Compound Nucleus Cross Sections Research Articles

Importance of the residual nucleus level density in the calculation of the 239Pu(n, 2n)238Pu excitation function

In parallel with the recent measurement by Méot et al. [1] of the 239Pu(n, 2n)238Pu reaction cross section in the [7-10] MeV neutron-incident energy range, a modeling work was undertaken to support the new measurement. This theoretical framework is here dedicated to study the impact of the type of level density for the 239Pu residual nucleus (RN) on the final shape of the low-energy tail of the (n, 2n) excitation function. For this purpose, the AVXSF-LNG program [4] has been upgraded to model second-chance reactions and coupled to the TALYS-ECIS06 nuclear reaction codes [3] that are used to provide the compound nucleus (CN) cross section to AVXSF-LNG as a function of the selected pre-equilibrium model . The spin-dependent population of the RN obtained after CN emission is commonly advertised when using an exciton-based model for calculating the total pre-equilibrium cross section. On the other hand a population based on a particle-hole state density is rather expected when using the MSD/MSC quantum mechanical description in place of the exciton-based model. As far as a spectrum of a few number of individual excitations is favored, the combinatorial Quasi-Particle-Vibrational-Rotational Level Density method [4] implemented in the AVXSF-LNG computer program is well suited to model the various alternatives. Several RN level densities have been tested in this work. It includes the testing of the Quasi-particle Random Phase Approximation-based result of Ref. [6]. As a guide line, the amount of pre-equilibrium flux in the total (n,2n) excitation function is being studied as a function of the type of level density selected for the residual nucleus.

Systematics of different quantities related to sequential prompt emission in fission

A deterministic treatment of sequential neutron emission, based on recursive equations of the residual temperatures, was applied to numerous fission cases (i.e. 49 cases including nuclei fissioning spontaneously or induced by thermal and fast neutrons) for which reliable experimental data of fragment distributions exist. This fact emphasizes systematics and correlations between different average quantities characterizing the initial and residual fission fragments and the sequential prompt neutron emission. The ratios of the average residual temperature following the emission of each neutron to the average temperature of initial fragments ($${ }/{ }$$) are almost constant for all studied fission cases. They do not depend on the prescriptions used for the compound nucleus cross-sections of the inverse process and the level density parameters of initial and residual fragments. This finding allows the determination of a general form of the residual temperature distribution for each emission sequence $${P}_{{k}}(T)$$ with the maximum temperature related only to the average temperature of initial fragments. In this way the sequential emission can be included into the Los Alamos model. Prompt neutron spectra in the center-of-mass and laboratory frames can be calculated for each emission sequence. The systematic of the ratios of average residual temperatures and energies to the initial ones together with other linear correlations between different prompt emission and residual quantities allow to obtain indicative values of different average prompt emission quantities in the absence of any prompt emission model.

Multiband coupling and nuclear softness in optical model calculations for even-even and odd-A actinides

A new dispersive multiband coupled channels optical model with soft-rotator “effective” deformations is proposed to describe nucleon scattering on even-even and odd-A actinides. The impact of the introduction of axial and non-axial dynamical deformations that describe nuclear softness is discussed. Softness and multiband coupling are shown to change compound-nucleus formation cross section by up to ≈ 10% for incident neutron energies below 1 MeV.

Non-coplanar compact configurations of nuclei and non-compound-nucleus contribution in the fusion cross section of theC12+Nb93reaction

Background: In our earlier study of the $^{12}\mathrm{C}+^{93}\mathrm{Nb}\ensuremath{\rightarrow}^{105}\mathrm{Ag}^{*}$ reaction at three near- and below-barrier energies (${E}_{\mathrm{c}.\mathrm{m}.}=41.097$, 47.828, and 54.205 MeV), using the dynamical cluster-decay model (DCM) with various nuclear interaction potentials (the Blocki et al. pocket formula and others derived from the Skyrme energy density formalism) for compact, coplanar $({\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0})$ nuclei, we found a large non-compound-nucleus (nCN) contribution in the measured fusion cross section of this reaction.Purpose: In the present work, we look for the effect of using non-coplanar, compact configurations $({\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0})$, in the Blocki et al. pocket formula of the nuclear proximity potential, on the non-compound-nucleus (nCN) contribution, using the DCM.Methods: Allowing the $\mathrm{\ensuremath{\Phi}}$ degree of freedom in the DCM formalism, we calculate the compound-nucleus (CN) and nCN cross sections. The only parameter of the DCM is the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$, which also fits the empirically determined nCN cross section nearly exactly, under the assumption of considering it like a quasifission process where the fragment preformation factor ${P}_{0}=1$.Results: With the $\mathrm{\ensuremath{\Phi}}$ degree of freedom included, at the higher two energies the nCN cross section gets enhanced, and hence the pure CN cross section is decreased, since the calculated (total) fusion cross section is fitted to experimental data. The parameter $\mathrm{\ensuremath{\Delta}}R$ for the nCN contribution is smaller, and hence the reaction time larger, than for the CN decay process. Also, the contributing angular momentum ${\ensuremath{\ell}}_{\mathrm{max}}$ value increases in going from ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$ to ${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0}$ for both the CN and nCN processes. The intermediate mass fragments (IMFs), measured up to mass 13 in this reaction, are shown extended up to mass 16, and the fusion-fission $(ff)$ region is identified as $A/2\ifmmode\pm\else\textpm\fi{}16$, the same as for the ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$ case.Conclusions: As a result of enhanced nCN cross section due to ${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0}$, the CN fusion probability ${P}_{\mathrm{CN}}$ for $^{105}\mathrm{Ag}^{*}$ changes its behavior from an increasing to a decreasing function of center-of-mass energy ${E}_{\mathrm{c}.\mathrm{m}.}$, and hence belongs to the group of weakly fissioning nuclei, instead of the strongly fissioning superheavy nuclei for ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$. On the other hand, with measured IMFs taken to represent the $ff$ component, non-coplanarity simply increases the magnitude of CN survival probability ${P}_{\mathrm{surv}}$, although its functional dependence on ${E}_{\mathrm{c}.\mathrm{m}.}$ remains the same as for weakly fissioning nuclei. In other words, on adding the $\mathrm{\ensuremath{\Phi}}$ degree of freedom, the inconsistent result of ${P}_{\mathrm{CN}}$ behaving like strongly fissioning superheavy nuclei and ${P}_{\mathrm{surv}}$ like the weakly fissioning nuclei for ${\mathrm{\ensuremath{\Phi}}}_{c}={0}^{0}$ changes to both ${P}_{\mathrm{CN}}$ and ${P}_{\mathrm{surv}}$ behaving consistently like those of weakly fissioning nuclei. Thus, our calculations advocate for ${\mathrm{\ensuremath{\Phi}}}_{c}$ as an important degree of freedom, like deformations of nuclei themselves.

Compound nucleus formation probabilityPCNdefined within the dynamical cluster-decay model

With in the dynamical cluster-decay model (DCM), the compound nucleus fusion/ formation probability PCN is defined for the first time, and its variation with CN excitation energy E* and fissility parameter χ is studied. In DCM, the (total) fusion cross section σfusion is sum of the compound nucleus (CN) and noncompound nucleus (nCN) decay processes, each calculated as the dynamical fragmentation process. The CN cross section σCN is constituted of the evaporation residues (ER) and fusion-fission (ff), including the intermediate mass fragments (IMFs), each calculated for all contributing decay fragments (A1, A2) in terms of their formation and barrier penetration probabilities P0 and P. The nCN cross section σnCN is determined as the quasi-fission (qf) process where P0=1 and P is calculated for the entrance channel nuclei. The calculations are presented for six different target-projectile combinations of CN mass A~100 to superheavy, at various different center-of-mass energies with effects of deformations and orientations of nuclei included in it. Interesting results are that the PCN=1 for complete fusion, but PCN <1 or ≪1 due to the nCN conribution, depending strongly on both E* and χ.

An algorithm for generating random variates from the Madland–Nix fission energy spectrum

An algorithm for generating random variates from the Madland–Nix fission energy spectrum assuming a constant compound nucleus cross section is given based on physics considerations. A program was written to generate variates using the algorithm developed, and it was shown that the generated variates match the probability density function. This algorithm can be used by Monte Carlo particle transport codes to sample secondary energies for neutrons born from fission when the underlying data is given as parameters to a Madland–Nix energy spectrum.

Compound nucleus formation probabilityPCNdetermined within the dynamical cluster-decay model for various “hot” fusion reactions

The compound nucleus (CN) fusion/formation probability ${P}_{CN}$ is defined and its detailed variations with the CN excitation energy ${E}^{*}$, center-of-mass energy ${E}_{\mathrm{c}.\mathrm{m}.}$, fissility parameter $\ensuremath{\chi}$, CN mass number ${A}_{CN}$, and Coulomb interaction parameter ${Z}_{1}{Z}_{2}$ are studied for the first time within the dynamical cluster-decay model (DCM). The model is a nonstatistical description of the decay of a CN to all possible processes. The (total) fusion cross section ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ is the sum of the CN and noncompound nucleus (nCN) decay cross sections, each calculated as the dynamical fragmentation process. The CN cross section ${\ensuremath{\sigma}}_{CN}$ is constituted of evaporation residues and fusion-fission, including intermediate-mass fragments, each calculated for all contributing decay fragments (${A}_{1}$, ${A}_{2}$) in terms of their formation and barrier penetration probabilities ${P}_{0}$ and $P$. The nCN cross section ${\ensuremath{\sigma}}_{\mathit{nCN}}$ is determined as the quasi-fission (qf) process, where ${P}_{0}=1$ and P is calculated for the entrance-channel nuclei. The DCM, with effects of deformations and orientations of nuclei included in it, is used to study the ${P}_{CN}$ for about a dozen ``hot'' fusion reactions forming a CN of mass number $A\ensuremath{\sim}100$ to superheavy nuclei and for various different nuclear interaction potentials. Interesting results are that ${P}_{CN}=1$ for complete fusion, but ${P}_{CN}&lt;1$ or ${P}_{CN}\ensuremath{\ll}1$ due to the nCN contribution, depending strongly on different parameters of the entrance-channel reaction but found to be independent of the nuclear interaction potentials used.

Investigation of deuteron breakup and deuteron-induced fission on actinide nuclei at low incident energies

An analysis of the $^{231}$Pa$(d,3n)$$^{230}$U reaction excitation function at energies around the Coulomb barrier has taken into account the pre-equilibrium and compound-nucleus cross sections corrected for the deuteron-breakup decrease of the total reaction cross section, as well as the inelastic breakup enhancement. The analysis reveals the dominance of the deuteron breakup mechanism unlike a former assessment in this respect of the deuteron-induced fission process.

Analysis of Deuteron Breakup and Induced Activation on Medium Nuclei

An extended analysis of the nuclear reaction mechanisms involved within deuterons interaction with Co and Nb is presented. First, the available elastic-scattering data analysis provided the optical potential for reaction cross sections calculations. An increased effort has been devoted to the breakup mechanism, both the elastic breakup and the breakup fusion contributions to the different activation cross sections being carefully considered. Next, the direct reaction contributions, namely the stripping and pick-up reaction cross sections have been calculated. Finally, the preequilibrium and compound-nucleus cross-section calculation, corrected for the breakup and stripping decrease of the total reaction cross section, completed the deuteron activation cross-section analysis. The overall agreement between the measured and calculated deuteron activation cross sections proves the adequacy of nuclear mechanisms suite.

Low and medium energy deuteron-induced reactions onCu63,65nuclei

The activation cross sections of (d,p), (d,2n), (d,3n), and (d,2p) reactions on 63,65Cu were measured in the energy range from 4 to 20 MeV using the stacked-foils technique. Then, following the available elastic-scattering data analysis that provided the optical potential for reaction cross sections calculations, an increased effort has been devoted to the breakup mechanism, the direct reaction stripping, and the pre-equilibrium and compound-nucleus cross section calculations, corrected for the breakup and stripping decrease of the total reaction cross section. The overall agreement between the measured and calculated deuteron activation cross sections proves the correctness of the nuclear mechanisms account, next to the simultaneous analysis of the elastic-scattering and reaction data.

On the accuracy of techniques for determining neutron compound-nucleus formation cross sections

We consider three methods for determining neutron nonelastic cross sections: direct measurement by transmission of neutrons through a spherical shell; subtraction of the angle-integrated elastic cross section from the total cross section; and a modification of the subtraction technique using Wick’s limit that in favorable cases can significantly reduce the errors in the subtraction method. We show new results using the modified subtraction technique for nonelastic cross sections at 21.6 MeV neutron energy over a wide mass range, and discuss criteria that should be satisfied in order for the modified subtraction technique to be reliable.

Assessment of deuteron-induced reaction mechanisms at low and medium energies

An extended analysis of the nuclear reaction mechanisms involved in the deuterons interaction with 63,65 Cu is presented. First, the available elastic-scattering data analysis provide d us the optical potential for reac- tion cross sections calculations. An increased effort has been devoted to the breakup mechanism, both the elastic breakup and the breakup fusion contributions to the different activation cross sections being carefully considered. Next, the direct reaction contributions through the one nucleon stripping re action cross sections have been cal- culated. Finally, the pre-equilibrium and compound-nucleus cross-section calculation, corrected for the breakup and stripping decrease of the total reaction cross section, completed the d euteron activation cross-section anal- ysis. The overall agreement between the measured and calculated deuteron activation cross sections proves the correctness of the nuclear mechanisms account.

Multistep proton scattering—towards higher energies

The multistep direct theory of Feshbach, Kerman and Koonin is applied to the analysis of nucleon inelastic scattering to the continuum. The one-step cross sections include contributions of incoherent particle-hole and collective excitations in the continuum. The multistep formalism is used with the non-DWBA matrix elements that involve the biorthogonally conjugated distorted waves. The multistep direct cross sections are combined with multistep compound and compound nucleus cross sections to give a complete analysis of proton inelastic scattering by iron at energies 29 MeV, 39 MeV and 62 MeV. The results show large contributions from the two-, three- and four-step reactions. A good agreement with experiment is obtained at all energies.

Prompt fission neutron multiplicity and spectrum evaluations for n+ 238U reaction

The prompt fission neutron multiplicity and spectra for n+ 238U reaction are calculated using an improved Los Alamos model which includes the linear relation between the average prompt gamma ray energy and the prompt neutron multiplicity and also the average fission fragment kinetic energy dependence on the incident neutron energy. The coefficients describing the quadratic variation of the fission fragment kinetic energy versus the incident energy are obtained by extrapolation of the data and procedure used for n+ 235U reaction. The inverse process compound nucleus cross-section of the fissioning nucleus is calculated using the coupled channel method. In the incident energy range where only the first fission chance is involved the comparison of present spectrum evaluation with spectrum calculation using multi-modal model is made too. The calculated prompt neutron multiplicity and spectra of 238U neutron induced fission are in good agreement with the experimental data for the entire incident energy range required in evaluations, proving the validity of the used procedure.

Effects of instantons on the YN interaction

Neutron inelastic scattering from thulium-169 has been studied for states above 100 keV via the (n,n′γ) reaction at incident energies in the 0.2- to 1.0-MeV range. A high-resolution Ge spectrometer in conjunction with the time-of-flight technique was utilized. Thirty-six gamma-ray transitions from 16 levels were observed. Gamma-ray angular distributions were measured at En=750 keV and excitation functions at 125 degrees were measured in 50 keV steps over the range of incident energies. Differential gamma-ray production cross sections and gamma-ray branching ratios were obtained. Inferred neutron inelastic level cross sections of the four lowest ground-state rotational band (Kπ=1/2+) members are compared to the sum of calculated compound nucleus and direct interaction cross sections. For the remaining levels, measurements are compared to compound nucleus calculations only. The comparison shows generally good agreement particularly near threshold.

Thulium-169 neutron inelastic scattering cross section measurements via the [formula omitted]Tm [formula omitted] reaction

Neutron inelastic scattering from thulium-169 has been studied for states above 100 keV via the (n,n′γ) reaction at incident energies in the 0.2- to 1.0-MeV range. A high-resolution Ge spectrometer in conjunction with the time-of-flight technique was utilized. Thirty-six gamma-ray transitions from 16 levels were observed. Gamma-ray angular distributions were measured at E n=750 keV and excitation functions at 125 degrees were measured in 50 keV steps over the range of incident energies. Differential gamma-ray production cross sections and gamma-ray branching ratios were obtained. Inferred neutron inelastic level cross sections of the four lowest ground-state rotational band (K π=1/2 +) members are compared to the sum of calculated compound nucleus and direct interaction cross sections. For the remaining levels, measurements are compared to compound nucleus calculations only. The comparison shows generally good agreement particularly near threshold.

Clustering-related aspects in the compound nucleus formation

A new approach to describe the compound nucleus formation process, where clustering aspects of the nucleus are taken into account, is worked out. It is shown that quantitative differences between the compound nucleus cross-section of232Th and238U, as observed in recent photofission experiments, could be due to the different cluster preformation probabilities of these nuclei.

A consistent analysis of , , and multistep reactions using the Feshbach - Kerman - Koonin theory

The multistep reaction theory of Feshbach, Kerman and Koonin is used to analyse data on nuclear reactions to the continuum. The multistep direct, multistep compound, collective and compound nucleus cross sections are calculated with the same set of parameters and it is found that it is possible to fit the , and data in a fully consistent way. The data, however, could only be fitted by approximately doubling the strength of the effective interaction. Several possible reasons for this were investigated including isospin effects, neutron - proton distinguishability, sensitivity to optical potentials and non-locality effects, but the difficulty still remains.

Collective reactions to the continuum in neutron scattering by niobium.

The preequilibrium cross sections for the direct excitation of collective states, including giant resonances, in the continuum region, are calculated and combined with the multistep direct, multistep compound, and compound nucleus cross sections to give a complete analysis of neutron scattering by niobium. These collective cross sections we calculated in the framework of DWBA. A good description of neutron emission spectra and angular distributions has been obtained at incident energies 14.1, 20, and 25.7 MeV.

Resonant characteristics of statistical fluctuations in 12C+12C reaction cross sections.

The effects of angular momentum conservation on the properties of Ericson fluctuations in cross sections for the [sup 12]C([sup 12]C,[sup 8]Be[sub 0])[sup 16]O(g.s.) reaction and [sup 12]C([sup 12]C,[alpha])[sup 20]Ne[sup *] reactions leading to the 12 lowest excitations in [sup 20]Ne are studied. Comparison of Hauser-Feshbach predictions to experimental measurements of the [sup 8]Be[sub 0] total cross section in the range 9[le][ital E][sub c.m.][le]20 MeV indicates that this reaction channel is populated primarily by a compound-nucleus mechanism. Similar results are obtained for the majority of the [alpha]-particle channels in the energy region from [ital E][sub c.m.]=6.5 to 12.6 MeV. The compound-nucleus cross sections for these reactions are dominated by a narrow range of angular momenta. A statistical model that includes predicted unequal contributions from compound-nucleus levels with different spins is used to synthesize angular distributions and excitation functions for comparison to data. The results of these simulations give overall quantitatively correct estimates of the size and frequency of the fluctuations observed in the measured total cross sections and of the spins that dominate the fluctuations. Consequences for the identification of resonances'' are discussed.