Systematics of neutron emission probabilities from delayed neutron precursors

A simple correlation based on the gross theory ofβ-decay is derived between the neutron emission probabilitiesP _n of delayed neutron precursors, theirβ-decay energies and the neutron binding energies of the daughter nuclei. The correlation is shown to be valid for delayed neutron precursors among the fission products. TheP _n-values of several expected but still unidentified neutron precursors are estimated together with their contributions to the delayed neutron groups in thermal-neutron induced fission of²³⁵U. Some aspects of theβ-strength function for transitions into highly excited states are discussed.     

Half-lives and delayed neutron emission probabilities of short-lived Rb and Cs precursors

Half-lives and delayed-neutron emission probabilities (P _n ) of short-lived Rb and Cs precursors in the mass chains 94–98 and 143–147 were measured. Sources of isotope separated nuclides were obtained from the on-line mass-separator OSTIS installed at the Grenoble high-flux reactor. A newP _n -value of (25.4±3.2)% is given for the (214±30) ms¹⁴⁷Cs; theP _n -values of nine alkali precursor nuclides were redetermined: (2,730±20) ms⁹⁴Rb with (9.7±0.5)%, (377 ±6)ms⁹⁵Rb with (8.6±0.5)%, (197±5)ms⁹⁶Rb with (12.5±0.9)%, (171±4) ms⁹⁷Rb with (25.2±1.8)%, (114±13)ms⁹⁸Rb with (18.4±2.9)%, (1,765±30)ms¹⁴³Cs with (1.74 ±0.12)%, (1,000±10)ms¹⁴⁴Cs with (2.95±0.25)%, (616±20) ms¹⁴⁵Cs with (12.2±0.9)%, (325±10)ms¹⁴⁶Cs with (13.2±0.8)%. The results are compared with the existing data, and theP _n -values are discussed within some simple model predictions.     

Does the simple statistical model describe delayed neutron emission?: The cases of 85As, 87Br, 135Sb and 137I

Delayed neutron spectra and branching ratios to excited states in final nuclei calculated with the statistical model are compared to experimental data for the decay of ⁸⁷Br, ¹³⁷I, ⁸⁵As and ¹³⁵Sb. For the first two precursors, the calculations support the experimental β-strength functions reported previously. For the latter two, it is shown that the statistical model cannot simultaneously reproduce both spectra and branching ratios for any choice of β-strength function when all levels populated by neutron emission are included in the calculations. The comparisons demonstrate that partial widths for neutron emission are not compatible with optical-model transmission coefficients. We conclude, as pointed out previously, that structure effects in the energy range probed by delayed neutron emission are not averaged out to the extent required by the statistical assumptions.     

A simple model calculation of pion condensation in neutron matter

The charged pion condensed state in pure neutron matter is described analytically in an approximate calculation based on the chirally invariant σ-model. The calculation includes s- and p-wave condensed pion-nucleon interactions, pi-pi interactions, the effect of the N¹ (1236) resonance, and the (Ericson-Ericson Lorentz-Lorentz) effect of nuclear correlations.     

Delayed neutron emission probabilities of the precursors89,90,91Br and139,140,141I

The delayed neutron emission probabilities of^89,90,91Br and^139,140,141I have been measured. The ions AlBr⁺ and AlI⁺ are formed in the OSIRIS integrated target-ion source giving improved conditions for study of the most neutron-rich isotopes of iodine and bromine. The half-life determinations of⁹⁰Br,¹³⁹I and¹⁴¹I have been improved.     

Intranuclear-Cascade model calculation of photofission probabilities for actinide nuclei

We have calculated the fission probabilities for ²³⁷Np, ^{233, 235, 238}U, ²³²Th, and ^natPb following the absorption of photons with energies from 68 MeV to 3.77 GeV using the RELDIS Monte Carlo code. This code implements the cascade-evaporation-fission model of intermediate-energy photonuclear reactions. It includes multiparticle production in photoreactions on intranuclear nucleons, pre-equilibrium emission, and the statistical decay of excited residual nuclei via competition of evaporation, fission, and multifragmentation processes. The calculations show that in the GeV energy region the fission process is not solely responsible for the entire total photoabsorption cross-section, even for the actinides. The fission probabilities are 80-95% for ²³³U, ²³⁵U, and ²³⁷Np, 70-80% for ²³⁸U, and only 55-70% for ²³²Th. This is because certain residual nuclei that are created by deep photospallation at GeV photon energies have relatively low fission probabilities. The results of those model calculations are in reasonable agreement (at the 10% level) with recent experimental data on relative photofission cross-sections for ²³⁷Np and ^{233, 235, 238}U (but not for ²³²Th or ^natPb) from the Saskatchewan and Jefferson Laboratories over a very wide range in photon energy. Using our calculated fission probabilities plus the total photoabsorption cross-sections per nucleon, estimated from previous cross-section data for nuclei from C to Pb, we can infer absolute photofission cross-sections for the actinide nuclei and compare them with the SAL and JLab results. The resulting discrepancies, however, clearly demonstrate the need for direct measurement of the total photoabsorption cross-sections for the heavy actinides.     

Measurement and statistical model analysis of pre-fission neutron multiplicities

The average number of neutrons preceding fission (ν_pre) was measured for the compound systems ¹⁶⁸YB, ¹⁷⁸W, ¹⁸⁸Pt, ¹⁹²Pb, ¹⁹⁸Pb, ²⁰⁰Pb, ²¹⁰Po, ²¹³At and ²⁵¹Es formed by reactions induced by ¹⁶O, ¹⁸O, ¹⁹F, ²⁸Si or ³⁰Si projectiles with energies (E) between 4.9 and 7.2 MeV/A In some cases ν_pre is seen to increase with increasing E above a threshold energy (E_th) whereas the statistical model indicates that it should decrease. For a given projectile, this threshold decreases with increasing fissility, becoming equal to the Coulomb barrier around A_CN∼213 for ¹⁶O projectiles. Below E_th the variation of ν_pre with E is consistent with statistical model predictions. The deviations above E_th have been attributed to dissipative effects not included in the model. Extensive statistical model and Xχ² analyses of the pre-fission data below E_th and of fission and fusion excitation function data, previously measured, were made. The diffuseness parameters of the fusion spin-distributions agreed reasonably well with those suggested by the zero-point motion model. The ratios of level densities at saddle and equilibrium deformations (a_f/a_v) were found to be consistent with a value of unity, and the fission barriers (E_f) consistent with the predictions of the finite-range rotating liquid-drop model. However these values for a_f/a_ν and E_f may not represent the true values. Inclusion of dissipation requires higher values, whilst inclusion of the temperature dependence of E_f in statistical model calculations is shown to result in a reduction in the value of a_f/a_ν. Since reliable theoretical calculations are unavailable for either effect the consistency of the data with the finite range fission barriers can only be demonstrated to within 10–15% and values for a_f/a_ν, have an uncertainty of at least 5%.     

On some properties of the neutron in the statistical model

Using the statistical model to arrive at |ψ(r)|² the square modulus of theS state wavefunction of the neutron, the electric dipole moment |d _n ^e | of the neutron as well as its baryon number violating lifetime have been estimated. The baryon asymmetry of the universe depending on |d _n ^e | has also been studied in this context.     

Measurements of effective delayed neutron fraction in a fast neutron reactor using the perturbation method

A perturbation method is proposed to obtain the effective delayed neutron fraction β_(eff) of a cylindrical highly enriched uranium reactor.Based on reactivity measurements with and without a sample at a specified position using the positive period technique,the reactor reactivity perturbation △ρ of the sample in β_(eff) units is measured.Simulations of the perturbation experiments are performed using the MCNP program.The PERT card is used to provide the difference dκ of effective neutron multiplication factors with and without the sample inside the reactor.Based on the relationship between the effective multiplication factor and the reactivity,the equation β~(eff)=dκ/△ρ is derived.In this paper,the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated.The average β_(eff) value of the reactor is given as 0.00645,and the standard uncertainty is 3.0%.Additionally,the perturbation experiments for β_(eff) can be used to evaluate the reliabilities of the delayed neutron parameters.This work shows that the delayed neutron data of ~(235)U and ~(238)U from G.R.Keepin's publication are more reliable than those from ENDF-B6.0.ENDF-B7.0,JENDL3.3 and CENDL2.2.     

Competition between fission and neutron emission by diffusion model

Magnitudes and relative signs of amplitudes for three inelastic proton channels have been determined for 42 3/2⁺ resonances in⁵⁷Co in the rangeE _p =3.1–4.0 MeV. Amplitude and width channel correlations have been obtained for each pair of channels. One of the amplitude correlations is large and highly significant. Comparisons between these data and statistical theories of nuclear levels are presented for both widths and products of amplitudes; in general, agreement is good. The widths for one channel and amplitude products for one pair of channels appear energy-dependent, with most of the strength concentrated in the lowest 200 keV.     

Pre-equilibrium neutron emission in the nucleon exchange transport model

We extend the nucleon exchange transport model to include the emission of pre-equilibrium neutrons as a result of nucleon transfer to unbound states. The treatment takes account of the heating of the two nuclei caused by the energy dissipation and the cooling due to the pre-equilibrium emission. Furthermore, the transferred nucleons may induce cascading in the receptor nucleus by means of direct two-body scattering with the resident nucleons, based on a reduced, Pauli-blocked, energy-dependent free NN cross section. Qualitative agreement with experimental data is achieved, but the absolute multiplicities are systematically underestimated by about a factor of two. The dependence of multiplicity on bombarding energy is reproduced. The energy spectra and their variation with angle are generally reproduced, although the yield of the highest energy particles is sometimes underestimated.     

Fundamental view on the calculation of internal partition functions using occupational probabilities

From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where occupational probabilities are used including those using the Planck–Larkin partition function (PLPF) within the chemical picture. Considering these rules is useful from conceptual and practical points of view. A solution is introduced to assure fulfilling the above mentioned rules when using occupational probabilities. Sample calculations are performed showing quantitative significance of inaccuracies caused by dishonoring such rules.     

Gamma-ray energies of short-lived Rb,Sr, and Y isotopes indicating delayed neutron emission to excited states

Gamma energies in the level schemes of ^95,96,97Sr, ^95,96,97Y, and ^95,97Zr are reported. Some of their excited levels are populated by delayed neutron emission. These nuclei were produced as daughters of Rb fission fragments originating from the reaction ²³⁵U(n, f). By thermal ionization they were separated from fission products having other nuclear charge states and by an on-line mass separator according to their respective masses.     

A simple molecular statistical treatment of a model for cholesterics

The cholesteric state is discussed in terms of a model consisting of the Maier-Saupe and a twist interaction. The model can be easily solved in the mean field approximation. In the practical case of a large pitch analytical expressions are obtained for relevant quantities like the order parameters and the free energy. Then it appears that the pitch is temperature independent, which is a general result, and does not influence the discontinuity of the main (nematic) order parameter at the isotropic-cholesteric transition. Interactions giving rise to a temperature-dependent pitch are discussed briefly.     

Burnup calculation by the method of first-flight collision probabilities using average chords prior to the first collision

A technique to calculate the burnup of materials of cells and fuel assemblies using the matrices of first-flight neutron collision probabilities rebuilt at a given burnup step is presented. A method to rebuild and correct first collision probability matrices using average chords prior to the first neutron collision, which are calculated with the help of geometric modules of constructed stochastic neutron trajectories, is described. Results of calculation of the infinite multiplication factor for elementary cells with a modified material composition compared to the reference one as well as calculation of material burnup in the cells and fuel assemblies of a VVER-1000 are presented.     

A revisit to the neutron skin thickness of neutron-rich nuclei in the statistical abrasion ablation model

The cross sections of the fragments produced in the projectile fragmentation reactions of the even calcium isotopes from A=36 to A=52 are calculated using the statistical abrasion ablation model.The neutron skin thickness are studied by investigating the fragments isotopic cross section distributions.The neutron-skin thicknesses of the calcium isotopes have a good linear correlation to the peak positions of their fragment isotopic cross section distributions.The correlation between the neutron skin thickness and the neutron density distributions of 48Ca is investigated by introducing a parameter to adjust the diffuseness parameter in the fermi-type density distribution.     

A revisit to the neutron skin thickness of neutron-rich nuclei in the statistical abrasion ablation model

The cross sections of the fragments produced in the projectile fragmentation reactions of the even calcium isotopes from A=36 to A=52 are calculated using the statistical abrasion ablation model.The neutron skin thickness are studied by investigating the fragments isotopic cross section distributions.The neutron-skin thicknesses of the calcium isotopes have a good linear correlation to the peak positions of their fragment isotopic cross section distributions.The correlation between the neutron skin thickness and the neutron density distributions of 48 Ca is investigated by introducing a parameter to adjust the diffuseness parameter in the fermi-type density distribution.