Prompt mass distributions in fission

A previously developed structure-sensitive statistical model, incorporating the nuclear structure and deformation effects, has been utilised to study the prompt mass distributions in fision and other related characteristics. The principle of detailed balance has been applied to calculate the yield probabilities. The fusion barriers and the penetrabilities of the fragments were estimated from a nuclear plus Coulomb interaction potential. The prompt fragment mass yields were then obtained as a product of three quantities: the product level densities of the conjugates at their most probable excitation energies, the barrier penetrabilities and the isobaric charge yields. The calculations are free from any arbitrary parameters. Comparison with experimental data for²²⁶Ra(p, f) atE _p =11.1MeV,²³²Th(n, f) atE _n =1.0 MeV,²³⁵U(n, f) and²³⁹Pu(n, f) at thermal neutron energies and for the spontaneous fission of²⁵²Cf shows fairly good agreement.     

The probability of prompt and delayed fission of muonic237Np

Fission fragments from the reaction²³⁷Np(μ ^?,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ ^?,γ,f)-data of the same experiment. The total fission probability perμ-stopP _t has been measured as well as the fission probabilities P_f of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P _t =(54±17)%,P _f (3d→1s)=(41±21)%,P _f (2p→1s,E=6.218 MeV)=(61±19)%, andP _f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a²³⁸U(³He,αf)-reaction.     

Influence of shell effects on the angular distributions of fission fragments

A dynamical-statistical model is used to analyze the experimental angular distributions of fission fragments in the reactions α + ²³⁸U, ²³⁷Np at E _α = 20–100 MeV, as well as to determine the Am isotope fission probabilities and the shape isomer yields in the reactions d + ^242,240Pu at E _d = 20–30 MeV. Manifestations of shell effects are found in the fission barrier structure up to the excitation energies of 50–60 MeV.     

Study of the reaction238U (α, α′f) atE α=480 MeV

The excitation function of the fission probability P _E E _x) for²³⁸U has been measured in the reaction²³⁸U(α, α′ f) at 480 MeV bombarding energy. The reaction mechanism of this reaction is discussed for excitation energies belowB _nf , the threshold for second chance fission, and aboveB _nf up toE _x =37 MeV. In comparing with results from fission induced by photons and by particle transfer reactions the (α, α′f) reaction gives too low values for the fission probabilityP _f at excitation energies well aboveB _nE . The role of the quasi-elastic knock-out process in this reaction is discussed.     

Effect of entrance channel parameters on fission fragment angular momentum in medium energy fission

Independent isomeric yield ratios of¹³²I were radiochemically determined in alpha particle induced fission of²³⁸U in the energy range 25–44 MeV. Fission fragment angular momenta were deduced from the measured isomeric yield ratios using spin dependent statistical model analysis. It was seen that angular momentum of¹³²I increases with increase of excitation energy and angular momentum of the fissioning nucleus. Comparison of the present data on¹³²I in²³⁸U(α,f) with the literature data for the same product in²³⁸U(p, f) and²³⁸U(γ, f) at various excitation energies show that fragment angular momentum strongly depends on the input angular momentum in the range of excitation energy considered. Experimental fragment angular momentum at all excitation energies were seen to be in agreement with the theoretical values calculated based on thermal equilibration of the various collective rotational degrees after considering the occurence of multichance fission. Thus, strong effect of input angular momentum as well as the statistical equilibration among the various collective rotational degrees of freedom in medium energy fission is corroborated.     

Cold deformed fission in232U(n,f) and239Pu(n,f)

Masses, charges and kinetic energies of light fission fragments from the reactions²³²U(n, f) and²³⁹Pu(n, f) induced by thermal neutrons have been measured on the Cosi fan tutte spectrometer of the Institut Laue-Langevin in Grenoble. Both at very high and very low kinetic energies marked fine structures in the mass yields and odd-even staggerings in the charge yields are observed. In the framework of a scission point model the results are shown to point to compact and deformed scission configurations, respectively, where at scission the fragments carry no intrinsic excitation energy. The two limiting processes may, therefore, be called cold compact fission (usually known as cold fission) and cold deformed fission. The latter process as a general phenomenon of low energy fission has come into focus only recently.     

Resonances in the isomeric and prompt fission probabilities of240Pu

The prompt and isomeric fission probabilities of²⁴⁰Pu have been studied using the²³⁹Pu(d,p) reaction. A number of resonances are observed in the subbarrier population of the 4 ns fission isomer for excitation energies between 4.0 and 6.2 MeV. Apart from a structure at 4.3 MeV, they do not coincide with transmission resonances found in prompt fission. Calculations with an extended doorway state model which simultaneously reproduce the measured delayed and prompt fission probabilities yield revised fission barrier parameters as well as spectroscopic information on fission and gamma widths of highly excited states in the second minimum.     

Beta-delayed fission and neutron emission: Consequences for the astrophysicalr-process and the age of the galaxy

Beta-delayed neutron emission and beta-delayed fission probabilities (P _n andP _{β d j} ) were calculated for neutron-rich nuclei between the beta stability line and the neutron-drip line in the range 10≦Z≦100 and 75≦Z≦100, respectively. These results were obtained by applying recentβ-strength function calculations, fission barrier height predictions, and a neutron optical potential from infinite nuclear matter calculations. An area of ～100% fission probability is predicted around Z=94,N=168 extending beyond the well-known island of spontaneous fission in that region. Astrophysicalr-process calculations were performed including the calculatedP _n and Pβ d f values. This puts the method to determine the age of the Galaxy by the actinide chronometers on a reliable basis. An excellent overall agreement with the observedr-abundance distribution is obtained. The predictedr-process production ratios for the Chronometrie pairs²³²Th/²³⁸U,²³⁵U/²³⁸U and²⁴⁴Pu/²³⁸U result in an age of the Galaxy oft _G =(20.8± ₄ ² )×10⁹ a, which is by almost a factor two larger than earlier predictions by this method, but in accordance with recent astronomical observations from globular clusters. The predicted island of 100%β-delayed fission acts as a sink to ther-process with the consequence that no superheavy elements are produced in nature.     

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%.     

Mass and energy dependence of pion-induced fission

Data for fission induced by pi meson beams from 80 to 500 MeV are presented for nuclei from Fe through Pu as measured by solid state track detectors. The general trends for binary fission withπ ⁺ are reproduced fairly well by a calculation in the ‘high excitation’ limit with standard level density and fission barrier parameters, butπ ^? data are underpredicted. A universal dependence of the binary fission probabilities with the fissility (Z±1)²/A is found to be valid for both pion beam charges for all beam energies below the delta resonance. Probabilities for observing three fragments withπ ⁺ are not reproduced by a ternary fission application of the model found to work for binary fission.     

Influence of collective rotational degrees of freedom in medium energy fission

In the present work rms angular momenta have been deduced for the fission fragments corresponding to¹³¹Te^m,g and¹³³Te^m,g in²³²Th(α _{40 MeV},f) and²³⁸U(α _{40 MeV},f) systems from the radiochemically determined independent isomeric yield ratios and statistical model based analysis. For¹³¹Te and¹³³Te the rms angular momenta deduced are 5.9±1.0 and 7.9±1.2 ? respectively in²³²Th(α _{40 MeV},f) and 7.2±0.6 and 8.0±0.8 ? respectively in²³⁸U(α ₄₀ MeV,f). Comparison of the present data with the literature data for these fragments in the same compound nuclei²³⁶U^* and²⁴²Pu^* at lower excitation energies shows increase in the fragment angular momentum with increasing excitation energy and angular momenta of the fissioning nuclei. Fragment angular momentum deduced theoretically for asymmetric and deformed fragments on the basis of thermal equilibration of the collective rotational degrees e.g., rigid rotation, wriggling, tilting, bending and twisting modes considering the effect of multichance fission, are in good agreement with the experimental observations.     

Mass dependence of statistical fission parameters

Statistical fission parameters B_f and $\text{a}{}_{\mathrm{<mtext>f</mtext>}}\text{a}{}_{\mathrm{\nu }}$ are extracted from analyses of recently measured heavy-ion induced fission and evaporation residue excitation functions for medium mass systems using a formalism with spin dependent level densities and multiple particle/fission competition. Results are compared with those of the less rigorous s-wave approximation as treated in the code ALICE.     

Symmetric and asymmetric fission of Ac isotopes near the fission threshold

Fission probabilities and fragment anisotropies were investigated for fission of ²²⁷Ac and ²²⁸Ac by means of direct reactions with a ³He beam on a ²²⁶Ra target. Triple-humped mass distributions are found also for excitation energies where second-chance fission is excluded. The fission barrier is higher for symmetric fission compared to that for asymmetric fission by 1.2 and 2.0 MeV, respectively, suggesting that the character of the mass split is already predetermined at the saddle point.     

Measurement of fast neutron induced fission cross section of thorium using Lexan plastic track detector

Fission-track registration characteristics of Lexan solid state nuclear track detectors have been used to measure the fast neutron induced fission cross section of²³²Th. The fast neutrons (?14.2MeV) were produced with the help of an AN-400 model Van-de-Graaff accelerator at Banaras Hindu University laboratory using³H(²H,n)⁴He reaction and were used to irradiate the fissile target deposited on the plastic detector. The track densityT, registered on the plastic detector is related to the fission cross sectionσ _f, through the relationT=knσ _føt wheren is the number of fissile atoms per cm² in the deposit, ø is the neutron flux,k is fission track registration efficiency andt is the time of irradiation. The fission cross sectionσ _f of²³²Th, relative to the well measured fission cross section of²³⁸U, was found to be 0.36±0.04 barn.     

Prompt neutron emission spectra and multiplicities in the thermal neutron induced fission of235U

The emission spectra of prompt fission neutrons from mass and kinetic energy selected fission fragments have been measured in²³⁵U(n _th,f). Neutron energies were determined from the measurement of the neutron time of flight using a NE213 scintillation detector. The fragment energies were measured by a pair of surface barrier detectors in one set of measurements and by a back-to-back gridded ionization chamber in the second set of measurements. The data were analysed event by event to deduce neutron energy in the rest frame of the emitting fragment for the determination of neutron emission spectra and multiplicities as a function of the fragment mass and total kinetic energy. The results are compared with statistical model calculations using shell and excitation energy dependent level density formulations to deduce the level density parameters of the neutron rich fragment nuclei over a large range of fragment masses.     

The study of prompt and delayed muon induced fission

The ratios of prompt to delayed fission yields for the isotopes²³³U,²³⁴U,²³⁵U,²³⁶U,²³⁸U,²³⁷Np,²⁴²Pu, and²⁴⁴Pu and the fission probabilities relative to each other have been investigated experimentally. Using the value of the total fission probability for²³⁷Np the absolute probabilities for prompt and delayed fission have been determined. The fission probabilities per muon captureP _fc have been derived for all the isotopes and compared with an evaluation based on excitation functions from theory.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

Effect of the initial excitation energy on the average fission lifetime of nuclei

The dependence of the fission time on the initial nuclear excitation energy E _{tot 0} ^* is studied on the basis of a refined combined dynamical and statistical model. It is shown that this dependence may be nonmonotonic, in which case it features a broad maximum. It turns out that the form of the average fission time 〈t _f 〉 as a function of E _{tot 0} ^* depends greatly on the orbital angular momentum L _n carried away by prescission neutrons.