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.     

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.     

The study of the (α, α′ f) reaction at 120 MeV on 232Th and 238U: (II). Fission barrier properties deduced from fission probabilities and angular distributions

The fission probabilities and angular distributions of the fission fragments for the (α, α'f) reaction on ²³²Th and ²³⁸U at a bombarding energy of 120 MeV have been measured from about 4 to 14 MeV excitation energy. Evidence for sub-barrier resonances has been found, the negativeparity ones occurring at the same excitation energy where photofission resonances have been observed. The data are analyzed with the two-humped barrier model. For ²³⁸U the data are reasonably well fitted with barriers similar to those known from the literature. For ²³²Th though, the outer barrier parameters are quite different: the height E_B = 6.6 MeV and the width (khω)_B = 1.2 MeV. Also for ²³²Th, introducing an additional mass symmetric and axially asymmetric outer barrier, as was previously found necessary for ²³⁸U, does not result in a good fit to the data at higher excitation energies.     

A study of reaction rates of (n, f ) , (n, \gamma) and (n, 2n) reactions in natU and 232Th by the neutron fluence produced in the graphite set-up (GAMMA-3) irradiated by 2.33 GeV deuteron beam

Spallation neutrons produced in the collision of a 2.33GeV deuteron beam with a large lead target are moderated by a thick graphite block surrounding the target and used to activate the radioactive samples of ^natU and Th put at three different positions, identified as holes “a”, “b” and “c” in the graphite block. Rates of the (n, f), (n, $ \gamma$ and (n, 2n) reactions in the two samples are determined using the gamma spectrometry. The ratios of the experimental reaction rates, R (n, 2n)/R (n, f), for ²³²Th and ^natU are estimated in order to understand the role of the (n, x n) kind of reactions in Accelerator-Driven Sub-critical Systems. For the Th-sample, the ratio is ～ 54 (10)% in the case of hole “a” and ～ 95 (57)% in the case of hole “b” compared to 1.73(20)% for hole “a” and 0.710(9)% for hole “b” in the case of the ^natU sample. Also the ratio of fission rates in uranium to thorium, ^natU (n, f)/ ²³²Th (n, f), is ～ 11.2 (17) in the case of hole “a” and 26.8(85) in hole “b”. Similarly, the ratio ²³⁸U (n, 2n)/ ²³²Th (n, 2n) is 0.36(4) for hole “a” and 0.20(10) for hole “b” showing that ²³²Th is more prone to the (n, x n) reaction than ²³⁸U . All the experimental reaction rates are compared with the simulated ones by generating neutron fluxes at the three holes from MCNPX 2.6c and making use of the LA150 library of cross-sections. The experimental and calculated reaction rates of all the three reactions are in reasonably good agreement. The transmutation power, P _norm as well as P _norm/P _beam of the set-up is estimated using the reaction rates of the (n, $ \gamma$ and (n, 2n) reactions for both the samples in the three holes and compared with some of the results of the “Energy plus Transmutation” set-up and TARC experiment.     

Experimentally determined transition probabilities of the systems 6p2→6p6d, 6p7s, 6p8s of neutral lead

Branching ratio measurements have been performed for all of the observed transitions from eight levels in neutral lead (6p²→6p6d, 6p²→ 6p7s, 6p²→6p8s) excited in a hollow cathode discharge in the 200–730 nm spectral range. From the relative emission intensity data, a set of absolute transition probabilities is derived for 28 lines, including lines for which transition probabilities have not been previously published. The absolute scales are obtained by averaging the measured lifetimes of the ³P⁰_1,2, ¹P_1⁰(6p7s), ³F^0_2,3, ³D^0_1,2(6p6d) levels.     

Parity violation at neutron p-wave resonances of238U and232Th and related questions

Parity violation effects have been studied at 40 neutron p-wave resonances of the even-even nuclei²³⁸U and²³²Th. Of these 11 show parity violation effects larger than 2 standard deviations, making parity violation a rather common phenomenon. Parity mixing up to 10% has been found. The root-mean squared matrix elements for parity violation derived from these resonances are M=0.58 (+0.50/-0.25) meV for²³⁸U, respectively 1.39 (+0.35/-0.38) meV for²³²Th.     

Determination of the spectroscopic quadrupole moments of 33 75 As and 29 63 Cu

The HFS-splitting of the 2s-2p and 3d-2p transitions of muonic arsenic and 3d-2p transitions of copper have been measured with high resolution Ge-semiconductor detectors to determine the nuclear quadrupole moments. A coincidence measurement was performed to separate the 2s-2p transition from the background. The nuclear spectroscopic quadrupole moments were found to be:Q _spec=0.314(6) b for ₃₃ ⁷⁵ AsQ _spec=0.220(15) b for ₂₉ ⁶³ Cu. In addition, generalized Barrett moments were determined in a model-independent analysis of muonic transition energies.     

Shell effects in the evolution of the mass asymmetry in heavy-ion collisions leading to composite systems withZ=108

Fragment mass distributions are presented obtained in the heavy-ion reactions²²Ne+²⁴⁹Cf,³²S+²³⁸U,⁴⁰Ar+²³²Th and⁵⁶Fe+²⁰⁸Pb leading to composite systems with equal nuclear charge numberZ=108. The experiments were performed at the heavy-ion cyclotron U 300 of the Laboratory of Nuclear Reactions in Dubna. The spectrometer DEMAS was used to measure the time-of-flight values and the laboratory angles of the correlated fragments. The shape of the mass distributions strongly depends on the initial mass asymmetry. When decreasing the bombarding energy down to values near the Coulomb barrier, the mass distributions obtained in the reactions³²S+²³⁸U and⁴⁰Ar+²³²Th exhibit relative maxima ofM≈205 interpreted to be due to stabilizing effects of nuclear shells during the fragmentation process.     

The PbPb collision

The reaction ²⁰⁸Pb on ²⁰⁸Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the ²⁰⁸Pb on ²³⁸U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ_z² versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.     

What can be learnt about nuclear polarization from a consistency analysis ofe − cross sections and muonic X-rays for208Pb and the isotone pair209Bi/208Pb?

A joint analysis of recent electron scattering cross sections and muonic atom X-ray energies is performed for²⁰⁸Pb and the isotone pair²⁰⁹Bi/²⁰⁸Pb. From the compatibility of the experimental data one can learn about the nuclear polarisation correction. However, we find this information not to be as accurate as other authors claimed when we take into consideration the ambiguities in the treatment of the corrections of the higher levels.     

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.     

Cross sections for nuclear reactions in collisions of238U+238U and238U +197Au near and below the coulomb barrier

Cross sections for nuclear reactions at beam energies near and below the spherical Coulomb barrier V _c were measured in the very heavy collision systems²³⁸U +²³⁸U and²³⁸U +¹⁹⁷Au. The most probable reaction channel with mass transfer is the one-neutron transfer. Its excitation function is understood in terms of Rutherford trajectories together with the quantal process of neutron tunnelling over large distances. In addition, the exchange of up to 15 nucleons is observed down to 0.90 V _c . The excitation functions for the multi-nucleon transfer products have much steeper slopes than that for one-neutron transfer, and are steeper for²³⁸U +¹⁹⁷Au than for²³⁸U +²³⁸U, suggesting that nuclear contact is established in the associated collisions. The angular distribution for one selected multi-nucleon transfer product,²²⁷Th, shows that its formation occurs in more central collisions within contact times shorter than about 10^?21 s. There is no evidence for very longlived di-nuclear systems in the these reactions.     

Dynamical approach to calculating angular distributions of fission fragments

A dynamical approach is proposed for calculating the angular distributions of fission fragments. The relaxation time for the degree of freedom associated with the projection of the total angular momentum of the nuclear system onto the symmetry axis and the coefficient of damping of the fission mode are the basic parameters of this approach. Experimental data on the anisotropy of the angular distributions of fission fragments and on the multiplicities of prescission neutrons are analyzed within the proposed model for ¹⁶O+²⁰⁸Pb (E _lab=110–148 MeV), ¹⁶O+²³²Th (120–160 MeV), ¹⁶O+²⁴⁸Cm (110–148 MeV), and ¹⁶O+²³⁸U (96–148 MeV). The relaxation time and the damping coefficient are estimated at τ_K=(5–6)×10^?21 s and β=4×10²¹ s^?1, respectively.     

Spin-forbidden transitions between 2p 2 and 2s2p states in the beryllium isoelectronic sequence

Fine-structure splittings, wavelengths and transition probabilities are evaluated for transitions 2p ^{2 1} S ₀→2s2p ³ P ₁ ⁰, 2p ^{2 1} D ₂→2s2p ³ P _J ⁰ (J=1, 2) and 2p ^{2 3} P _J →2s2p ¹ P ₁ ⁰ (J =0, 1, 2) in beryllium-like ions using configuration interaction wavefunctions. Some significant differences with previous calculations are obtained. At present there are no experimental results. However, from calculations reported here it should clearly be worthwhile to search for these lines in laboratory and astrophysical spectra. The decay of the 2p ^{2 1} D ₂ level is discussed.     

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.     

Quasi-free electron scattering in a relativistic model of the nucleus

Longitudinal and transverse response functions of quasi-free electron scattering have been calculated in mean field approximation for a relativisticσ-ω model, including non-linearities in theσ-field. As a consequence of the completely consistent and fully relativistic treatment of wave functions and current operators, gauge invariance is perfectly satisfied throughout the calculation. The results indicate that models with the same nuclear bulk properties lead to similar response functions within 10%. Our results agree with the experimental data for¹²C and²³⁸U, but cannot describe the longitudinal response in the Ca-Fe region. Predictions for²⁰⁸Pb are given for comparison with future experiments.     

Hybrid model analysis of intermediate energy (20<E γ<140 MeV) photonuclear reactions on232Th and235,238U

The hybrid model code ALICE/LIVERMORE 82 (with fission option) has been used in the study of photonuclear reactions on²³²Th and^235,238U (20<E _γ<140 MeV). The total fission probabilitiesP _f were calculated. A model was established for the decay of the fission fragments. This model, together with the code ALICE, allowed the calculation of the cross sectionsσ ⁽ⁱ⁾ for emission of at leasti neutrons, and of the average multiplicity¯v and widthW of the neutron distribution for²³⁸U. The theoretical results forP _f ,σ ⁽ⁱ⁾ ,¯v andW show very good agreement with existing experimental data. It is shown that a comparison of the calculations with the available experimental data does not allow for a discrimination between the various photon absorption mechanisms proposed (single-particle absorption vs. quasi-deuteron mechanism).     

The level structures of the nuclei232Th and238U

Time-of-flight gating techniques have been used to study the decay γ-rays from states excited by inelastic scattering of neutrons from²³²Th and²³⁸U. Neutron energies up to 1900 MeV have been used. From accurate determinations of the γ-ray energies, intensities and thresholds, detailed level and decay schemes have been obtained for²³²Th and²³⁸U. New levels in both nuclei are observed at larger excitations than before and the present work is incompatible with some previously accepted spin and collective band assignments derived from Coulomb excitation studies.     

Stochastic model of tilting mode in nuclear fission

A model of induced nuclear fission was developed with consideration of thermodynamically fluctuating orientation degree of freedom (tilting) of deformed nuclei. This model was applied to analysis of the experimental angular anisotropy of fission fragments in the ¹⁶O + ²³²Th, ²³⁸U, ²⁴⁸Cm, ²⁰⁸Pb, ²⁰⁹Bi; ¹²C + ²³⁶U; ¹⁹F + ²⁰⁸Pb; and ¹¹B + ²³⁷Np reactions. Information on the equilibrating time of the tilting mode was obtained. The text was submitted by the authors in English.     

Pairing-energy coefficients of neutron-rich fragments in spallation reactions

The ratio of pairing-energy coefficient to temperature(a_p/T)of neutron-rich fragments produced in spallation reactions has been investigated by adopting an isobaric yield ratio method deduced in the framework of a modified Fisher model.A series of spallation reactions,0.5A and 1A Ge V~(208)Pb+p,1A Ge V~(238)U+p,0.5A Ge V~(136)Xe+d,0.2A,0.5A and 1A Ge V~(136)Xe+p,and~(56)Fe+p with incident energy ranging from 0.3A to 1.5A Ge V,has been analysed.An obvious odd-even staggering is shown in the fragments with small neutron excess(I≡N-Z),and in the relatively small-A fragments which have large I.The values of a_p/T for the fragments,with I from 0 to36,have been found to be in a range from-4 to 4,and most values of a_p/T fall in the range from-1 to 1.It is suggested that a small pairing-energy coefficient should be considered in predicting the cross sections of fragments in spallation reactions.It is also concluded that the method proposed in this article is not good for fragments with A/A_s85%(where A_(s )is the mass number of the spallation system).