Precompound Decay Research Articles

Measurement and analysis of the excitation function and isomeric cross section ratios forα-induced reaction on Ir, Au, Re and Ta nuclei

Excitation functions and a few isomeric cross-section ratios for production of (1)192Au,193Au,194Au,195Au and192Ir nuclides inα-induced reactions on191,193Ir, (2)197Tl,197m Hg,198m,g Tl,199Tl and200Tl nuclides inα-induced reaction in197Au and (3)183Re and184m,g Re nuclides inα-induced reaction in181Ta and185Re are obtained from the measurements of the residual activities by the conventional stacked-foils technique from threshold to 50MeV. The excitation function and isomeric cross-section ratios for nuclear reaction181Ta(α,n)184m,g Re are compared with the theoretical calculation using the code Stapre which is based on exciton model for pre-equilibrium phase and Hauser-Feshbach formalism taking angular momentum and parity into account for the equilibrium phase of the nuclear reaction. All other experimental excitation functions are compared with the calculations considering equilibrium as well as pre-equilibrium reaction mechanism according to the geometry dependent hybrid (GDH) model and hybrid model of Blann using the code Alice/91. The high energy part of the excitation functions are dominated by pre-equilibrium reaction mechanism whereas the low energy parts are dominated by equilibrium evaporation with its characteristic peak. The GDH model provides a potentially better description of the physical process (i.e., a higher probability for peripheral collisions to undergo precompound decay than for central collisions) compared to hybrid model. However in the energy range of present measurement most of the excitation functions are fitted reasonably well by both GDH model and hybrid model with initial exciton numberN 0=4(N n=2,N p=2,N h=0). Barring a few reactions we have found the overall agreement between theory and experiment is reasonably good taking the limitations of the theory into account.

New precompound decay model: Angular distributions

A new Monte Carlo precompound decay model is used to calculate double-differential spectra using an approach based on conservation of linear momentum between an incident nucleon and the three quasiparticles activated in the collisions of the equilibration process. The angular distribution theory is presented as it is applied to the individual three-exciton cascades of the precompound model. The importance of multiple precompound decay beyond two nucleons per nucleus is illustrated for ${}^{90}$Zr$(p,xn)$ reactions for incident protons up to 256 MeV. These components are shown to be important for extending the useful range of the precompound approach to energies beyond 80 MeV. The contribution to nucleon spectra due to hole conversion processes is illustrated. We compare results of the formulation described with experimental angular distributions for ${}^{90}$Zr$(p,xn)$ reactions at incident energies of 45, 80, and 160 MeV, and for the ${}^{90}$Zr$(p,xp)$ reactions at incident energies of 80, 160, and 200 MeV. Additionally, ${}^{208}$Pb$(p,xn)$ spectra at 7.5\ifmmode^\circ\else\textdegree\fi{}, 30\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}, 120\ifmmode^\circ\else\textdegree\fi{}, and 150\ifmmode^\circ\else\textdegree\fi{} are compared with two experimental data sets for 256 MeV incident proton energy, and ${}^{90}$Zr$(p,xn)$ spectra at the same five angles are compared with predicted results for 256 MeV incident protons. At 256 MeV incident proton energy, the higher energy emission spectra are seriously overpredicted at 60\ifmmode^\circ\else\textdegree\fi{}. All other results are reproduced quite well, including back-angle yields. The quasielastic peak measured at 7.5\ifmmode^\circ\else\textdegree\fi{} at 256 MeV incident proton energy is shown to be in quite reasonable agreement with experimental results.

New precompound decay model.

A new precompound Monte Carlo simulation model is presented. It permits unlimited multiple precompound emission for each interaction, may be used to give exclusive spectra and yields, and does not rely upon those exciton state densities shown to be inconsistent with the assumed two body transitions in the hybrid and exciton model formulations. Results of the new model are compared with $^{90}\mathrm{Zr}$ (p,xn) single differential spectra for incident energies from 25 to 160 MeV, and for $^{59}\mathrm{Co}$ (p,x) and $^{51}\mathrm{V}$ (p,x) excitation functions for incident proton energies up to 200 MeV. The new model gives significant improvement over the hybrid model for calculation of excitation functions. Multiple precompound decay predictions are compared for the two models. It is shown that the restriction to two precompound nucleons per decay in the hybrid model becomes a poor approximation for incident proton energies above \ensuremath{\approxeq}80 MeV. \textcopyright{} 1996 The American Physical Society.

Comparison of fast cascade plus statistical models for heavy ion induced multifragmentation reactions.

We consider the reaction [sup 36]Ar+[sup 197]Au at incident [sup 36]Ar energies of 35, 50, 80, and 110[ital A] MeV, comparing calculations of precompound decay using the Boltzmann master equation (BME) and quantum molecular dynamics (QMD) models. We then estimate quasiequilibrated nuclei and excitations using the BME, and use these values as input into statistical multifragmentation models. For the latter we compare sequential binary decay as an extension of the Weisskopf-Ewing evaporation model, and a simultaneous multifragmentation for an expanded low density gas. The exclusive multiplicities predicted by these models are compared with experimental results.

Measurement of excitation functions and mean projected recoil ranges of nuclei in α-induced reactions on F, Al, V, Co and Re nuclei

Excitation function and mean projected recoil ranges of nuclei produced in theα-particle induced reactions on F, Al, V, Co and Re targets were measured by conventional thick target thick recoil catcher technique for bombarding energiesE α≤65 MeV. The measured cross-sections are compared with calculations considering equilibrium as well as pre-equilibrium reaction mechanism according to the hybrid and geometry dependent hybrid (GDH) model of Blann using the code Alice/85/300. High energy part of the excitation functions are dominated by pre-equilibrium reaction mechanism whereas the low energy parts are dominated by evaporation with its characteristic peak. In this paper emphasis will be placed on the GDH model, for it provides a potentially better description of the physical process i.e., a higher probability of peripheral collisions to undergo precompound decay than for central collisions. Geometry dependent model with initial exciton numbern 0=4 (n n=2,n p=2,n k=0) gives better fits compared to hybrid model with same initial exciton configuration andmfp parameterk=1.0 forα-induced reactions on F, V, Co and Re. Whereas forα-induced reaction on Al comparatively large initial exciton configurations (8/4/4/0) or (10/5/5/0) were required to fit the excitation functions reasonably well. Recoil ranges were converted into recoil momentum and vice versa using Lindhard, Scharff and Schiott (LSS) and Blaugrund theories. These theories were also used to calculate projected recoil ranges for full momentum transfer pertaining to fusion reactions. The momentum transfer information was used to get clues about some aspect of the interaction from the trends and magnitudes of the observed ranges.

Giant resonances and intermediate energy heavy ions: Electromagnetic decay experiments

We briefly explore how large cross sections for excitation of both isoscalar and isovector giant multipole resonances which can be obtained using intermediate energy heavy-ion reactions can be utilized in photon-decay coincidence experiments to provide new information on subjects ranging from basic nuclear structure properties to resonance damping and pre-compound decay. We also discuss experiments in which photon-decay techniques are used as a tag to isolate and identify very weakly excited modes, enabling us to explore such diverse subjects as hadronic excitation of the giant dipole resonance, the distribution of isovector quadrupole strength in 208Pb, and the excitation of two-phonon giant resonance strength.

Emission of energetic protons at backward angles in He+U reactions within a cooperative model with coulomb effects

The emission of backward angle protons in the collisions between 3,4He and 238U are investigated within the cooperative model which involves the multiple collisions among the projectile and target nucleons. As the charge of the target is large, the Coulomb distortion of the emitted protons by the remaining charges has been included by following a covariant formulation. In contrast to intranuclear cascade and precompound decay models, the cooperative model gives a good overall description of the data. The Coulomb distortion effects in the final channel are found to be important.

The quantum statistics of pre-equilibrium phenomenology

It is shown how the widely used phenomenological models of multi-step direct precompound decay can be given a quantum-mechanical interpretation on the basis of what we call leading-particle statistics.

Emission of energetic protons at backward angles in central collisions

Backward-angle protons produced in collisions between intermediate-energy complex projectiles and 238U are shown to originate from reactions which involve large linear momentum transfers to the target. Spectral slopes yield apparent temperatures that are 2–3 times larger than for a fully equilibrated, complete-fusion source. Comparisons with intranuclear cascade and precompound decay calculations suggest a multiple-collision mechanism that is intermediate between quasi-free scattering and complete thermalization.

Numerical test of approximations in the hybrid precompound decay model

We review inconsistencies in expressions which are used for exciton distribution functions in precompound decay models utilizing the Ericson type of partial state density. We then compare results of one formulation, the hybrid model, with and without corrected distribution functions for the second hierarchy of configurations. Results are shown for93Nb (n, n′) and (n, p) reactions at 14.7, 45 and 90 MeV incident nucleon energies. The corrected distribution functions change hybrid model predictions by less than 10% for angle integrated spectra, but certain cases are discussed for which the improved treatment should be used due to larger errors from the use of the Ericson expression.

Precompound decay in heavy ion reactions via the hybrid model.

The hybrid model for precompound decay is applied to the calculation of neutron spectra following the $^{20}\mathrm{Ne}$ and $^{12}\mathrm{C}$ bombardment of $^{165}\mathrm{Ho}$ at 220, 292, ${(}^{20}$Ne), and 300 ${(}^{12}$C) MeV. Results are compared with experimentally deduced angle integrated spectra and with results of the Boltzmann master equation. Both models give excellent agreement with experimentally deduced spectra.

Angular momentum effects in preequilibrium cluster emission.

The preequilibrium emission of \ensuremath{\alpha} particles was studied by observing the precompound decay of the $^{65}\mathrm{Zn}^{\mathrm{*}}$ composite system. Several entrance channels were used, covering a range of angular momenta up to about 40\ensuremath{\Elzxh}. A model interpretation is presented which does not employ cluster preformation assumptions or parameters. The results suggest that angular momentum conservation governs preequilibrium cluster emission to a large extent.

The pre-equilibrium hybrid and exciton models revisited

Abstract We develop a new perspective upon the differences between the hybrid and exciton models for precompound decay. Their difference in status regarding the type of cross-section being calculated, is demonstrated. Here, the treatment of multiple emission plays an important role. Statistical a priori hypotheses and possible future development of the considered models are discussed.

Comments on the state densities and the transition rates in the pre-equilibrium exciton model

It is proposed to renormalize the exciton-state densities used in models for precompound decay such that the summed state densities agree with the expressions employed in equilibrium statistical models. In this way a close fit can be guaranteed between preequilibrium model calculations and the results of equilibrium statistical models for the evaporative stage of the reaction. The consequences of this proposal for the internal transition rates of the pre-equilibrium exciton model are analyzed. The matrix element for the residual interaction is obtained not from a phenomenological parametrization, but from the nucleon mean free path in nuclear matter. It is demonstrated that the proposed renormalization, from one-component Fermi-gas formulas to two-fermion expressions for the state densities, leads to strongly improved agreement of the effective exciton-model values for the nucleon mean free path in nuclear matter with realistic estimates. It is proved that the particle-hole state densities for a two-component Fermi gas, summed over the allowed exciton-state numbers, agree with the phenomenological state-density expressions used in statistical Hauser-Feshbach models.

Linear momentum transfer in 40-150 MeV proton-induced reactions with 238U.

Angular correlations between coincident fission fragments have been measured for 40-, 90-, and 150-MeV proton-induced reactions on a /sup 238/U target. From these data linear momentum transfer distributions have been derived, which are then compared with other results for protons and more complex projectiles. On a per nucleon basis, protons exhibit the largest average linear momentum transfer values of any projectile over the energy range from E/A = 40 to 1000 MeV. This can be understood in terms of fundamental scattering cross sections, and is qualitatively demonstrated by intranuclear cascade calculations. Both cascade and precompound decay calculations reproduce the linear momentum transfer distributions with moderate success.

Analysis of continuum gamma-ray emission in precompound-decay reactions

Abstract A model is developed for the statistical description of continuum γ-ray emission in precompound reactions. Consistency requirements are derived and discussed. An ambiguity in the generalization of the Brink-Axel hypothesis to precompound decay is pointed out.

Precompound evaporation analyses of excitation functions for (α,xn) reactions

Calculated ($\ensuremath{\alpha},x\mathrm{n}$) excitation functions ($x=1 \mathrm{to} 4$) for $^{233,234,235}\mathrm{U}$ and $^{237}\mathrm{Np}$ targets, for incident $^{4}\mathrm{He}$ energies to 45 MeV, have been compared with experimental results. Calculations used experimental fission barriers with single particle ratios which were deduced by fitting experimentally deduced fission probabilities at excitations up to 12 MeV. Standard precompound parameters used for fitting spectra of nucleon-induced reactions were used, changing only the initial exciton number to four, appropriate for $\ensuremath{\alpha}$-induced reactions. Agreement with experimental results was good to excellent, without the need of multiple precompound decay, nor of variation of precompound decay parameters from those required for nonfissile systems.

Global test of modified precompound decay models

A single parameter set was adopted for the hybrid and geometry dependent hybrid models. The nuclear density profile was modified for consistency with results of the Myers nuclear droplet model. Optical model parameters were modified to give better global results for inverse reaction cross sections in the precompound energy range up to 90 MeV. Two types of multiple precompound decay processes are defined, and the more important of the two is incorporated into the precompound decay formalism. This results in two to five orders of magnitude improvement in predicting $^{202}\mathrm{Hg}$(p,2p) and $^{202}\mathrm{Hg}$(p,2pn) product yields for proton energies up to 86 MeV. The global parameter set and formulation of this work is compared with (n, $x\mathrm{n}$) and (n,p) spectra for 14 MeV incident neutrons, for (p,n) spectra with 18-90 MeV protons, and with (p,p\ensuremath{'}) spectra for 39-90 MeV protons. The geometry dependent hybrid model gives the better overall agreement, in most cases within the 20-30% limit of significance attached to the model. Some discussion is given of methods by which the calculations might be further improved.NUCLEAR REACTIONS Hybrid, geometry dependent hybrid precompound decay models, improve global parameter set, implement multiple precompound decay. Test new formulation vs spectra from reactions induced by 14 MeV neutrons to 90 MeV protons.

Precompound analyses ofNi58−64(n, px)reactions

Data for the inclusive (n, $\mathrm{p}x$) reaction for 60 MeV neutrons on $^{58,60,62,64}\mathrm{Ni}$ are presented. Angular distributions for $Q$-value bins show a decrease of the forward peaking of the proton emission with increasing neutron excess. A marked dependence of the angle integrated spectra on ($N\ensuremath{-}Z$) is observed. The data are compared to hybrid and geometry dependent hybrid model calculations. Although these results predict the general shape of the spectra, they do not account for ($N\ensuremath{-}Z$) dependence. A neutron skin, as given by a hydrodynamic model, is added to the geometry dependent hybrid model, which predicts a higher precompound decay for high impact parameters. These results agree much better with the $N\ensuremath{-}Z$ dependence of the data.NUCLEAR REACTIONS $^{58,60,62,64}\mathrm{Ni}$(n,p), ${\ensuremath{\epsilon}}_{\mathrm{n}}=60$ MeV, measured $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$, $\frac{d\ensuremath{\sigma}}{d\ensuremath{\epsilon}}$; analyze via hybrid and geometry dependent hybrid models; explore importance of neutron skin.

Random-walk model of precompound decay II: Stochastic uncertainties in the lifetimes and cross-sections

The uncertainties arising from the stochastic nature of precompound decay nuclear reactions are analyzed in the framework of the preequilibrium exciton and random-walk models. It is demonstrated that the standard deviations and the mean values of the exciton-state lifetimes are of the same order of magnitude. Their correlations are weakly positive, except for exciton states near the equilibrium number, where the correlations are significant. The usefulness and the limitations of the never-come-back approximation are discussed. A general proof is presented of the conditions under which the master-equation and random-walk approaches to Markov processes are equivalent. Connections between different preequilibrium models, e.g. the multi-step compound model and the microscopic statistical theory of precompound decay, are pointed out. It is shown that the waiting time between subsequent collisions is governed by a Poisson process, suggesting that the variance associated with the nucleon mean free path in nuclear matter, as estimated from preequilibrium models, is considerable. The stochastic uncertainties in the emission cross-sections correspond to those of a Bernoulli process.