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Reply to "Comment on `Statistical significance of spreading widths for doorway states"'

William M. MacDonald

Phys. Rev. C 21, 1642 (1980) - Published 1 April, 1980

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In response to the Comment of Lane, Lynn, and Moses, I demonstrate that my strength function analysis of fine structure in doorways is not sensitive to "imperfections" of data in the "wings." The "error weighting function" which relates errors in reduced widths ${γ_{λ}}^{2}$ to an error in the spreading width $Γ^{↓}$ is derived for least-squares fitting based either on the Lorentz-weighted strength function or on the summed strength function favored by Lane, Lynn, and Moses. The spreading width derived from the summed strength function is shown to be more sensitive to errors in ${γ_{λ}}^{2}$ in the wings of the fine structure pattern.

NUCLEAR REACTIONS Isobaric analog resonances, fine structure, doorway states.

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Axial blocking measurement of the ${}^{28}{Si}$ 12.291 MeV level width

E. Fuschini, F. Malaguti, A. Uguzzoni, and E. Verondini

Phys. Rev. C 21, 1646(R) (1980) - Published 1 April, 1980

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The width of the 12.291 MeV level of ${}^{28}{Si}$ was measured by the axial blocking of $α$ particles from the ${}^{27}{Al}$ ( $p$ , $α_{0}$ ) resonance at $E_{p} = 731.4$ keV. The result $Γ = 28_{- 6}^{+ 13}$ eV compares very favorably with that obtained from yield measurements but not with a previous planar blocking experiment.

NUCLEAR REACTIONS ${}^{27}{Al}$ ( $p$ , $α_{0}$ ) ${}^{24}{Mg}$ , $E = 0.731$ MeV; measured blocking effect. ${}^{28}{Si}$ deduced level width. Single crystal thick Al targets. LR 115 cellulose nitrate detectors.

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${}^{12}C$ - ${}^{12}C$ resonances studied through $γ$ decay

G. Andritsopoulos, X. Aslanoglou, P. Bakoyeorgos, and G. Vourvopoulos

Phys. Rev. C 21, 1648(R) (1980) - Published 1 April, 1980

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Resonances in the ${}^{12}C$ - ${}^{12}C$ system and in the energy range $E_{c . m .} = 7 - 10$ MeV were studied through $γ$ decay. Excitation functions of the $γ$ decay of the first excited states of ${}^{20}{Ne}$ , ${}^{23}{Na}$ , and ${}^{23}{Mg}$ seen through the ${}^{12}C$ ( ${}^{12}C$ , $α$ ) ${}^{20}{Ne}$ , ${}^{12}C$ ( ${}^{12}C$ , $p$ ) ${}^{23}{Na}$ , and ${}^{12}C$ ( ${}^{12}C$ , $n$ ) ${}^{23}{Mg}$ reactions corroborated the existence of resonances observed through various particle reactions. With the help of angular distributions from the ${}^{12}C$ ( ${}^{12}C$ , $α$ ) ${}^{20}{Ne}_{g . s .}$ reaction, one other resonance was established at $E_{c . m .} = 9.65$ MeV with $J^{π} = 8^{+}$ .

NUCLEAR REACTIONS ${}^{12}C$ ( ${}^{12}C$ , $α$ ) ${}^{20}{Ne}$ , ${}^{12}C$ ( ${}^{12}C$ , $p$ ) ${}^{23}{Na}$ , ${}^{12}C$ ( ${}^{12}C$ , $n$ ) ${}^{23}{Mg}$ ; $E ({}^{12}C) = 14 - 20$ MeV; measured $σ_{γ} (E)$ , $σ_{α} (E, ϑ)$ , deduced ${}^{24}{Mg}$ resonances; natural target.

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Elastic cross sections for $e^{-}$ + ${}^{48}{Ca}$ at 757.5 MeV

J. B. Bellicard, P. Bounin, R. F. Frosch, R. Hofstadter, J. S. McCarthy, F. J. Uhrhane, B. C. Clark, and R. Herman

Phys. Rev. C 21, 1652(R) (1980) - Published 1 April, 1980

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Interpretation of a recent neutron-proton analyzing power measurement

A. Chisholm, J. C. Duder, R. Garrett, and J. L. Poletti

Phys. Rev. C 21, 1653(R) (1980) - Published 1 April, 1980

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In a recent paper on the analyzing power for neutrons elastically scattered by protons at 16.9 MeV the authors of that paper conclude that $F$ waves make a significant contribution to the reaction even at that low energy. This conclusion is examined and discussed.

NUCLEAR REACTIONS ${}^{1}H$ ( $n$ , $n$ ) ${}^{1}H$ , $E = 16.9$ MeV; $F$ -wave contributions to $A_{y} (θ)$ .

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Optical potential for ${}^{6}{Li}$ + ${}^{28}{Si}$ elastic scattering at 154 MeV

P. Schwandt, S. Kailas, W. W. Jacobs, M. D. Kaitchuck, W. Ploughe, and P. P. Singh

Phys. Rev. C 21, 1656(R) (1980) - Published 1 April, 1980

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The differential cross section angular distribution for ${}^{6}{Li}$ elastic scattering from ${}^{28}{Si}$ was measured at 154 MeV lab energy for center-of-mass angles up to 66°. The data exhibit forward-angle diffractive structure and a large-angle falloff similar to that of refractive nuclear scattering. An optical-model analysis with Woods-Saxon form factors and standard fitting criterion yields a broad continuum of admissible real central potential depths $| V | \sim 120 - 200$ MeV rather than the multitude of discrete parameter families encountered at lower bombarding energies. The best fit to the data selects a $| V |$ near 160 MeV. A Woods-Saxon squared form factor as well as a microscopic folding-model potential have also been investigated in fitting the data.

NUCLEAR REACTIONS ${}^{28}{Si}$ ( ${}^{6}{Li}$ , ${}^{6}{Li}$ ), $E_{L} = 154$ MeV: measured $\frac{d σ}{d Ω}$ ; optical-model analysis.

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Character of the low-lying $0^{-}$ and $0^{+}$ states in the even Rn, Ra, Th, U, and Pu isotopes

R. K. Sheline

Phys. Rev. C 21, 1660(R) (1980) - Published 1 April, 1980

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The systematics of the energies and inverse moments of inertia are compared for the ground state and low-lying $K = 0^{+}$ and $K = 0^{-}$ bands in the even Rn, Ra, Th, U, and Pu nuclei. This comparison suggests a structural relationship between the excited $K = 0^{+}$ band and the well known $K = 0^{-}$ band as expected from the calculations of Chasman.

NUCLEAR STRUCTURE Systematics of energies and $\frac{h}{2}$ values of low-lying $K = 0^{+}$ and $K = 0^{-}$ bands in even Rn, Ra, Th, U, and Pu isotopes.

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Search for naturally occurring superheavy element $Z = 110$ , $A = 294$

William Stephens, Jeffrey Klein, and Robert Zurmühle

Phys. Rev. C 21, 1664(R) (1980) - Published 1 April, 1980

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A search for the superheavy element $Z = 110$ and $A = 294$ has been made using the Tandem accelerator as a highly sensitive mass spectrometer. The observed background leads to an upper limit on the presence of ${}^{294}110$ in a sample of placer platinum of 1 in $10^{11}$ . This result implies that ${}^{294}110$ either has a lifetime less than about 2 × $10^{8}$ yr, or was not produced in the amounts predicted by Schramm and Fowler, or did not follow its homolog platinum in the geophysical and chemical processing of the material.

NUCLEAR STRUCTURE Search for superheavy element (110, 294), upper limit found, use of Tandem accelerator as sensitive mass spectrometer.

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${}^{111}{In}$ - ${}^{109}{In}$ mass difference

E. M. Takagui and O. Dietzsch

Phys. Rev. C 21, 1667(R) (1980) - Published 1 April, 1980

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A measurement of the difference of $Q$ values for the ${}^{108}{Cd}$ ( ${}^{3}{He}$ , $d$ ) ${}^{109}{In}$ and the ${}^{110}{Cd}$ ( ${}^{3}{He}$ , $d$ ) ${}^{111}{In}$ reactions shows a significant discrepancy with the value from the 1977 Atomic Mass Tables. We find $Q [{}^{110}{Cd} ({}^{3}{He}, d) {}^{111}{In}] - Q [{}^{108}{Cd} ({}^{3}{He}, d) {}^{109}{In}] = 806.5 \pm 2.6$ keV, leading to a new improved mass excess difference for ${}^{111}{In}$ - ${}^{109}{In}$ of - 1904.5±7.5 keV.

NUCLEAR REACTIONS ${}^{108}{Cd}$ ( ${}^{3}{He}$ , $d$ ); ${}^{110}{Cd}$ ( ${}^{3}{He}$ , $d$ ); measured $Q$ values, deduced ${}^{111}{In}$ - ${}^{109}{In}$ mass excess difference.

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$g$ factor of the 14 ms $8^{+}$ isomeric state in ${}^{88}Y$

A. Kleinrahm, C. Günther, and H. Hübel

Phys. Rev. C 21, 1670(R) (1980) - Published 1 April, 1980

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The method of in-beam perturbation of gamma ray angular distribution by nuclear magnetic resonance was applied to remeasure the $g$ factor of the $I^{π} = 8^{+}$ , $T_{\frac{1}{2}} = 14$ ms isomeric state in ${}^{88}Y$ with the result $g = 0.609 (6)$ .

NUCLEAR REACTIONS ${}^{87}{Rb} (α, 3 n) {}^{88}Y^{m}$ , $E_{α} = 40.1$ MeV; rf field; measured $I_{γ} (⊖, H)$ ; deduced ${}^{88}Y^{m}$ $g$ factor.

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Transverse electromagnetic form factor in ${}^{12}C$

D. Cha

Phys. Rev. C 21, 1672(R) (1980) - Published 1 April, 1980

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We calculate the contribution from the convection current to the recently measured transverse form factor of the ${}^{12}C$ $2^{+}$ level at 4.44 MeV. The convection current dominates for small momentum transfer and is determined by the $B (E 2)$ . In this region, theory agrees with experiment. At intermediate momentum transfer, agreement with experiment is only possible assuming a coherent sum of the convection current and magnetization density contributions.

NUCLEAR STRUCTURE ${}^{12}C$ , $E = 4.44$ MeV; calculated ${F_{T}}^{2}$ .

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Second and third backbending in ${}^{160}{Yb}$

A. Ansari and S. C. K. Nair

Phys. Rev. C 21, 1674(R) (1980) - Published 1 April, 1980

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In the cranked Hartree-Fock-Bogoliubov method with the pairing + $Q \cdot Q$ interaction, we find two backbends due to antipairing among protons: one at $J \approx 24$ and the other stronger one at $J \approx 38$ . The proton pairing gap does not vanish even at $J = 44$ .

NUCLEAR STRUCTURE Cranked Hartree-Fock-Bogoliubov calculations of yrast levels in ${}^{160}{Yb}$ , prediction of a third backbend at $J \approx 38$ .

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Analyticity and model-independent determination of the nuclear charge density

Olgierd Dumbrajs

Phys. Rev. C 21, 1677(R) (1980) - Published 1 April, 1980

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Erratum: Angular momentum transfer in the deep inelastic reactions of 237 MeV ${}^{40}{Ar}$ with ${}^{89}Y$

M. N. Namboodiri, J. B. Natowitz, P. Kasiraj, R. Eggers, L. Adler, P. Gonthier, C. Cerruti, and S. Simon

Phys. Rev. C 21, 1680 (1980) - Published 1 April, 1980

Neutron-proton elastic scattering between 200 and 500 MeV. III. Phase shift analysis

D. V. Bugg, J. A. Edgington, W. R. Gibson, N. Wright, N. M. Stewart, A. S. Clough, D. Axen, G. A. Ludgate, C. J. Oram, L. P. Robertson, J. R. Richardson, and C. Amsler

Phys. Rev. C 21, 1004 (1980) - Published 1 March, 1980

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Proton spectra from 800 MeV protons on selected nuclides

R. E. Chrien, T. J. Krieger, R. J. Sutter, M. May, H. Palevsky, R. L. Stearns, T. Kozlowski, and T. Bauer

Phys. Rev. C 21, 1014 (1980) - Published 1 March, 1980

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The emission of protons from targets of ${}^{6}{Li}$ , Li, ${}^{12}C$ , ${}^{27}{Al}$ , ${}^{40}{Ca}$ , ${}^{51}V$ , ${}^{90}{Zr}$ , and Pb under bombardment from 800 MeV protons has been studied using a high resolution proton spectrometer. Spectra were measured at laboratory scattering angles of 5°, 7°, 9°, 11°, 13°, 15°, 20°, 25°, and 30° with special emphasis on the quasifree region. Outgoing momenta corresponding to the region of pion production were examined at 11° and 15°. Absolute cross sections have been derived by reference to known ( $p$ , $p$ ) scattering data at 800 MeV. The quasifree scattering has been compared to a distorted-wave impulse approximation analysis by summing over the unobserved (struck) nucleon. The systematics of proton production and the applicability of the distorted-wave impulse approximation analyses are discussed.

NUCLEAR REACTIONS ( $p$ , $p^{'}$ ) on ${}^{6}{Li}$ , Li, ${}^{12}C$ , ${}^{27}{Al}$ , ${}^{40}{Ca}$ , ${}^{51}V$ , ${}^{90}{Zr}$ , Pb; $E_{p} = 800$ MeV, $θ_{L} = 5 ° to 30 °$ ; quasielastic scattering, DWIA analysis.

Spin and isospin transfer in the ${}^{12}C$ ( $π^{+}$ , $π^{+'}$ ) reaction

R. J. Peterson, R. L. Boudrie, J. J. Kraushaar, R. A. Ristinen, J. R. Shepard, G. R. Smith, C. F. Moore, W. J. Braithwaite, N. S. P. King, C. L. Morris, H. A. Thiessen, and J. Piffaretti

Phys. Rev. C 21, 1030 (1980) - Published 1 March, 1980

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Inelastic scattering cross sections from ${}^{12}C$ were measured for the 12.7 MeV ( $1^{+}$ ;0), 15.1 MeV ( $1^{+}$ ;1), and 16.1 MeV ( $2^{+}$ ;1) levels for positive pion beam energies of 100, 116, 140, 160, 180, 200, 230, 260, and 291 MeV. Clearly oscillatory angular distributions were measured for the $1^{+}$ states, and these are shown to be explained by very general considerations of the scattering amplitudes. The 16.1 MeV data show little structure at the lower beam energies, but the falling angular dependence at the higher beam energies is very like that observed for the 4.4 MeV ( $2^{+}$ ;0) state. A prediction for the ratio of the $T = 0$ and $T = 1$ $1^{+}$ cross sections is derived from a specific two-step calculation, and found to agree with the data at the 3-3 resonance.

NUCLEAR REACTIONS ${}^{12}C$ ( $π^{+}$ , $π^{+'}$ ) ${}^{12}C$ , $E_{π^{+}} = 100, 116, 140, 160, 180, 200, 230, 260, 291$ MeV. Measured $σ (θ)$ for 12.7, 15.1, and 16.1 MeV states.

Role of Gamow-Teller suppression and $M 1$ radiative widths on $π^{-}$ photoproduction from ${}^{14}N$

M. K. Singham and F. Tabakin

Phys. Rev. C 21, 1039 (1980) - Published 1 March, 1980

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Total and differential cross sections are presented for the reaction ${}^{14}N$ ( $γ$ , $π^{-}$ ) ${}^{14}O_{g . s}$ . for 0-200 MeV pions, using the Blomqvist-Laget photoproduction operator and including all requisite pion distorted waves. It is found that phenomenological $p$ -shell wave functions obtained from fits to inelastic electron scattering data from ${}^{14}N$ , when used in the photoproduction calculation, give good agreement with experiment. This agreement is a result of using nuclear wave functions that not only suppress the Gamow-Teller matrix element but also agree with $M 1$ radiative widths. As in the photoproduction of pions off other light nuclei, the total cross section shows a peak at energies far below the (3, 3) resonance energy, which arises from the recoil nuclei being constrained to discrete final states. As a result of the suppression of the Gamow-Teller matrix element for this transition, the reaction is sensitive (even at threshold) to the higher order terms in the photoproduction operator and hence to the curvature of the pion waves and the Fermi motion of the nucleons in the nuclei. This suggests that this reaction provides a sensitive probe of pion distortions and of the Ericson-Ericson effect.

NUCLEAR REACTIONS ${}^{14}N$ ( $γ$ , $π^{-}$ ) ${}^{14}O_{g . s .}$ , $E = 145 - 325$ MeV; calculated $σ_{T}$ , $σ (θ)$ ; compared with $σ (θ)$ for ${}^{12}C$ ( $γ$ , $π^{-}$ ) ${}^{12}N_{g . s .}$ for $E = 187$ MeV; nuclear structure, pion distortions, photoproduction operator effects.

Angular and energy distributions of ${}^{24}{Na}$ fragments formed by the reaction of 11.5-GeV protons with ${}^{197}{Au}$

J. A. Urbon, S. B. Kaufman, D. J. Henderson, and E. P. Steinberg

Phys. Rev. C 21, 1048 (1980) - Published 1 March, 1980

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The angular distribution and the range distributions at three angles have been measured for the light nuclear fragment ${}^{24}{Na}$ formed by the interaction of 11.5-GeV protons with ${}^{197}{Au}$ . The angular distribution has a peak at a laboratory angle $θ_{L} = 70 °$ and is thus quite different from the forward-peaked angular distribution previously observed for ${}^{24}{Na}$ at a bombarding energy of 2.9 GeV. The velocity distributions derived from the range distributions are relatively narrow, and the mean velocity decreases from 2.11 ( ${M e V / A)}^{½}$ at $θ_{L} = 30 ° to 1.86$ ( ${M e V / A)}^{½}$ at 156.5°. The data are analyzed in terms of the two-step model of nuclear reactions and are found to be consistent with that model. The model parameters derived from this analysis are $〈 v_{∥} 〉 = 0.14$ ( ${M e V / A)}^{½}$ and $〈 V 〉 = 2.00$ ( ${M e V / A)}^{½}$ .The angular distribution in the frame moving with the velocity $v_{∥}$ is found to be symmetric about 90°, with an intensity ratio $\frac{I (90 °)}{I (0 °)} = 1.43$ . The implications of this analysis for the reaction mechanism are discussed.

NUCLEAR REACTIONS ${}^{197}{Au}$ ( $p$ , $x$ ) ${}^{24}{Na}$ , $E_{p} = 11.5$ GeV; measured angular distribution and range distributions at 30°, 90°, and 156.5°; inferred parameters of two-step model.

Effect of the pion and $Δ$ optical potential on deep inelastic pion-nuclear reactions

Joseph N. Ginocchio and Mikkel B. Johnson

Phys. Rev. C 21, 1056 (1980) - Published 1 March, 1980

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The effect of the pion and $Δ$ optical potentials on the propagation of the pion and delta in a semiclassical transport model of pion-nuclear reactions is studied. It is shown that the reaction and true absorption cross sections are increased to become closer to the measured cross sections. The derivative terms in the optical potential are shown to be particularly important. However, the distribution of final products produced still has some discrepancies compared to experiment, indicating that the mechanism for the deposition of the pion energy in the nucleus is not completely understood.

NUCLEAR REACTIONS The effect of optical potential on mean free paths in pion-nucleus reactions. Total reaction and absorption cross section calculated for pions incident on ${}^{12}C$ .

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Reply to "Comment on `Statistical significance of spreading widths for doorway states"'

Axial blocking measurement of the ${}^{28}{Si}$ 12.291 MeV level width

${}^{12}C$ - ${}^{12}C$ resonances studied through $γ$ decay

Elastic cross sections for $e^{-}$ + ${}^{48}{Ca}$ at 757.5 MeV

Interpretation of a recent neutron-proton analyzing power measurement

Optical potential for ${}^{6}{Li}$ + ${}^{28}{Si}$ elastic scattering at 154 MeV

Character of the low-lying $0^{-}$ and $0^{+}$ states in the even Rn, Ra, Th, U, and Pu isotopes

Search for naturally occurring superheavy element $Z = 110$ , $A = 294$

${}^{111}{In}$ - ${}^{109}{In}$ mass difference

$g$ factor of the 14 ms $8^{+}$ isomeric state in ${}^{88}Y$

Transverse electromagnetic form factor in ${}^{12}C$

Second and third backbending in ${}^{160}{Yb}$

Analyticity and model-independent determination of the nuclear charge density

Erratum: Angular momentum transfer in the deep inelastic reactions of 237 MeV ${}^{40}{Ar}$ with ${}^{89}Y$

Neutron-proton elastic scattering between 200 and 500 MeV. III. Phase shift analysis

Proton spectra from 800 MeV protons on selected nuclides

Spin and isospin transfer in the ${}^{12}C$ ( $π^{+}$ , $π^{+'}$ ) reaction

Role of Gamow-Teller suppression and $M 1$ radiative widths on $π^{-}$ photoproduction from ${}^{14}N$

Angular and energy distributions of ${}^{24}{Na}$ fragments formed by the reaction of 11.5-GeV protons with ${}^{197}{Au}$

Effect of the pion and $Δ$ optical potential on deep inelastic pion-nuclear reactions

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