Recent Articles

Single-particle component of the first excited state of ${}^{211}{Bi}$

E. R. Flynn, R. E. Anderson, N. J. DiGiacomo, R. J. Peterson, and G. R. Smith

Phys. Rev. C 16, 139 (1977) - Published 1 July, 1977

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The first excited state of ${}^{211}{Bi}$ is located at 410 keV and, in spite of the relatively simple structure of this nucleus relative to the ${}^{208}{Pb}$ closed shell, this level is presently not understood theoretically. In order to increase the available information about this state, we report here on the ${}^{208}{Pb} (α, p) {}^{211}{Bi}$ reaction, which can provide a measure of the proton particle strength to such levels. The yields from the ${}^{206}{Pb} (α, p) {}^{209}{Bi}$ reaction are used as a strength calibration after distorted-wave Born approximation corrections. It is found that the 410 keV state contains 52% of the $f_{\frac{7}{2}}$ single-particle strength although it has been displaced downward by 500 keV from the unperturbed $f_{\frac{7}{2}}$ position in ${}^{209}{Bi}$ .

[NUCLEAR REACTIONS ${}^{206, 208}{Pb} (α, p)$ , $E_{α} = 35.5$ MeV, measured $σ (θ, E_{p})$ , DWBA analysis, deduced $C^{2} S_{lj}$ .]

Optical model description of anomalous elastic and inelastic $α - {}^{40}{Ca}$ scattering between 20 and 50 MeV

F. Michel and R. Vanderpoorten

Phys. Rev. C 16, 142 (1977) - Published 1 July, 1977

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An optical model analysis of the anomalous large angle elastic $α - {}^{40}{Ca}$ scattering between 20 and 50 MeV has been performed on the basis of a single fit at 29 MeV incident energy. The resulting potential gives a good description of the characteristic energy dependence of the angular distributions. A nonresonant interpretation of the phenomenon is proposed. A distorted wave Born approximation analysis of some inelastic transitions is presented.

[NUCLEAR REACTIONS ${}^{40}{Ca} (α, α)$ , ${}^{40}{Ca} (α, α^{'})$ , $E = 20 - 50$ MeV; calculated $σ (θ)$ ; optical model analysis; DWBA analysis.]

Neutron source reaction cross sections

Nelson Jarmie and J. H. Jett

Phys. Rev. C 16, 15 (1977) - Published 1 July, 1977

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Accurate differential cross sections have been measured for the reactions ${}^{2}H {(d, {}^{3}{He})}_{n}$ at 12.305 MeV, for ${}^{3}H {(p, {}^{3}{He})}_{n}$ at 13.600 MeV, and ${}^{2}H {(t, {}^{4}{He})}_{n}$ at 20.000 MeV. The relative error for most of the data is on the order of 1% and the scale error is less than 1%. The data are used to give absolute normalizations to the measured neutron spectra from these reactions and will be useful in the analysis of mass-4 and mass-5 systems.

[NUCLEAR REACTIONS ${}^{2}H (d, {}^{3}{He})$ , $E = 12.305$ MeV, $θ (c . m .) = 24 - 96^{\circ}$ ; ${}^{3}H (p, {}^{3}{He})$ , $E = 13.600$ MeV, $θ (c . m .) = 25 - 103^{\circ}$ ; ${}^{2}H (t, {}^{4}{He})$ , $E = 20.000$ MeV, $θ (c . m .) = 36 - 104^{\circ}$ ; $Δ θ = \pm {0.03}^{\circ}$ , measured differential cross sections $σ (θ)$ ; $Δ σ = 1 %$ .]

Doorway state structure in neutron cross sections for ${}^{56}{Fe}$

G. J. Kirouac

Phys. Rev. C 16, 153 (1977) - Published 1 July, 1977

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Intermediate structures in the $s$ - and $d$ -wave elastic and inelastic neutron scattering cross sections of ${}^{56}{Fe}$ are explained on the basis of a doorway state model. A particle-vibrator coupling model is used to calculate the cross sections from which resonance energies and widths of the doorway states are extracted. No adjustable parameters are used in the calculations. Doorway state resonances in both the ${1 / 2}^{+}$ elastic scattering channel and the ${3 / 2}^{+}$ elastic and inelastic scattering channels can be accounted for by a ( $d_{\frac{5}{2}} \otimes 2^{+}$ ) doorway state configuration in which a single quasibound $d_{\frac{5}{2}}$ neutron in ${}^{57}{Fe}$ is coupled to the first $2^{+}$ state of the ${}^{56}{Fe}$ target. The agreement obtained between the calculations and the observed intermediate structure widths as well as the summed compound nucleus fine structure widths is good. Doorway state resonances in the $p$ -wave neutron channels which result from ( $d_{\frac{5}{2}} \otimes 3^{-}$ ) configurations are also calculated.

[NUCLEAR REACTIONS ${}^{56}{Fe} + n$ ; calculated doorway state structure in $σ (E) E_{n} = 0 - 2.2$ MeV; coupled channels for $s$ -, $p$ -, $d$ -wave neutrons.]

Absolute cross sections and isomeric cross-section ratios for the ${}^{148}{Nd} (d, 2 n)$ , ${}^{148}{Nd} (p, n)$ , and ${}^{146}{Nd} (α, p n)$ reactions producing the isomeric pair ${}^{148}{Pm}^{m, g}$

D. C. Aumann and W. Gückel

Phys. Rev. C 16, 160 (1977) - Published 1 July, 1977

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Excitation functions and isomeric cross-section ratios were determined for the ${}^{148}{Nd} (d, 2 n)$ , ${}^{148}{Nd} (p, n)$ , and ${}^{146}{Nd} (α, p n)$ reactions producing the isomeric pair ${}^{148}{Pm}^{m, g}$ . The experimental isomer ratios of 41.3-day ${}^{148}{Pm}^{m}$ (6-) and 5.37-day ${}^{148}{Pm}^{g}$ (1-) were compared with statistical model calculations wherein spin cutoff parameters $μ$ were obtained assuming that $σ$ is either independent or varying with excitation energy. The spin cutoff parameters and the effective moments of inertia deduced from these calculations were $σ = 4.2$ and $θ = 0.70 θ_{r}$ , respectively, for the reaction ${}^{148}{Nd} (p, n) {}^{148}{Pm}^{m, g}$ , and $σ = 3.9$ and $θ = 0.65 θ_{r}$ , respectively, for the reaction ${}^{148}{Nd} (d, 2 n) {}^{148}{Pm}^{m, g}$ .

[NUCLEAR REACTIONS ${}^{148}{Nd} (p, n)$ , ( $d, 2 n$ ), ${}^{146}{Nd} (α, p n)$ , $E_{P} = 9 - 45$ MeV, $E_{d} = 6.5 - 52$ MeV, $E_{α} = 29 - 59$ MeV; measured $σ (E)$ , isomer ratio; deduced spin cutoff parameter, moment of inertia.]

( ${}^{12}C$ , ${}^{8}{Be}$ ) reaction on even calcium isotopes

G. R. Morgan and N. R. Fletcher

Phys. Rev. C 16, 167 (1977) - Published 1 July, 1977

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The ( ${}^{12}C$ , ${}^{8}{Be}$ ) reaction on even calcium isotopes results in selectively populated energy spectra similar to those for the ( ${}^{6}{Li, d}$ ) and ( ${}^{16}O$ , ${}^{12}C$ ) reactions on the same target nuclei. The ( ${}^{12}C$ , ${}^{8}{Be}$ ) cross sections are larger than those for ( ${}^{6}{Li, d}$ ) and comparable to those for ( ${}^{16}O$ , ${}^{12}C$ ), and the cross sections decrease in magnitude for the heavier residual isotopes. Both effects are due largely to differences in the matching of $Q$ value and angular momentum. The ( ${}^{12}C$ , ${}^{8}{Be}$ ) angular distributions have characteristics typical of direct reactions and the distributions are well reproduced by finite range distorted-wave Born-approximation calculations assuming direct transfer of an $α$ particle.

[NUCLEAR REACTIONS ${}^{40}{Ca}$ ( ${}^{12}C$ , ${}^{8}{Be}$ ), measured $σ (θ)$ at $E_{lab} = 45$ MeV and $σ (E)$ from 35 to 46 MeV; ${}^{42, 44, 48}{Ca}$ ( ${}^{12}C$ , ${}^{8}{Be}$ ), measured $σ (θ)$ at $E_{lab} = 45$ MeV, enriched targets. Finite range DWBA analyses, deduced $S$ .]

Experimental evidence of multistep processes in the ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{76}{Ge}$ and ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ) ${}^{74}{Ge}$ reactions

P. D. Bond, H. J. Korner, M.-C. Lemaire, D. J. Pisano, and C. E. Thorn

Phys. Rev. C 16, 177 (1977) - Published 1 July, 1977

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Angular distributions of the ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{76}{Ge}$ and ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ) ${}^{74}{Ge}$ reactions have been measured at incident energies of 75 and 77.6 MeV, respectively. The time-reversed reaction cross sections leading to the Ge ground states are nearly identical bell shaped curves. Stripping and pickup angular distributions to the Ge $2^{+}$ states show a strong shape difference suggesting interference between direct and two-step transfer. Angular distributions for which ${}^{18}O$ is in its first $2^{+}$ state are similar in shape to those with ${}^{18}O$ in its ground state. Data are also presented for elastic and inelastic scattering in both entrance and exit channels as well as for single-neutron transfer.

[NUCLEAR REACTIONS ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ), ( ${}^{18}O$ , ${}^{17}O$ ), ( ${}^{18}O$ , ${}^{18}O$ ) $E = 75$ MeV; ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ), ( ${}^{16}O$ , ${}^{16}O$ ) $E = 77.6$ MeV; measured $σ (θ)$ .]

Reaction measurements and analyses for ${}^{3}{He}$ + ${}^{4}{He}$ at 15.95 MeV (c.m.)

J. A. Koepke and Ronald E. Brown

Phys. Rev. C 16, 18 (1977) - Published 1 July, 1977

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A study has been made of the proton and $α$ -particle yields from the 28-MeV (lab) bombardment of ${}^{4}{He}$ by ${}^{3}{He}$ . From these measurements a total reaction cross section $σ_{R}$ of $433 \pm 10$ mb was deduced. A reaction-model analysis of the $α$ -particle continuum revealed a significant contribution from the sequential reaction ${}^{3}{He} + {}^{4}{He} \to {}^{6}{Li} (2.18) + p \to α + d + p$ in which the breakup of the excited ${}^{6}{Li}$ nucleus is nearly isotropic in its rest system. A phase-shift study was performed for ${}^{3}{He}$ + ${}^{4}{He}$ elastic scattering at this energy using our $σ_{R}$ value as a constraint. A pronounced odd-even dependence of the real parts of the phase shifts on the orbital angular momentum was found. The results of this work are compared with other experiments, optical-model and phase-shift analyses, and resonating-group calculations.

[NUCLEAR REACTIONS ${}^{4}{He} ({}^{3}{He}, p)$ , ( ${}^{3}{He}, α$ ), $E = 28.00$ MeV; measured $σ (E_{p}, θ)$ , $σ (E_{α}, θ)$ ; deduced $σ_{R}$ . $α$ -continuum analysis. Phase-shift analysis. Resonating-group comparison.]

Analysis of the ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{76}{Ge}$ and ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ) ${}^{74}{Ge}$ reactions in terms of exact finite-range coupled-channel Born approximation

M.-C. Lemaire and K. S. Low

Phys. Rev. C 16, 183 (1977) - Published 1 July, 1977

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An exact finite-range coupled-channel Born-approximation analysis of the ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{76}{Ge}$ and ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ) ${}^{74}{Ge}$ reactions has been performed. It shows that the shape change between the angular distributions of different final states is well reproduced by using BCS—random-phase-approximation wave functions to describe the Ge states. The measured transfer cross sections are rather well described by calculations using optical model parameters and deformation values which fit the experimental data on ${}^{18}O$ and ${}^{16}O$ elastic and inelastic scattering. It has been found that the excitation of the ${}^{18}O^{*}$ $2^{+}$ state has to be included in the coupled-channel Born-approximation analysis in order to reproduce the experimental angular distributions of the ${}^{74}{Ge}$ and ${}^{76}{Ge}$ ground states. A unique factor of 2.3 can be used to normalize the calculated cross section to the experimental data.

[NUCLEAR REACTIONS ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ), ( ${}^{18}O$ , ${}^{18}O$ ); ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ), ( ${}^{16}O$ , ${}^{16}O$ ); deduced optical model parameters; CCBA analysis.]

Yrast decay schemes from heavy ion + ${}^{48}{Ca}$ fusion-evaporation reactions. I. ${}^{54 - 56}{Mn}$ , ${}^{56}{Cr}$ , and ${}^{52 - 53}V$

A. M. Nathan, J. W. Olness, E. K. Warburton, and J. B. McGrory

Phys. Rev. C 16, 192 (1977) - Published 1 July, 1977

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Fusion-evaporation reactions induced by a beam of 25-50 MeV ${}^{11}B$ on an isotopically enriched ${}^{48}{Ca}$ target have been used to populate high-spin yrast levels in ${}^{54 - 56}{Mn}$ , ${}^{56}{Cr}$ , and ${}^{52 - 53}V$ . Measurements consisted of $γ$ - ray excitation functions, angular distributions, $γ - γ$ coincidences, and recoil-distance and Doppler shift lifetime measurements, from which were deduced the energy levels, $γ$ -ray branching ratios, most probable spin-parity assignments, and level lifetimes.

[NUCLEAR REACTIONS ${}^{48}{Ca} ({}^{11}B, x n, y p, z α) {}^{54 - 56}{Mn}$ , ${}^{56}{Cr}$ , and ${}^{52 - 53}V$ . $E = 25 - 50$ MeV; measured $σ (E, E_{γ})$ and coin.; deduced levels; measured $σ (E_{γ}, θ)$ ; deduced $J^{π}$ for high-spin levels; measured RDM and Doppler shifts; deduced $t_{\frac{1}{2}}$ , ${| M (M 1) |}^{2}$ and ${| M (E 2) |}^{2}$ . Enriched targets, Ge(Li) detectors.]

Bombarding energy dependence of deep inelastic fragment kinetic energies

T. M. Cormier, P. Braun-Munzinger, P. M. Cormier, J. W. Harris, and L. L. Lee, Jr.

Phys. Rev. C 16, 215 (1977) - Published 1 July, 1977

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The bombarding energy dependence of deep inelastic fragment kinetic energies has been measured for ${}^{35}{Cl}$ + ${}^{27}{Al}$ collisions at $E ({}^{35}{Cl}) = 140, 150, 160, and 170$ MeV. The results are compared with a simple classical model to show that the observed energy dependence is in reasonable agreement with a classical picture of strong tangential friction leading to rigid rotation of a very extended intermediate dinuclear system.

[NUCLEAR REACTIONS ${}^{35}{Cl}$ + ${}^{27}{Al}$ ; quasifission, $E = 140, 150, 160, 170$ Mev; measured fragment energies, $θ = 15^{\circ}, 20^{\circ}, 25^{\circ}, 30^{\circ}$ .]

Structure in the ${}^{12}C ({}^{12}C, d) {}^{22}{Na}$ reaction near $E_{c . m .} = 14.3$ MeV

A. H. Lumpkin, G. R. Morgan, and K. W. Kemper

Phys. Rev. C 16, 220 (1977) - Published 1 July, 1977

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Enhancements are observed in the ${}^{12}C ({}^{12}C, d) {}^{22}{Na}$ reaction for the population of the $J^{π} = 5^{+} and 7^{+}$ states at $E_{x} = 1.53 and 4.52$ MeV in the energy region from 13.0 to 16.8 MeV (c.m.). A comparison of ${}^{12}C$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) and ${}^{12}C ({}^{12}C, d)$ suggests that the selective population of the states in ${}^{22}{Na}$ arises from the deuteron exit channel penetrabilities for grazing partial waves rather than nuclear structure similarities between the ${}^{12}C$ + ${}^{12}C$ and $d + {}^{22}{Na}$ systems.

[NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, d)$ , $E_{c . m .} = 13.0 to 16.8$ MeV; measured $E_{d}$ and $\frac{d σ}{d Ω}$ at $θ_{1 a b} = 10^{\circ} and 20^{\circ}$ .]

Mutual excitation near the Coulomb barrier in the ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C^{}$ + ${}^{12}C^{}$ reaction

W. J. Braithwaite and A. W. Obst

Phys. Rev. C 16, 224 (1977) - Published 1 July, 1977

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An excitation function has been measured for ${}^{12}C$ + ${}^{12}C$ mutually excited to both first excited states, using $γ$ pairs detected in any two of four closely packed 12.5-cm × 12.5-cm NaI detectors. Both $\frac{\bar{W} (90^{\circ})}{\bar{W} (180^{\circ})}$ and $\bar{W} (90^{\circ}) + \bar{W} (180^{\circ})$ vary smoothly with bombarding energy, in disagreement with recent predictions of sharp resonant structure.

[NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, {}^{12}C_{4.44}^{*}) {}^{12}C_{4.44}^{*}$ , $E = 10 - 15$ MeV, $γ - γ$ coin for $θ_{γ γ} = 90^{\circ} and 180^{\circ}$ , no sharp resonances observed.]

Band structure in ${}^{147, 149, 151}{Eu}$ observed via ( $HI, x n$ ) reactions

J. G. Fleissner, E. G. Funk, F. P. Venezia, and J. W. Mihelich

Phys. Rev. C 16, 227 (1977) - Published 1 July, 1977

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$γ$ rays from levels in ${}^{147, 149, 151}{Eu}$ have been studied using primarily ( ${}^{6, 7}{Li}, x n γ$ ) reactions. Prompt and delayed $γ - γ$ coincidences, excitation functions, and angular distributions were used to study the in-beam $γ$ rays. Bands with $Δ I = 2$ built on an ${11 / 2}^{-}$ isomeric state have been observed in all three nuclei and since the energy spacings strongly resemble those of the core nuclei they are interpreted as decoupled bands. The maximum spin observed in the decoupled band is ${27 / 2}^{-}$ for ${}^{151}{Eu}$ and ${23 / 2}^{-}$ for ${}^{149, 147}{Eu}$ . Possible unfavored states associated with the $π h_{\frac{11}{2}}$ system have also been identified. High spin positive parity states have been observed for ${}^{147}{Eu}$ and ${}^{149}{Eu}$ . The maximum spin observed for each nucleus is ( ${33 / 2}^{+}$ ) at 4178.1 keV for ${}^{147}{Eu}$ , ( ${29 / 2}^{+}$ ) at 3042.0 keV for ${}^{149}{Eu}$ , and ( ${27 / 2}^{-}$ ) at 2118.9 keV for ${}^{151}{Eu}$ . The experimental results for the negative parity bands of ${}^{149, 151}{Eu}$ have been compared with predictions of the triaxial rotor plus particle model incorporating a variable moment of inertia. The results of the model calculations give some indication of triaxial shapes for ${}^{149}{Eu}$ and ${}^{151}{Eu}$ although the predictions for the symmetric case are not significantly different from those of the asymmetric case.

[NUCLEAR REACTIONS ${}^{143, 145}{Nd} ({}^{7}{Li}, 3 n γ)$ , ${}^{146, 148}{Nd} ({}^{6}{Li}, 3 n γ)$ , $E = 26.0 - 34.0$ MeV; ${}^{139}{La} ({}^{12}C, 4 n γ)$ , $E = 60, 63$ MeV; measured $σ (E, E_{γ}, θ)$ , $γ - γ$ coin, $γ - γ$ delay. ${}^{147, 149, 151}{Eu}$ deduced levels, $J, π$ . Enriched targets. Ge(Li) detectors. Triaxial rotor-plus-particle calculations including VMI.]

Electrofission of ${}^{206}{Pb}$ , ${}^{207}{Pb}$ , and ${}^{208}{Pb}$

A. Kernohan, T. E. Drake, A. Chung, and L. Pai

Phys. Rev. C 16, 239 (1977) - Published 1 July, 1977

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Electrofission yield curves for incident electron energies of 28-44 MeV were measured for the lead isotopes ${}^{206}{Pb}$ , ${}^{207}{Pb}$ , and ${}^{208}{Pb}$ , with aluminized polycarbonate track damage detectors. The fission barrier energies and the level densities at the fission saddle point were deduced from the yield curves. An anomalous sharp resonance-like feature was discovered at 35 MeV in the ${}^{206}{Pb}$ yield.

[NUCLEAR REACTIONS, FISSION ${}^{206}{Pb}$ , ${}^{207}{Pb}$ , ${}^{208}{Pb} (e, e^{'} f)$ , $E = 30 - 44$ MeV; measured fission yield; deduced level density parameter and fission barrier energy.]

Scission point configuration of thermal-neutron induced fission of ${}^{235}U$

Charles S. Brown and Peter Fong

Phys. Rev. C 16, 243 (1977) - Published 1 July, 1977

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Trajectory calculations of the long-range $α$ particles emitted in thermal-neutron induced fission of ${}^{235}U$ have been carried out based on the initial conditions determined by the statistical theory of fission. The results agree very well with the experimental results of angular and energy distributions of the $α$ particle and thus lend strong support to the statistical theory. The discrepancy of this calculation with the best-fit trajectory calculations is resolved by showing that the latter are mathematically correct but physically wrong because they contradict with the experimental results of the number of prompt neutrons emitted per fission.

[NUCLEAR REACTIONS, FISSION LRA fission, statistical theory.]

Scission point configuration of ${}^{252}{Cf}$ fission

Peter Fong

Phys. Rev. C 16, 251 (1977) - Published 1 July, 1977

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The Fossati-Pinelli study of the scission point configuration of ${}^{252}{Cf}$ based on the calculations of trajectories of long-range $α$ particles emitted in fission provides previously unavailable experimental evidence supporting the basic assumption of the statistical theory of nuclear fission. However, their stated conclusion and that of a similar analysis by Krishnarajulu and Mehta need modification. It is found that the broad and fluctuating distributions of initial energies of the $α$ particle and the fission fragments obtained by these two groups might not be real even though they are mathematically valid. Nevertheless, together with other information available to us, the unreal part may be eliminated and both works then yield results that are wholly consistent with the statistical theory of fission. The validity of the dynamical theories will be discussed.

[NUCLEAR REACTIONS, FISSION LRA-fission, statistical theory.]

Independent isomeric yield ratio of ${}^{148}{Pm}$ in fission of the moderately excited ${}^{236}U$ compound nucleus as a measure of fragment angular momentum

D. C. Aumann, W. Gückel, E. Nirschl, and H. Zeising

Phys. Rev. C 16, 254 (1977) - Published 1 July, 1977

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The independent yield ratio of 41.3-day ${}^{148}{Pm}^{m}$ (6-) and 5.37-day ${}^{148}{Pm}^{g}$ (1-) has been measured radiochemically for fission of ${}^{233}U$ and ${}^{235}U$ induced by thermal neutrons and for fission of ${}^{232}{Th}$ by ${}^{4}{He}$ ions of 26-42 MeV. The values of the ${}^{148}{Pm}$ isomer ratios were 3.0 ± 0.5 and ${2.6}_{- 0.5}^{+ 0.9}$ for the thermal-neutron-induced fission of ${}^{233}U$ and ${}^{235}U$ , respectively, and 6.8 ± 1.2, 6.6 ± 0.7, 5.3 ± 0.5, 8.5 ± 0.9, and 8.5 ± 0.9 for fission of ${}^{232}{Th}$ by ${}^{4}{He}$ ions of 25.8, 29.1, 31.8, 37.0, and 41.4 MeV, respectively. On the basis of the measured independent yield ratios the average intrinsic angular momentum of the primary fission fragments (which lead by the emission of prompt neutrons and $γ$ rays to the secondary fragment ${}^{148}{Pm}$ ) was estimated by means of a simple statistical-model analysis based on the formalism developed by Huizenga and Vandenbosch. The following values for the average intrinsic spin of the primary fragment were obtained: $(10.8 \pm 0.9) ℏ$ and $({10.0}_{- 1.1}^{+ 1.6}) ℏ$ for thermal-neutron-induced fission of ${}^{233}U$ and ${}^{235}U$ , respectively, and $(16.5 \pm 1.5) ℏ$ , $(16.3 \pm 0.9) ℏ$ , $(14.6 \pm 0.7) ℏ$ , $(19.9 \pm 1.1) ℏ$ , and $(19.9 \pm 1.1) ℏ$ for fission of ${}^{232}{Th}$ by ${}^{4}{He}$ ions of 25.8, 29.1, 31.8, 37.0, and 41.4 MeV, respectively. The results show that a fraction of the angular momentum of the fissioning nucleus appears as intrinsic spin of the primary fragments when the angular momentum of the fissioning nucleus is increased as in the case of the ${}^{4}{He}$ -ion-induced fission. A summary of all published independent isomer-yield ratio studies which were used for deducing fission fragment angular momenta is given.

[NUCLEAR REACTIONS, FISSION ${}^{233, 235}U (n, f)$ , $E = thermal$ , ${}^{232}{Th} ({}^{4}{He}, f)$ , $E = 25.8 - 41.4$ MeV; measured ${}^{148}{Pm}$ independent isomer yields; deduced primary angular momenta.]

Independent yields of fast-neutron fission of ${}^{232}{Th}$ : Observation of proton odd-even effect and neutron shell effect on the yields

Talma Izak-Biran and Saadia Amiel

Phys. Rev. C 16, 266 (1977) - Published 1 July, 1977

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Elemental yields in the fission of ${}^{232}{Th}$ induced by reactor neutrons were measured and found to disclose a pronounced odd-even effect. Independent and cumulative yields of isotopes of Kr, Xe, Sn, and Sb were measured and the independent yields of isotopes of Rb, Cs, and Sb were subsequently derived. A comparison of the yield values obtained with the calculated "normal" yields reveals a constant enhancement of products with an even number of protons, relative to those with an odd number. An average amplitude of 30(±12)% in the fluctuation of proton pairing was established for all isotopes measured, except for the doubly magic ${}^{132}{Sn}$ , which shows an extreme effect, apparently due to its closed neutron shell. The odd-even effect is discussed in connection with the mass distribution, excitation, and total kinetic energies. The neutron shell effect on the yields is discussed with regard to the primary mass split and the neutron emission probabilities.

[NUCLEAR REACTIONS, FISSION Fission yields ${}^{232}{Th} (n, f)$ , calculated proton odd-even effect, calculated neutron closed shell effect.]

Second-order pion-nucleus optical potential

Tsung-Shung H. Lee and Soumya Chakravarti

Phys. Rev. C 16, 273 (1977) - Published 1 July, 1977

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The second-order pion-nucleus optical potential is expressed in momentum space in terms of the $π N$ off-shell $t$ matrix and the $NN$ correlation function. The dependence of the $π N t$ matrix on the total $π N$ momentum is determined within the framework of relativistic particle quantum mechanics. Numerical results are presented for $π - {}^{4}{He}$ scattering. It is found that the $NN$ correlations tend to decrease the forward elastic cross sections by a factor of about 1.5 at low energy, $E_{π} ≃ 60$ MeV. At higher energies the main effect of the $NN$ correlations is to increase the differential cross section at large angles. The effect of $NN$ correlations on the total cross section and the pion wave function is also found to be important. A study of the dependence of the calculated cross sections on the range parameters of the $π N t$ matrix and of the $NN$ correlations suggests that the $low$ -energy pion-nucleus scattering data cannot be adequately described by an optical model constructed from the first- and second-order terms in an expansion in terms of the $π N t$ matrix.

[NUCLEAR REACTIONS Second-order $π$ -nucleus optical potential studied in the multiple-scattering theory.]

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Single-particle component of the first excited state of ${}^{211}{Bi}$

Optical model description of anomalous elastic and inelastic $α - {}^{40}{Ca}$ scattering between 20 and 50 MeV

Neutron source reaction cross sections

Doorway state structure in neutron cross sections for ${}^{56}{Fe}$

Absolute cross sections and isomeric cross-section ratios for the ${}^{148}{Nd} (d, 2 n)$ , ${}^{148}{Nd} (p, n)$ , and ${}^{146}{Nd} (α, p n)$ reactions producing the isomeric pair ${}^{148}{Pm}^{m, g}$

( ${}^{12}C$ , ${}^{8}{Be}$ ) reaction on even calcium isotopes

Experimental evidence of multistep processes in the ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{76}{Ge}$ and ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ) ${}^{74}{Ge}$ reactions

Reaction measurements and analyses for ${}^{3}{He}$ + ${}^{4}{He}$ at 15.95 MeV (c.m.)

Analysis of the ${}^{74}{Ge}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{76}{Ge}$ and ${}^{76}{Ge}$ ( ${}^{16}O$ , ${}^{18}O$ ) ${}^{74}{Ge}$ reactions in terms of exact finite-range coupled-channel Born approximation

Yrast decay schemes from heavy ion + ${}^{48}{Ca}$ fusion-evaporation reactions. I. ${}^{54 - 56}{Mn}$ , ${}^{56}{Cr}$ , and ${}^{52 - 53}V$

Bombarding energy dependence of deep inelastic fragment kinetic energies

Structure in the ${}^{12}C ({}^{12}C, d) {}^{22}{Na}$ reaction near $E_{c . m .} = 14.3$ MeV

Mutual excitation near the Coulomb barrier in the ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C^{}$ + ${}^{12}C^{}$ reaction

Band structure in ${}^{147, 149, 151}{Eu}$ observed via ( $HI, x n$ ) reactions

Electrofission of ${}^{206}{Pb}$ , ${}^{207}{Pb}$ , and ${}^{208}{Pb}$

Scission point configuration of thermal-neutron induced fission of ${}^{235}U$

Scission point configuration of ${}^{252}{Cf}$ fission

Independent isomeric yield ratio of ${}^{148}{Pm}$ in fission of the moderately excited ${}^{236}U$ compound nucleus as a measure of fragment angular momentum

Independent yields of fast-neutron fission of ${}^{232}{Th}$ : Observation of proton odd-even effect and neutron shell effect on the yields

Second-order pion-nucleus optical potential

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