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Study of the reaction ${}^{26}{Mg} (p, α γ) {}^{23}{Na}$ through $α - γ$ angular correlations

R. Prasad, A. Hofmann, and F. Vogler

Phys. Rev. C 10, 1577(R) (1974) - Published 1 October, 1974

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In the reaction ${}^{26}{Mg} (p, α γ)$ the angular distributions of the $α$ particles leading to the ground state, first, second, fourth plus fifth excited states, and absolute double differential cross sections for $α_{1}, γ_{1 \to 0}$ , $α_{2}, γ_{2 \to 1}$ , and $α_{5}, γ_{5 \to 2}$ have been measured at an average proton energy of 9.88 MeV. The emergent $α$ particles were detected with a multidetector arrangement consisting of eight silicon surface-barrier detectors. For the coincidence measurements a Ge(Li) detector placed in the reaction plane was used for the detection of $γ$ rays. It has been found that the averaged differential and double differential cross sections can be described with the Hauser-Feshbach theory. An additional correlation measurement has been done in order to check the symmetry predicted for compound-nuclear reactions. The measurements agree with the predicted symmetry.

NUCLEAR REACTIONS ${}^{26}{Mg} (p, α γ)$ , $\bar{E}$ MeV, measured differential and double differential cross sections. Hauser-Feshbach analyses of angular distributions and angular correlations; enriched target.

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Pauli corrections for correlated wave functions

Paul Goldhammer and James A. Pintar

Phys. Rev. C 10, 1581(R) (1974) - Published 1 October, 1974

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Variational calculation of the on- and off-shell $T$ matrix

G. L. Payne and J. D. Perez

Phys. Rev. C 10, 1584(R) (1974) - Published 1 October, 1974

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The use of a Schwinger-type variational principle for the evaluation of the two-body $T$ matrix $T (p^{'}, p, E)$ is shown to be an efficient and accurate method both on and off the energy shell. Using standard trial functions all of the matrix elements for the Reid soft-core interaction can be determined by simple recursion relations, and the evaluation of the $T$ matrix is reduced to solving a set of simultaneous equations.

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Lifetimes of the first two excited states of ${}^{66}{Ga}$

F. S. Dietrich, L. F. Hansen, and R. P. Koopman

Phys. Rev. C 10, 1587(R) (1974) - Published 1 October, 1974

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The 44- and 66-keV levels of ${}^{66}{Ga}$ have been excited by the ${}^{66}{Zn} (p, n) {}^{66}{Ga}$ reaction, and their decay $γ$ rays timed with respect to the pulsed proton beam. The extracted half-lives are 17.3 ± 2.0 ns for the 44-keV level, and 15.4 ± 0.4 ns for the 66-keV level.

NUCLEAR REACTIONS ${}^{66}{Zn} (p, n γ)$ , $E_{p} = 7.5 - 10$ MeV, pulsed beam. Measured $E_{γ}$ , $p - γ$ timing. ${}^{66}{Ga}$ deduced $T_{\frac{1}{2}}$ . Enriched target.

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Attempted Coulomb excitation of the spontaneous-fission isomeric state in ${}^{239}{Pu}$

C. E. Bemis, Jr., F. Plasil, R. L. Ferguson, E. E. Gross, and A. Zucker

Phys. Rev. C 10, 1590(R) (1974) - Published 1 October, 1974

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Attempts to Coulomb excite the 8.5 μsec spontaneous-fission isomeric state in ${}^{239}{Pu}$ with 100- and 117-MeV ${}^{20}{Ne}$ ions have led to negative results. A cross section upper limit of 3.2 × $10^{- 34}$ ${cm}^{2}$ , integrated over ${}^{20}{Ne}$ laboratory scattering angles 90° → 180°, was determined.

NUCLEAR REACTIONS ${}^{239}{Pu}$ ( ${}^{20}{Ne}$ , ${}^{20}{Ne'}$ ) spontaneous-fission isomer, $E = 100 and 117$ MeV; measured $T_{\frac{1}{2}}$ , coinc, Coulomb excitation yield; deduced upper limit $σ (E, θ)$ for $θ = 90 - 180 °$ . Enriched target.

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Analog transitions in the $A = 30$ system

E. Kuhlmann and S. S. Hanna

Phys. Rev. C 10, 1593(R) (1974) - Published 1 October, 1974

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The $T = 1$ -ray decay of the $2^{+}$ , $γ$ state at $E_{x} = 4.183$ MeV in ${}^{30}P$ was investigated. A new branch (2 ± 1)% to the $0^{+}$ , $T = 1$ state at $E_{x} = 0.677$ MeV was found. The decay mode is discussed in terms of isospin and an estimate of the lifetime of this state is derived.

NUCLEAR REACTION ${}^{29}{Si} (p, γ)$ , $E = 0.70 - 0.75$ MeV, measured $σ (E; E_{γ}; θ)$ , deduced ${}^{30}P$ level branching. Enriched ${}^{29}{Si}$ target.

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Distortions in angular correlations for the reaction ${}^{11}B (d, p γ) {}^{12}B^{*}$ (0.95 MeV) at low energy

U. Karfunkel, J. P. F. Sellschop, and M. C. Stemmet

Phys. Rev. C 10, 1596(R) (1974) - Published 1 October, 1974

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For the reaction ${}^{11}B (d, p γ) {}^{12}B^{*}$ (0.95 MeV) at $E_{d} = 1$ MeV, 15 angular correlation measurements covering the range $θ_{d p} = 22 ° to 160 °$ give values of the anisotropy ( $ε$ ) and the deviation of the measured symmetry axis from the recoil axis ( $Δ Φ$ ). The values of $Δ Φ$ remain small and constant throughout, whereas the values of $ε$ increase sharply at backward angles to a high, possibly constant value. These results are surprising in the simplicity of their behavior and are contrary to some features and anticipations of previously reported measurements.

NUCLEAR REACTIONS ${}^{11}B (d, p γ) {}^{12}B^{*}$ (0.95), $E_{d} = 1.0$ MeV, measured $p - γ$ coin., $θ_{p} = 20 - 160 °$ , $Δ θ = 10 °$ . Calculated anisotropies, phase shifts; deduced distortions.

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Autoionization in the beta decays of ${}^{210}{Bi}$ and ${}^{204}{Tl}$

B. P. Pathak

Phys. Rev. C 10, 1599(R) (1974) - Published 1 October, 1974

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Autoionization accompanying $β$ decays of ${}^{204}{Tl}$ and ${}^{210}{Bi}$ has been studied. The $K -$ and $L -$ shell autoionization probabilities for ${}^{204}{Tl}$ have been found to be (1.06 ± 0.03) × $10^{- 4}$ and (19 ± 1) × $10^{- 4}$ , respectively. The $K$ -shell autoionization probability for the ${}^{210}{Bi}$ has been obtained as (1.21 ± 0.05) × $10^{- 4}$ .

RADIOACTIVITY ${}^{204}{Tl}$ , ${}^{210}{Bi}$ , measured $P_{K}$ , $P_{L}$ , Ge(Li) detector.

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Oscillating forward angle cross sections for the ${}^{60}{Ni}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{62}{Ni}_{g . s .}$ transition

M. J. LeVine, A. J. Baltz, P. D. Bond, J. D. Garrett, S. Kahana, and C. E. Thorn

Phys. Rev. C 10, 1602(R) (1974) - Published 1 October, 1974

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The yield of the ${}^{60}{Ni}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{62}{Ni}_{g . s .}$ reaction at an incident energy of 65 MeV has been measured to forward angles using a QDDD spectrometer. Predicted, strong oscillations in the forward angle differential cross section are indeed observed. The detailed shape of this angular distribution can be reproduced by distorted-wave Born-approximation calculations employing an optical potential more strongly absorbing in the nuclear interior, and more weakly absorbing at the nuclear surface than previously used.

NUCLEAR REACTIONS ${}^{60}{Ni}$ ( ${}^{18}O$ , ${}^{16}O$ ); $E = 65$ MeV measured $σ (θ)$ ; DWBA analysis.

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Cross sections for the production of mass-6 and mass-7 nuclides in the proton-induced spallation of ${}^{20}{Ne}$

Lolo M. Panggabean, Sam M. Austin, and Helmut Laumer

Phys. Rev. C 10, 1605(R) (1974) - Published 1 October, 1974

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Cross sections for proton-induced spallation of ${}^{20}{Ne}$ leading to nuclides with mass 6 or mass 7 were measured at proton energies between 30 and 40 MeV. Time-of-flight techniques were used for mass identification.

NUCLEAR REACTIONS ${}^{20}{Ne} + p$ $E = 30.0, 35.0, 40.0$ MeV; measured spallation $σ$ for producing masses 6, 7; gas targets. Discuss astrophysical significance.

Erratum: Collective multipole expansion of the inelastic scattering continuum

M. B. Lewis

Phys. Rev. C 10, 1609 (1974) - Published 1 October, 1974

Erratum: Nuclear $g$ factor of the 204-keV level in ${}^{95}{Mo}$

D. A. Garber, M. Behar, Z. W. Grabowski, and Wm. C. King

Phys. Rev. C 10, 1609 (1974) - Published 1 October, 1974

( $p, {}^{3}{He}$ ) and ( $p, t$ ) reactions on ${}^{29}{Si}$

H. Nann, W. Benenson, W. A. Lanford, and B. H. Wildenthal

Phys. Rev. C 10, 1001 (1974) - Published 1 September, 1974

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Differential cross sections of the ${}^{29}{Si} (p, {}^{3}{He}) {}^{27}{Al}$ and ${}^{29}{Si} (p, t) {}^{27}{Si}$ reactions between $θ_{lab} = 4 and 60 °$ have been measured at 40.1 MeV bombarding energy. Assignments of the $L$ transfers on the basis of comparisons to distorted-wave Born approximation (DWBA) calculations yield several new spin and parity assignments for states in ${}^{27}{Si}$ . The experimental differential cross sections of the transitions to several of the low-lying mirror pairs of final states in ${}^{27}{Al}$ and ${}^{27}{Si}$ are compared to the results of microscopic DWBA calculations in order to study the spin-isospin dependence of the interaction potential in the two-nucleon transfer reaction and to test current shell-model wave functions for the nuclear states involved.

NUCLEAR REACTIONS ${}^{29}{Si} (p, t)$ , ${}^{29}{Si} (p, {}^{3}{He})$ , $E_{p} = 40.1$ MeV; measured $σ (E_{t}, E_{{}^{3}{He}}, θ)$ ; enriched target, deduced energies, $L$ values, normalization factors for states of ${}^{27}{Al}$ and ${}^{27}{Si}$ .

Structure of ${}^{42}{Ti}$ from the ${}^{40}{Ca} ({}^{3}{He}, n) {}^{42}{Ti}$ reaction

W. P. Alford, R. A. Lindgren, D. Elmore, and R. N. Boyd

Phys. Rev. C 10, 1013 (1974) - Published 1 September, 1974

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The structure of ${}^{42}{Ti}$ has been investigated using the ${}^{40}{Ca} ({}^{3}{He}, n) {}^{42}{Ti}$ reaction at a beam energy of 15 MeV. Comparisons between measured angular distributions and distorted wave Born approximation (DWBA) calculations provide a number of new spin assignments. The DWBA analysis also provides an estimate of $p$ state admixtures in the low-lying states of the ${(f_{\frac{7}{2}})}^{2}$ configuration. A comparison with the results of the ${}^{40}{Ca} (t, p) {}^{42}{Ca}$ reaction demonstrates the analog character of many levels in ${}^{42}{Ti}$ and ${}^{42}{Ca}$ up to about 6.5 MeV. Above 3 MeV, in states involving large $p^{2}$ or $f p$ components in the wave function, transition strengths are comparable in both two-proton and two-neutron transfers. The states in ${}^{42}{Ca}$ generally occur at an excitation energy several hundred keV above the corresponding analog in ${}^{42}{Ti}$ , suggesting that the $f_{\frac{7}{2}} - p_{\frac{3}{2}}$ single particle splitting is slightly greater in ${}^{42}{Ca}$ .

NUCLEAR REACTIONS, STRUCTURE ${}^{40}{Ca} ({}^{3}{He}, n)$ $E = 15$ MeV; measured angular distributions, DWBA deduced $J$ , $π$ . Comparison ${}^{42}{Ti}$ , ${}^{42}{Ca}$ analog states.

Finite-range distorted-wave Born-approximation analysis of strongly oscillating angular distributions of heavy-ion reactions

M. F. Werby and W. Tobocman

Phys. Rev. C 10, 1022 (1974) - Published 1 September, 1974

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Angular distributions of the ${}^{32}S$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{36}{Ar}$ reaction are characterized by strong oscillations for the ground state and to a lesser extent for the first excited state for $E_{lab} = 45$ MeV. We show that such a process can be described by a finite-range no recoil distorted-wave Born-approximation analysis using weakly absorbing optical model potentials and an $α$ -particle cluster model description of the nuclei involved. Good fits to the data were obtained with this model. The influence of different choices of optical model potentials is examined.

NUCLEAR REACTIONS ${}^{32}S$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{36}{Ar}$ ; $E = 45$ MeV, calculated differential cross sections; ground state, first excited state; finite-range, no recoil, DWBA.

Differential cross sections for charged-particle emission in reactions of 58-MeV $α$ particles with ${}^{12}C$ , ${}^{16}O$ , and ${}^{54}{Fe}$ : Comparison with the exciton model of pre-equilibrium particle emission

F. E. Bertrand, R. W. Peelle, and C. Kalbach-Cline

Phys. Rev. C 10, 1028 (1974) - Published 1 September, 1974

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Cross sections differential in energy and angle are presented for the proton, deuteron, triton, and $α$ particles from reactions of 58-MeV $α$ particles on C, O, and ${}^{54}{Fe}$ , and the angle-integrated differential spectra are compared with the predictions of an extended exciton model of pre-equilibrium reactions. The experimental results were obtained with a semiconductor telescope and cover the whole energy range above a few MeV. Except for oxygen, the results are given with uncertainties of 5-10%; for oxygen, relative intensities are valid at a given angle, but the absolute uncertainty is about 50%. The high-energy segment of the spectrum is highly anisotropic for all emitted particles, but for low energies the evaporation mechanism may be important for proton and perhaps $α$ -particle emission. The inelastic $α$ spectra from ${}^{54}{Fe}$ are more similar in shape to previous observations of the ${}^{54}{Fe} (p, x p)$ spectra than to the presently reported ${}^{12}C (α, x α)$ results. Comparisons are made between the data and the exciton model assuming an initial configuration of four particles. The model was extended to recognize that for reactions of incident $α$ particles, emitted $α$ particles and even deuteron, triton, and ${}^{3}{He}$ particles may contribute a significant fraction of the pre-equilibrium emission. The empirical internormalization factor for the relative intensity of various exit particles (mass number $p_{β}$ ) is found to be consistent with the ( $p_{β}!$ ) value deduced previously from results with incident protons. Using matrix elements deduced from systematics, the predictions for ${}^{12}C$ yield qualitatively correct shapes with normalization for the various particle types correct to within a factor of 6. For ${}^{54}{Fe}$ , the magnitude and shape of the predicted integral spectra are good for secondary protons and deuterons, but the predicted spectra fall off far too rapidly at high energies for tritons and $α$ particles.

NUCLEAR REACTIONS ${}^{12}C$ , ${}^{16}O$ , ${}^{54}{Fe}$ , ( $α, α^{'} x$ ), ( $α, t x$ ), ( $α, d x$ ), ( $α, p x$ ), $E = 58$ MeV; Ge(Li); measured $σ (E_{α^{'}}, E_{t}, E_{d}, E_{p}, θ)$ ; deduced $σ (E)$ . $2 ≲ E_{α}$ , $E_{t}$ , $E_{d}$ , $E_{p} ≲ 60$ MeV. Comparison with extended exciton model of preequilibrium particle emission.

Analytic distorted waves for intermediate-energy alpha particles

R. T. Janus and I. E. McCarthy

Phys. Rev. C 10, 1041 (1974) - Published 1 September, 1974

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It is shown that physically consistent and realistic values of all the parameters can be found for a model that represents the distorted waves in the distorted-wave Born approximation for collective $α$ inelastic scattering by a properly normalized decaying plane wave. The significance of this achievement in a thoroughly understood reaction is that we are now able to obtain analytic distorted waves that are sufficiently realistic and sufficiently simple to use in off-shell distorted-wave impulse approximation calculations of reactions of current interest requiring microscopic descriptions of the reaction mechanism.

NUCLEAR REACTIONS ${}^{62}{Ni} (α, α^{'})$ , $E = 33, 50, 100$ MeV; ${}^{24}{Mg}$ , ${}^{48}{Ti} (α, α^{'})$ , $E = 41$ MeV; ${}^{32}S$ , ${}^{88}{Sr} (α, α^{'})$ , $E = 42$ MeV; analytic DWBA, calculated $σ (θ)$ .

Production of the light elements lithium, beryllium, and boron by proton-induced spallation of ${}^{16}O$

Helmut Laumer, Sam M. Austin, and Lolo M. Panggabean

Phys. Rev. C 10, 1045 (1974) - Published 1 September, 1974

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Astrophysically important cross sections for the production of isotopes of lithium, beryllium, and boron in the proton-induced spallation of ${}^{16}O$ were measured for proton energies between 30 and 42 MeV. A time-of-flight method was used for mass identification. The astrophysical significance of the results is discussed.

NUCLEAR REACTIONS ${}^{16}O + p$ ; $E = 30.0, 33.7, 37.9, 41.9$ MeV; measured spallation $σ$ for producing masses 6, 7, 10, 11. Gas targets. Discuss astrophysical significance.

Vector analyzing power and cross section for the reaction ${}^{36}{Ar} (\vec{d}, p) {}^{37}{Ar}$

S. Sen, W. A. Yoh, and M. T. McEllistrem

Phys. Rev. C 10, 1050 (1974) - Published 1 September, 1974

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Cross section and vector analyzing power for the reaction ${}^{36}{Ar} (\vec{d}, p) {}^{37}{Ar}$ have been measured for an incident deuteron energy of 10.02 MeV. The data have been analyzed in the framework of the distorted-wave Born approximation. The $J$ dependence of the vector analyzing power permits unambiguous spin-parity assignments to be made for 19 states in ${}^{37}{Ar}$ with excitation energies up to 8.40 MeV. Tentative spin assignments are made to the states with excitation energies 8.093 and 8.399 MeV. Most probable spin-parity values for the constituents of the unresolved (5.880 + 5.961) MeV and (7.246 + 7.282) MeV groups in the spectra are suggested from an analysis of the data. Spectroscopic factors are extracted using deuteron optical model potential parameters obtained from a simultaneous analysis of the elastic cross section and vector analyzing power data. Results of the analysis for the 2.217 and 7.131 MeV states indicate the possible importance of reaction processes other than the one-step stripping mechanism.

NUCLEAR REACTIONS ${}^{36}{Ar} (\vec{d}, d)$ , $\vec{d}, p$ , $E = 10.02$ MeV; measured $σ (θ)$ , $i T_{11} (θ)$ ; deduced $J$ , $π$ , $S$ by DWBA analysis. Enriched target.

Statistical analysis of the energy dependence of ${}^{12}C$ + ${}^{12}C$ cross sections

D. Shapira, R. G. Stokstad, and D. A. Bromley

Phys. Rev. C 10, 1063 (1974) - Published 1 September, 1974

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A statistical analysis has been made of the narrow structure appearing in the excitation functions for ${}^{12}C$ + ${}^{12}C$ induced interactions for elastic scattering ( $13.5 \leq E_{c . m .} \leq 37.5$ MeV), inelastic scattering ( $20 \leq E_{c . m .} \leq 30$ MeV), and $α$ particle production ( $16 \leq E_{c . m .} \leq 21$ MeV). Average fluctuation widths, strengths and cross correlations predicted by the statistical models of nuclei and of nuclear reactions are compared with those obtained from the analysis of suitably reduced experimental data. Good agreement is found. The effects of gross structure, possible structure of intermediate width, and a small ratio of level width to spacing ( $\frac{Γ}{D}$ ) on the analysis of the narrow structure were studied using synthetic excitation functions. Appropriate correction factors were obtained in this way for application to parameters extracted directly from the reduced data. The results of the studies with synthetic excitation functions support the validity of the present statistical analysis. Compound processes are found to contribute up to ∼20% of the measured elastic scattering cross section at 90° c.m. New experimental results reported herein for ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}^{*}$ reactions also suggest a large direct component, in contrast to earlier measurements on this reaction at lower energies. Hauser-Feshbach predictions of absolute compound cross sections show over-all good agreement with the average fluctuating cross sections deduced from the experimental data. It is concluded that the structure with widths ∼0.3 MeV observed in the experimental excitation functions studied here is of statistical origin, and that the statistical model can also explain the occasional structural features with individual widths up to ∼0.8 MeV. Apart from the gross structure associated with potential scattering, no evidence is found in the elastic scattering data for structure requiring nonstatistical mechanisms for its explanation.

NUCLEAR REACTIONS Statistical model analysis of ${}^{12}C$ ( ${}^{12}C$ , ${}^{12}C$ ) ${}^{12}C$ , $13.5 \leq E_{c . m .} \leq 37.5$ MeV; ${}^{12}C$ ( ${}^{12}C$ , ${}^{12}C$ ) ${}^{12}C$ (4.43) $20 \leq E_{c . m .} \leq 30$ MeV; ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}^{*}$ $16 \leq E_{c . m .} \leq 21$ MeV. Deduced average widths, fluctuation intensity, cross correlations. Hauser-Feshbach calculations. Measured $\frac{d σ}{d Ω}$ for ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}^{*}$ at $θ_{α} ≃ 0 °$ , $16 \leq E_{c . m .} \leq 21$ MeV.

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Study of the reaction ${}^{26}{Mg} (p, α γ) {}^{23}{Na}$ through $α - γ$ angular correlations

Pauli corrections for correlated wave functions

Variational calculation of the on- and off-shell $T$ matrix

Lifetimes of the first two excited states of ${}^{66}{Ga}$

Attempted Coulomb excitation of the spontaneous-fission isomeric state in ${}^{239}{Pu}$

Analog transitions in the $A = 30$ system

Distortions in angular correlations for the reaction ${}^{11}B (d, p γ) {}^{12}B^{*}$ (0.95 MeV) at low energy

Autoionization in the beta decays of ${}^{210}{Bi}$ and ${}^{204}{Tl}$

Oscillating forward angle cross sections for the ${}^{60}{Ni}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{62}{Ni}_{g . s .}$ transition

Cross sections for the production of mass-6 and mass-7 nuclides in the proton-induced spallation of ${}^{20}{Ne}$

Erratum: Collective multipole expansion of the inelastic scattering continuum

Erratum: Nuclear $g$ factor of the 204-keV level in ${}^{95}{Mo}$

( $p, {}^{3}{He}$ ) and ( $p, t$ ) reactions on ${}^{29}{Si}$

Structure of ${}^{42}{Ti}$ from the ${}^{40}{Ca} ({}^{3}{He}, n) {}^{42}{Ti}$ reaction

Finite-range distorted-wave Born-approximation analysis of strongly oscillating angular distributions of heavy-ion reactions

Differential cross sections for charged-particle emission in reactions of 58-MeV $α$ particles with ${}^{12}C$ , ${}^{16}O$ , and ${}^{54}{Fe}$ : Comparison with the exciton model of pre-equilibrium particle emission

Analytic distorted waves for intermediate-energy alpha particles

Production of the light elements lithium, beryllium, and boron by proton-induced spallation of ${}^{16}O$

Vector analyzing power and cross section for the reaction ${}^{36}{Ar} (\vec{d}, p) {}^{37}{Ar}$

Statistical analysis of the energy dependence of ${}^{12}C$ + ${}^{12}C$ cross sections

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