Recent Articles

( $\vec{t}$ , $p$ ) reaction on ${}^{56}{Fe}$ , ${}^{58, 60, 64}{Ni}$ : Structure and reaction-mechanism effects

W. P. Alford, R. N. Boyd, E. Sugarbaker, D. L. Hanson, and E. R. Flynn

Phys. Rev. C 21, 1203 (1980) - Published 1 April, 1980

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Differential cross sections and analyzing powers have been measured for the ( $\vec{t}$ , $p$ ) reaction on ${}^{56}{Fe}$ , ${}^{58, 60, 64}{Ni}$ at an incident energy of 17 MeV. Data were obtained for states up to an excitation of 3.7, 3.13, 2.8, and 4.9 MeV in ${}^{58}{Fe}$ , ${}^{60, 62, 66}{Ni}$ , respectively, including about ten states each with spin and parity $0^{+}$ , $2^{+}$ , and $4^{+}$ , and two states each with $3^{-}$ and $5^{-}$ . The measured analyzing powers show angular distributions characteristic of the $L$ transfer, with variations from state to state comparable to those observed for cross sections of a given $L$ . Angular distributions of the differential cross sections for strong transitions were generally fitted well by a standard distorted-wave Born approximation calculation. There appear to be significant discrepancies between the data and distorted-wave Born approximation predictions for excited $0^{+}$ states and for most $4^{+}$ states. Distorted-wave Born approximation predictions of analyzing power were in qualitative agreement with the data for ground-state transitions and for strong $L = 2$ transitions but this was not true for $L = 0$ transitions to excited states and for transitions with $L > 2$ . The effect of varying the optical parameters used in the distorted-wave Born approximation calculations was investigated; it was found that predictions of analyzing power for $L > 0$ were quite sensitive to the choice of proton potential. The effects of two-step reaction processes were also investigated. These were found to produce large changes in predicted cross sections and analyzing powers, which could account for some of the discrepancies between these results and distorted-wave Born approximation predictions.

NUCLEAR REACTIONS ${}^{56}{Fe}$ , ${}^{58, 60, 64}{Ni}$ ( $\vec{t}$ , $p$ ) $E = 17$ MeV; polarized beam; enriched targets; measured $σ (E_{p}, θ)$ , $A_{y} (E_{p}, θ)$ ; DWBA; coupled reaction channel analysis.

Giant resonance for the actinide nuclei: Photoneutron and photofission cross sections for ${}^{235}U$ , ${}^{236}U$ , ${}^{238}U$ , and ${}^{232}{Th}$

J. T. Caldwell, E. J. Dowdy, B. L. Berman, R. A. Alvarez, and P. Meyer

Phys. Rev. C 21, 1215 (1980) - Published 1 April, 1980

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The photoneutron cross sections $σ (γ, n)$ and $σ (γ, 2 n)$ , and total photofission cross sections $σ (γ, F)$ have been measured for ${}^{235}U$ , ${}^{236}U$ , ${}^{238}U$ , and ${}^{232}{Th}$ from threshold to 18.3 MeV using monoenergetic photons from the annihilation in flight of fast positrons and neutron-multiplicity detection in an efficient $4 π$ neutron detector. Use of the ring-ratio technique allowed both the average photofission neutron energy for each nucleus to be obtained as a function of photon energy and, for ${}^{236}U$ and ${}^{238}U$ , the determination of the partial cross sections for first-chance $σ (γ, f)$ and second-chance $σ (γ, n f)$ photofission as well. Information extracted from the data includes integrated cross sections and their moments, giant-resonance parameters, deformation and radius parameters, and relative and absolute neutron and fission probabilities.

NUCLEAR REACTIONS ${}^{235, 236, 238}U$ and ${}^{232}{Th}$ ( $γ$ , $n$ , $2 n$ , $F$ ), $E_{γ} = 5 - 18.3$ MeV; measured $4 π$ neutron yield, neutron multiplicities, and average energies for monoenergetic photons; $σ (E_{γ}, 1 n)$ , $σ (E_{γ}, 2 n)$ , $σ (E_{γ}, F)$ , integrated cross sections and moments, GDR parameters, nuclear shape parameters, neutron and fission probabilities.

States in ${}^{193}{Pt}$ using the ( $p$ , $t$ ) reaction

G. Rotbard, G. Berrier-Ronsin, M. Vergnes, J. Kalifa, J. Vernotte, and R. K. Sheline

Phys. Rev. C 21, 1232 (1980) - Published 1 April, 1980

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Levels in ${}^{193}{Pt}$ were populated by the ( $p$ , $t$ ) reaction using 25 MeV protons and an isotopically enriched ${}^{195}{Pt}$ target. A number of low-lying negative parity states are observed. By far the most strongly populated is the $\frac{1}{2^{-}}$ ground state. Some of these states are qualitatively interpreted assuming Coriolis coupling and rotation-vibration coupling between the $\frac{1}{2^{-}} | 530 |$ , $\frac{3}{2^{-}} | 532 |$ , and $\frac{5}{2^{-}} | 532 |$ Nilsson states and an oblate core. $L = 0$ angular distributions for states in ${}^{193}{Pt}$ appear to be associated with the excited $J^{π} = 0^{+}$ states in the even-even Pt cores.

NUCLEAR REACTION ${}^{195}{Pt}$ ( $p$ , $t$ ) ${}^{193}{Pt}$ , $E (p) = 25$ MeV, excitation energies, $σ (E_{t}, θ)$ $θ = 5 ° - 55 °$ , ${}^{193}{Pt}$ $l$ , $J$ , $π$ , deduced; enriched target; magnetic spectrograph; analyses, strong coupling model, oblate shpae.

Nuclear sizes of ${}^{40, 42, 44, 48}{Ca}$ from elastic scattering of 104 MeV alpha particles. I. Experimental results and optical potentials

H. J. Gils, E. Friedman, H. Rebel, J. Buschmann, S. Zagromski, H. Klewe-Nebenius, B. Neumann, R. Pesl, and G. Bechtold

Phys. Rev. C 21, 1239 (1980) - Published 1 April, 1980

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Differential cross sections for elastic scattering of 104 MeV $α$ particles from ${}^{40, 42, 44, 48}{Ca}$ have been measured with high angular accuracy over a wide angular range. Optical model analysis based on a Fourier-Bessel description of the real potential reveals isotopic differences which, in particular for ${}^{48}{Ca}$ , indicate a small neutron skin.

NUCLEAR REACTIONS ${}^{40, 42, 44, 48}{Ca}$ ( $α$ , $α$ ), $E_{α} = 104$ MeV, measured $σ (θ)$ ; $θ_{c . m .} = 3 - 110 °$ ; enriched targets; optical model analysis using Fourier-Bessel method, deduced isotopic differences in the real potentials.

Nuclear sizes of ${}^{40, 42, 44, 48}{Ca}$ from elastic scattering of 104 MeV alpha particles. II. Nuclear density distributions

H. J. Gils, E. Friedman, Z. Majka, and H. Rebel

Phys. Rev. C 21, 1245 (1980) - Published 1 April, 1980

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The elastic scattering of 104 MeV $α$ particles from ${}^{40, 42, 44, 48}{Ca}$ has been analyzed by a single-folding model with a density-dependent effective interaction. Nuclear density distributions have been extracted using various descriptions including Fourier-Bessel series which distinctly reduces the model dependence of the results and enables realistic estimates of errors. Differences of the density shapes of the Ca isotopes are well determined showing evidence for a neutron skin in ${}^{48}{Ca}$ . The resulting root mean square radii are compared to the results obtained from other methods. The sensitivity and limitations of various methods are discussed.

NUCLEAR REACTIONS ${}^{40, 42, 44, 48}{Ca}$ ( $α$ , $α$ ), $E_{α} = 104$ MeV; folding model analyses of $σ (θ)$ , density-dependent interaction, Fourier-Bessel densities, deduced isotopic differences of nuclear density distributions.

Isoscalar breathing mode state in ${}^{90}{Zr}$ and ${}^{116}{Sn}$

C. M. Rozsa, D. H. Youngblood, J. D. Bronson, Y. -W. Lui, and U. Garg

Phys. Rev. C 21, 1252 (1980) - Published 1 April, 1980

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Beams of 96- and 129-MeV $α$ particles were used to excite the giant resonance region in ${}^{90}{Zr}$ and ${}^{116}{Sn}$ . From the analysis of data obtained from 0° to 8°, two distinct components of the giant resonance peak were resolved in each nucleus. The upper component is well described by a distorted-wave Born-approximation calculation for $L = 0$ exhausting 90% (180%) of the energy weighted sum rule and has $E_{x} = 16.2$ MeV (15.6 MeV), $Γ = 3.5$ MeV (4.1 MeV) for ${}^{90}{Zr}$ ( ${}^{116}{Sn}$ ). The nuclear incompressibility is extracted from these data and from that available for ${}^{144}{Sm}$ and ${}^{208}{Pb}$ . The lower component is the giant quadrupole resonance exhausting 66% (84%) of the isoscalar quadrupole sum rule and has $E_{x} = 14.0$ MeV (13.2 MeV), $Γ = 3.4$ MeV (3.3 MeV) for ${}^{90}{Zr}$ ( ${}^{116}{Sn}$ ).

NUCLEAR REACTIONS ${}^{90}{Zr}$ , ${}^{116}{Sn}$ ( $α$ , $α^{'}$ ), $E_{α} = 96, 129$ MeV. Measured $E_{x}$ , $σ (θ)$ , giant resonances; deduced $L$ , $β$ , nuclear incompressibility.

Barrier to complete fusion for ${}^{4}{He}$ and ${}^{1}H$ and that for evaporation from ${}^{194}{Hg}$

M. A. McMahan and John M. Alexander

Phys. Rev. C 21, 1261 (1980) - Published 1 April, 1980

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A reference set of transmission coefficients for ${}^{1}H$ and ${}^{4}{He}$ reactions is obtained by systematic fits to data for fusion cross sections. Comparisons to other sets, obtained from elastic scattering data, show some significant differences. A comparison is made of calculated to measured evaporation spectra for ${}^{4}{He}$ from ${}^{194}{Hg}$ ( $E^{*} = 98$ MeV, $l_{crit} = 45$ ). There appears to be a significant reduction in the barrier to evaporation for this excited nucleus.

NUCLEAR REACTIONS Fusion cross sections for ${}^{1}H$ - and ${}^{4}{He}$ -induced reactions are systematized to provide reference values for transmission coefficients. Evaporation spectrum analysis made for ${}^{4}{He}$ from ${}^{194}{Hg}$ ( $E^{*} = 98$ MeV, $l_{crit} = 45$ ).

Breakup of strongly absorptive projectiles: Application to ( $h$ , $dp$ ) reaction

T. Udagawa and T. Tamura

Phys. Rev. C 21, 1271 (1980) - Published 1 April, 1980

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The well known distorted-wave Born-approximation formula for breakup processes was first simplified by introducing several approximations, all of which are believed justified for strongly absorptive high-energy projectiles. This made the theory very transparent and the ensuing numerical calculations rather easy to perform. This new formula, which was applied earlier with success to the breakup of ${}^{20}{Ne}$ , is applied in the present work to that of ${}^{3}{He}$ , again with success.

NUCLEAR REACTION Distorted-wave Born approximation; breakup reaction of strongly absorptive projectiles; ${}^{51}V$ ( ${}^{3}{He}$ , $dp$ ) reaction, calculated $\frac{d^{3} σ}{dE d Ω d Ω}$ ; $E ({}^{3}{He}) = 90$ MeV.

Binary decay process in the reaction ${}^{84}{Kr}$ + ${}^{238}U$ within the dynamical fragmentation theory

Raj K. Gupta

Phys. Rev. C 21, 1278 (1980) - Published 1 April, 1980

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A complete dynamical calculation of the ${}^{84}{Kr}$ + ${}^{238}U$ reaction is carried out within the fragmentation theory based on the two-center shell model. A time-dependent Schrödinger equation in the mass-fragmentation coordinate is solved for the collision process by using the classical orbit results. It is shown that this reaction is a peripheral collision with reaction times of the order of 6 × $10^{- 21}$ sec. The mass fragmentation gives large probabilities only for a few nucleon transfer, as is observed experimentally in this reaction.

NUCLEAR REACTIONS ${}^{84}{Kr}$ + ${}^{238}U$ , mass fragmentation, time-dependent Schrödinger equation, classical orbits, two-center shell model.

High-spin $E 2$ bands in Kr isotopes

J. S. Clements, L. R. Medsker, L. H. Fry, Jr., and L. V. Theisen

Phys. Rev. C 21, 1285 (1980) - Published 1 April, 1980

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Bands of $E 2$ transitions are assigned to ${}^{79}{Kr}$ and ${}^{81}{Kr}$ on the basis of $γ$ -ray singles, $γ - γ$ coincidence, angular distribution, and excitation function measurements. These bands can be interpreted as arising from the decoupling of $g_{\frac{9}{2}}$ neutrons from the ${}^{78}{Kr}$ and ${}^{80}{Kr}$ cores, respectively, and a comparison is made with the previously reported ${}^{77}{Kr}$ decoupled band. Relative reaction cross sections are in fair agreement with evaporation model calculations.

NUCLEAR REACTIONS ${}^{72}{Ge}$ ( ${}^{10}B$ , $x γ$ ) and ${}^{73}{Ge}$ ( ${}^{11}B$ , $x γ$ ), $E = 31, 34, 37, 40$ MeV; measured $σ (E_{γ}, E)$ , $σ (E_{γ}, θ)$ . ${}^{73}{Ge}$ ( ${}^{11}B$ , $x γ$ ) $E = 37$ MeV, measured Si(Li)-Ge(Li) $γ - γ$ coin. ${}^{74, 72}{Ge}$ ( ${}^{10}B$ , $x γ$ ) $E = 40$ MeV; measured Ge(Li)-Ge(Li) $γ - γ$ coin. ${}^{79, 81}{Kr}$ deduced levels, $J^{π}$ . Enriched targets.

Gamma-ray studies in ${}^{45}V$

S. A. Gronemeyer, L. Meyer-Schützmeister, A. J. Elwyn, and G. Hardie

Phys. Rev. C 21, 1290 (1980) - Published 1 April, 1980

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The level scheme of ${}^{45}V$ was studied with the reaction ${}^{40}{Ca}$ ( ${}^{7}{Li}$ , $2 n$ ) ${}^{45}V$ using ${}^{7}{Li}$ beams of 14-16-MeV energies. Prompt and delayed $n - γ$ and $γ - γ$ coincidences revealed a doublet at an excitation energy of about 57 keV with a separation energy of only 800 eV. The half-life of the upper member, a $\frac{3}{2^{-}}$ state, was measured to be 430±80 nsec. This state decays strongly via internal conversion to the lower member of the doublet, a $\frac{5}{2^{-}}$ state. The half-life of the latter level was measured to be ≲4.2 nsec. Since ${}^{45}V$ is a $T = \frac{1}{2}$ nucleus and the mirror of the well-known ${}^{45}{Ti}$ nucleus, Coulomb displacement energies could be deduced. A comparison of these Coulomb displacement energies with those of neighboring nuclei, the measured lifetimes, and the observed $γ - γ$ and $n - γ$ prompt and delayed coincidence spectra established nearly all the ${}^{45}V$ levels expected below the proton separation energy of 1.62 MeV, namely, $\frac{7}{2^{-}} (g . s .)$ , $\frac{5}{2^{-}} (56.4 keV)$ , $\frac{3}{2^{-}} (57.2 keV)$ , $\frac{3}{2^{+}} (386.1 keV)$ , $\frac{5}{2^{+}} (796.8 keV)$ , and $\frac{7}{2^{+}} (1273 keV)$ . The expected four highest bound levels, in particular the $\frac{9}{2^{-}}$ and $\frac{11}{2^{-}}$ states, are not seen in the present experiment. The latter two states are supposed to decay either completely or predominantly to the ground state and hence are not observable in these $γ - γ$ coincidence studies. The third and fourth levels were not seen in ${}^{45}{Ti}$ $γ$ -ray spectra which exhibit much higher counting rates than those of ${}^{45}V$ . They are therefore not expected to be observable in the present ${}^{45}V$ spectra. ${}^{45}V$ gamma rays were also seen in the ${}^{40}{Ca}$ ( ${}^{6}{Li}$ , $n$ ) ${}^{45}V$ reaction with a 10- and a 13.5-MeV ${}^{6}{Li}$ beam. This reaction has a smaller production cross section and is therefore less suited for detailed studies.

NUCLEAR REACTIONS ${}^{40}{Ca}$ ( ${}^{7}{Li}$ , $2 n$ ) ${}^{45}V$ : singles spectra, prompt and delayed $n - γ$ and $γ - γ$ coincidences with $E_{{}^{7}{Li}} = 14, 15, 16$ MeV. ${}^{40}{Ca}$ ( ${}^{6}{Li}$ , $n$ ) ${}^{45}V$ with 10, 13.5 MeV ${}^{6}{Li}$ : $n - γ$ and $γ - γ$ coincidences. Measurement of $T_{\frac{1}{2}} = 430 \pm 80$ nsec for the 57.2-keV state and ≲4.2 nsec for the 56.4-keV state. Deduced ${\frac{7}{2}}^{-} (g . s .)$ ; ${\frac{5}{2}}^{-} (56.4)$ ; ${\frac{3}{2}}^{-} (57.2)$ ; ${\frac{3}{2}}^{+} (386.1)$ ; ${\frac{5}{2}}^{+} (796.8)$ ; ${\frac{7}{2}}^{+} (1273)$ , and $γ$ decay of these states.

Mechanisms for deuteron production in relativistic nuclear collisions

Joseph I. Kapusta

Phys. Rev. C 21, 1301 (1980) - Published 1 April, 1980

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A variety of mechanisms for deuteron production in relativistic nuclear collisions are considered. These include the coalescence model, the sudden approximation model, and the static thermal model. A new model based on time dependent perturbation theory is presented. A solution of the rate equations for a hydrodynamically expanding fireball suggests that chemical equilibrium might be achieved in central collisions. Emphasis is placed on the physical assumptions of the various models, their limitations, and their subtly different predictions. Of some importance is the effect of impact parameter averaging which, when written in terms of the usual power law relationship, introduces the necessity for measuring various two particle correlation functions to check the self-consistency of these models.

NUCLEAR REACTIONS Relativistic heavy ions, models for deuteron production $p - n$ correlations.

High-spin states in ${}^{65}{Ga}$ and possible triaxial structure

H. Kawakami, A. P. de Lima, R. M. Ronningen, A. V. Ramayya, J. H. Hamilton, R. L. Robinson, H. J. Kim, and L. K. Peker

Phys. Rev. C 21, 1311 (1980) - Published 1 April, 1980

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Level structure of ${}^{65}{Ga}$ was investigated by in-beam $γ$ -ray spectroscopy. Excitation function, $γ$ -ray angular distribution, and $γ - γ$ coincidence measurements were performed. From $γ$ -ray energies and intensities and $γ - γ$ coincidence relations, eleven new excited states were established and parities and spins up to $\frac{21}{2^{+}}$ were assigned. Bands of levels built on $f_{\frac{5}{2}}$ and $g_{\frac{9}{2}}$ orbitals were observed with spacings that suggest triaxial structure.

NUCLEAR STRUCTURE ${}^{58}{Ni}$ ( ${}^{12}C$ , $α p$ ) $E = 39$ MeV, ${}^{60}{Ni}$ ( ${}^{7}{Li}$ , $2 n$ ) $E = 18 - 21$ MeV; measured $I_{γ}$ , $E_{γ}$ , $I_{γ} (θ)$ , $γ γ_{coin}$ , $γ γ_{DCO}$ , $I_{γ}$ (Ex. $E_{{}^{7}{Li}}$ ); deduced ${}^{65}{Ga}$ levels, $J$ , $π$ , $γ$ multipolarity.

Spectra of $p$ , $d$ , and $t$ from relativistic nuclear collisions

A. Sandoval, H. H. Gutbrod, W. G. Meyer, R. Stock, Ch. Lukner, A. M. Poskanzer, J. Gosset, J. -C. Jourdain, C. H. King, G. King, Nguyen Van Sen, G. D. Westfall, and K. L. Wolf

Phys. Rev. C 21, 1321 (1980) - Published 1 April, 1980

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Inclusive energy spectra of protons, deuterons, and tritons were measured with a telescope of silicon and germanium detectors with a detection range for proton energies up to 200 MeV. Fifteen sets of data were taken using projectiles ranging from protons to ${}^{40}{Ar}$ on targets from ${}^{27}{Al}$ to ${}^{238}U$ at bombarding energies from 240 MeV/nucleon to 2.1 GeV/nucleon. Particular attention was paid to the absolute normalization of the cross sections. For three previously reported reactions, He fragment cross sections have been corrected and are presented. To facilitate a comparison with theory the sum of nucleonic charges emitted as protons plus composite particles was estimated and is presented as a function of fragment energy per nucleon in the interval from 15 to 200 MeV/nucleon. For low-energy fragments at forward angles the protons account for only 25% of the nucleonic charges. The equal mass ${}^{40}{Ar}$ plus Ca systems were examined in the center of mass. Here at 0.4 GeV/nucleon ${}^{40}{Ar}$ plus Ca the proton spectra appear to be nearly isotropic in the center of mass over the region measured. Comparisons of some data with firestreak, cascade, and fluid dynamics models indicate a failure of the first and a fair agreement with the latter two. In addition, associated fast charged particle multiplicities (where the particles had energies larger than 25 MeV/nucleon) and azimuthal correlations were measured with an 80 counter array of plastic scintillators. It was found that the associated multiplicities were a smooth function of the total kinetic energy of the projectile.

NUCLEAR REACTIONS U( ${}^{20}{Ne}$ , $X$ ), $\frac{E}{A} = 240$ MeV/nucleon; U( ${}^{40}{Ar}$ , $X$ ), Ca( ${}^{40}{Ar}$ , $X$ ), U( ${}^{20}{Ne}$ , $X$ ), Au( ${}^{20}{Ne}$ , $X$ ), Ag( ${}^{20}{Ne}$ , $X$ ), Al( ${}^{20}{Ne}$ , $X$ ), U( ${}^{4}{He}$ , $X$ ), Al( ${}^{4}{He}$ , $X$ ), $\frac{E}{A} = 390$ MeV/nucleon; U( ${}^{40}{Ar}$ , $X$ ), Ca( ${}^{40}{Ar}$ , $X$ ), U( ${}^{20}{Ne}$ , $X$ ), U( ${}^{4}{He}$ , $X$ ), U( $p$ , $X$ ), $\frac{E}{A} = 1.04$ GeV/nucleon; U( ${}^{20}{Ne}$ , $X$ ), $\frac{E}{A} = 2.1$ GeV/nucleon; measured $σ (E, θ)$ , $X = p, d, t$ .

Inelastic scattering of ${}^{6}{Li}$ from ${}^{58}{Ni}$ at 71 MeV

C. Williamson, A. Galonsky, R. Huffman, and R. Markham

Phys. Rev. C 21, 1344 (1980) - Published 1 April, 1980

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Nine excited states of ${}^{58}{Ni}$ were studied via the ${}^{58}{Ni}$ ( ${}^{6}{Li}$ , ${}^{6}{Li}$ ) reaction at 71.2 MeV. Two methods were employed to analyze the data. They were the distorted wave Born approximation, and the method of coupled channels. A comparison of their predictions and the information they provide about the nuclear deformation lengths is presented. In agreement with the Austern-Blair model for strongly absorbed particles, all five parameter sets produced equally good fits to the inelastic data.

NUCLEAR REACTIONS ${}^{58}{Ni}$ ( ${}^{6}{Li}$ , ${}^{6}{Li}$ ′) for ${}^{58}{Ni}^{*}$ energies $E^{*} = 1.45, 2.46, 2.78, 3.04, 3.26, 3.62, 3.90, 4.48, and 4.75$ MeV. Angular distributions measured, deformation lengths extracted.

Time-dependent— $S$ -matrix Hartree-Fock theory of complex reactions

James J. Griffin, Peter C. Lichtner, and Maria Dworzecka

Phys. Rev. C 21, 1351 (1980) - Published 1 April, 1980

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Some limitations of the conventional time-dependent Hartree-Fock method for describing complex reactions are noted, and one particular ubiquitous defect is discussed in detail: the post-breakup spurious cross channel correlations which arise whenever several asymptotic reaction channels must be simultaneously described by a single determinant. A reformulated time-dependent— $S$ -matrix Hartree-Fock theory is proposed, which obviates this difficulty. Axiomatic requirements minimal to assure that the time-dependent— $S$ -matrix Hartree-Fock theory represents an unambiguous and physically interpretable asymptotic reaction theory are utilized to prescribe conditions upon the definition of acceptable asymptotic channels. That definition, in turn, defines the physical range of the time-dependent— $S$ -matrix Hartree-Fock theory to encompass the collisions of mathematically well-defined "time-dependent Hartree-Fock droplets." The physical properties of these objects then circumscribe the content of the Hartree-Fock single determinantal description. If their periodic vibrations occur for continuous ranges of energy then the resulting "classical" time-dependent Hartree-Fock droplets are seen to be intrinsically dissipative, and the single determinantal description of their collisions reduces to a "trajectory" theory which can describe the masses and relative motions of the fragments but can provide no information about specific asymptotic excited states beyond their constants of motion, or the average properties of the limit, if it exists, of their equilibrization process. If, on the other hand, the periodic vibrations of the time-dependent Hartree-Fock droplets are discrete in energy, then the time-dependent— $S$ -matrix Hartree-Fock theory can describe asymptotically the time-average properties of the whole spectrum of such periodic vibrations of these "quantized" time-dependent Hartree-Fock droplets which are asymptotically stationary on a time-averaged basis. Such quantized time-dependent Hartree-Fock droplet spectra promise the closest analog to the rich array of asymptotic channel eigenstates in the exact Schrödinger theory which single time-dependent Hartree-Fock self-consistent determinants might describe. Whether the time-dependent Hartree-Fock droplets are classical or quantized is determined by the mathematical properties of the periodic solutions of the time-dependent Hartree-Fock equation. If the droplets are in fact classical, then the question remains open whether an explicit requantization, by assumption, could consistently restore the close structural analogy with the exact theory. We argue that if the statistical interpretation of the single determinantal wave function, which is central to the present restructuring of the conventional time-dependent Hartree-Fock description, were to be found inadmissible, then no basis would remain for considering the determinant as a "wave function" in the Schrödinger sense. Finally, we note that the conceptual basis of this time-averaged $S$ -matrix theory need not be restricted to the time-dependent Hartree-Fock theory, but might apply as well to other nonlinear Schrödinger-type models which purport to provide an approximate wave function to describe physical reaction processes.

NUCLEAR REACTIONS Structural analysis of scattering theory for time-dependent Hartree-Fock single determinantal wave functions; scattering matrix defined as a time average; channels labeled by time-averaged properties of periodic solutions; time-averaged channel orthogonality; classical and quantal time-dependent Hartree-Fock droplets.

Neutron emission in deep-inelastic collisions induced by ${}^{86}{Kr}$ on ${}^{166}{Er}$ at 5.7, 7.0, and 7.9 MeV/nucleon

Y. Eyal, A. Gavron, I. Tserruya, Z. Fraenkel, Y. Eisen, S. Wald, R. Bass, C. R. Gould, G. Kreyling, R. Renfordt, K. Stelzer, R. Zitzmann, A. Gobbi, U. Lynen, H. Stelzer, I. Rode, and R. Bock

Phys. Rev. C 21, 1377 (1980) - Published 1 April, 1980

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Neutron emission associated with deep-inelastic collisions of 496-, 602-, and 675-MeV ${}^{86}{Kr}$ with ${}^{166}{Er}$ has been studied as a function of kinetic energy loss, fragment mass, and neutron scattering angles. The major de-excitation process is neutron evaporation from fully accelerated fragments. The excitation energy is shared between the fragments in proportion to their mass, indicating energy equilibration in the intermediate dinuclear composite system for the completely damped as for the quasielastic components. Within limits imposed by the systematic uncertainties, the angular and velocity distributions of the neutrons in the laboratory frame are consistent with isotropic emission of neutrons in the c.m. frame of the fragments. We find no evidence for pre-equilibrium effects. The observed multiplicities and energy spectra of the neutrons are consistent with predictions of statistical-model calculations.

NUCLEAR REACTIONS ${}^{166}{Er} ({}^{86}{Kr}, A_{L}) A_{H}$ $E_{lab} = 496, 602, and 675$ MeV; $66 <~ A_{L} <~ 126$ , $A_{H} = 252 - A_{L}$ , $θ \sim 21 ° - 75 °$ , $- 250 <~ Q value <~ 0$ MeV; measured $σ_{n} (E_{lab}, Q value, θ, A_{L}, A_{H}, E_{n}, θ_{n}, φ_{n})$ ; deduced neutron c.m. energy spectra, out-of-plane anisotropy and multiplicities; degree of energy equilibration.

Alpha-particle doorway states in ${}^{28}{Si}$

Kenji Katori, Kohei Furuno, Takao Ooi, and Susumu Hanashima

Phys. Rev. C 21, 1387 (1980) - Published 1 April, 1980

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Excitation functions for the ${}^{12}C$ ( ${}^{16}O$ , ${}^{12}C_{g . s .}$ ) ${}^{16}O$ reaction feeding the $0^{+}$ , 6.049-, $3^{-}$ , 6.131-, $2^{+}$ , 6.919-, $1^{-}$ , 7.117-, $4^{+}$ , 10.353-, and $4^{+}$ , 11.095-MeV states of ${}^{16}O$ have been measured at $θ_{lab} = 7.0 °$ over the energy range $22.7 \leq E_{c . m .} \leq 37.7$ MeV in 86- or 173-keV steps. The Ericson-fluctuation type analysis was performed and nonfluctuating enhancements with a width of 700 keV are observed at $E_{c . m .} = 23.6, 24.6, 28.4, and 32.2$ MeV for the $0^{+}$ , 6.049- MeV states. The most probable total spins for the lowest three states are assigned to be $J^{π} = 14^{+}, 14^{+}, and 15^{-}$ , respectively. These enhancements are strongly correlated to those for the $2^{+}$ , 6.919- MeV state, but anticorrelated to those for the $3^{-}$ , 6.131-MeV state. Model calculations based on Hauser-Feshbach and band-crossing theories were performed and none of them have succeeded to reproduce the data in a consistent way. Alpha-particle doorway states embedded in the high excitation of ${}^{28}{Si}$ (39-54 MeV) are indicative to describe these intermediate-structure resonances.

NUCLEAR REACTIONS ${}^{12}C$ ( ${}^{16}O$ , ${}^{12}C$ ) ${}^{16}O$ ; $E = 53 - 88$ MeV, $θ_{lab} = 5 ° - 16.5 °$ : measured $σ (E, θ)$ , deduced resonances, $J^{π}$ ; correlation analysis of fluctuations.

${}^{238}U$ neutron-induced fission cross section for incident neutron energies between 5 eV and 3.5 MeV

F. C. Difilippo, R. B. Perez, G. de Saussure, D. K. Olsen, and R. W. Ingle

Phys. Rev. C 21, 1400 (1980) - Published 1 April, 1980

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A measurement of the ${}^{238}U$ neutron-induced fission cross section has been performed in the neutron energy range between 5 eV and 3.5 MeV. The favorable signal-to-background ratio and high resolution of this experiment resulted in the identification of 85 subthreshold fission resonances or clusters of resonances in the neutron energy region between 5 eV and 200 keV. The fission data below 100 keV are characteristic of a weak coupling situation between Class I and Class II levels. The structure of the fission levels at the 720- and 1210-eV fission clusters is discussed. There is an apparent enhancement of the fission cross section at the opening of the $2^{+}$ neutron inelastic channel in ${}^{238}U$ at 45 keV. An enhancement of the subthreshold fission cross section between 100 and 200 keV has been tentatively interpreted in terms of the presence of a Class II, partially damped vibrational level. There is a marked structure in the fission cross section above 200 keV up to and including the plateau between 2 and 3.5 MeV.

NUCLEAR REACTIONS, FISSION ${}^{238}U$ ( $n$ , $f$ ). $E = 5 eV - 3.5 MeV$ ; measured $σ (E)$ ; deduced parameters second well fission barrier.

Charge distribution in the thermal neutron fission of ${}^{245}{Cm}$ : Fractional cumulative yields of ${}^{135}I$ and ${}^{140}{Ba}$

Tarun Datta, S. P. Dange, S. B. Manohar, A. G. C. Nair, Satya Prakash, and M. V. Ramaniah

Phys. Rev. C 21, 1411 (1980) - Published 1 April, 1980

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Fractional cumulative yields for ${}^{135}I$ and ${}^{140}{Ba}$ have been determined in the thermal neutron induced fission of ${}^{245}{Cm}$ following the respective daughter product activities. The fractional cumulative yield values obtained are 0.951±0.014 and 0.969±0.006 for ${}^{135}I$ and ${}^{140}{Ba}$ , respectively. The fractional cumulative yield value for ${}^{135}I$ has been compared with the one reported earlier and an attempt has been made to correlate the value to the neutron to proton ratio of the fissioning nucleus. The data have been analyzed to examine the effect of shells on the width of the charge distribution. This indicates a narrower width of charge distribution for mass chain 135 and a broader width for mass chain 140 compared to normal width of the distribution.

NUCLEAR REACTIONS, FISSION Thermal neutron fission of ${}^{245}{Cm}$ , measured FCY, data analyzed in terms of neutron to proton ratio, odd-even effect and shell effect.

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