Geometry Dependent Hybrid Model Research Articles

Double differential cross sections for (p, xn) reactions of64Zn,65Cu and89Y with 26MeV protons

Double differential cross sections for the inclusive production of neutrons from64Zn,65Cu and89Y bombarded with 26.0 MeV protons have been measured with time-of-flight techniques. The data reduction is discussed with respect to the influence of background corrections in the continuous part of the spectra, and a short comparison with preequilibrium model calculations is presented, showing good agreement with predictions of both, the hybrid and the geometry-dependent hybrid model including multiple particle emission. The question of how to treat pairing remains open.

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.

Analysis of 14MeV (n,p) cross sections with pre-equilibrium model and effective Q-Values.

The measured cross sections of 14 MeV (n,p) reaction for nuclei with mass number larger than 90 are analyzed in terms of the pre-equilibrium exciton model and an effective Q-value, that is derived from a semi-empirical mass formula whose parameters are smooth functions of mass number and are free from fluctuations near closed shells. The deviations from 1.0 of the ratios of experimental to theoretical cross sections calculated using the effective Q-values are markedly reduced as compared with the use of the true Q-values. The use of the effective Q-values also gives a better agreement between the experimental and calculated cross sections in the calculations based on the geometry-dependent hybrid model.

The (p, n) Reaction on 209Bi and Pre-Compound Process

Cross sections and mean projected ranges of the recoil ions for 209 Bi( p , n ) reaction with E p from 18 MeV to 64 MeV were obtained. The cross sections were analysed both by the hybrid model and by the geometry dependent hybrid model. The geometry dependent hybrid model was found to reproduce the experimental ( p , n ) cross sections upto E p of 64 MeV, while the calculated cross sections by the hybrid model deviate from the experimental ones at the proton energies higher than 40 MeV. Dependence of decay rates of the exciton states on the nuclear density was discussed and it was concluded that the pre-compound model is essentially concerned with averaging of the doorway states. Recoil ranges of the reaction residuals were analysed, introducing a 90° asymmetry term P 1 (cos θ) for the angular distributions of the residuals in CM system.

Investigation of 54- to 99-MeVLi6-induced reactions on rare earth targets

Cross section measurements for the reactions $^{150}\mathrm{Sm}$ and $^{142,146,150}\mathrm{Nd}(^{6}\mathrm{Li},xn+yp)$ have been performed in the 50-100-MeV energy range. The experimental excitation functions have been compared to the predictions of the geometry dependent hybrid model. Reasonable agreement between theory and experiment is achieved for the ($\mathrm{xn}$) exit channels while significant differences exist for charged particle exit channels. These differences can be attributed to a contribution from breakup of the $^{6}\mathrm{Li}$ projectile with reactions being induced by the breakup fragments.NUCLEAR REACTIONS $^{150}\mathrm{Sm}$, $^{142,146,150}\mathrm{Nd}(^{6}\mathrm{Li},xnyp\ensuremath{\gamma})$, enriched targets, $E=54\ensuremath{-}99$ MeV; measured in-beam, decay $\ensuremath{\gamma}$ rays. Deduced Eu, Sm isotopic yields. Geometry-dependent hybrid model; breakup of $^{6}\mathrm{Li}$.

Angular-momentum effects in pre-equilibrium processes

Cross sections and the first three moments of the $\ensuremath{\gamma}$-ray multiplicity distribution were measured for many transitions corresponding to $\mathrm{xn}$ and $\mathrm{xn}\ensuremath{\alpha}$ products from bombardments of $^{166}\mathrm{Er}$ with $^{4}\mathrm{He}$, $^{150}\mathrm{Nd}$ with $^{20}\mathrm{Ne}$, and $^{130}\mathrm{Te}$ with $^{40}\mathrm{Ar}$. The $^{4}\mathrm{He}$ and $^{20}\mathrm{Ne}$ bombarding energies were chosen to produce $^{170}\mathrm{Yb}$ compound nuclei at similar excitation energies, approximately 63, 77, and 92 MeV. A Ge(Li)-NaI anti-Compton spectrometer was used in coincidence with nine 5.1-cm by 7.6-cm NaI(Tl) detectors. For the reactions ($^{20}\mathrm{Ne},xn$) and ($^{40}\mathrm{Ar},xn$), the average $\ensuremath{\gamma}$-ray multiplicity ${〈M〉}_{x}$ increases linearly with decreasing $x$ as expected from the statistical decay of compound nuclei. In the ($^{4}\mathrm{He},xn$) reactions, ${〈M〉}_{x}$ is similar for large $x$ but for small $x$ it decreases substantially with decreasing $x$. The latter corresponds to a shift in the population toward the low $J$ values of levels in $^{170\ensuremath{-}x}\mathrm{Yb}$ prior to $\ensuremath{\gamma}$ decay. Also, in the few-neutron channels the average multiplicity associated with a given gating transition in the residual nucleus is much smaller for transitions between low-lying levels. These features, absent in the heavy-ion bombardments, indicate a strong contribution from pre-equilibrium neutron emission. The measured ($^{4}\mathrm{He},xn$) cross sections are in reasonable agreement with those calculated from the geometry-dependent hybrid model of pre-equilibrium emission except for the smallest values of $x$; the latter results and the low ${〈M〉}_{x}$ values for $x\ensuremath{\le}4$ suggest that more than one pre-equilibrium neutron is emitted in these channels.[NUCLEAR REACTIONS $^{150}\mathrm{Nd}(^{20}\mathrm{Ne},xn\ensuremath{\gamma})$, ($^{20}\mathrm{Ne},xn\ensuremath{\alpha}\ensuremath{\gamma}$), $x=4\ensuremath{-}8$, $E=94.2, 110.7$ MeV; $^{130}\mathrm{Te}(^{40}\mathrm{Ar},xn\ensuremath{\gamma})$, $x=3\ensuremath{-}5$, $E=154.5$ MeV; $^{166}\mathrm{Er}(^{4}\mathrm{He},xn\ensuremath{\gamma})$, ($^{4}\mathrm{He},xn\ensuremath{\alpha}\ensuremath{\gamma}$), $x=2\ensuremath{-}8$, $E=67.6\ensuremath{-}95.3$ MeV; measured $\ensuremath{\sigma}(E,E\ensuremath{\gamma})$, $\ensuremath{\gamma}$-ray multiplicities; deduced $J$ distributions in evaporation residues. Enriched target, anti-Compton Ge(Li)-NaI spectrometer.]

Preequilibrium analysis of (p, n) spectra on various targets at proton energies of 25 TO 45 MeV

Thin target (p, n) spectra are reported for incident proton energies of 25, 35 and 45 MeV on 48Ca, 90Zr and 120Sn, and at proton energies of 35 and 45 MeV on 208Pb. Angle-integrated spectra are compared with predictions of the geometry-dependent hybrid model, the hybrid model, and the hybrid model with average state lifetime. The geometry-dependent hybrid model, when combined with evaporation components, gives an excellent prediction of the overall shapes and magnitudes of the experimental results. The simpler hybrid model fails in both respects, paralleling results of earlier comparisons of (p, p') spectra with model calculations.

A priori pre-equilibrium decay models

Intranuclear transition rates for a priori calculations of pre-equilibrium decay have been calculated using both the imaginary optical potential and a nucleon-nucleon scattering approach which is improved over earlier results used in the geometry dependent hybrid model. Spectra calculated using these intranuclear transition rates in several formulations of the hybrid model are compared with each other and with experimental results for the reactions 209Bi(p, p') and 54Fe(p, p') at incident proton energies of 39 and 62 MeV. Results calculated in several ways are found to be in reasonable agreement with data in view of the uncertainties of the calculation. It is shown that the initial target-projectile interaction may be treated as a direct reaction term for which it is essential to consider the geometry of the reaction with respect to the nuclear density distribution but, based on estimated nucleon mean free paths, higher order pre-equilibrium terms may be treated in a non-localized fashion. It is also shown that the relative lifetime dependences assumed in many exciton model calculations are in reasonable agreement with results from nucleon-nucleon scattering calculations at excitation energies below 25 MeV, but get progressively poorer at higher excitations.