Imprints of compound-nucleus and direct-interaction processes in energy-averaged cross sections and durations of nuclear reactions

New analytical expressions for the energy-averaged S-matrix and nuclear-reaction cross sections are obtained on the basis of the unitary S-matrix parametrization. Some approximations are analyzed when compound-nucleus cross sections are described with and without the Hauser-Feshbach formula with the partial-width-fluctuation correction. The connection of the S-matrix parameters in the Simonius representation with the dynamics of compound-nucleus processes is clarified. An explicit expression for the averaged duration of the nuclear reaction is obtained for the range of closely situated resonances. Possible methods of obtaining information on some compound-nucleus and direct-interaction characteristics from the averaged cross sections and durations are examined.     

A study of 14N using the 13C(d,n)14N reaction

Absolute differential cross sections for the ¹³C(d, n)¹⁴N reaction were measured at deuteron bombarding energies of 4.5, 5.0 and 5.5 MeV. Spectroscopic factors and statistical compound-nucleus contributions are obtained by treating the observed cross sections as an incoherent sum of distorted-wave Born approximation and compound-nucleus contributions. Energy-averaged spectroscopic factors are derived. An anomaly is observed in the yield for the 2.313 MeV T= 1 state.     

Fluctuations in the total cross sections of Y,Zr, La,Ce, Pr,Gd, Ho,Ta and Hg for 1.0 TO 2.0 MeV neutrons

Results of an analysis of the fluctuations observed in the neutron total cross sections of nine different nuclei in the energy range between 1.0 and 2.0 MeV are presented. It has been found that in general these may be explained to be due to fluctuations in the widths and spacings of the compound-nucleus level. The cross section data for some of the nuclei seem to indicate the presence of structures with widths much larger than the compound-nucleus width.     

On the anisotropy of multi-chance, high-spin fission

Inclusion of the fission-fragment anisotropy in statistical-model analyses is shown to provide significant constraints on the spin and chance distributions for high-spin fission. Selective anisotropy measurements which should enhance sensitivity to shell or pairing corrections in the late stages of compound-nucleus decay are suggested.     

Possible parity-violating effects in ternary fission

Possible parity-violating effects are considered in ternary fission and estimated for different assumptions regarding the mechanism of the process. Here we shall consider differentP-violating effects in neutron-induced ternary fission. As shown in [1], all theP-violating effects in nuclear reactions proceeding via the compound-nucleus stage bear some features in common. All of them are characterized by the factors of dynamical enhancement (caused by the large density of compound-nucleus states), resonance enhancement defined by the ratio of the level spacing for the states of opposite of opposite parity to the width these states [1], and structural enhancement (or hindrance) factors in the exit or entrance channels. Since we believe that neutron-induced ternary fission proceeds via the compound-nucleus stage, one can apply here the basic methods and results [1] used for binary fission, with some modifications necessitated by the presence of 3 particles in the exit channel. Since, however, the analytic analysis of the 3-body problem is rather abstruse and difficult even in classical mechanics, we shall use some reasonable hypothesis about the mechanism of ternary fission in order to obtain the order of magnitude estimates forP-violating effects.     

A level-density-dependent imaginary potential for heavy ions

Under the assumption that compound-nucleus formation is the only channel competing with elastic scattering, an L-dependent imaginary potential is defined with the help of the compound-nucleus level density. For the latter an expression is used which seems to be accurate enough for excitation energies of several tens of MeV and with a substantial part of rotational energy. Associated with a double-folded real part, this imaginary potential is shown to reproduce well the elastic scattering data of eight systems of medium size (total mass between 36 and 72) at various energies not very high above the Coulomb barrier. The results are equivalent to those obtained with a folding real potential and a Woods-Saxon imaginary potential with parameters adjusted for each set of data with the advantage that our approach only needs two parameters to fit the data for a wide range of energies for each scattering system.     

Enhancement ofT-noninvariant effects in neutron-induced nuclear reactions

The previously developed approach to P-nonconservation in nuclear reactions is applied to the investigation of P- and T-noninvariant effects in neutron-induced reactions. Dynamical and resonance enhancement effects for T-noninvariant quantities are considered. The estimate is given of the expected effect in the compound-nucleus p-resonance.     

Fast fission phenomenon,deep inelastic reactions and compound nucleus formation described within a dynamical macroscopic model

We present a dynamical model to describe dissipative heavy ion reactions. It treats explicitly the relative motion of the two ions, the mass asymmetry of the system and the projection of the isospin of each ion. The deformations, which are induced during the collision, are simulated with a time-dependent interaction potential. This is done by a time-dependent transition between a sudden interaction potential in the entrance channel and an adiabatic potential in the exit channel. The model allows us to compute the compound-nucleus cross section and multidifferential cross sections for deep inelastic reactions. In addition, for some systems, and under certain conditions which are discussed in detail, a new dissipative heavy ion collision appears: fast-fission phenomenon which has intermediate properties between deep inelastic and compound nucleus reactions. The calculated properties concerning fast fission are compared with experimental results and reproduce some of those which could not be understood as belonging to deep inelastic or compound-nucleus reactions.     

Statistical theory of precompound reactions: The multistep compound process

Using a quantum-statistical framework, the method of the generating function involving both commuting and anticommuting variables, and the saddle-point approximation followed by the loop expansion, we derive a theoretical framework for multistep-compound reactions. Our statistical input distinguishes between several classes of states of increasing complexity; this distinction is possible only at the expense of relinquishing the orthogonal invariance of the distribution of Hamiltonian matrix elements usually required in compound-nucleus theories. Our result contains both the compound-nucleus scattering cross section and the theory of Agassi Weidenmüller, and Montzouranis (Phys. Lett. C22 (1975), 145.) developed earlier as special cases. It goes beyond this theory, and extends the framework of precompound theories in general, by allowing the couplings between classes, and to the channels, to be reasonably strong. A self-consistency condition embodied in the saddle-point equation implies in this case that the level densities used in precompound calculations must be modified. We investigate the modification in simple model cases. Our results suggest that the modification may be relevant for the high-energy tail of the spectrum of precompound particles.     

Parity non-conservation effects in neutron elastic scattering reactions

Energy dependence of parity non-conservation effects is derived for neutron elastic scattering on nuclei: emission asymmetry and the rotation of the polarization plane for the polarized neutron beam and longitudinal polarization for unpolarized neutrons. Both potential scattering and scattering through the compound-nucleus resonances (multi-level approximation) are taken into account. The expressions obtained are compared with experimental data on thermal neutron scattering.     

United-atomK x-ray production in nuclear reactions

The probability for compound-nucleus x-ray productionP _cnx in atomic collisions where long-lived compound nuclei are formed is calculated using the second-order distorted wave Born Approximation. The results are compared with a semi-classical formula which relatesP _cnx to the product of theK-vacancy decay rateГ _K , the compound-nucleus lifetime τ, the probability of creating aK vacancy on the incoming part of the collision, and the fraction of reaction productsr _cn that have formed a compound nucleus. For an isolated resonance, we find that τ is just the inverse of the resonance widthqG, and for the compound-nucleus reactions involving many unresolved resonances, τ is the inverse of the Erison correlation widthГ _C . For isobaric analog resonancesГ _C is expected to be larger on resonance than off resonance. The fraction of reaction productsr _cn is given in terms of squares of complex reaction amplitudes.     

Breakdown of the compound-nucleus model in the fusion-evaporation process for110Pd+110Pd

The fusion of the massive systems¹¹⁰Pd+¹⁰⁴Ru and¹¹⁰Pd+¹¹⁰Pd was uniquely identified by observing the a decay of the evaporation residues. The observed distribution of the fusion cross section on the different evaporation-residue channels is in clear contradiction to calculations based on the compound-nucleus model. As a possible explanation the precompound evaporation of a particles is proposed.     

An analysis of runs tests as indicators of nonstatistical structure in the compound nucleus

Runs tests were applied to computer-generated elastic-scattering excitation functions in order to examine their sensitivity to nonstatistical structure in the compound nucleus. The scattering amplitudes were either purely statistical or else they included contributions from additional resonances about 1 MeV broad. Our aim was to determine whether the runs tests could distinguish between the two cases. The tests were successful once trends producing correlations between the datum points were removed. Spurious nonstatistical effects were thus eliminated, demonstrating that if the trend-reduction problem is dealt with propertly, runs tests are effective in searches for nonstatistical structure beneath the compound-nucleus fluctuations in experimental excitation functions.     

A consistent study of precompound and compound-nucleus emission mechanisms in neutron-induced reactions

The exciton model in its closed form and the Weisskopf-Ewing model have been consistently applied to neutron-induced reactions. The analysis has been performed for 12 nuclei in the rangeA=45–209. The primary particle-emission is considered to be governed by an admixture of precompound and compound-nucleus mechanisms, while all consecutive particles are considered to undergo pure compound-nucleus emission. The calculated primary-neutron spectra and excitation functions for (n, p), (n, 2n) and (n, 3n) reactions atE _n=4–24 MeV have been compared with experimental data. The average best-fit values of the exciton-model free parameterK have been found to be ¯K=700 MeV³. Departures form this value appear to cancel out structure effects introduced into transition rates through the structure-sensitive single-particle level density.     

Theory of time-reversal symmetry breaking in compound-nucleus reactions

The interpretation of experimental tests of time-reversal symmetry in compound-nucleus reactions requires the theoretical calculation of a correlation coefficientR. We evaluateR in the framework of a statistical model, and relate it to the observables.     

A scenario for the 220-MeV40Ar+238U reaction

Singles and coincidence charge distributions are combined to illustrate the mechanism for the 220-MeV⁴⁰Ar+²³⁸U reaction. It is found that the apparent peak in the coincidence fragment distribution corresponding toZ=82 (A=208) can be explained in terms of the fissionability of the target-like fragments produced in deep-inelastic collisions rather than as a manifestation of shell effects in compound-nucleus fission, as has been postulated for a similar system.     

Electromagnetic decay of the giant quadrupole resonances: (I). Reaction mechanism and angular distributions of the emitted photons

A study is made of the electromagnetic decay of the ²⁰⁸Pb giant quadrupole resonance excited by inelastic scattering of ¹⁷O at 380 MeV. Due to the instability of the giant quadrupole resonance with respect to compound-nucleus formation and to neutron emission, the time over which the radiation is produced is not much greater than the time in which the direct reaction occurs. Angular distributions of the γ-rays produced in transitions to several low-lying states of the residual nucleus are calculated and their dependence on effects due to the proximity of the interacting nuclei is discussed.     

Pre-scission particle and gamma-ray emission in heavy-ion-induced fission

An introduction is given to the physics of the equilibrium transition-state model and of dissipative nuclear dynamics. Experimental data on pre-scission particle and gamma-ray emission and their interpretation are reviewed. They appear to indicate overdamped motion of the nuclear fluid. A time scale for compound-nucleus fission of about 30 × 10⁻²¹ s or greater is indicated, whilst that for quasi- or fast-fission is somewhat shorter.     

Isospin breaking matrix elements in compound nuclei

The study of compound-nucleus reactions that are isospin forbidden yields information on the average Coulomb matrix element, that mixes states of different isospin in the domain of highly excited overlapping levels. A prerequisite for this is, however, the calculation and subtraction of “external” mixing. In the present work, an approximate calculation is carried through. It is based on a transport theory of statistical nuclear reactions developed in recent years. Coulomb matrix elements are derived in 18 cases for which experimental data are available.     

Investigation of 16O excited states via the 14N(3He,p) reaction

The reaction ¹⁴N(³He, p)¹⁶O has been investigated at a bombarding energy of 15.0 MeV, using a differentially pumped gas target. Angular distributions were measured for 30 levels below 16.5 MeV in excitation. Data were compared with shell-model calculations of Zuker, Buck and McGrory for states whose correspondence with theory is established. Many states are found to possess a large compound-nucleus reaction component. Several previously unreported levels are observed at high excitation. Angular distributions for all except the weakest levels have been compared with DWBA calculations.