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Pairing backbending

M. S. Hussein and Hsi-Tseng Chen

Phys. Rev. C 12, 2103(R) (1975) - Published 1 December, 1975

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Excitation of deep lying hole states in ${}^{11}C$ , ${}^{15}O$ , ${}^{27}{Si}$ , and ${}^{57}{Ni}$ with the ( ${}^{3}{He}$ , $α$ ) reaction at 216 MeV

E. Gerlic, H. Langevin-Joliot, P. Roos, J. Van de Wiele, J. P. Didelez, and G. Duhamel

Phys. Rev. C 12, 2106(R) (1975) - Published 1 December, 1975

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The $α$ spectra were investigated in the discrete and continuum regions. In addition to the well known low lying levels, peaks and broad structures are observed for each nucleus at higher excitation energies. The bumps location and spreading, and their forward peaked distributions, suggest that they arise from neutron pickup in the deeper shells, i.e., $1 s$ for ${}^{12}C$ and ${}^{16}O$ , $1 p_{\frac{3}{2}}$ for ${}^{28}{Si}$ and $1 d + (1 p)$ for ${}^{58}{Ni}$ .

NUCLEAR REACTIONS ${}^{12}C$ , ${}^{16}O$ , ${}^{28}{Si}$ , ${}^{58}{Ni} ({}^{3}{He}, α)$ , $E = 216$ MeV; measured $σ (E α; θ)$ ; high excitation energy observed levels and broad structure in ${}^{11}C$ , ${}^{15}O$ , ${}^{27}{Si}$ , and ${}^{57}{Ni}$ .

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Shape implications of unhindered ${\frac{11}{2}}^{-} \to {\frac{11}{2}}^{-}$ $β$ decays in the region with $N < 82$ and $Z > 50$

J. van Klinken and S. J. Feenstra

Phys. Rev. C 12, 2111(R) (1975) - Published 1 December, 1975

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Unhindered ${\frac{11}{2}}^{-} \to {\frac{11}{2}}^{-}$ $β$ -ray transitions with $log ft$ values of 5.0 to 5.4 have been observed in the decay of ${}^{139}{Eu}$ , ${}^{139}{Sm}^{m}$ ,, and a new isotope ${}^{135}{Pm}$ . These transitions show no noticeable retardation and are not "shape forbidden." The shape of ${\frac{11}{2}}^{-}$ states with odd $N$ is not very different from the (prolate) shape of adjacent ${\frac{11}{2}}^{-}$ states with odd $Z$ .

RADIOACTIVITY $β$ decay between ${\frac{11}{2}}^{-}$ states of ${}^{139}{Eu}$ , ${}^{139}{Sm}$ , ${}^{139, 137, 135}{Pm}$ , ${}^{137, 135}{Nd}$ . Deduced $log ft$ values and shape differences.

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Excited analogs in ${}^{62}{Ni}$ and ${}^{63}{Cu} (p, n)$ and the weak-coupling model

C. Wong, J. D. Anderson, V. R. Brown, J. C. Davis, S. M. Grimes, V. A. Madsen, and C. H. Poppe

Phys. Rev. C 12, 2115(R) (1975) - Published 1 December, 1975

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The ground- and $2^{+}$ excited-state analog cross sections in ${}^{62}{Ni} (p, n)$ have been measured at bombarding energies of 16, 19, and 22 MeV. The measurements at 19 and 22 MeV confirm the weak coupling and Thankappan-True prediction of ∼ 0.4 for the fractionation of the $2^{+}$ strength into the ${\frac{7}{2}}^{-}$ excited analog transition in ${}^{63}{Cu} (p, n)$ . At 16 MeV, agreement with the weak-coupling model is poor. The discrepancy is possibly due to a preequilibrium contribution to the ${\frac{7}{2}}^{-}$ excited analog transition in ${}^{63}{Cu} (p, n)$ .

NUCLEAR REACTIONS ${}^{62}{Ni} (p, n)$ , $E = 16, 19, 22$ MeV; measured $σ (θ)$ ground-state and $2^{+}$ excited-state analog; calculated $σ (θ)$ $2^{+}$ using weak-coupling model.

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${}^{51}V (d, n_{0}) {}^{52}{Cr}$ reaction with polarized deuterons

P. A. Quin and J. A. Thomson

Phys. Rev. C 12, 2118(R) (1975) - Published 1 December, 1975

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The vector analyzing power of the ${}^{51}V (d, n_{0}) {}^{52}{Cr}$ reaction has been measured for laboratory angles between 5° and 40° at a deuteron energy of 11 MeV. Distorted-wave calculations are in qualitative agreement with the observed angular dependence of the vector analyzing power.

NUCLEAR REACTION ${}^{51}V (d, n_{0})$ , $E_{d} = 11.0$ MeV; measured polarization parameter $i T_{11} (θ)$ . Natural target. DWBA analysis.

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Level structure of ${}^{60}{Co}$

P. L. Jolivette, J. D. Goss, and C. P. Browne

Phys. Rev. C 12, 2121(R) (1975) - Published 1 December, 1975

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Level energies of ${}^{60}{Co}$ were measured using the ${}^{59}{Co} (d, p) {}^{60}{Co}$ reaction and the 100 cm broad range magnetic spectrograph. In order to excite nearly all states the data were taken at $θ_{lab} \geq 60 °$ . Energies for 89 states having $E_{x} \leq 3.2$ MeV were measured with uncertainties of 1 keV or less.

NUCLEAR REACTION ${}^{59}{Co} (d, p)$ , $E = 5 - 8$ MeV; measured $E_{x}$ in ${}^{60}{Co}$ .

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Further evidence for the recently discovered doublet in ${}^{48}{Ca}$

J. W. Tape, M. Ulrickson, N. Benczer-Koller, and Jack R. MacDonald

Phys. Rev. C 12, 2125(R) (1975) - Published 1 December, 1975

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Energy-dependent Hamiltonians, charge densities, and recoil effects

J. L. Friar

Phys. Rev. C 12, 2127(R) (1975) - Published 1 December, 1975

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Erratum: Extraction of $a_{nn}$ from the reaction $π^{-} d \to γ nn$

W. R. Gibbs, B. F. Gibson, and G. J. Stephenson, Jr.

Phys. Rev. C 12, 2130 (1975) - Published 1 December, 1975

Nonperturbative three-dimensional formalism for the study of the nucleon-nucleon interaction

Abraham Klein and Tsung-Shung H. Lee

Phys. Rev. C 12, 1381 (1975) - Published 1 November, 1975

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As an alternative to the dispersion theoretic approach to the two-nucleon interaction, we outline an improved version of an older method which derives both an interaction and the wave equation of which it is a part on an equal footing. This is done by reducing the Bethe-Salpeter equation to an equal time equation. The main improvement is that the interaction is given in nonperturbative form rather than as a sum of Feynman diagrams. As an illustration of the formalism, we test the validity of a simple version of the isobar model for the nucleon-nucleon problem and find it quantitatively inadequate. We discuss parenthetically how the existence of classes of reduction schemes is reflected as an ambiguity in the definition of the interaction.

NUCLEAR REACTIONS Theory of nucleon-nucleon interaction. Non-perturbative field theoretical method.

Lifetimes of the 2893- and 3464-keV levels of ${}^{40}{Ar}$

E. K. Warburton, J. W. Olness, and J. J. Kolata

Phys. Rev. C 12, 1392 (1975) - Published 1 November, 1975

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The recoil-distance method has been used in conjunction with the ${}^{27}{Al} ({}^{18}O, p α) {}^{40}{Ar}$ and ${}^{37}{Cl} (α, p) {}^{40}{Ar}$ reactions to measure mean lifetimes of 4.2±2.0 and 930±50 ps for the ${}^{40}{Ar}$ 2893- and 3464-keV levels, respectively. The excitation energies of these two levels were deduced to be 2892.60±0.11 and 3464.48±0.13 keV, respectively. The 3464-keV level is assigned $J^{π} = 6^{+}$ on the basis of the lifetime, the $γ$ -ray angular distribution, and previous ${}^{38}{Ar} (t, p) {}^{40}{Ar}$ results. The $E 2$ transition strengths of the ${}^{40}{Ar}$ $0^{+}$ - $2^{+}$ - $4^{+}$ - $6^{+}$ ground-state band are compared to those of ${}^{42}{Ca}$ and to shell-model calculations.

NUCLEAR REACTIONS ${}^{37}{Cl} (α, p)$ , $E = 12$ MeV, ${}^{27}{Al} ({}^{18}O, p α)$ , $E = 35$ MeV; measured recoil distance, $E_{γ}$ , and $σ_{γ} (θ)$ . Deduced $J^{π}$ , $T_{\frac{1}{2}}$ , $B (E 2)$ , $E_{x}$ . Natural and enriched targets, Ge(Li) detector.

( $p, 2 p$ ) and ( $p, pd$ ) reactions on ${}^{3}{He}$ at 45.0 MeV

S. N. Bunker, Mahavir Jain, C. A. Miller, J. M. Nelson, and W. T. H. van Oers

Phys. Rev. C 12, 1396 (1975) - Published 1 November, 1975

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The reactions ${}^{3}{He} (p, 2 p) d$ , ${}^{3}{He} (p, p d) p$ , and ${}^{3}{He} (p, 2 p) p n$ have been studied at 45.0 MeV using a coplanar symmetric geometry. Angular correlations have been obtained for both the ${}^{3}{He} (p, 2 p) d$ and ${}^{3}{He} (p, 2 p) d^{*}$ reactions. Within the framework of the plane-wave impulse approximation (PWIA) the extracted momentum distributions of the $p + d$ and $p + d^{*}$ systems in ${}^{3}{He}$ are compared with predictions calculated using relatively simple wave functions for ${}^{3}{He}$ , $d$ , and $d^{*}$ . Reasonable agreement between the shapes of the extracted and theoretical momentum distributions has been obtained. There exist differences between the momentum distributions extracted from the angular correlation and energy-sharing data. The PWIA predictions overestimate the cross sections by appreciable factors. The ${}^{3}{He} (p, p d)$ quasi-free scattering enhancements exhibit shifts in the peak position away from the minimum in the momentum of the spectator proton. The ${}^{3}{He} (p, 2 p) p n$ continua are to first approximation in agreement with differential phase-space distribution predictions if the kinematic region of low energy for the relative motion of the unobserved $n - p$ pair is excluded.

NUCLEAR REACTIONS ${}^{3}{He} (p, 2 p) {}^{2}H$ , ${}^{3}{He} (p, 2 p) p n$ , ${}^{3}{He} (p, p d) {}^{1}H$ , $T_{1} = 45.0$ MeV; measured $\frac{d σ}{(d T_{3} d Ω_{3} d Ω_{4})}$ in coplanar geometry; deduced momentum distributions using PWIA; compared with theoretical momentum distributions; investigated four-body continua.

Lifetime of the 3464-keV level in ${}^{40}{Ar}$

A. R. Poletti, D. C. Radford, and J. R. Southon

Phys. Rev. C 12, 1407 (1975) - Published 1 November, 1975

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Direct electronic timing has been used to measure the mean life of the 3464-keV state in ${}^{40}{Ar}$ . The state was populated by the ${}^{37}{Cl} (α, p) {}^{40}{Ar}$ reaction at 10.6 MeV, and the mean life was determined to be 1.00 ± 0.03 nsec. The measured lifetime in conjunction with other $γ$ -ray angular distributions and previous ${}^{38}{Ar} (t, p) {}^{40}{Ar}$ results allows an assignment of $J^{π} = 6^{+}$ to the level. The $E 2$ transition strengths of the ${}^{40}{Ar}$ $6^{+}$ → $4^{+}$ , $4^{+}$ → $2^{+}$ ′ and $2^{+}$ → $0^{+}$ transitions are compared to those in ${}^{42}{Ca}$ and to a weak-coupling calculation.

NUCLEAR REACTIONS ${}^{37}{Cl} (α, p)$ , $E = 10.6$ MeV. Measured particle- $γ$ time delay. Deduced $T_{\frac{1}{2}}$ , $B (E 2)$ , $J^{π}$ . Enriched target.

$E 1$ excitations in $A = 15$ nuclei

M. H. Harakeh, P. Paul, H. M. Kuan, and E. K. Warburton

Phys. Rev. C 12, 1410 (1975) - Published 1 November, 1975

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The ${}^{14}C (p, γ) {}^{15}N$ reaction was studied from $E_{p} = 2.8 to 30$ MeV corresponding to $E_{x} = 13 to 38$ MeV in ${}^{15}N$ covering the region of the lowest $T = \frac{3}{2}$ states as well as the giant dipole resonance (GDR). The ${}^{14}N (p, γ) {}^{15}O$ reaction measurements were extended for excitation regions from $E_{x} = 24 - 33.5$ MeV thus covering the analogous regions in ${}^{15}O$ and ${}^{15}N$ . Angular distributions obtained in the first reaction at the resonance energies of $E_{p} = 4.83, 5.62, 6.65, 6.925, 10.0, 11.0, 12.35, 13.6, and 16.4$ MeV indicated large negative $a_{2}$ coefficients in all cases. The new narrow ( $Γ_{c . m .} = 90$ keV) resonance at 6.925 MeV has $J^{π} = {\frac{3}{2}}^{+}$ and $T = \frac{1}{2}$ . A careful comparison of the ${}^{15}N (γ, p_{0}) {}^{14}C$ and ${}^{15}O (γ, p_{0}) {}^{14}N$ reactions is used to extract the $T = \frac{3}{2} and \frac{1}{2}$ components of the GDR in $A = 15$ . Most of the $T = \frac{3}{2}$ $E 1$ strength is located near $E_{x} = 26$ MeV. A microscopic calculation of $J^{π} \leq {\frac{5}{2}}^{+}$ states with $T = \frac{1}{2} and \frac{3}{2}$ in a 2h-1p and 1h basis of good isospin gives good agreement with the observed depleted $B (E 1)$ values from the lowest $T = \frac{3}{2}$ states and reproduces the location of the collective $T = \frac{3}{2}$ $E 1$ states near 26 MeV. It also describes well the distribution of $T = \frac{1}{2}$ collective $E 1$ strength. Using this agreement with the theory which contains no adjusted parameters an effective symmetry potential of $U = 28$ MeV is extracted from the isospin energy splitting. This value is smaller than the typical 60 MeV found in heavier nuclei but agrees with a recent model-independent limit and with other cases of $| T_{z} | = \frac{1}{2}$ nuclei.

NUCLEAR REACTIONS ${}^{15}N$ , ${}^{14}C (p, γ)$ , $E_{p} = 2.8 - 30$ MeV, measured $\frac{d σ}{d Ω (90 °)}$ , angular distributions. ${}^{15}O$ , ${}^{14}N (p, γ)$ , $E_{x} = 24 - 33.5$ MeV, measured $\frac{d σ}{d Ω (90 °)}$ . Calculated 2h-1p, 1h states of $A = 15$ and $B (E 1)$ . Deduced location of $T = \frac{3}{2} and \frac{1}{2}$ component of GDR and effective symmetry potential.

Cross section of slow neutrons on parahydrogen

J. Callerame, D. J. Larson, S. J. Lipson, and R. Wilson

Phys. Rev. C 12, 1423 (1975) - Published 1 November, 1975

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The total cross section of slow neutrons on gaseous parahydrogen has been measured at several temperatures near 20 K and with pressures ranging from 250 to 750 Torr. A previous experiment had suggested that the cross section would exhibit a significant pressure dependence. However, no such pressure dependence was observed. The data give a value for the neutron-proton coherent scattering length of (-3.733±0.004) × $10^{- 13}$ cm, in agreement with the latest liquid mirror measurements.

NUCLEAR REACTIONS ${}^{1}H (n, n)$ ; $E = 4.2 - 4.6$ meV; parahydrogen; measured total neutron cross section; deduced coherent scattering length.

Cross section of slow neutrons on orthodeuterium

J. Callerame, D. J. Larson, S. J. Lipson, and R. Wilson

Phys. Rev. C 12, 1428 (1975) - Published 1 November, 1975

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The total cross section of slow neutrons on gaseous orthodeuterium has been measured near 22 K and at pressures ranging from 145 to 300 Torr. The results give rise to a set of values for the neutron-deuteron scattering lengths that are in significant disagreement with the latest liquid mirror measurements. The relationship between the scattering lengths was found to be: ${(2 a_{4} + a_{2})}^{2} + (\frac{5}{4}) {(a_{4} - a_{2})}^{2} = (2.313 \pm 0.003) \times 10^{- 24}$ ${cm}^{2}$ .

NUCLEAR REACTIONS ${}^{2}H (n, n)$ ; $E = 4.2$ meV; orthodeuterium; measured total neutron cross section; deduced relationship between $a_{2}$ and $a_{4}$ .

Resonating-group study of $N$ + ${}^{16}O$ scattering with a generator-coordinate technique

D. R. Thompson and Y. C. Tang

Phys. Rev. C 12, 1432 (1975) - Published 1 November, 1975

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The scattering of nucleons by ${}^{16}O$ is studied with the resonating-group method. The ${}^{16}O$ wave function used is a translationally invariant antisymmetrized product of single-particle wave functions of ${(1 s)}^{4} {(1 p)}^{12}$ configuration in a harmonic-oscillator well having an appropriately chosen width parameter. A generator-coordinate technique is employed to facilitate the computation of the nonlocal interaction between the nucleon and the ${}^{16}O$ nucleus. This technique is discussed in some detail in order to demonstrate its utility in a nuclear problem involving a relatively large number of nucleons. Calculated results are compared with experimental data over a wide range of energies, and it is found that the agreement is in general quite satisfactory. Also, the result shows that in this particular problem the heavy-particle pickup process, which is properly taken into consideration by the use of a totally antisymmetric wave function, has a relatively small contribution.

NUCLEAR REACTIONS ${}^{16}O (N, N)$ ; calculated phase shifts, $σ (θ)$ , and $P (θ)$ . Resonating-group method with generator-coordinate technique.

Back-angle elastic alpha scattering from ${}^{89}Y$ and ${}^{90, 91, 94}{Zr}$

M. Wit, J. Schiele, K. A. Eberhard, and J. P. Schiffer

Phys. Rev. C 12, 1447 (1975) - Published 1 November, 1975

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Excitation functions and angular distributions for elastic $α$ scattering from target nuclei around $A = 90$ have been measured in an effort to obtain a precise picture of the cross sections at backward angles. Excitation functions between $E_{α} (lab) = 18 through 25$ MeV for $α$ + ${}^{89}Y$ and $α$ + ${}^{90, 91, 94}{Zr}$ have been measured in steps of 500 keV or less at angles between 141° and 176° (lab). Near 180°, narrow (about 1 MeV) minima, with a drop in cross section by more than an order of magnitude, are observed around $E_{α} = 23$ MeV for the $α$ + ${}^{89}Y$ and $α$ + ${}^{90, 91}{Zr}$ elastic scattering. A similar, but less pronounced, structure is seen in the excitation function for $α$ + ${}^{94}{Zr}$ . Angular distributions between 48.5° and 176° (lab) measured at several energies in 2.5° steps show a regular diffractionlike pattern over the entire angular range. A standard four-parameter Woods-Saxon potential is found to be sufficient to provide a detailed fit to the experimental data including the minima in the excitation functions at back angles.

NUCLEAR REACTIONS ${}^{89}Y (α, α_{0})$ , ${}^{90, 91, 94}{Zr} (α, α_{0})$ , $E = 18 - 25$ MeV; measured $σ (E, θ)$ ; optical-model analysis. Enriched targets; $θ = 48.5 ° - 176 °$ ; $Δ θ = 2.5 °$ ; calculated $σ (E, θ)$ .

Proton states in ${}^{85}Y$

L. R. Medsker, G. S. Florey, H. T. Fortune, and R. M. Wieland

Phys. Rev. C 12, 1452 (1975) - Published 1 November, 1975

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The ${}^{84}{Sr} ({}^{3}{He}, d) {}^{85}Y$ reaction has been studied at a bombarding energy of 18 MeV to extend the systematics of proton states in the odd- $A$ yttrium nuclei. Thirty-seven states in the previously uninvestigated ${}_{39}^{85}Y_{46}$ were observed. A distorted-wave analysis was used to determine $l$ values and spectroscopic strengths. The ground state of ${}^{85}Y$ is assigned $J^{π} = \frac{1}{2^{-}}$ and the first excited state (at 20 keV) $\frac{9}{2^{+}}$ . The results are compared with previous ( ${}^{3}{He}$ , $d$ ) reaction studies on ${}^{86}{Sr}$ and ${}^{88}{Sr}$ .

NUCLEAR REACTIONS ${}^{84}{Sr} ({}^{3}{He}, d)$ , $E = 18$ MeV; enriched target; measured $σ (E_{d}, θ)$ ; deduced ${}^{85}Y$ levels, $l$ , $j$ , $G_{lj}$ .

Neutron-capture gamma rays from ${}^{116}{Sn}$ and ${}^{122}{Sn}$ and the valence model

M. R. Bhat, R. E. Chrien, G. W. Cole, and O. A. Wasson

Phys. Rev. C 12, 1457 (1975) - Published 1 November, 1975

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Capture $γ$ -ray intensities from resonances of ${}^{116}{Sn}$ and ${}^{122}{Sn}$ have been measured. The results lead to binding energies of 6944 ± 2.0 keV for the product nucleus ${}^{117}{Sn}$ and 5948 ± 3.0 keV for the product nucleus ${}^{123}{Sn}$ . Resonance spins were determined: in ${}^{116}{Sn}$ , $E_{0} = 147.9$ and $E_{0} = 632$ eV resonances are $J = \frac{3}{2}$ , $l = 1$ ; in ${}^{122}{Sn}$ , $E_{0} = 106.9$ eV resonance is $J = \frac{3}{2}$ , $l = 1$ ; $E_{0} = 259.9$ eV resonance is $J = \frac{1}{2}$ , $l = 1$ . The measured partial widths are compared to single-particle transition model predictions. The model fails to predict the observed widths.

NUCLEAR REACTIONS Resonance capture in ${}^{116}{Sn}$ , ${}^{122}{Sn}$ , partial widths, spins, parities, angular distributions, valence model predictions.

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Pairing backbending

Excitation of deep lying hole states in ${}^{11}C$ , ${}^{15}O$ , ${}^{27}{Si}$ , and ${}^{57}{Ni}$ with the ( ${}^{3}{He}$ , $α$ ) reaction at 216 MeV

Shape implications of unhindered ${\frac{11}{2}}^{-} \to {\frac{11}{2}}^{-}$ $β$ decays in the region with $N < 82$ and $Z > 50$

Excited analogs in ${}^{62}{Ni}$ and ${}^{63}{Cu} (p, n)$ and the weak-coupling model

${}^{51}V (d, n_{0}) {}^{52}{Cr}$ reaction with polarized deuterons

Level structure of ${}^{60}{Co}$

Further evidence for the recently discovered doublet in ${}^{48}{Ca}$

Energy-dependent Hamiltonians, charge densities, and recoil effects

Erratum: Extraction of $a_{nn}$ from the reaction $π^{-} d \to γ nn$

Nonperturbative three-dimensional formalism for the study of the nucleon-nucleon interaction

Lifetimes of the 2893- and 3464-keV levels of ${}^{40}{Ar}$

( $p, 2 p$ ) and ( $p, pd$ ) reactions on ${}^{3}{He}$ at 45.0 MeV

Lifetime of the 3464-keV level in ${}^{40}{Ar}$

$E 1$ excitations in $A = 15$ nuclei

Cross section of slow neutrons on parahydrogen

Cross section of slow neutrons on orthodeuterium

Resonating-group study of $N$ + ${}^{16}O$ scattering with a generator-coordinate technique

Back-angle elastic alpha scattering from ${}^{89}Y$ and ${}^{90, 91, 94}{Zr}$

Proton states in ${}^{85}Y$

Neutron-capture gamma rays from ${}^{116}{Sn}$ and ${}^{122}{Sn}$ and the valence model

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