) reaction on ${}^{12}C$ , ${}^{24}{Mg}$ , and ${}^{40}{Ca}$

R. G. Markham and M. A. M. Shahabuddin

Phys. Rev. C 14, 2037 (1976) - Published 1 December, 1976

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Angular distributions have been obtained for the ( $α, {}^{6}{Li}$ ) reaction at 46 MeV on targets of ${}^{12}C$ , ${}^{24}{Mg}$ , and ${}^{40}{Ca}$ . A finite-range distorted-wave Born-approximation analysis is performed using shell model wave functions to describe the target and various cluster wave functions to describe ${}^{6}{Li}$ . Finite-range effects are evident in the predicted absolute magnitudes but not in the shapes of the angular distributions, which are poorly fitted. Reasonable agreement between measured and predicted absolute cross sections is obtained if the product of the $α - d$ wave function and potential for the ${}^{6}{Li}$ has no node away from the origin.

NUCLEAR REACTIONS ${}^{12}C$ , ${}^{24}{Mg}$ , ${}^{40}{Ca} (α, {}^{6}{Li})$ , $E = 46$ MeV; measured $σ (E_{6_{Li}}, θ)$ : Finite-range DWBA analysis with microscopic wave functions.

Variational principle for the bloch unified reaction theory

W. MacDonald and R. Raphael

Phys. Rev. C 14, 2044 (1976) - Published 1 December, 1976

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The unified reaction theory formulated by Bloch uses a boundary value operator to write the Schrödinger equation for a scattering state as an inhomogeneous equation over the interaction region. As suggested by Lane and Robson, this equation can be solved by using a matrix representation on any set which is complete over the interaction volume. Lane and Robson have proposed, however, that a variational form of the Bloch equation can be used to obtain a "best" value for the $S$ matrix when a finite subset of this basis is used. We first consider the variational principle suggested by Lane and Robson, which gives a many-channel $S$ matrix different from the matrix solution on a finite basis, and show that the difference results from the fact that their variational principle is not, in fact, equivalent to the Bloch equation. We then present a variational principle which is fully equivalent to the Bloch form of the Schrödinger equation and show that the resulting $S$ matrix is the same as that obtained from the matrix solution of this equation.

NUCLEAR REACTIONS Variational principle for the Bloch equation.

Unitarity constraints with the Kapur-Peierls formalism

D. B. Adler

Phys. Rev. C 14, 2050 (1976) - Published 1 December, 1976

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It is well known that the Kapur-Peierls formalism, as currently used for the analysis of resonance reactions, fails to provide a manifestly unitary collision matrix expansion, in contrast to the $R$ -matrix theory. This drawback, and the presence of a number of parameters generally larger than in the $R$ -matrix theory, inhibits the general use of the Kapur-Peierls formalism, except for special cases in which it was possible to establish explicit relations to the $R$ -matrix formalism. It is shown here that the basic properties of the Kapur-Peierls eigenfunctions provide relations among the parameters, which express in general the condition of unitarity. These relations, obtained without need of imposing limits to the number of resonances and of reaction channels, and retaining the general nature of the parameters of being energy dependent, establish constraints among the Kapur-Peierls parameters. As a result, the number of real independent parameters for the Kapur-Peierls formalism is reduced to be the same as in the $R$ -matrix theory. From the same relations is derived also a transformation from the Kapur-Peierls parameters to the $R$ -matrix parameters, in an equally general form. The basic feature of unitarity for the Kapur-Peierls parameters is retained if in applications only limited numbers of resonances and channels are introduced. Analytical procedures based on an iteration-perturbation scheme are presented so as to provide for the explicit use of the unitarity constraints in numerical applications and data analysis. The same procedures provide $R$ -matrix parameters unitarily related to the Kapur-Peierls parameters, and representing the same collision matrix.

NUCLEAR REACTIONS Kapur-Peierls formalism, unitarity constraints, iteration procedures in numerical applications, data analysis.

Approximate distorted-wave Born-approximation methods for ( $d, p$ ) stripping reactions

E. V. Ivash and R. J. Kulkarni

Phys. Rev. C 14, 2063 (1976) - Published 1 December, 1976

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In order to take into account in a consistent manner the effect of the $D$ state of the deuteron on ( $d, p$ ) and ( $d, n$ ) stripping reactions, and to study the effect on the vector and tensor polarizations, it is essential to include finite range in the distorted-wave Born-approximation calculations. To reduce the complexity of the exact finite-range calculations two approximations have been developed. The first is based essentially on an expansion of the finite-range form factor and the double-radial integral of the exact theory in powers of the $n - p$ separation distance. The second uses a $δ$ potential over a spherical shell, and is a generalization of the usual zero-range approach. Computational aspects of the problem are also discussed.

NUCLEAR REACTIONS Two approximate treatments of finite-range, $D$ -state DWBA effects in stripping reactions; using $n - p$ separation expansions and spherical $δ$ -shell assumption.

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Recent Issues

Determination of the half-life of the 56.5-keV level in ${}^{74}{Ga}$ by delayed coincident summing

Beta radiations from ${}^{59}{Fe}$ and ${}^{60}{Co}$ nuclei polarized in iron foils cooled by dilution refrigeration

Resonances in ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$

Reexamination of the $β^{-}$ decay of ${}^{130}{Sn}$

Sensitivity of the reaction ${}^{40}{Ca}$ ( ${}^{13}C$ , ${}^{14}N$ ) ${}^{39}K$ to the ${}^{39}K$ + $p$ form factor

Structure in gamma-ray yields from the ${}^{12}C$ + ${}^{16}O$ reaction above the Coulomb barrier

Nuclear model-independent matter density from 1.04 GeV proton elastic scattering

Isotope shifts of $1 f_{\frac{7}{2}}$ radii from nucleon-transfer reactions

Interpretation of fission fragment anisotropies in the fission of ${}^{238}U$ induced by intermediate energy ${}^{4}{He}$ ions

Erratum: New alternative to the resonating group method

Systematic dependence of the slowing-down environment on nuclear lifetime measurements by the Doppler-shift attenuation method

Normalization of the ( $d$ , ${}^{3}{He}$ ) reaction

Distorted-wave impulse-approximation calculations for quasifree cluster knockout reactions

Absolute spectroscopic factors from the ( $p, p α$ ) reaction at 100 MeV on $1 p$ -shell nuclei

Cluster spectroscopic factors for the $p$ -shell nuclei

High-spin levels in ${}^{191}{Pt}$ and ${}^{193}{Pt}$ and the triaxial rotor model

Finite-range distorted-wave Born-approximation study of the ( ${}^{4}{He}$ , ${}^{6}{Li}$ ) reaction on ${}^{12}C$ , ${}^{24}{Mg}$ , and ${}^{40}{Ca}$

Variational principle for the bloch unified reaction theory

Unitarity constraints with the Kapur-Peierls formalism

Approximate distorted-wave Born-approximation methods for ( $d, p$ ) stripping reactions

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