Exciton Model Calculations Research Articles

A systematics for negative pion induced nuclear fission cross-sections: Experimental data fitting and cascade exciton model validation

The developed fission systematics depicts the projectile energy and the target mass dependence of fission cross-sections of heavy nuclei. The developed model is fitted using experimental fission cross-section data of 500–1665 MeV negative pion induced fission in [Formula: see text]Sn, [Formula: see text]Au and [Formula: see text]Bi. The same systematics is further fitted using the cascade exciton model (CEM) calculations of the above-mentioned fission reactions. Parameterization of the model is performed by calculating its parameters and uncertainties in them. A comparison of the systematics predictions with experimental data and CEM calculations is made. Validation of the systematics using new target nuclei [Formula: see text]Eu, [Formula: see text]Ta, [Formula: see text]Hg and [Formula: see text]At (not included in the systematics development) over an extended range of pion energies, from 80 MeV to 2500 MeV, builds trust in it. The systematics is not valid for [Formula: see text]Th and [Formula: see text]U. The systematics is found to be valid for target nuclei from [Formula: see text]Sn to [Formula: see text]At and for incident negative pion energies from 80 MeV to 2500 MeV. Results are discussed in detail. Merits and demerits of the developed systematics have been concisely described. Valid conclusions and future perspectives are also given.

Incomplete fusion analysis of the Li7 -induced reaction on Nb93 within 3–6.5 MeV/nucleon

It is understood from the recent experimental studies that prompt/resonant breakup, and transfer followed by breakup in the weakly bound $^{6,7}$Li-induced reactions play a significant role in the complete-incomplete fusion (CF-ICF), suppression/enhancement in the fusion cross section around the Coulomb barrier. Investigation of ICF over CF was done by measuring cross sections of the populated residues in the $^{7}$Li-induced reaction on $^{\text{nat}}$Nb target within 3--6.5 MeV/nucleon energy region. Measured excitation functions of different channels were compared with different equilibrium (EQ) and preequilibrium (PEQ) models. The enhancement in cross sections in the proton ($\sim$ 20--30 MeV) and $\alpha$-emitting channels, which may be ascribed to ICF, was observed in the measured energy range when compared to the Hauser-Feshbach and exciton model calculations using EMPIRE, which satisfactorily reproduces the neutron channels, compared to the Weisskopf-Ewing model and Hybrid Monte Carlo calculations. The increment of the incomplete fusion fraction was observed with rising projectile energy.

Excitonic Properties of Ordered Metal Nanocluster Arrays: 2D Silver Clusters at Multiporphyrin Templates.

The design of ordered arrays of metal nanoclusters such as, for example, two-dimensional cluster-organic frameworks might open a new route toward the development of materials with tailored optical properties. Such systems could serve as plasmonically enhanced light-harvesting materials, sensors, or catalysts. We present here a theoretical approach for the simulation of the optical properties of ordered arrays of metal clusters that is based on the ab initio parametrized Frenkel exciton model. We demonstrate that small atomically precise silver clusters can be assembled in one- and two-dimensional arrays on suitably designed porphyrin templates exhibiting remarkable optical properties. By employing explicit time-dependent density functional theory calculations on smaller homologues, we show that the intrinsic optical properties of metal clusters are largely preserved but undergo J- and H-type excitonic coupling that results in controllable splitting of their excited states. Furthermore, ab initio parametrized Frenkel exciton model calculations allow us to predict an energetic splitting of up to 0.77 eV in extended two-dimensional square arrays and 0.79 eV in tilted square aggregates containing up to 25 cluster-porphyrin subunits.

Preequilibrium Models for 63Cu(n, xp) Reaction in Neutrons at 9, 11, 14.8, and 15 MeV Using the EMPIRE 3.2 Code

In this study, the calculations of proton emission spectra and of the excitation function produced by 63Cu(n, xp) and 63Cu(n, p)63Ni reactions, respectively, are used in the framework of preequilibrium models with the new version of the EMPIRE 3.2 code. Exciton Model predictions combined with the Kalbach angular distribution systematics and the Hybrid Monte Carlo Simulation (HMS) were used, and some necessary parameters have been investigated for our calculations. The comparison with experimental data shows clear improvement over the Exciton Model and HMS calculations.

Production cross–section calculations of medical 32P, 117Sn, 153Sm and 186,188Re radionuclides used in bone pain palliation treatment

Abstract In this study, production cross–section calculations of 32P, 117Sn, 153Sm and 186,188Re radionuclides used in bone pain palliation treatment produced by 30Si(d,γ)32P, 118Sn(γ,n)117Sn, 116Sn(n,γ)117Sn, 150Nd(α,n)153Sm, 154Sm(n,2n)153Sm, 152Sm(n,γ)153Sm, 186W(d,2n)186Re, 187Re(γ,n)186Re, 185Re(n,γ)186Re and 187Re(n,γ)188Re reactions have been investigated in the different incident energy range of 0.003–34 MeV. Two-component exciton and generalised superfluid models of the TALYS 1.6 and exciton and generalised superfluid models of the EMPIRE 3.1 computer codes have been used to pre-equilibrium (PEQ) reaction calculations. The calculated production cross–section results have been compared with available experimental results existing in the experimental nuclear reaction database (EXFOR). Except the 118Sn(γ,n)117Sn, 150Nd(α,n)153Sm and 185Re(n,γ)186Re reactions, the two-component exciton model calculations of TALYS 1.6 code exhibit generally good agreement with the experimental measurements for all reactions used in this present study.

Missing final states and the spectral endpoint in exciton model calculations

Recent studies of (n, xp) spectra at incident energies of 28 to 63 MeV have emphasized a previously noted trend that exciton model calculations do not extend to high enough emission energies in some (p, xn) and (n, xp) reactions. Improved agreement between experiment and calculation is achieved by including in the residual nucleus state density those configurations that can be populated but were not being counted because the Fermi level moves down during particle emission. This necessitates minor adjustments in other model parameters. The situation is generalized to reactions with complex particle channels, and significant effects are seen in the calculations for a few reactions on light targets, though the average level of agreement with experiment is unchanged from earlier work.

Preequilibrium reactions with complex particle channels

Investigations of nucleon induced reactions at incident energies of $14--90\phantom{\rule{0.3em}{0ex}}\text{MeV}$ resulting in the emission of complex particles ($A=2--4$) have provided insights which complement those previously obtained from ($N,\mathit{xN}$) reactions. The description of the preequilibrium energy spectra required modifications to an earlier phenomenological model for direct pickup reactions. This model supplements the usual exciton preequilibrium model. Work on complex particle induced reactions confirms some of these results, extends them to include stripping and exchange reactions, and provides evidence for a projectile dependence of the average effective matrix elements for the residual interactions in the exciton model. A full description of reactions with complex projectiles will require the inclusion of a realistic breakup component and the resulting reduction of the cross section available for the exciton model calculations. Reactions with complex particles in the entrance and/or exit channels have provided indirect evidence for the amount of surface peaking of the initial target-projectile interaction. A summary of additional data needed to help resolve remaining questions is presented.

Surface and collective effects in preequilibrium reactions

Surface localization of the initial target-projectile interaction has been investigated for incident protons and neutrons at bombarding energies of 14--100 MeV within the framework of the exciton preequilibrium model. Incident neutrons, at least at energies up to around 30 MeV, show a greater amount of surface peaking than do incident protons as judged by the effective well depth available to the hole degree of freedom created. With this difference included, exciton model calculations can describe the energy spectra in all four $(N,N)$ reaction channels with a consistent set of model input. To aid in this study, the excitation of strong spectroscopic collective states was included in the calculations. The addition of giant resonance state excitation has a small but helpful effect. There is a need for additional data, especially for incident neutrons above 26 MeV.

Consistent exciton model calculations with shell structure, pairing and isospin effects

Shell structure effects are included in a consistent way for all stages of preequilibrium particle emission in the exciton model. Also included are pairing, isospin, and finite well depth effects. Calculations have been performed for a variety of (N,N) reactions around N=50 and Z=50 at 18 and 25 MeV incident energies. Comparisons with experimental angle-integrated energy spectra demonstrate the utility of the current methodology for including shell effects when pairing and isospin are also included. They also show that shell structure effects wash out in about D/2d mass units. The sensitivity to and interconnectedness of model input were studied, and adjusted parameter values were applied uniformly to all systems. In particular, in order to reproduce the relative yields in the inelastic and exchange channels, the effective residual interaction between like nucleons must be larger than between a neutron and a proton. This is contrary to earlier assumptions.

Comparison of two- and one-component preequilibrium exciton model calculations for some neutron induced reactions

Two-component preequilibrium, used by Gupta, and analogously one-component exciton model descriptions are applied to neutron induced reactions such as46Ti(n,n′),46Ti(n,xp) and27Al(n,xp) at 14.6 MeV. This is the first complete calculation made by the two-component approach of Gupta. In order to obtain mean lives the time-integrated form of master equations is used.

Computational comparison of quantum-mechanical models for multistep direct reactions.

We have carried out a computational comparison of all existing quantum-mechanical models for multistep direct (MSD) reactions. The various MSD models, including the so-called Feshbach-Kerman-Koonin, Tamura-Udagawa-Lenske and Nishioka-Yoshida-Weidenm\"uller models, have been implemented in a single computer system. All model calculations thus use the same set of parameters and the same numerical techniques; only one adjustable parameter is employed. The computational results have been compared with experimental energy spectra and angular distributions for several nuclear reactions, namely, $^{90}\mathrm{Zr}$(p,p') at 80 MeV, $^{209}\mathrm{Bi}$(p,p') at 62 MeV, and $^{93}\mathrm{Nb}$(n,n') at 25.7 MeV. In addition, the results have been compared with the Kalbach systematics and with semiclassical exciton model calculations. All quantum MSD models provide a good fit to the experimental data. In addition, they reproduce the systematics very well and are clearly better than semiclassical model calculations. We furthermore show that the calculated predictions do not differ very strongly between the various quantum MSD models, leading to the conclusion that the simplest MSD model (the Feshbach-Kerman-Koonin model) is adequate for the analysis of experimental data.

MEASUREMENT AND ANALYSIS OF EXCITATION FUNCTIONS FOR ALPHA-INDUCED REACTIONS IN BISMUTH

Excitation functions for 209 Bi (α, 3n), 209 Bi (α, 4n) and 209 Bi (α, 5n) reactions have been measured in the energy range threshold to ≈50 MeV using stacked foil technique. Excitation functions have also been theoretically calculated and as expected, inclusion of pre-equilibrium contribution based on exciton model calculations along with compound nucleus calculations using Hauser–Feshbach formalism reproduces well the measured excitation functions. Interesting trend in the ratio of pre-equilibrium to equilibrium component with projectile energy has been observed.

Two-component exciton model: Basic formalism away from shell closures.

A closed form version of the two-component exciton model is derived. Discussions of corrections for the Pauli exclusion principle, of the expected behavior of the residual two-body matrix elements, and of the relative merits of different types of reaction calculations within the exciton model are presented. Calculations verify the validity of the equal a priori probabilities assumption underlying exciton model calculations and demonstrate that the one- and two-component models produce very similar results when similar assumptions are made about the relative probabilities of exciting proton and neutron degrees of freedom.

Proton-induced fission ofTh232and Ir: Exciton model calculations

Exciton model calculations within the geometry-dependent hybrid model have been performed to study the proton-induced fission of /sup 232/Th and Ir. After adjusting the parameters of the model to reproduce observed (p,xn) and total fission cross section, isotopic distributions of Rb and Cs have been evaluated and compared with experimental distributions measured by on-line mass spectrometry. With simplifying assumptions on the charge division mechanism, the experimental Cs distributions are very well reproduced in the /sup 232/Th(p,f) case. Observed structures are explained in terms of reaction mechanisms. The fission of medium-heavy elements (e.g., Ir(p,f)) appears to be promising for studying high excitation energy fission events and angular momentum effects.

The pre-equilibrium process of the 165Ho( α, xn yp) reaction at Eγ = 109 MeV studied by particle-gamma coincidence measurements

Exclusive proton spectra for individual reaction channels of the 165Ho( α, p xn) reaction at E α = 109 MeV were measured in coincidence with discrete γ-rays characteristic of the residual nuclei. The proton spectra for individual reaction channels of the 165Ho( α, p xn) reaction with small x clearly show two proton groups. One is the proton group appearing as a peak at the highest-energy region of the spectrum. It arises from proton emission at the pre-equilibrium (PEQ) stage, being followed by the evaporating neutrons at the equilibrium (EQ) stage. The other is the proton group seen as a bump (or tail) at the lower-energy side of the peak. It is due to proton emission at the PEQ stage and at least one-neutron emission at the PEQ stage as well. This shows that there exists a threshold energy for the PEQ particle emission. The exclusive spectra as well as the inclusive ones are compared with exciton model calculations where all particles emitted at the PEQ stage of the reaction are properly taken into account. The calculation starting with the initial 4p1h exciton state was found to reproduce well the observed proton spectra. The escape probability Γ↑/( Γ↑ + Γ↓) was found to be about 30% for the doorway state (initial exciton state) with about 100 MeV excitation energy produced by α-particle bombardment on 165Ho.

Isotopic effects in the (n, p) reaction cross section on heavy targets and the statistical preequilibrium model

The systematic decrease in (n,p) cross sections with increasing neutron number for isotopes in reactions induced by 14 MeV neutrons on heavy targets is explained in terms of the preequilibrium model. The relevant physical quantities responsible for this behavior are proton and neutron separation energies, similarly to (n, p) reactions on lighter nuclei, in which proton emission is governed by the compound-nucleus model. The principal transition rateλ+ in the preequilibrium exciton-model calculations should be kept constant (for a given number of excitons and constant energy) in order to obtain a good description of data. The calculations are compared with experimental (n,p) cross sections for series of Te, Xe, W, and Os isotopes.

Energy and angular distributions of neutrons from 90 MeV proton and 140 MeV alpha-particle bombardment of nuclei

We measured neutron time-of-flight spectra from 90 MeV protons and 140 MeV alpha particles bombarding thin targets of Al, Ni, Zr, and Bi at laboratory angles between 20\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{}. The lowenergy (5 to 45 MeV) portions of the spectra were measured with 5 cm diameter by 5 cm deep NE-213 counters at 1 m flight paths with n-$\ensuremath{\gamma}$ pulse-shape discrimination. The high-energy (35 to 150 MeV) portions of the spectra were measured with 12.7 cm diameter by 10.2 cm deep NE-102 counters at flight paths of 2.0 to 5.0 m. The proton-induced measured neutron spectra reveal three distinct energy regions: a low-energy evaporation region, a high-energy region dominated by the quasifree scattering process, and an intermediate-energy region dominated by multistep, preequilibrium processes. In the latter two regions, the spectra show strong angular dependence. The alpha-particle induced neutron spectra show these same distinct energy regions plus an exponential falloff above the beam energy per nucleon. The neutron spectra are compared with earlier proton spectra produced also by 90 MeV protons and 140 MeV alpha particles. It is observed that the high-energy portions of the forward-angle neutron and proton cross sections are in ratios consistent with the idea that single nucleon-nucleon scattering dominates. For the heavy-mass targets, the low-energy evaporation regions show neutron yields larger than proton yields. The proton-to-neutron ratios observed in the high-energy continua are interpreted with a quasifree calculation fitted simultaneously to the proton and the neutron spectra. Preequilibrium calculations with the exciton model and the hybrid model reproduce the shape of the experimental angle-integrated energy spectra down to lower energies than the quasifree calculations. The exciton model calculations underestimate the magnitudes of the cross sections, while the hybrid model provides better absolute agreement. One of the preequilibrium calculations uses the method of Mantzouranis and Weidenm\"uller to predict angular distributions; we find that the predicted angular distributions overestimate the neutron yields at forward angles. The intranuclear-cascade model predicts proton-to-neutron ratios much smaller than experimentally observed in the high-energy forward-angle continua.NUCLEAR REACTIONS $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{209}\mathrm{Bi}$(p,n), ($\ensuremath{\alpha}$, n), ${E}_{\mathrm{p}}=90$ MeV; ${E}_{\ensuremath{\alpha}}=140$ MeV; ${\ensuremath{\theta}}_{L}=20\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}135\ifmmode^\circ\else\textdegree\fi{}$; measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}\mathrm{dE}}$; compared with available experimental proton spectra and with theoretical calculations including PWIA quasifree scattering, preequilibrium exciton, geometry-dependent hybrid, and intranuclear-cascade models.

Decay modes of the isoscalar giant quadrupole resonance in the Zn isotopes

Particle-particle coincidence measurements have been performed to study directly the particle decay modes of the isoscalar giant quadrupole resonance in $^{64}\mathrm{Zn}$, $^{66}\mathrm{Zn}$, and $^{68}\mathrm{Zn}$. The resonance was excited via inelastic alpha particle scattering at 160 MeV and decay protons, neutrons, and alpha particles were detected in coincidence at a number of angles. The importance of statistical processes in the decay of the giant quadrupole resonance is shown by the similarity of the measured branching ratios to statistical model predictions, which vary systematically across the Zn isotopes. This result is consistent with exciton model calculations which predict that the giant quadrupole resonance width in Zn isotopes is predominantly a spreading width rather than an escape width.[NUCLEAR REACTIONS $^{64}\mathrm{Zn}(\ensuremath{\alpha},\ensuremath{\alpha}x)$, $^{66}\mathrm{Zn}(\ensuremath{\alpha},\ensuremath{\alpha}x)$, $^{68}\mathrm{Zn}(\ensuremath{\alpha},\ensuremath{\alpha}x)$, $x=p,n,\ensuremath{\alpha}$, ${E}_{\ensuremath{\alpha}}=160$ MeV; measured $\frac{{d}^{4}\ensuremath{\sigma}}{d{\ensuremath{\Omega}}_{\ensuremath{\alpha}}d{\ensuremath{\Omega}}_{x}d{E}_{\ensuremath{\alpha}}d{E}_{x}}$; deduced giant quadrupole resonance branching ratios; compared with branching ratios calculated in statistical model.]

Fission ofTh232at energies up to 90 MeV

In a recent work, the yields of spallation residues from 8-90 MeV proton induced fission of $^{232}\mathrm{Th}$ were reproduced by exciton model calculations to which a fission option had been added. This allowed evaluation of the spectrum of fissioning nuclei. In this work, an extension of that calculation to the properties of the fission products is presented. Dividing the fissioning nuclei according to their fissionability, an approach is introduced which accounts for the percentage of symmetric and asymmetric fission, allows calculation of the most probable charge for a given fission product mass chain, and evaluates the numbers of pre- and post-fission neutrons. A comparison of the results of this calculation is made with extensive amounts of experimental data, and the implications of the calculation discussed.[NUCLEAR REACTIONS, FISSION $^{232}\mathrm{Th}(p,f) E=8\ensuremath{-}90$ MeV; interpretation of mass distribution and charge dispersion based on calculations of model proposed.]

Angular distributions in a unified model of preequilibrium and equilibrium neutron emission

An alternative mathematical formulation is presented for the generalized master equation of the exciton model, introduced by Mantzouranis et al. to describe preequilibrium effects in angular distributions of emitted particles in nuclear reactions. The exciton model proposed in this paper includes internal transitions with $\ensuremath{\Delta}n=2, 0, \ensuremath{-}2$, and describes both the preequilibrium and the stages of the reaction process. A simple, but exact formula is given to calculate mean lifetimes of exciton states and their Legendre coefficients, from which double differential cross sections can be easily calculated. The mathematical improvements of the generalized exciton model greatly facilitate a systematical comparison with experimental data. In this paper the neutron inelastic scattering data for 34 elements measured by Hermsdorf et al. at 14.6 MeV were used for such intercomparison. The results show underestimation of angular distributions at backward angles. However, a good overall fit of all angular distributions is obtained by adjustment of only two global parameters. It is concluded that further study with regard to the physics of the model is required. Some local variations in the angular distribution coefficients as a function of the mass number might be ascribed to level-density effects. Although it appeared that the presently adopted formulas and parameters in exciton model calculations are not adequate to give detailed predictions of the energy and angular distributions, meaningful improvements were obtained by variation of final-state parameters. Finally, some attention was devoted to the unification of the exciton and Hauser-Feshbach models. By introducing a proper definition of equilibrium emission it is shown that consistent results are obtained for neutron emission spectra calculated with the two models.NUCLEAR REACTIONS Be, C, Na, Mg, Al, Si, P, S, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Se, Br, Zr, Nb, Cd, In, Sn, Sb, I, Ta, W, Au, Hg, Pb, Bi ($n, \mathrm{nx}$), $E=14.6$ MeV; calculated $\ensuremath{\sigma}$ (${E}_{n}, \ensuremath{\theta}$), Legendre coefficients. Generalized exciton model, preequilibrium and analysis, Hauser-Fesh-bach model.