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.     

The study of prompt and delayed muon induced fission

The mean life times of negative muons bound to actinide nuclei have been measured by detecting the time difference between a stopped muon and the arrival of fragments from delayed fission after muon capture. The deduced capture ratesΛ _c are 1.392(4)·10⁷/s for²³⁷Np, 1.290(7)·10⁷/s for²⁴²Pu and 1.240(7)·10⁷/s for²⁴⁴Pu. The results are compared with published data for the fission and the neutron decay channels and for the electron decay of the bound muon. Including a former measurement ofΛ _c for²³⁹Pu, an isotopic dependence of the muon capture rates in the Pu isotopes is clearly observed.     

The muon attachment probability after prompt fission

We calculate the attachement probability of muons to the fission fragments of ²³⁸U. The problem is reduced to a one-dimensional wave equation with an effective potential, which allows one to investigate the weight of several dynamical factors. We find that the attachment probability is rather insensitive to the fission time, the dominant roles being played by the final kinetic energy and the asymmetry of the fragments. The attachment probability to the light fragment in the most likely configuration $\text{(E}{}_{\mathrm{<mtext>fin</mtext>}}\text{= 165}\text{MeV}\text{,}\text{A}{}_{\mathrm{<mtext>L</mtext>}}\text{A}{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.83)}\text{is}\text{P}{}_{\mathrm{<mtext>L</mtext>}}\text{? 0.10}$, in agreement with the experimen data.     

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.     

AnomalousE1 conversion in octupole-deformed nuclei and muon shake-off in prompt fission

It has been shown that the coexistence of octupole and quadrupole deformation in nuclei gives rise to strong penetration effects in internal conversion for theE1 transitions. This idea has been applied for evaluating the muon shake-off probabilityW _sh. The value obtained,W _sh/–0.5% per prompt fission, is in good agreement with the experimental result. Possibilities for further experimental studies of this effect are discussed.The author would like to acknowledge fruitful discussions of the problem together with Prof. Yu.P. Gangrsky, Dr. V. Yu. Denisov and Prof. D.F. Zaretsky. He is also grateful to Prof. G.Ye. Belovitsky, Prof. P. David and Dr. Ch. Rösel for discussions of the experimental situation. This work was completed at the University of Bonn in the frame of a fellowship from the Heinrich Hertz Foundation.     

Contribution of prompt muon production to total muon fluxes

Summary The flux of prompt cosmic-ray muons coming from charmed particles which are produced in both nondiffractive and diffractive processes of primary-air collisions is computed. Its maximum contribution is estimated by stressing the diffractive character of produced charmed particles. We compare the observed results on angular distributions of muon intensities at a given depth with the calculated results. There is no clear evidence for prompt muons. In a more quantitative analysis, χ² tests with regard to the expected form of the muon spectrum are performed. The expectation is based on a formula of Thompson and Walley for muons coming from pion and kaon decay which shows a sec θ enhancement plus a part of prompt muons. From these quantitative analysis, it is concluded that prompt muons may contribute to the total flux in the energy range between several TeV and several hundreds of TeV but are not beyond the maximum prediction.

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Riassunto Si calcola il flusso di muoni pronti dei raggi cosmici che derivano da particelle cariche che sono prodotte in processi sia diffrattivi che non diffrattivi di collisioni primariearia. Si stima il suo contributo massimo sottolineando il carattere diffrattivo delle particelle con charm prodotte. Si confrontano i risultati osservati sulle distribuzioni angolari delle intensità muoni a una data profondità con i risultati calcolati. Non c'è una chiara evidenza per i muoni pronti. In un'analisi piú qualititativa si calcolano test χ² con riferimento alla forma prevista dello spettro muonico. La previsione è basata su una formula di Thompson e Walley per muoni che derivano dal decadimento di pioni e kaoni che mostra un incremento di sec θ piú una parte di muoni pronti. Da questa analisi quantitativa si conclude che i muoni pronti possono contribuire al flusso totale nell'intervallo di energia da alcuni TeV a parecchie centinaia di TeV ma non sono al di sotto della previsione massima.

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Резюме Вычисляется поток быстрых мюонов космических лучей, происходящих от очарованных частиц, которые были образованы в недифракционных и дифракционных процессах первичных соударений. Оценивается максимальная величина вклада быстрых мюонов, отмечая дифракционный характер образованных очарованных частиц. Мы сравниваем наблюденные результаты для угловых распределений мюонных интенсивностей на данной глубине с результатами вычислений. Не обнаружено явного подтверждения для быстрых мюонов. Проводится количественный анализ, χ² проверка ожидаемой формы мюонного спектра. Ожидаемая величина определяется из формулы Томпсона и Валлея для мюонов, возникающих из распадов пионов и каонов, которая обнаруживает sec θ возрастание плюс вклад от быстрых мюонов. На основании этого количественного анализа делается вывод, что быстрые мюоны могут давать вклад в полый поток в области энергий от нескольких ТэВ до нескольких сотен ТэВ.

     

Muon-induced prompt fission of uranium

The prompt-fission probabilities of muonic ²³⁸U in radiationless dipole and quadrupole transitions of the muon are calculated. The 3d → 1s transition is found to dominate, in agreement with experiment. A measured drastic enhancement in the $\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}$ ratio compared to photofission data is reproduced in terms of the increase of the fission barrier in the presence of the muon.     

Delayed muon induced fission of209Bi and the role of meson-exchange currents

The probability for delayed muon induced fission of²⁰⁹Bi has been determined from a ( ^–,f ₁ f ₂) measurement. The measured fission probability P _f =(4.2±0.7)×10^–5 is compared with theoretical predictions. The high fission threshold reaction seems well suited for studying the influence of two-body meson-exchange currents in nuclear muon capture.We are indebted to the following institutes or organizations for financial support: Bundesministerium für Forschung und Technologie der Bundesrepublik Deutschland contract number 06 BN 271 (HP, PD, HH, FR, CR), Foundation for Fundamental Research on Matter (FOM) and the Netherlands Organization of the Advancement of Pure Research (NWO) (JK, CTAMdL, WL, AT) and the Schweizer Nationalfonds (LS).     

Muon attachment in prompt fission of237Np

The probabilities of muon attachment to fission fragments in the prompt fission of²³⁷Np have been determined as a function of fragment mass and total kinetic energy release in a ( ^–,f ₁ f ₂ e ^–)-coincidence measurement. A strong dependence of the attachment probability on the fragment mass is observed. The experimental results are compared with theoretical predictions.It is a pleasure to thank Professor T. Mayer-Kuckuk for his co-operation in performing the project. We gratefully acknowledge the permanent support of Professor J.P. Blaser and his staff at PSI. We thank Professor R. Engfer, Dr. A.v.d. Schaaf, and Dr. H.C. Walter for their support in using the electron spectrometer SIN-DRUM I. We are thankful to Professor S. Polikanov (GSI) and to Dr. T. Krogulski (University of Warsaw, Bialystok) for intensive and fruitful discussions. We appreciate the collaboration of Professor W. Müller and Dr. J. Pauwels (CBNM-Mol) in the target preparation. This work has been funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 06BN271 (PD, HH, FR, ChR, WS). We thank the following institutions and organisations for financial support: Foundation for Fundamental Research on Matter (FOM), the Netherlands Organisation of the Advancement of Pure Research (NWO) (JK, CdL, AT), and the Swiss National Foundation (SNF) (WB, EH; HP, DV). One of the authors is grateful for a fellowship granted by the Studienstiftung des deutschen Volkes (FR).     

Nuclear excitation and prompt fission in muonic238U

A study of muonic²³⁸U has been performed in a combined (μ ^?,γ f) and (μ ^?,γγ) coincidence experiment to investigate the role of non-radiative transitions and their fission probabilities. An augmentation of the outer fission barrier ofΔE _b =(0.6±0.1) MeV due to the presence of the muon is deduced. A significant contribution to the prompt fission yield not only results from the (2p→1s) and (3d→1s) non-radiative transitions, but also from other radiationless transitions. Specifically, the measured fission probabilities of the transitions (2p→1s), (3d→1s), and (3p→1s) are (1.5±0.4)%, (5.7±1.7)%, and (5.3±1.9)%, respectively.     

Observation of the delayed fission induced by antiproton annihilation in 238U

Delayed fission following the annihilation of antiprotons at rest in ²³⁸U nuclei has been observed with a yield of approximately 10⁻³. By means of the recoil-distance technique a lifetime of about 10⁻¹⁰ s has been determined for the delayed fission; this is interpreted as due to the non-mesonic decay of heavy hypernuclei.     

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.     

Left-right asymmetry of the angular distribution of prompt neutrons from 235U fission induced by polarized thermal neutrons

Left-right asymmetry of the angular distribution of prompt neutrons from ²³⁵U fission induced by polarized thermal neutrons was measured. This asymmetry is caused by the interference of the s and p waves in the input reaction channel and was found to be equal to b=(?5.8±1.4)×10^?5.     

Born-Oppenheimer expansion: From muon distribution to dissipation in fission

It is shown that a consistent treatment of momentum translation by a muon in the problem of the distribution of muons among prompt-fission fragments modifies the nonadiabatic transition operator in the Born-Oppenheimer expansion and removes difficulties indicated in earlier calculations. The muon distribution for very asymmetric prompt fission proves to be highly sensitive to the velocity of the primary fragments at the scission point. The mean collective energy dissipated during saddle-to-scission descent due to the one-body mechanism is calculated within the same approach.     

瞬发超临界系统内持续裂变链的发展过程

根据基本的概率理论和瞬发临界附近有限裂变链的发展规律, 推导了单脉冲源条件下脉冲堆引发持续裂变链过程中的中子数与时间关系式, 并得到CFBR-Ⅱ堆上实验的验证. 该关系式进一步发展了Hansen理论模型, 除了可以描述裂变链后期的发展趋势, 还可以描述持续裂变链产生初期中子数的快速增长行为. 讨论了引发时间与源强的关系, 指出在弱源条件下, 引发时间几乎不依赖于源强. 关键词： 持续裂变链 脉冲堆 引发时间     

Search for sp interference in the emission of prompt neutrons from 235U fission induced by polarized thermal neutrons

It is shown that the softening of the acoustic mode and the ensuing ferroelastic phase transition are due to the linear-quadratic interaction between the symmetric and antisymmetric deformations, which is presently neglected in the literature. An expression is obtained which can be used to predict the phase transition pressure if the initial elastic moduli are known.     

Muon induced fission

Fission probabilities following muon capture are calculated for nuclei in the actinide region. The capture process is described in a simple model and cross sections of photon as well as neutron reactions are considered. The energy dependence of both is taken into account. A comparison with experimental data is made.     

Pion induced fission

Fissilities induced by the absorption ofπ ^? at rest in nuclei ranging from rare earth region to Uranium are evaluated by means of the Exciton Model. The theoretical results satisfactorily reproduce the experimental findings provided the ratioa _f/a_n is greater than unity and equal to 1.1.