Neutron deexcitation mechanism through pre-equilibrium and equilibrium phases of the ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}$($\alpha$,$\mathrm{xn}\gamma$) reaction at $E\left(\alpha \right)=120\mathrm{}$ MeV was studied as a function of the neutron multiplicity $x$. The deexciting neutrons with a wide range of the multiplicity $x$ showed energy and angular distributions characteristic of the pre-equilibrium process followed by equilibrium evaporation. The pre-equilibrium neutrons were found to carry away considerable amounts of angular momenta. The energy and angular distributions of the emitted neutrons were analyzed in terms of a simple two phase deexcitation model of the pre-equilibrium phase and the equilibrium phase. It gives the mean number of pre-equilibrium neutrons (∼1.7), pre-equilibrium quasitemperature (∼6 MeV), the average exciton particles number around 20, and the equilibrium temperature (1.6 MeV).

NUCLEAR REACTIONS ${}_{}{}^{164}{}_{}{}^{}\mathrm{Dy}(\alpha ,xn\gamma ){}_{}{}^{168-x}{}_{}{}^{}\mathrm{Er}$, $x=6-11\mathrm{}$, $E\left(\alpha \right)=120\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(x\right)\mathrm{}$, $\sigma (E_n,{\theta }_n)$; deduced angular momentum removal by neutrons, pre-equilibrium effects, properties of pre-equilibrium phase. Two phase deexcitation model analysis. Enriched target.

High resolution neutron transmission and differential scattering measurements have been performed on ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and the results for $E=25-600\mathrm{}$ keV are presented. Data analyses were performed utilizing multilevel $R$-matrix codes. Resonance parameters (i.e., $E$, 1, $J$, and ${\Gamma }_n$) were deduced for a large fraction of the 223 resonances observed. In addition to the previously known doorway in the $s$-wave channel, the $p$-wave neutron strength function exhibits significant changes near 40 and 145 keV indicative of doorway states in the $p_{\frac{1}{2}}$ and $p_{\frac{3}{2}}$ channels, respectively. These results are in good agreement with those observed in a study of the ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$+$n$ reaction. It is suggested that these doorway states arise from a ($d_{\frac{5}{2}}$, $3^{-}$) particle-core excitation. The $d$-wave strength function shows indications of a doorway at about $E=425\mathrm{}$ keV. The latter represents doorway resonances in the $d_{\frac{3}{2}}$ and $d_{\frac{5}{2}}$ channels which probably arise from a recoupling of the particle-core excitation that has been used to explain the $s$-wave doorway. A cumulative plot of the number of $s$-wave resonances vs $E$ shows considerable curvature which indicates an increase of about 12% in the level density per 100 keV of excitation. These data were analyzed in terms of a constant temperature model with a nuclear temperature of about 0.9 MeV. The model reproduced the cumulative plot of $d$-wave resonances reasonably well up to $E\approx 500$ keV, but underestimated the number of $p$-wave resonances. This indicates a parity dependence of the level density formula for this nucleus. Many of the resonances which had previously been thought to contribute to the ground-state $M1\mathrm{}$ radiative strength are in fact formed by $s$ and $d$ waves, and hence, decay by $E1$ radiation. We deduce a considerably smaller amount of $M1\mathrm{}$ radiation for $E_x=6738-7340\mathrm{}$ keV in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ than had been reported earlier.

NUCLEAR REACTIONS ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}\mathrm{}\left(n\right)\mathrm{}$, ($n$,$n$), $E=25-600\mathrm{}$ keV; measured ${\sigma }_T\mathrm{}\left(E\right)\mathrm{}$, $\sigma (E,\theta )$. ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ deduced doorway states, resonance parameters, $J^{\pi }$, ${\Gamma }_n$, neutron strength functions, level densities, $M1\mathrm{}$ ground-state radiative strength.

Inelastic electron scattering cross sections for the excited states at 6.43, 6.74, and 7.06 MeV in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ were measured with high resolution. The measurements were done in forward and backward directions covering the momentum transfer range of $0.3<q<\mathrm{}2.5\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$. The state at 7.06 MeV was identified as the $\pi {\left(i_{\frac{13}{2}}{h_{\frac{11}{2}}^{-}}^1\right)}_{12-}$ and the states at 6.74 and 6.43 MeV as the $\nu {\left(j_{\frac{15}{2}}{i_{\frac{13}{2}}^{-}}^1\right)}_{14-,12-}$, respectively. The identification was based on four criteria: (a) the agreement between the $q$ dependence of the measured form factor with that of Hartree-Fock single particle-hole prediction, with no adjustment of radial parameters, (b) the absence of a longitudinal form factor, (c) the relative magnitude of the observed levels, and (d) the excitation energies being close to the single p-h energies. The measured strength of each state was found to be 50% of the single p-h prediction.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$($e$,$e^{\prime }$) $E=50-335\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, $\theta =90\mathrm{}°,160\mathrm{}°$. ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ deduced, levels $J^{\pi }={12}^{-}, {14}^{-}$. DWBA calculation with Hartree-Fock single particle wave functions.

The low-energy part of the radiation emitted after thermal neutron capture in ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ has been investigated by different experimental techniques: Gamma-ray measurements were performed with a diffraction spectrometer. The conversion electron spectrum was recorded with a $\beta$ spectrograph and measurements of gamma-gamma coincidences were carried out. For ten rotational bands in ${}_{}{}^{182}{}_{}{}^{}\mathrm{Ta}$, which were already proposed in an earlier work, a large amount of new decay data has been obtained and for most of these bands higher rotational levels have been found. These ten bands have for their lowest level the following energies and $I^{\pi }K$ values: 0 keV $3^{-}$3, 16 keV $5^{+}$5, 114 keV $4^{-}$4, 150 keV $4^{+}$4, 173 keV $5^{-}$5, 250 keV $3^{+}$3, 270 keV $2^{-}$2, 402 keV $2^{+}$2, 547 keV $3^{-}$3, and 558 keV $1^{-}$0. New rotational bands with the following band head energies and structure have been established: 443.6 keV ${\{\frac{5}{2^{+}}{\mathrm{}\left[402\right]\mathrm{}}_p, \frac{3}{2^{-}}{\mathrm{}\left[512\right]\mathrm{}}_n\}}_{K=1\mathrm{}}$, 593.0 keV ${\{\frac{7}{2^{+}}{\mathrm{}\left[404\right]\mathrm{}}_p, \frac{9}{2^{+}}{\mathrm{}\left[624\right]\mathrm{}}_n\}}_{K=1\mathrm{}}$, and 647.6 keV ${\{\frac{5}{2^{+}}{\mathrm{}\left[402\right]\mathrm{}}_p, \frac{1}{2^{-}}{\mathrm{}\left[510\right]\mathrm{}}_n\}}_{K=2\mathrm{}}$. Tentative band heads have been proposed at 390, 740, and 749 keV with $I^{\pi }K$ values $6^{+}$6, $2^{-}$2, and $3^{+}$3. For the sake of completeness, previously found levels with $K$ values ranging from seven to ten are also discussed.

NUCLEAR REACTIONS ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$($n$,$\gamma$), $E=\mathrm{thermal}$; measured $E_{\gamma }$, $I_{\gamma }$, $I_{\mathrm{ce}}$, $\gamma \gamma$ co-incidences. ${}_{}{}^{182}{}_{}{}^{}\mathrm{Ta}$ deduced levels $J$, $\pi$, $K$, $\mathrm{cc}$, $\gamma$ multipolarities, $J$ of ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ neutron resonances. Natural targets.

Recent measurements of the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ neutron capture cross section show a considerable amount of fluctuation between 5 and 100 keV. Statistical tests performed on the measured cross section suggest that the fluctuations are not compatible with the statistical model of nuclear reactions and imply the existence of intermediate structure, which is interpreted in terms of doorway states. The validity of the statistical tests used here is confirmed by numerical experiments with simulated cross sections generated by the Monte Carlo method, in accordance with the statistical method. The behavior of the capture cross section is compared to those of the subthreshold fission cross section and of the inelastic scattering cross section. The threshold anomaly at the opening of the inelastic channel at 45 keV is seen in the form of a rounded step.

NUCLEAR REACTIONS Neutron capture ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$($n$,$\gamma$). $E=5\mathrm{} \mathrm{keV}-0.1\mathrm{} \mathrm{MeV}$ measured $\sigma \mathrm{}\left(E\right)\mathrm{}$; statistical tests for intermediate structure; doorway states.

In-beam, time-sorted measurements of internal conversion electrons and $\gamma$ rays are reported for ${}_{}{}^{203}{}_{}{}^{}\mathrm{Pb}$ formed by the ${}_{}{}^{204}{}_{}{}^{}\mathrm{Hg}$($\alpha$,$5n$) reaction at $E_{\alpha }=53.5\mathrm{}$ MeV. The multipolarity of the 153 keV transition deexciting the $\frac{29}{2^{-}}$ isomer is determined to be $E3$. The 239-keV transition, in the cascade connecting the $\frac{23}{2^{+}}$ and $\frac{21}{2^{+}}$ states, is determined to be $M1$. The 874-keV transition is found to have an $\frac{M1}{E2\mathrm{}}$ $\gamma$ intensity ratio of ${0.4}_{-0.15\mathrm{}}^{+0.20\mathrm{}}$. Thus, the state at 2796 keV is assigned $J^{\pi }=\frac{23}{2^{+}}$ and has a probable configuration ${p_{\frac{1}{2}}}^{-1\mathrm{}}{f_{\frac{5}{2}}}^{-3\mathrm{}}{i_{\frac{13}{2}}}^{-1\mathrm{}}+{p_{\frac{1}{2}}}^{-2\mathrm{}}{f_{\frac{5}{2}}}^{-1\mathrm{}}{f_{\frac{7}{2}}}^{-1\mathrm{}}{i_{\frac{13}{2}}}^{-1\mathrm{}}$. The other measured multipolarities are $E2\left(258 \mathrm{keV}\right)$, $M1\left(635\mathrm{} \mathrm{keV}\right)$, $E2\left(839\mathrm{} \mathrm{keV}\right)$, and $M4\left(1027\mathrm{} \mathrm{keV}\right)$ with no measurable admixture of multipoles.

NUCLEAR REACTIONS ${}_{}{}^{204}{}_{}{}^{}\mathrm{Hg}$($\alpha$,$5n$)${}_{}{}^{203}{}_{}{}^{}\mathrm{Pb}$, $E_{\alpha }=53.5\mathrm{}$ MeV. Measured $\gamma$ and conversion electron spectra 30-1300 keV in eight time bands between beam bursts. Deduced ICC, $J$, $\pi$. Si(Li) and Ge(Li) detectors.

Cross sections for the radiative capture and one nucleon emission reactions have been obtained by mass identification of reaction products at 0° using thin targets for the systems ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (70 and 59 MeV), ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (70 and 59 MeV) and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (59 MeV). The cross sections for radiative capture are in all cases < 500 nb. The measurement of the ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ cross section is in disagreement with previous work performed using thick targets. This discrepancy is discussed.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (70 and 59 MeV), ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (70 and 59 MeV), ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (59 MeV) upper limits radiative capture cross sections + estimate of one nucleon emission cross section for ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ (70 MeV).

Structure in the energy spectra of specific final fragments produced in symmetric heavy-ion damped collisions is shown to correlate with statistical evaporation processes from primary fragments. The calculations are applied and described for ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ produced by the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ reaction at a bombarding energy of 400 MeV. The calculated energy spectrum has structure at the same energies as the experimental spectrum.

NUCLEAR REACTIONS Calculated isotopic energy spectra from heavy-ion damped collisions. Origin of structure.

The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,${}_{}{}^8{}_{}{}^{}\mathrm{Be}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$* reactions to the low lying $0^{+}$, $2^{+}$, $4^{+}$ and $3^{-}$, $1^{-}$ states have been studied for $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=18.5\mathrm{} \mathrm{to} 22.7$ MeV at intervals of ∼86 keV. Excitation functions indicate the presence of twelve resonances in this energy region, eight of which are given $J^{\pi }$ assignments based on angular distributions of the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ + ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$($0^{+}$) channel measured at each energy interval. A high degree of resonance energy correspondence between these and other reaction cross section anomalies is noted. It is apparent that the density of resonant states for the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ + ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ exit channel is much higher than reported in other channels.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$*; $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\simeq 18.5 \mathrm{to} 22.7$ MeV, ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\simeq 13° \mathrm{to} 73°$; measured $\sigma (\theta ,E)$ to low lying states, deduced resonance energies and $J^{\pi }$ values.

The $\gamma$-ray yield functions for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ reaction have been studied from $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=15\mathrm{} \mathrm{to} 23.7$ MeV and the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction from $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=20\mathrm{} \mathrm{to} 34.9$ MeV. Structure in the form of a broad oscillation was observed for some channels of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ reaction, but for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction no structure was detected. It was also noted that the fusion-evaporation processes to high spin states of the residual nuclei play a greater role in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ reaction than for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$. These observations are consistent with a greater surface transparency in the case of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ system.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E_{{}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}}=45-71\mathrm{}$ MeV; ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, $E_{{}_{}{}^{28}{}_{}{}^{}\mathrm{Si}}=55-96\mathrm{}$ MeV. Natural carbon and oxygen targets. Measured $I_{\gamma }\mathrm{}\left(E\right)\mathrm{}$.

Neutron emission and $\alpha$-particle emission in the ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$ + ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ reaction have been measured for the damped-collision and fusion-fission components of this reaction at a bombarding energy of 8.5 MeV/u. The c.m. neutron energy spectra for damped collisions indicate equal temperatures for the light and heavy fragments, a result consistent with the equilibration of the excitation energy during the interaction time. Pre-equilibrium neutron emission is found to contribute less than 5%. An out-of-plane neutron anisotropy $A_2=0.2\mathrm{}\pm 0.1$ is found. The measured ratios of the neutron multiplicities for the light and heavy fragments suggest a rapid approach of the fragment $\frac{N}{Z}$ ratios during the collision to that corresponding to minimum potential energy of the composite system.

NUCLEAR REACTIONS ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$(${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, $\mathrm{HI}\mathrm{xn}$)$E_{\mathrm{lab}}=476\mathrm{}$ MeV; measured ${\sigma }_n(E_n,{\theta }_n,{\phi }_n)$; deduced nuclear temperatures, neutron multiplicities, neutron-to-proton ratio $\frac{N}{Z}$, neutron out-of-plane anisotropy $A_2$.

The set of coupled linear second-order differential equations which has to be solved for quantum-mechanical calculations of inelastic scattering processes with multiple excitation can be rewritten as an equivalent set of coupled first-order integral equations. When Airy functions are used as piecewise analytic reference solutions, it makes it possible to evaluate analytically the integrals that arise in the set of integral equations. This set can be solved iteratively with a considerable reduction of computation time in cases of heavy ion scattering, when compared to quantum-mechanical coupled-channel calculations of the conventional type. The efficiency of two iteration schemes, an inward-outward and a perturbative one, has been investigated for some test cases dealing with multiple Coulomb excitation of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ by Kr and Pb. It turns out that, for heavy ion scattering, only the inward-outward iteration scheme has a practical importance. Finally, the excitation probabilities for ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, Coulomb excited by 385 MeV Kr up to $I=24\mathrm{}\hslash$, are shown for a reduced $E2\mathrm{}$ transition matrix element of 3.5 eb and they are compared with the excitation probabilities calculated according to the semiclassical theory.

NUCLEAR REACTIONS Solving coupled equations by iteration; quantum mechanically calculated excitation probabilities for heavy ion multiple Coulomb excitation.

High spin states and isomers in ${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$ have been studied using the ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$,$3n$)${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$ and ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$,$4n$)${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$ reactions. Levels up to $J=\frac{53}{2}$ have been assigned, and two isomers at 4904 keV ($J=\frac{41}{2}$, ${\tau }_{\frac{1}{2}}=7\mathrm{}\pm 2$ ns) and 6032 keV ($J=\frac{49}{2}$, ${\tau }_{\frac{1}{2}}=10.9\mathrm{}\pm 0.6$ ns) have been identified. Gamma transitions de-exciting the isomers have $B\left(E2\mathrm{}\right)\mathrm{}$ values characteristic of single-particle transitions. The yrast sequence exhibits an irregular dependence on excitation energy characteristic of an independent particle model rather than a deformed rotor. In addition, above $J=\frac{25}{2}$ it exhibits an effective moment of inertia of 138 Me${\mathrm{V}}^{-1\mathrm{}}$ which is 1.18 times the rigid sphere value. These data are compared to recent spherical and deformed shell model predictions and a qualitative agreement is found between experiment and calculation.

NUCLEAR REACTIONS ${}_{}{}^{122}{}_{}{}^{}\mathrm{Sn}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$,$3n$) ${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$, $E=115-165\mathrm{}$ MeV; ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, $4n$) ${}_{}{}^{151}{}_{}{}^{}\mathrm{Dy}$, $E=60-101\mathrm{}$ MeV. Measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, $I\left(\theta \right)$, $\gamma -\gamma$ coinc. with pulsed beam. Deduced levels, branching ratios, spin assignments, lifetimes. Enriched targets, Ge(Li) detectors. Comparison with spherical and oblate spheroidal model calculations.

The mean lives of the ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ $\frac{1}{2^{+}}$, $\frac{7}{2^{+}}$, and $\frac{9}{2^{+}}$ levels at 2796, 1747, and 2867 keV have been measured using the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$,$n$)${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ reaction near threshold and the Doppler shift attenuation method. The results were 7.9±1.0, 74±6, and 61±6 fs, respectively. In order to obtain a result for the 8-fs 2796-keV level, four different targets were used. These consisted of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ implanted in thick backings of Mg, Al, Ta, and Au. The analysis developed for measuring this fast lifetime is described in detail. Excitation energies of 1747.2±0.3, 2788.87±0.10, 2795.8±0.7, and 2867.2±0.4 keV were obtained for the second-to-fifth excited states. The lifetime results are compared to recent shell-model predictions.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$,$n$)${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$, $E=20-27\mathrm{}$ MeV; measured Doppler-shift attenuation and lineshape. ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ 2796-, 1747-, and 2867-keV levels; deduced ${\tau }_m$. Implanted targets.

Time-dependent Hartree-Fock calculations are carried out for the systems ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. Cross sections for the formation of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ are qualitatively similar in both cases, although there exist significant quantitative differences which reflect the importance of the entrance channel. Both systems exhibit an angular momentum window for fusion. The results of the calculations are compared with currently available experimental data.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $x$) and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, $x$) in time-dependent Hartree-Fock approximation. Fusion and strongly damped collisions.

Excitation functions for ${}_{}{}^{16}{}_{}{}^{})\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}$ scattering were measured for ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28,30}{}_{}{}^{}\mathrm{Si}$ at several angles in the energy range $20 \mathrm{MeV}\lesssim E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\lesssim 35 \mathrm{MeV}$. Detailed angular distributions were obtained for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ (${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$) at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=21\mathrm{} \mathrm{}\left(21.7\right), 24 \mathrm{}\left(24.8\right), 27 \mathrm{}\left(27.9\right), \mathrm{and} 30 \mathrm{}\left(31.0\right)\mathrm{}$ MeV. The data were analyzed with a conventional optical model with a shallow, and energy-dependent real, and a weakly absorbing and energy-dependent imaginary potential.

NUCLEAR REACTIONS ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$), ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$), ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$), ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$). Measured elastic scattering cross section $20 \mathrm{MeV}<~E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~35 \mathrm{MeV}$. Fitted optical models to data.

Differential cross sections for the elastic scattering, single excitation ($Q=-4.43\mathrm{}$ MeV), and mutual excitation ($Q=-8.86\mathrm{}$ MeV) of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured at 14 bombarding energies in the range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=35-63\mathrm{}$ MeV. The angular distributions extend typically from 16° to 90° c.m. The results have been analyzed with the optical model, the distorted-wave approximation, and the method of coupled equations. The optical model analysis of the elastic scattering reveals a sensitivity of the predicted cross sections at large angles to the strength and shape of the real part of the nuclear potential in the region 4 to 6 fm. The potentials predicted by the double-folding model fit the data remarkably well over the entire angular range, whereas the shallow potentials which we have explored generally fit the data only in the forwardangle region. The results thus indicate that the real potential for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ system is more attractive in the region of 4 to 6 fm than would have been expected on the basis of previous analyses of comparable systems at lower bombarding energies.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=35-63\mathrm{}$ MeV; measured $\sigma (E,\theta )$ for elastic, single, and mutual excitation of $2^{+}$. Optical model, DWBA analyses.

Angular distributions of the most intense one- and two-nucleon transfer reactions induced by 93.8 MeV ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions on a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ target were measured over the angular range 10-65°. The reactions are selective in that only a few of the available states are strongly excited. For both single proton and single neutron transfer, $p_{\frac{1}{2}}$ and $d_{\frac{5}{2}}$ shells are populated with about equal probability; for $\mathrm{pn}$ transfer the strongest peak corresponds to the $5^{+}$ level of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The sum of the cross sections for all of these transfer reactions, integrated over the measured angular range, is 7.5 mb. This may be compared with 23 mb for the inelastic scattering to the $2^{+}$ level of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and 7 mb for mutual excitation of the $2^{+}$ level in the target and projectile. Distorted-wave Bornapproximation calculations are compared with the measured angular distributions for a number of the transfer reactions.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$), ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$), ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$) $E=93.8\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; DWBA analyses.

The possibility of a simple parametrization of the energy density functionals derived from a two-body effective interaction by expanding them in a Taylor series about the saturation density is proposed. Carrying out this procedure for a two-body effective interaction constructed in an earlier work, it is shown that the Taylor series expansions, truncated at the quadratic terms, give a quite satisfactory description of the exact energy density functionals. The resulting simple energy density has been used to calculate the real part of ion-ion interaction potential for several pairs of spherical nuclei in the framework of Brueckner's sudden approximation. The shape of the calculated potentials together with the positions and heights of interaction barriers are in good agreement with those referred to in the literature.

NUCLEAR REACTIONS Parametrized energy density, calculated ion-ion interaction potentials, and interaction barriers of spherical nuclei.

Analysis of 0.8 GeV proton inelastic scattering by ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ has yielded the angular distribution of a broad peak located at $32A^{-\frac{1}{3}}$ MeV with a width of approximately 2.2 MeV. The angular distribution, extending from 1.0 to 3.2 ${\mathrm{fm}}^{-1\mathrm{}}$, agrees well with $L=3\mathrm{}$ collective distorted-wave Born approximation calculations. A deformation length $\beta R$ of 0.80 fm is obtained. The isoscalar energy weighted sum rule fraction exhausted by an octupole excitation at 7.2 MeV in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ with this deformation length is 23%. The $3^{-}$ state at 2.75 MeV in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ is found to exhaust 8% of the isoscalar energy weighted sum rule. These results are in excellent agreement with recent ($\alpha$,${\alpha }^{\prime }$) work which established the existence of the low-energy octupole resonance.

NUCLEAR REACTIONS ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$($p$,$p^{\prime }$) $E_p=0.8\mathrm{}$ GeV, measured $E_x$, $\sigma \left(\theta \right)$; low-energy octupole resonance; determined $l$,$\beta$.