Statistical Reaction Model Research Articles

Vortex photon induced nuclear reaction: Mechanism, model, and application to the studies of giant resonance and astrophysical reaction rate

The vortex photon beam induced nuclear reaction is studied. The interaction formalism of nuclei with vortex photons is developed and incorporated into the statistical reaction model to calculate reaction cross-sections. For 138 nuclei of high nuclear astrophysics and structure interest, the cross-sections of γ-ray emission and neutron production from the decay of the giant resonances (GR) populated by vortex photons, e.g., (γvo,γemit) and (γvo,nprod.), are computed. It is shown that for the (γvo,γemit) and (γvo,nprod.) cross-sections, the GR contribution of an individual L is either enhanced or suppressed depending on the parameters of vortex γ-rays, and the contribution from the GR of a specific L can be identified and deduced. To this end, a novel method to exclusively determine the γ-strength function (γSF) for the GR of a specific L is proposed considering the (γvo,γemit) and (γvo,nprod.) measurements, and the feasibility studies demonstrate that the γSF for the giant quadrupole resonance can be extracted. Furthermore, the astrophysical reaction rates of the vortex photon induced reactions in p-process are investigated. It is indicated that photo-nuclear reactions induced by vortex photons will bring new insights in nuclear physics and astrophysics research.

Continuum random-phase approximation for (n,γ) reactions on neutron-rich nuclei: Collective effects and resonances

We formulate a microscopic theory to calculate cross section of the radiative neutron capture reaction on neutron-rich nuclei using the continuum random-phase approximation (cRPA) to the time-dependent density functional theory (TDDFT). With an intention of applying to the $r$ process, for which the statistical reaction model may not be appropriate, we describe the transition between a initial state of incident neutron and a final state of the $\ensuremath{\gamma}$ decay by means of a single many-body framework of the cRPA-TDDFT. With the cRPA approach, it is possible to describe various excitation modes present in the $(n,\ensuremath{\gamma})$ reaction, including soft dipole excitation, the giant resonances, as well as noncollective excitations and the single-particle resonances. Furthermore, it enables us to describe the $(n,\ensuremath{\gamma})$ reaction where the the final states of the $\ensuremath{\gamma}$ transition are low-lying surface vibrational states. We demonstrate the theory by performing numerical calculation for the reaction $^{139}\mathrm{Sn}(n,\ensuremath{\gamma})^{140}\mathrm{Sn}$. We discuss various new features which are beyond the single-particle model: the presence of narrow and wide resonances originating from noncollective and collective excitations and roles of low-lying quadrupole and octupole vibrational states.

Photoexcitation of Ge76

The dipole strength of the nuclide $^{76}$Ge was studied in photon-scattering experiments using bremsstrahlung produced with electron beams of energies of 7.8 and 12.3 MeV at the $\gamma$ELBE facility. We identified 210 levels up to an excitation energy of 9.4 MeV and assigned spin $J$ = 1 to most of them. The quasicontinuum of unresolved transitions was included in the analysis of the spectra and the intensities of branching transitions were estimated on the basis of simulations of statistical $\gamma$-ray cascades. The photoabsorption cross section up to the neutron-separation energy was determined and is compared with predictions of the statistical reaction model. The derived photon strength function is compared with results of experiments using other reactions.

Electric and magnetic dipole strength in Zn66

The dipole strength of the $N=28$ closed-shell nuclide $^{54}\mathrm{Fe}$ was studied in photon-scattering experiments using bremsstrahlung produced with electron beams of kinetic energies of 7.5 and 13.9 MeV at the $\ensuremath{\gamma}\mathrm{ELBE}$ facility as well as using quasimonoenergetic and linearly polarized photon beams of 26 different energies within the range from 5.5 to 11.4 MeV at the $\mathrm{HI}\ensuremath{\gamma}\mathrm{S}$ facility. About 100 $J=1$ states were newly identified, out of them 19 with ${1}^{+}$ and 30 with ${1}^{\ensuremath{-}}$ assignments. The quasicontinuum of unresolved transitions was included in the analysis of the spectra and the intensities of branching transitions were estimated on the basis of simulations of statistical $\ensuremath{\gamma}$-ray cascades. As a result, the photoabsorption cross section up to the neutron-separation energy was determined and compared with predictions of the statistical reaction model. The experimental $M1$ strengths from resolved ${1}^{+}$ states are compared with results of large-scale shell-model calculations.

Electric and magnetic dipole strength in Fe54

The dipole strength of the $N=28$ closed-shell nuclide $^{54}\mathrm{Fe}$ was studied in photon-scattering experiments using bremsstrahlung produced with electron beams of kinetic energies of 7.5 and 13.9 MeV at the $\ensuremath{\gamma}\mathrm{ELBE}$ facility as well as using quasimonoenergetic and linearly polarized photon beams of 26 different energies within the range from 5.5 to 11.4 MeV at the $\mathrm{HI}\ensuremath{\gamma}\mathrm{S}$ facility. About 100 $J=1$ states were newly identified, out of them 19 with ${1}^{+}$ and 30 with ${1}^{\ensuremath{-}}$ assignments. The quasicontinuum of unresolved transitions was included in the analysis of the spectra and the intensities of branching transitions were estimated on the basis of simulations of statistical $\ensuremath{\gamma}$-ray cascades. As a result, the photoabsorption cross section up to the neutron-separation energy was determined and compared with predictions of the statistical reaction model. The experimental $M1$ strengths from resolved ${1}^{+}$ states are compared with results of large-scale shell-model calculations.

Estimation of production yield of 93mMo and other residues from a 7Li-induced reaction

The crux of the present work is to analyze the yield of the residues produced in the 7Li-induced reaction on 89Y target in the low energy range. The experimental yields of 93mMo, which is a significant product in the energy range considered, and other coproduced radionuclides, such as 92mNb, 89Zr, 91mY, and 90mY have been measured within 19–40 MeV energy, and are compared with the compound and pre-compound models in the framework of the statistical reaction model code EMPIRE. The maximum measured yield for 93mMo is 374 MBq/C at 31.3 MeV in a 3 mg/cm2 thick 89Y target corresponding to a cross-section of 396.8 ± 38.6 mb from the 89Y(7Li,3n)93mMo reaction. The model estimations well reproduce the experimental yields of 93mMo. The possible production of stable isotopes has also been estimated theoretically from the model over the experimental energy range. The reaction could be an alternative route for the production of no-carrier-added 93mMo radionuclide provided that the radionuclides are chemically separated from the bulk 89Y matrix.

Dipole strength inSe80forsprocess and nuclear transmutation ofSe79

The dipole strength distribution of $^{80}\mathrm{Se}$ was studied in a photon-scattering experiment by using bremsstrahlung produced with an electron beam of energy 11.5 MeV at the linear accelerator ELBE. We identified $180\phantom{\rule{0.28em}{0ex}}\ensuremath{\gamma}$ transitions up to an energy of 9.6 MeV, and analyzed the strength in the quasicontinuum of the spectrum. Simulations of statistical $\ensuremath{\gamma}$-ray cascades were performed to estimate intensities of inelastic transitions and to correct the intensities of the ground-state transitions for their branching ratios. The photoabsorption cross section below the neutron-separation energy derived in this way was combined with the photoabsorption cross section obtained from an earlier $(\ensuremath{\gamma},n)$ experiment and used as an input for the calculation of $^{79}\mathrm{Se}(n,\ensuremath{\gamma})$ reaction rates on the basis of the statistical reaction model.

Extended optical model for fission

A comprehensive formalism to calculate fission cross sections based on the extension of the optical model for fission is presented. It can be used for description of nuclear reactions on actinides featuring multi-humped fission barriers with partial absorption in the wells and direct transmission through discrete and continuum fission channels. The formalism describes the gross fluctuations observed in the fission probability due to vibrational resonances, and can be easily implemented in existing statistical reaction model codes. The extended optical model for fission is applied for neutron induced fission cross-section calculations on $^{234,235,238}\mathrm{U}$ and $^{239}\mathrm{Pu}$ targets. A triple-humped fission barrier is used for $^{234,235}\mathrm{U}(n,f)$, while a double-humped fission barrier is used for $^{238}\mathrm{U}(n,f)$ and $^{239}\mathrm{Pu}(n,f)$ reactions as predicted by theoretical barrier calculations. The impact of partial damping of class-II/III states, and of direct transmission through discrete and continuum fission channels, is shown to be critical for a proper description of the measured fission cross sections for $^{234,235,238}\mathrm{U}(n,f)$ reactions. The $^{239}\mathrm{Pu}(n,f)$ reaction can be calculated in the complete damping approximation. Calculated cross sections for $^{235,238}\mathrm{U}(n,f)$ and $^{239}\mathrm{Pu}(n,f)$ reactions agree within 3% with the corresponding cross sections derived within the Neutron Standards least-squares fit of available experimental data. The extended optical model for fission can be used for both theoretical fission studies and nuclear data evaluation.

Impact of low-energy multipole excitations and pygmy resonances on radiative nucleon captures

Nuclear structure theory is considered in the framework of the development of a microscopic model for nucleon-capture astrophysical implementations. In particular, microscopically obtained strength functions from a theoretical method incorporating density functional theory and quasiparticle-phonon model are used as an input in a statistical reaction model. The approach is applied in systematic investigations of the impact of low-energy multipole excitations and pygmy resonances on dipole photoabsorption and radiative neutronand proton-capture cross sections of key s- and r-process nuclei which is discussed in comparison with the experiment. For the cases of the short-lived isotopes 89 Zr and 91 Mo theoretical predictions are made.

Pygmy resonances and radiative nucleon captures for stellar nucleosynthesis

The impact of low-energy multipole excitations and pygmy resonances on radiative neutron and proton-capture cross sections in nuclei close to the $\ensuremath{\beta}$-stability line is investigated. For this purpose, a microscopic theoretical approach based on self-consistent density functional theory and quasiparticle-random-phase-approximation formalism extended with multiphonon degrees of freedom is implemented in a statistical reaction model. The advantage of the method is the microscopic nuclear structure input for unified description of low-energy multiphonon excitations and pygmy and giant resonances. This is found to be important for the understanding of the fine structure and dynamics of the nuclear response function at low energies, which strongly influences nuclear reaction rates of astrophysical relevance. Calculations of the radiative capture cross sections of the reactions $^{85}\mathrm{Kr}(n,\ensuremath{\gamma})^{86}\mathrm{Kr}, ^{87}\mathrm{Sr}(n,\ensuremath{\gamma})^{88}\mathrm{Sr}$, and $^{89}\mathrm{Y}(p,\ensuremath{\gamma})^{90}\mathrm{Zr}$ are discussed in comparison with experimental data. For the reactions $^{89}\mathrm{Zr}(n,\ensuremath{\gamma})^{90}\mathrm{Zr}$ and $^{91}\mathrm{Mo}(n,\ensuremath{\gamma})^{92}\mathrm{Mo}$ theoretical predictions of the reaction cross sections are made.

Alkene Hydroboration: Hot Intermediates That React While They Are Cooling

Non-TST behavior has recently attracted a great deal of attention. If such behavior is general, then the standard way in which synthetic chemists rationalize and predict reactivity and selectivity would be at least partially invalid. The work in this article was inspired by recent results which highlighted a departure from the predictions of TST for rationalization of the regiochemical outcome of the hydroboration reaction mechanism, suggesting that the isomeric product ratios arise because of nonstatistical dynamical effects (J. Am. Chem. Soc. 2009, 131, 3130-3131). We suggest, based on new calculations using a weak collision RRKM-Master Equation (ME) model, an alternative interpretation of the experimental results which preserves a statistical reaction model. While it is a common assumption that all intermediates and transition states along the reaction path are in thermal equilibrium with solvent, our ME results show that hot intermediates may react while they are undergoing stepwise relaxation through weak collisions, even in solution. To our knowledge, this work represents the first application of master equation methodology to a solution phase thermal reaction in organic chemistry that cannot be otherwise explained using conventional TST. Explicit modeling of solvent and solute dynamics is often prohibitively expensive; however, the master equation offers a computationally tractable model with considerable predictive power that may be utilized to investigate whether stepwise collisional relaxation is prevalent in other polyatomic systems.

Light charged particle decay in the reaction7Li+16O

Angular distributions and excitation functions for the emission of a large number of proton, deuteron, triton, andα-particle groups in7Li+16O reactions have been measured in the vicinity of the Coulomb barrier. Within the framework of the statistical reaction model, two approaches are presented that can reproduce the only weakly anisotropic shape of the angular distributions and the absolute cross section for those groups of ejectiles where contributions from direct reaction modes are small. When a standard Woods-Saxon potential deduced from elastic scattering is used, the entrance channel angular momentum distribution must be limited to values below critical angular momental cr which are smaller than the grazing angular momental gr if fusion is to be described. A global proximity potential with a parameter set that has been adjusted to reproduce the fusion reactions of a variety of p- and sd-shell nuclei yields very similar results when applied to7Li+16O. The proximity potential effectively introduces a similar angular-momentum limitation. This analysis proves the existence of a fusion cross section limitation and the importance of strong direct reaction modes (transfer and possibly inelastic processes) in7Li+16O reactions at energies close to and even below the Coulomb barrier. Another aspect of7Li+16O is addressed briefly. The resonance-like structure observed in the heavy-ion radiative capture reaction7Li(16O,γ 0+1)23Na atE x (23Na)=25.4 MeV is not observed in the particle decay channels investigated in the present work.

Propagation of k-body forces from k-to N-particle space

In the dilute gas approximation closed-form expressions are derived for (i) the propagation of k -body forces from k -to N -particle space and (ii) transition strengths between different spaces ( N ≠ N ′). They are presented in their local and global-averaged form for any k ⩾2. For k = 2 the local average leads to the final state density used in statistical reaction models. In this way, the link is given between state densities in reaction theory and random-matrix physics.

Computation of correlation characteristics of nuclear reactions induced by semi-heavy ions

The present paper suggests a consistent approach to the calculation of different characteristics of nuclear reactions with the production of high-lying quasistationary states of nuclei induced by light and semi-heavy ions with an incident energy up to 10 MeV/nucleon. To investigate this subject it is expedient to analyze the angular correlations of nuclear reaction products. The approach is based on some basic theoretical statements, namely, the general theory of angular correlations in terms of the density matrix and its spin-tensors, two supplementary nuclear reaction models — direct and statistical reaction models — on some methods of computation of quasistationary state characteristics such as the cluster wave functions, width, spectroscopic factors, and, the experimentally observable quantities — differential cross-sections, spin-tensors of the density matrix of the final nuclear state, particle-particle and particle-γ-quantum angular correlation functions and populations of magnetic sublevels of the final nucleus. The approach has been implemented as a package of FORTRAN programs, applied to the analysis of concrete nuclear reactions.

Statistical model calculation of the (n, xn) and (n, f) reaction cross sections for nuclei232th,238u and237Np

Statistical reaction model including preequilibrium emission as well as Hauser-Feshbach type contributions was applied to calculate the excitation function for the (n, xn) and (n, f) reactions up to 22 MeV bombarding energy using computer code STAPREF. The level density parameters were kept constant in excitation energy. Smalll variations of the fission threshold and the level density parameters from nuclide to nuclide within the experimental errors make it possible to achieve quite satisfactory agreement with the compilated cross sections above 3 MeV. The theoretical description of the isomeric ratio and the cross sections as a function of the neutron energy for the237Np(n, 2n) reaction may help to give recommendations for the excitation functions. Rotational parameters and decoupling constants were also calculated for ground state deformation and extrapolated to transition state.

Sol-gel kinetics III. Test of the statistical reaction model

The distribution of functional groups, -OCH 3, -OH, -OSi, about a silicon atom, undergoing concurrent hydrolysis and condensation in an acid catalyzed Si(OH 3) 4:CH 3OH:H 2O sol-gel, were measured by 29Si NMR. These NMR results were compared to predictions based on a statistical reaction model which assumes that all the hydrolysis and condensation rate constant depend only on the functional group reactivity and not on the local silicon environment. The hydrolysis and condesation reactions of monomeric species were successfully predicted by the model. The greater than predicted population of silicon species bonded to one other silicon via an SiOSi bond and the less than expected population of silicon species bonded to two other silicons via SiOSi bonds indicates that the condensation of partially condensed species is slower than the condensation of monomeric species.

Sol-gel kinetics: II. Chemical speciation modeling

We present an exact theoretical kinetic formalism which specifically treats the temporal evolution of the various chemical functional groups about a specific silicon atom undergoing concurrent hydrolysis and condensation reactions. This formalism is applied to the chemical kinetics of a typical sol-gel reaction system. We also present a simplified statistical reaction model which reduces the number of chemically distinct rate coefficients necessary to describe the kinetics from 165 to 3. Experimental results which support this statistical model are also presented.

Sol-Gel Kinetics: 29Si NMR and a Statistical Reaction Model

ABSTRACTThe early time behavior of an acid catalyzed Si(OCH3),4 (TMOS) sol-gel was studied by high resolution 29Si nuclear magnetic resonance (NMR). Both the water producing and the alcohol producing condensation reactions were found to contribute significantly to the overall condensation rate. A general theoretical kinetic formalism which specifically treats the temporal evolution of the various chemical function groups about a specific silicon atom was developed. The experimentally observed functional group distribution was in agreement with the distribution predicted by a simplified statistical reaction model. The mathematical framework for the study of chemical speciation at the next-to-nearest functional group level was developed. This framework was used to assign several fine structure resonances, and to show that the formation of various dimeric species is also largely statistical in nature.

Energy dependence ofBe9+C12cross sections: Resonances or fluctuations

266 excitation curves for the emission of protons, deuterons, tritons, ..cap alpha.. particles, and /sup 8/Be and /sup 9/Be ions have been measured in the system /sup 9/Be+/sup 12/C. Data were taken in 107 keV steps in the energy range from 5.9 to 15.4 MeV (c.m.) at several angles between 5/sup 0/ and 175/sup 0/ (lab). The results were analyzed on the basis of the statistical reaction model and various statistical methods for localizing possible correlated structures were used. The fluctuations are shown to be in agreement with the predictions of the statistical model and no marked correlations between different channels were found.