Recent Articles

Spin-parity determinations from the ${}^{48}{Ca} (\vec{d}, α) {}^{46}K$ reaction near 0°

S. Angelo, A. A. Pilt, and J. A. Kuehner

Phys. Rev. C 22, 427 (1980) - Published 1 August, 1980

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The tensor analyzing powers $T_{20}$ have been measured for a number of excited states of ${}^{46}K$ following the ${}^{48}{Ca} (\vec{d}, α) {}^{46}K$ reaction, leading to the following spin-parity determinations: g.s., $2^{-}$ ; 0.587 MeV, $3^{-}$ ; 0.691 MeV, $4^{-}$ ; 0.886 MeV, N; 1.370 MeV, $3^{-}$ ; 1.738 MeV, $4^{-}$ ( $0^{-}$ ); and 1.941 MeV, U (where N denotes natural and U, unnatural parity).

NUCLEAR REACTIONS ${}^{48}{Ca}$ (polarized $d$ , $α$ ), $E_{d} = 7.5, 8.0, 8.5, and 9.0$ MeV; measured tensor analyzing power $T_{20} (θ_{α} = 4 °)$ ; ${}^{46}K$ levels deduced $J^{π}$ . Enriched target.

Octupole modes of oscillation via analyzing power measurements

D. Ardouin, Ronald E. Brown, J. A. Cizewski, E. R. Flynn, J. W. Sunier, P. Alford, and E. Sugarbaker

Phys. Rev. C 22, 432 (1980) - Published 1 August, 1980

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Measurements of the analyzing power in the two-nucleon transfer reactions ${}^{70, 72}{Ge} (\vec{t}, p)$ have been carried out. This is a region where a shape transition has been previously proposed. Contrary to recent ( $\vec{p}$ , $t$ ) results, no strong interference effects between direct and two-step processes leading to the $2_{1}^{+}$ states have been observed. However, a marked difference has been revealed for the $3_{1}^{-}$ octupole transition. A microscopic interpretation of this effect is proposed.

NUCLEAR REACTIONS ${}^{70, 72}{Ge} (\vec{t}, p)$ measured $σ (θ)$ , $A_{y}$ , DWBA analysis.

Anomalous optical potential for sub-Coulomb barrier protons

S. M. Grimes

Phys. Rev. C 22, 436 (1980) - Published 1 August, 1980

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Measurements of the ( $p, n$ ) cross section on targets near $A = 100$ have been previously shown to require a rapid change in the imaginary potential with $A$ . Two possible explanations of this behavior are examined. Since the large values for the absorption are found midway between closed shells, it is possible that either collective effects or a modulation of the density of intermediate states could provide the explanation for this result. Calculations which explicitly include the collective states are presented, as are calculations of the two-particle one-hole state densities in these nuclei. We conclude that both effects play some role in explaining the "anomaly."

NUCLEAR REACTIONS ${}^{104}{Pd}$ , ${}^{116}{Cd}$ , $E = 3 - 6$ MeV, calculated proton absorption cross section with coupled channel formalism.

NUCLEAR STRUCTURE ${}^{90}{Zr}$ , ${}^{94}{Mo}$ , ${}^{104}{Pd}$ , ${}^{106}{Ag}$ , ${}^{107}{Ag}$ , ${}^{108}{Cd}$ , ${}^{109}{Ag}$ , ${}^{110}{Cd}$ , ${}^{111}{Ag}$ , ${}^{112}{In}$ , ${}^{113}{In}$ , ${}^{114}{In}$ , ${}^{115}{In}$ , and ${}^{117}{In}$ , calculated two-particle one-hole state densities, 0-15 MeV.

${}^{209}{Bi} ({}^{3}{He}, d) {}^{210}{Po}$ and ${}^{209}{Bi} ({}^{4}{He}, t) {}^{210}{Po}$ reactions and some matrix elements of the residual interaction

R. Groleau, W. A. Lanford, and R. Kouzes

Phys. Rev. C 22, 440 (1980) - Published 1 August, 1980

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The ( ${}^{3}{He}$ , $d$ ) and ( ${}^{4}{He}$ , $t$ ) single proton transfer reactions on ${}^{208}{Pb}$ and ${}^{209}{Bi}$ were studied using 30 and 40 MeV He beams. The outgoing reaction products were detected by a position sensitive proportional counter in the focal plane of a quadrupole-three-dipole spectrometer. The resolution varied between 10 and 14 keV full width at half maximum. Using the ratio of cross sections for the ( ${}^{3}{He}$ , $d$ ) and ( ${}^{4}{He}$ , $t$ ) reactions to determine $l$ transfers, spectroscopic factors for the reactions on ${}^{209}{Bi}$ have been measured relative to the transitions to the single-particle states observed in reactions on ${}^{208}{Pb}$ . Sum rules are applied and diagonal matrix elements of the effective interaction between valence protons around the ${}^{208}{Pb}$ core are deduced. The matrix elements obtained from empirical interactions and from realistic calculations are compared to these extracted matrix elements.

NUCLEAR REACTIONS ${}^{209}{Bi} ({}^{3}{He}, d) {}^{210}{Po}$ , ${}^{208}{Pb} ({}^{3}{He}, d) {}^{209}{Bi}$ $E_{{}^{3}{He}} = 30$ MeV and ${}^{209}{Bi} ({}^{4}{He}, t) {}^{210}{Po}$ , ${}^{208}{Pb} ({}^{4}{He}, t) {}^{209}{Bi}$ $E_{{}^{4}{He}} = 40$ MeV. Measured differential cross sections with a resolution of 10-14 keV (FWHM). Sum rule analysis and deduction of matrix elements of the residual interaction in nuclei.

${}^{48}{Ca} (d, n) {}^{49}{Sc}$ reaction at $E_{d} = 20$ MeV; proton single-particle states in ${}^{49}{Sc}$

Y. Iwasaki, A. Galonsky, and D. J. Weber

Phys. Rev. C 22, 456 (1980) - Published 1 August, 1980

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The ${}^{48}{Ca} (d, n) {}^{49}{Sc}$ reaction has been studied at $E_{d} = 20$ MeV. Angular distributions of differential cross sections have been obtained for 14 transitions to states in ${}^{49}{Sc}$ up to an excitation energy of 7.1 MeV. A distorted-wave Born-approximation analysis has been made of the experimental data. With respect to states corresponding to the same proton single-particle orbital, relative values of derived spectroscopic factors are generally in good agreement with those obtained from ( ${}^{3}{He}$ , $d$ ) reaction data. There are remarkable differences between the results from the ${}^{48}{Ca} (d, n) {}^{49}{Sc}$ reaction and the ${}^{48}{Ca} ({}^{3}{He}, n) {}^{49}{Sc}$ , however, regarding the dependence of the relative spectroscopic factors on proton single-particle orbitals.

NUCLEAR REACTIONS ${}^{48}{Ca} (d, n) {}^{49}{Sc}$ , $E = 20$ MeV, neutron time of flight, $Δ E = 120$ keV. Measured differential cross sections, 7.5°-50° lab. DWBA analysis, derived spectroscopic factors.

Spin-parity combinations and low-lying 2p-4h states in ${}^{54}{Mn}$

A. A. Pilt, J. A. Cameron, and J. A. Kuehner

Phys. Rev. C 22, 462 (1980) - Published 1 August, 1980

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The tensor analyzing powers $T_{20}$ of outgoing $α$ particles at $θ = 4 °$ have been measured in the ${}^{56}{Fe} (\vec{d}, α) {}^{54}{Mn}$ reaction at incident energies of 7.5, 8.0, 8.5, 9.0, and 9.5 MeV. The resulting determination of natural or unnatural parity led to the following new unambiguous $J^{π}$ assignments: 839 keV, $4^{+}$ ; 1073 keV, $6^{+}$ ; 1137 keV, $5^{+}$ ; 1391 keV, $1^{+}$ ; 1454 keV, $1^{+}$ ; 1.51 MeV, $2^{+}$ ; and 1.87 MeV, $3^{+}$ . In addition, natural or unnatural parity assignments were made to several levels above 2 MeV excitation for which no spin information existed prior to this experiment. A measurement of the angular distribution of outgoing $α$ particles in an unpolarized ( $d, α$ ) reaction led to a tentative $0^{+}$ assignment to a state at 1.68 MeV on the basis of decreasing cross section at forward angles. The results are compared to 1p3h + 2p4h shell model calculations and we suggest that the 1.51, 1.68, and 1.85 MeV levels are largely 2p-4h states.

NUCLEAR REACTIONS ${}^{56}{Fe} (\vec{d}, α)$ , $E = 7.5, 8.0, 8.5, 9.0, and 9.5$ MeV; measured $T_{20} (4 °)$ ; ${}^{54}{Mn}$ deduced levels, $J$ , $π$ . ${}^{56}{Fe} (d, α)$ , $E = 9.0$ MeV; measured $σ (E_{α}, θ)$ ; ${}^{54}{Mn}$ level deduced $J^{π} = (0^{+})$ . Comparison with shell-model calculations.

High-spin states of ${}^{83}{Rb}$

W. Gast, K. Dey, A. Gelberg, U. Kaup, F. Paar, R. Richter, K. O. Zell, and P. von Brentano

Phys. Rev. C 22, 469 (1980) - Published 1 August, 1980

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The decay scheme of ${}^{83}{Rb}$ was studied by gamma-ray spectroscopy with the ${}^{81}{Br} (α, 2 n) {}^{83}{Rb}$ , ${}^{70}{Zn} ({}^{16}O, p 2 n) {}^{83}{Rb}$ , ${}^{74}{Ge} ({}^{12}C, p 2 n) {}^{83}{Rb}$ , and ${}^{80}{Se} ({}^{6}{Li}, 3 n) {}^{83}{Rb}$ reactions. New energy levels and spins and parities were established. A stretched spin band built on the isomeric $\frac{9}{2^{+}}$ level at 42.3 keV, a $\frac{5}{2^{-}}$ ground state quasirotational band, and a three-quasiparticle band were found.

NUCLEAR REACTIONS ${}^{81}{Br} (α, 2 n)$ , $E_{α} = 19 - 25$ MeV, ${}^{80}{Se} ({}^{6}{Li}, 3 n)$ , $E_{{}^{6}{Li}} = 23 - 29$ MeV, measured $E_{γ}$ , $I_{γ}$ , $γ - γ$ -coincidence, $γ$ -angular distribution, ${}^{70}{Zn} ({}^{16}O, p 2 n) {}^{83}{Rb}$ , $E_{{}^{16}O} = 52$ MeV, ${}^{74}{Ge} ({}^{12}C, p 2 n) {}^{83}{Rb}$ , $E_{{}^{12}C} = 35 - 49$ MeV, measured $E_{γ}$ , ${}^{83}{Rb}$ deduced levels, $J$ , $π$ . Enriched targets, Ge(Li).

Limits on model-independent descriptions of elastic alpha-particle scattering

P. L. Roberson

Phys. Rev. C 22, 482 (1980) - Published 1 August, 1980

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Nearly unconstrained parametrizations of local optical-model potentials are used to investigate potential shapes which best reflect experimental data. The model dependence of optical-model analyses is investigated by removing as much of the parametrization bias as is practical, so that the analyses are mostly dependent on the sensitivity of the alpha-nucleus interaction and the precision of the experimental data. It is found that real- versus imaginary-potential correlations are the dominant limitation on model-independent analyses using local potentials; correlations decrease the effective sensitivity of the interaction to the interior of the real potential and are responsible for ambiguous solutions to the problem.

NUCLEAR REACTIONS $α$ -nucleus optical potentials; model-independent parametrization. ${}^{50}{Ti} (α, α)$ , $E_{α} = 140$ MeV.

Giant monopole and quadrupole resonances and other multipole excitations in ${}^{208}{Pb}$ studied in 43 MeV/nucleon $α$ -particle and deuteron scattering

H. P. Morsch, C. Sükösd, M. Rogge, P. Turek, H. Machner, and C. Mayer-Böricke

Phys. Rev. C 22, 489 (1980) - Published 1 August, 1980

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Inelastic excitations of ${}^{208}{Pb}$ up to the giant resonance region were investigated in 172 MeV $α$ and 86 MeV $d$ scattering. In the spectra, the giant resonance bump exhibits a double structure; the well known isoscalar giant quadrupole resonance at 10.9 ± 0.3 MeV, and the new resonance at 13.8 ± 0.3 MeV, for which evidence exists for $L = 0$ . Both resonances have a full width at half maximum of 2.6 ± 0.3 MeV. Below the giant resonances two new structures were found at excitation energies of 7.4 and 8.1 MeV which were identified as hexadecapole excitations with a strength of 3 and 2.7 single particle units, respectively. Angular distributions have been obtained for highlying excitations as well as for the low-lying $3^{-}$ , $5^{-}$ , $2^{+}$ , and $4^{+}$ states. Microscopic distorted-wave Born-approximation calculations have been performed using double folding form factors. In this approach a good description of our scattering data has been achieved. For low-lying excitations our results are consistent with electron and proton scattering analyses. For the giant quadrupole resonance the angular distributions cannot be described assuming pure $L = 2$ excitation. Different assumptions about other contributing multipole strengths are discussed. Assuming the 13.8 MeV resonance to be the giant monopole excitation, several models yield differential cross sections which are inconsistent with the data. A consistent description of $α$ and $d$ scattering is obtained if, in addition to the compressional $L = 0$ mode, diffuseness effects are considered as well as other contributing multipole strength ( $L = 1$ ). With the transition density used, the monopole strength corresponds to about 90% of the energy weighted sum rule limit. The result of a recent ${}^{16}O$ scattering experiment suggesting a pronounced $L = 3 and 5$ resonance at $E_{x} ≃ 20$ MeV in ${}^{208}{Pb}$ is not confirmed.

NUCLEAR REACTIONS ${}^{208}{Pb} (α, α^{'})$ , $E_{α} = 172$ MeV, ${}^{108}{Pb} (d, d^{'})$ , $E_{d} = 86$ MeV, measured $σ (θ)$ . Deduced strength of multipole excitation up to the giant resonance region.

Variation of ground-state $α$ -particle strengths for $sd$ - and $fp$ -shell nuclei

N. Anantaraman, H. W. Fulbright, and P. M. Stwertka

Phys. Rev. C 22, 501 (1980) - Published 1 August, 1980

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It is shown that when ( ${}^{6}{Li}$ , $d$ ) experimental results are reduced via a distorted-wave Born approximation procedure taking into account the finite size of ${}^{6}{Li}$ , the systematic variation in $α$ -particle transfer strengths in the $A = 20$ to $A = 68$ region agrees with recent theoretical strength predictions based on shell-model wave functions.

NUCLEAR REACTIONS DWBA analyses of ( ${}^{6}{Li}$ , $d$ ) reactions on 19 $sd$ - and 17 $fp$ -shell targets. Derived $S_{α}$ (g.s.). Compared with the shell-model predictions.

Resonant and average behavior of the ${}^{12}C$ + ${}^{12}C$ total reaction cross section: $5.6 \leq E_{c . m .} \leq 10.0$ MeV

K. A. Erb, R. R. Betts, S. K. Korotky, M. M. Hindi, P. P. Tung, M. W. Sachs, S. J. Willett, and D. A. Bromley

Phys. Rev. C 22, 507 (1980) - Published 1 August, 1980

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The gamma-radiation yields from the ${}^{12}C$ + ${}^{12}C$ interaction were measured in steps of 50 keV over the bombarding energy range $11.8 \leq E_{lab} \leq 20$ MeV in order to study the energy dependence of the total reaction cross section. Several new resonances, occurring at $E_{c . m .} = 6.49, 7.30, 7.45, 9.33, and 9.67$ MeV, were identified in these yields. Carbon partial widths were determined for a number of resonances, and these widths demonstrate the quasimolecular nature of the corresponding structures. The average or background trend of the energy dependence of the reaction cross section was found to be adequately described by an incoming-waves boundary condition model, however, and no evidence was found in the energy-averaged yields for anomalous absorption in the ${}^{12}C$ + ${}^{12}C$ system.

NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, γ)$ , $E = 11.8 - 20.0$ MeV; measured $σ (E)$ , deduced total ${}^{12}C$ + ${}^{12}C$ reaction cross section. Located five new narrow resonances. Measured total widths, estimated carbon partial widths of resonances. Optical model analysis of $σ_{React}$ , using incoming-wave boundary condition model.

Statistical analysis of the reaction ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ in the energy range 7-15 MeV

W. Galster, P. Dück, H. Fröhlich, W. Treu, H. Voit, and S. M. B. Lee

Phys. Rev. C 22, 515 (1980) - Published 1 August, 1980

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Statistical analyses involving deviation functions, channel cross correlations, and the number of maxima method were applied to the ${}^{12}C ({}^{12}C, α)$ reaction in the energy range 7.4-15 MeV. They show that the structures found in the angle integrated excitation functions are not consistent with a pure statistical reaction mechanism.

NUCLEAR REACTIONS Statistical analysis of the reaction ${}^{12}C ({}^{12}C, α)$ , $E = 7.4 - 15$ MeV; existence of nonstatistical features deduced.

${}^{11}B$ + ${}^{40}{Ca}$ single-nucleon transfer reactions $E_{lab} = 51.5$ MeV

C. W. Glover, K. W. Kemper, and A. D. Frawley

Phys. Rev. C 22, 522 (1980) - Published 1 August, 1980

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Angular distributions for the single-nucleon transfer reactions ${}^{40}{Ca}$ ( ${}^{11}B$ , ${}^{12}C$ ) ${}^{39}K$ ( $J^{π} = \frac{3}{2^{+}} and \frac{1}{2^{+}}$ and ${}^{40}{Ca} ({}^{11}B, {}^{10}B (J^{π} = 3^{+} and 1^{+})) {}^{41}{Ca}$ have been measured at 51.5 MeV. The distorted-wave Born approximation was used to analyzed the data. The distorted waves used in the distorted-wave Born-approximation calculations were generated from both Woods-Saxon and double-folding optical potentials which describe elastic scattering data. The standard distorted-wave Born-approximation calculations reproduced the forward angle data, including the $l = 1$ pickup reaction, but overpredicted the back-angle data. Distorted-wave Born-approximation calculations carried out with distorted waves obtained from double-folded potentials were in much better agreement with the data. The extracted spectroscopic factors for the proton pickup reaction are much larger than those obtained from light-ion data while for the neutron stripping case they agree, even for the case where ${}^{10}B$ was in its first excited state.

NUCLEAR REACTIONS ${}^{40}{Ca}$ ( ${}^{11}B$ , ${}^{12}C$ ), ${}^{40}{Ca}$ ( ${}^{11}B$ , ${}^{10}B$ ), $E = 51.5$ MeV, measured $σ (θ)$ . DWBA analysis with Woods-Saxon and double-folding optical potentials.

Intermediate structures and their dominant $l$ values in ${}^{16}O$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{20}{Ne}$ reactions, $E_{c . m .} = 11.5 to 18.6$ MeV

J. R. Hurd, N. R. Fletcher, A. D. Frawley, and J. F. Mateja

Phys. Rev. C 22, 528 (1980) - Published 1 August, 1980

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Measurements of $σ (θ, E)$ are reported for ${}^{16}O$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{20}{Ne}$ * reactions to the low lying $0^{+}$ , $2^{+}$ , $4^{+}$ and unresolved $3^{-}$ , $1^{-}$ final states. The energy range is $E_{c . m .} ≃ 11.5 to 18.6$ MeV with measurements at ∼ 86 keV intervals. Up to 38 angles between $θ_{c . m .} = 12 ° and 167 °$ are measured for each energy. A large number of resonances are identified by their appearance over a broad range of forward and backward angles and by their energy correlation over exit channels. Many $J^{π}$ assignments are inferred from the behavior of back angle $σ (θ)$ across the resonance. All $J$ values are from one to three units less than the optical model grazing angular momentum for the ${}^{16}O$ + ${}^{12}C$ channel.

NUCLEAR REACTIONS ${}^{16}O$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{20}{Ne}$ *; measured $σ (θ, E)$ to low-lying states for $E_{c . m .} ≃ 11.6 - 18.6$ MeV and $θ_{c . m .} ≃ 12 ° - 167 °$ . Deduced resonant energies and $J^{π}$ values.

Spin-flip systematics and spin-orbit potentials in heavy-ion inelastic scattering

Q. K. K. Liu and P. J. Ellis

Phys. Rev. C 22, 540 (1980) - Published 1 August, 1980

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Systematics of the $| m | = 1$ population probability $P_{1}$ of ${}^{24}{Mg}$ ( $2^{+}$ ) in the reaction ${}^{24}{Mg}$ ( ${}^{13}C$ , ${}^{13}C$ ′) ${}^{24}{Mg}$ ( $2^{+}$ ) were studied using the coupled channels formalism. It was found that $P_{1}$ is sensitive only to the parameters of the spin-orbit potential and is determined essentially by the magnitude and the shape of the spin-orbit potential in the region of the strong absorption radius. The data require a significantly larger spin-orbit potential than that given by the folding model.

NUCLEAR REACTIONS ${}^{24}{Mg}$ ( ${}^{13}C$ , ${}^{13}C$ ′), $E = 35$ MeV; coupled channels calculation of spin-flip probability for the ${}^{24}{Mg}$ 1.37 MeV $2^{+}$ level.

Compound nucleus fission at high angular momentum studied in the reaction ${}^{132}{Xe}$ + ${}^{30}{Si}$

H. Oeschler, H. Freiesleben, K. D. Hildenbrand, P. Engelstein, J. P. Coffin, B. Heusch, and P. Wagner

Phys. Rev. C 22, 546 (1980) - Published 1 August, 1980

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Reaction products from the bombardment of ${}^{132}{Xe}$ onto ${}^{30}{Si}$ at energies between 5.4 MeV/u and 8.2 MeV/u have been measured by a time-of-flight system combined with an ionization chamber. At all energies fission fragments are found to be well separated from deep inelastic reaction products. The rapidly increasing excitation function for fission shows an onset at $65 - 70 ℏ$ . This value and an $l_{crit}$ of $98 ℏ$ at 8.2 MeV/u are compatible with the concept of a fissioning compound nucleus. However, at the highest bombarding energies the $Z$ distributions indicate the emission of charged particles which is difficult to reconcile with the idea of a fully equilibrated compound nucleus. Incomplete momentum transfer reactions (incomplete fusion) followed by fission are considered as an explanation for the strong increase of the width of the $Z$ distribution with excitation energy. Consequences for the formation of compound nuclei at high angular momenta are discussed.

NUCLEAR REACTIONS ${}^{132}{Xe}$ + ${}^{30}{Si}$ ; $\frac{E}{A} = 5.4 - 8.2$ MeV/u; measured $Z$ and $A$ distributions of fission fragments and $σ_{fission} (E)$ ; compound nucleus fission and nonequilibrium effects. Enriched target.

Lifetime and $E 0$ decay of the first excited $0^{+}$ state in ${}^{14}C$

M. Toulemonde, K. H. Souw, J. C. Adloff, and N. Schulz

Phys. Rev. C 22, 553 (1980) - Published 1 August, 1980

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The reaction ${}^{2}H ({}^{13}C, p) {}^{14}C$ has been used to measure the lifetime of the ${}^{14}C$ (6.59 MeV, $0^{+}$ ) state. From recoil distance and Doppler shift attenuation measurements a value $τ = (4.6 \pm 0.7)$ ps was found. The reaction ${}^{13}C (d, p) {}^{14}C$ has been used to study the $E 0$ $π$ decay of the $0^{+}$ state. The branching ratio $\frac{Γ_{π}}{Γ}$ was measured to be (1.1±0.1) × $10^{- 2}$ . When this value is combined with the determined lifetime an $E 0$ matrix element ${〈 M 〉}_{π} = (0.36 \pm 0.06)$ ${fm}^{2}$ is obtained.

NUCLEAR REACTIONS $d ({}^{13}C, p)$ , $E = 18.9$ MeV; ${}^{13}C (d, p)$ , $E = 2.7$ MeV; ${}^{14}C$ measured lifetime and $E 0$ branching ratio, deduced $E 0$ matrix element. Enriched targets.

Spin assignments for the resonant structures in the ${}^{12}C$ + ${}^{12}C$ system through the reaction ${}^{12}C$ ( ${}^{12}C$ , ${}^{16}O_{g . s .}$ ) ${}^{8}{Be}_{g . s .}$ at $E_{c . m .} = 6 - 11$ MeV

R. Wada, T. Murakami, E. Takada, M. Fukada, and K. Takimoto

Phys. Rev. C 22, 557 (1980) - Published 1 August, 1980

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The resonant structures in the ${}^{12}C$ + ${}^{12}C$ system have been studied through the reaction ${}^{12}C$ ( ${}^{12}C$ , ${}^{16}O_{g . s .}$ ) ${}^{8}{Be}_{g . s .}$ at $E_{c . m .} = 6 - 11$ MeV. Excitation functions of the reaction have been measured in 50-keV steps at 14 angles between $θ_{c . m .} \sim 29 ° and \sim 90 °$ . Resonant structures have been found at 5.94, 6.41, 6.68, 7.47, 7.90, 8.10, 8.37, 8.58, 8.88, 9.08, 9.34, 9.56, 9.70, 9.99, 10.29, 10.43, 10.68, and 10.98 MeV. Some of these are new resonances. Their $J^{π}$ values have been assigned to be $4^{+}$ (5.94 MeV), $2^{+}$ (6.41 MeV), $2^{+}$ (6.68 MeV), $4^{+}$ (7.90 MeV), $2^{+}$ + $4^{+}$ (8.10 MeV), $4^{+}$ (8.37 MeV), $4^{+}$ (8.58 MeV), $6^{+}$ (8.88 MeV), $6^{+}$ (9.08 MeV), $6^{+}$ (9.34 MeV), $6^{+}$ (9.56 MeV), $6^{+}$ (9.70 MeV), $6^{+}$ (9.99 MeV), ( $8^{+}$ )(10.29 MeV), ( $8^{+}$ )(10.43 MeV), $8^{+}$ (10.68 MeV), and $8^{+}$ (10.98 MeV). An interesting relation between this exit channel and the $α$ , $γ$ exit channels has been found. This may give us important information about the structure of the resonances. Good correspondence has been found with several levels appearing in the reaction ${}^{12}C ({}^{16}O, α) {}^{24}{Mg}^{*}$ . This fact suggests that the resonances in the ${}^{16}O$ - ${}^{8}{Be}$ channel are true states of ${}^{24}{Mg}$ .

NUCLEAR REACTIONS ${}^{12}C$ ( ${}^{12}C$ , ${}^{16}O_{g . s .}$ ) ${}^{8}{Be}_{g . s .}$ , $E_{c . m .} = 6 - 11$ MeV; $θ_{c . m .} = 29 - 90 °$ ; measured $σ (θ, E)$ ; deduced resonance energies, $J^{π}$ values, total widths, partial-width products ( $Γ_{c} \cdot Γ_{0}$ ).

Structure in the excitation functions of the ${}^{12}C$ ( ${}^{12}C$ , ${}^{10}B$ ) and ${}^{12}C$ ( ${}^{12}C$ , ${}^{11}B$ ) reactions

T. M. Cormier and B. R. Fulton

Phys. Rev. C 22, 565 (1980) - Published 1 August, 1980

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The one- and two-nucleon transfer reactions ${}^{12}C$ ( ${}^{12}C$ , ${}^{11}B$ ) ${}^{13}N$ and ${}^{12}C$ ( ${}^{12}C$ , ${}^{10}B$ ) ${}^{14}N$ have been studied in the energy range of the ${}^{12}C$ + ${}^{12}C$ gross structure resonances in a search for related phenomena. Resonances are observed which are correlated with those seen in ${}^{12}C$ + ${}^{12}C$ inelastic scattering. Using Coulomb wave functions to estimate barrier penetrabilities, it is found that the reduced partial widths of the nucleon transfer channels are comparable to those of the inelastic channels.

NUCLEAR REACTIONS ${}^{12}C$ ( ${}^{12}C$ , ${}^{10}B$ ) and ${}^{12}C$ ( ${}^{12}C$ , ${}^{11}B$ ). Measured: $σ (E, θ)$ $E_{lab} = 44 to 80$ MeV for ${}^{10}B$ and $E_{lab} = 54 to 68$ MeV for ${}^{11}B$ . Deduced: resonance structure, reduced partial widths.

Markovian and non-Markovian effects in heavy-ion reactions at 10 -200 MeV per nucleon

E. S. Hernández and G. Mantzouranis

Phys. Rev. C 22, 575 (1980) - Published 1 August, 1980

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We have derived simplified formulas for the transition probability from an entrance channel $| i 〉$ to an exit channel $| f 〉$ that corresponds to a heavy-ion reaction. It is shown that a rearrangement of the perturbation series leads to an expansion of the cross section in terms of the ratio $y$ between the duration of a nucleon-nucleon collision and the elapsed time between two successive interactions. The cross section splits into two contributions, the Markovian part independent of $y$ , and the non-Markovian one containing explicit $y$ dependence. Such a decomposition allows us to demonstrate that a transition from the Markovian to the non-Markovian behavior is to be expected around 20 MeV per particle in the initial channel. This transition manifests itself in a change in the slope of the width of the mass distribution as a function of the incident energy. This fact seems to be in agreement with existing data.

NUCLEAR REACTIONS Heavy-ion reactions, Gaussian random matrix ensembles, perturbative expansion, ratio between characteristic times. Mark-ovian and non-Markovian contributions to the cross section.

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Spin-parity determinations from the ${}^{48}{Ca} (\vec{d}, α) {}^{46}K$ reaction near 0°

Octupole modes of oscillation via analyzing power measurements

Anomalous optical potential for sub-Coulomb barrier protons

${}^{209}{Bi} ({}^{3}{He}, d) {}^{210}{Po}$ and ${}^{209}{Bi} ({}^{4}{He}, t) {}^{210}{Po}$ reactions and some matrix elements of the residual interaction

${}^{48}{Ca} (d, n) {}^{49}{Sc}$ reaction at $E_{d} = 20$ MeV; proton single-particle states in ${}^{49}{Sc}$

Spin-parity combinations and low-lying 2p-4h states in ${}^{54}{Mn}$

High-spin states of ${}^{83}{Rb}$

Limits on model-independent descriptions of elastic alpha-particle scattering

Giant monopole and quadrupole resonances and other multipole excitations in ${}^{208}{Pb}$ studied in 43 MeV/nucleon $α$ -particle and deuteron scattering

Variation of ground-state $α$ -particle strengths for $sd$ - and $fp$ -shell nuclei

Resonant and average behavior of the ${}^{12}C$ + ${}^{12}C$ total reaction cross section: $5.6 \leq E_{c . m .} \leq 10.0$ MeV

Statistical analysis of the reaction ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ in the energy range 7-15 MeV

${}^{11}B$ + ${}^{40}{Ca}$ single-nucleon transfer reactions $E_{lab} = 51.5$ MeV

Intermediate structures and their dominant $l$ values in ${}^{16}O$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{20}{Ne}$ reactions, $E_{c . m .} = 11.5 to 18.6$ MeV

Spin-flip systematics and spin-orbit potentials in heavy-ion inelastic scattering

Compound nucleus fission at high angular momentum studied in the reaction ${}^{132}{Xe}$ + ${}^{30}{Si}$

Lifetime and $E 0$ decay of the first excited $0^{+}$ state in ${}^{14}C$

Spin assignments for the resonant structures in the ${}^{12}C$ + ${}^{12}C$ system through the reaction ${}^{12}C$ ( ${}^{12}C$ , ${}^{16}O_{g . s .}$ ) ${}^{8}{Be}_{g . s .}$ at $E_{c . m .} = 6 - 11$ MeV

Structure in the excitation functions of the ${}^{12}C$ ( ${}^{12}C$ , ${}^{10}B$ ) and ${}^{12}C$ ( ${}^{12}C$ , ${}^{11}B$ ) reactions

Markovian and non-Markovian effects in heavy-ion reactions at 10 -200 MeV per nucleon

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