Combined dynamical and statistical approach to describing induced fission of heavy nuclei

A combined dynamical and statistical approach to describing induced fission of heavy nuclei is proposed. This approach takes into account the nuclear-dissipation phenomenon and the double-humped structure of the fission barrier. A method that is intended for calculating the angular distribution of fission fragments and which is applicable over a broad range of excitation energies is discussed. The potential of the approach is demonstrated by addressing the problems of self-consistently describing experimental data on fission probabilities for plutonium and americium isotopes, the yields of shape isomers in the α+²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV and the d+^242,240Pu reactions at deuteron energies in the range E _d = 20–30 MeV, fission times in the α + ²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV, and angular distributions of fission fragments in the α + ²³⁸U, ²³⁷Np reactions at alpha-particle energies in the range E _α = 20–100 MeV.     

Mechanism of reactions induced by 7 MeV deuterons on9Be [(d,p), (d,d), (d,t), (d,4He)]

Angular distributions of protons, deuterons, tritons and alpha-particles emitted from the reactions in thed+⁹Be-system atE _d =7 MeV as well as excitation functions at selected angles in the energy rangeE _d =6.5–7.5 MeV (LAB) were measured. The potential part of the elastic scattering is described by the phenomenological optical model. The compound nucleus contribution to all exit channels is determined using the Hauser-Feshbach model. The collective excitation of the 2.43 MeV excited state of⁹Be and transfer processes are analysed within the DWBA formalism. The analyses suggest a significant contribution of five-nucleon transfer to the (d,⁴He) channel.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

Deuteron elastic scattering and (d,p) reactions on 208Pb at Ed = 22 MeV and j-dependence of T20 in (d,p) reaction

An experimental study of deuteron elastic scattering and (d,p) reactions at E_d = 22 MeV was made for ²⁰⁸Pb target. A new j-dependence of T₂₀ for (d,p) reaction at backward angles was observed. A “model independent” optical potential method was applied to analyze deuteron elastic scattering in the 10–22 MeV energy range. A continuum discretized coupled channels (CDCC) analysis was performed for deuteron elastic scattering at 22 MeV and the deuteron breakup effect was elucidated. DWBA and CDCC (d,p) analyses were made for (d,p) reactions.     

Investigation of the 208Pb(18O, f) fission reaction: Mass-energy distributions of fission fragments and their correlation with the gamma-ray multiplicity

The mass-energy distributions of fragments originating from the fission of the compound nucleus ²²⁶Th and their correlations with the multiplicity of gamma rays emitted from these fragments are measured and analyzed in ¹⁸O + ²⁰⁸Pb interaction induced by projectile oxygen ions of energy in the range E _lab = 78–198.5 MeV. Manifestations of an asymmetric fission mode, which is damped exponentially with increasing E _lab, are demonstrated. Theoretical calculations of fission valleys reveal that only two independent valleys, symmetric and asymmetric, exist in the vicinity of the scission point. The dependence of the multiplicity of gamma rays emitted from both fission fragments on their mass, M_γ(M), has a complicated structure and is highly sensitive to shell effects in both primary and final fragments. A two-component analysis of the dependence M_γ(M) shows that the asymmetric mode survives in fission only at low partial-wave orbital angular momenta of compound nuclei. It is found that, for all E _lab, the gamma-ray multiplicity M_γ as a function of the total kinetic energy (TKE) of fragments, M_γ(TKE), decreases linearly with increasing TKE. An analysis of the energy balance in the fission process at the laboratory energy of E _lab = 78 MeV revealed the region of cold fission of fragments whose total kinetic energy is TKE ～Q _max.     

Dynamic picture of the formation of spins of induced fission fragments

A way of calculating the average spins of induced fission fragments is developed, based on the dynamic model of their angular distributions. The range of relaxation times for the degree of freedom associated with the orientation of the axis of symmetry of a fissioning nucleus relative to its total angular momentum is determined by analyzing experimental data on the energy dependences of average spins and the anisotropy of the angular distributions of fission fragments for the ¹²C, ¹⁶O + ²³²Th reactions at E _сm = 55–150 MeV.     

Dynamic approach to the analysis of angular distributions of fission and quasi-fission fragments

A dynamic approach to the calculation of angular distributions of fission and quasi-fission fragments is proposed. The approach is tested in the analysis of the experimental data for the ²⁸Si, ³²S + ²⁰⁸Pb reactions at E _lab = 160–280 MeV. Dependence of the relaxation time for the degree of freedom related to the projection of the angular momentum onto the symmetry axis of the decaying system on the deformation and the angular momentum is discussed.     

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.     

Quasifree processes in the 2H + 3He interaction

Quasifree scattering and quasifree reaction processes have been examined in the ³He+ ²H → p+d+d, ³He + ²H → n+p+³He and ³He+²H → p+p+t reactions. Beam energies of E_d = 22.3 and 35 MeV and of E_3He = 30, 33.5, and 52.5 MeV were used. The experimental results are compared with PWIA calculations and Fourier transforms of the wave functions are extracted. The quasifree processes are described qualitatively by the PWIA, but some features cannot be described by either PWIA or DWIA.     

Evaporation residue cross sections from the fusion of52Cr+110Pd

Evaporation residue cross sections for the fusion of⁵²Cr and¹¹⁰Pd were studied at four energies close to the barrier (up toE _CM ?E _B =26 MeV). The cross sections were analysed using a multiple-chance fission/evaporation calculation. Agreement with the data is obtained with a fission barrier reduced by 40 to 20%, depending on incident energy.     

A study of the (d, α) reaction in 56Fe at 12 MeV

The (d, α) reaction in ⁵⁶Fe is studied at E_d = 12 MeV and angular distributions of the α-particles are obtained over the angular range 13°–83° (c.m.s.); the results are analysed in terms of the DWBA theory of direct reactions using the two-nucleon pick-up mechanism of Glendenning. Spectroscopic information on ⁵⁴Mn levels up to 4.3 MeV excitation is obtained.     

Electrofission of238U and232Th

Absolute electrofission cross sections for²³⁸U and²³²Th in the energy regionE _e =7 ?65 MeV and fission fragment angular distributions forE _e =7–30 MeV have been measured. The angular distributions show strong anisotropies for low energies. The relative dipole and quadrupole contributions as a function of excitation energy are discussed in terms of the low lying fission transition states above the fission barriers. The cross sections show significant deviations from the results of some earlier measurements, in particular in the energy region above the giant dipole resonance. From the difficulties of absolute electrofission cross section measurements and the ambiguities in their interpretation it is concluded that by this time the quantitative analysis of electrofission cross sections with respect to the contributions of the giant quadrupole resonances to the fission decay channel should be regarded as rather tentative.     

Analysis of fragment mass distribution in asymmetric area at fission of <Superscript>235</Superscript>U induced by thermal neutrons

The fragment mass yields in fission of ²³⁵U induced by thermal neutrons for A = 145–160 and E_K = 50–75 MeV were measured using a mass spectrometer. The fine structure is observed at A = 153, 154 and E_K = 50–60 MeV. The obtained results were described in the framework of a model based on the dinuclear system concept. The analyzed correlation between the total kinetic energy and mass distribution of fission fragments is connected with the shell structure of the formed fragments of fission. From this correlation and the time dependence of the calculated mass distribution of the binary reaction products, one can conclude that the descent time from a saddle point to a scission point for the more deformed fragments is longer than that for fragments of more compact shape.     

Effect of the Input Channel of Heavy-Ion Reactions on Fission-Fragment Spins

Within a dynamical approach, the average spins of fission fragments originating from the ¹²C + ^235,236U and ¹³C + ²³⁵U complete fusion reactions at c.m. energies in the range of E_c.m. = (55–75) MeV are analyzed as a function of energy. Particular attention is given to the process of formation of initial distributions for the components of the total angular momentum of compound nuclei. It is shown that substantial distinctions in the behavior of average spins of fission fragments for different fusion reaction channels are expected to be observed in the range of subbarrier energies.

     

Boron+boron sub-Coulomb energy total reaction cross sections

Total reaction cross sections have been measured for the following reactions and energy intervals: ¹¹B+¹¹B, E_c.m. = 1.56–3.65 MeV; ¹⁰B+¹¹B, E_c.m. = 1.61–3.94 MeV; ¹⁰B+¹⁰B, E_c.m. = 1.84–3.66 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by large NaI detectors. The absolute accuracy of the method is thoroughly discussed and tested via a measurement of the ¹²C+¹²C reaction. For all three boron cases measured neither intermediate nor giant type resonances were observed. The cross sections are well described by optical model calculations based on lowenergy ¹¹B+¹¹B elastic scattering parameter sets.     

Measurement and MIA analysis of the neutron differential cross section and polarization in the α-D break-up at 33 MeV c.m.

Differential cross sections at 0° and 20° and polarizations at 20° have been measured for the ²H(α, n) αp reaction at E_α = 100 MeV and the ⁴He(d, n) αp reaction at E_d = 50 MeV. Data have been analyzed by the Modified Impulse Approximation (MIA). Satisfactory agreement was obtained but some discrepancy remained in the analysis of polarization data.     

Studies on strongly damped components in relatively light heavy ion reaction systems

Strongly damped components have been studied in relatively light heavy ion reaction systems;²⁰Ne(E _lab=93, 120 and 146MeV)+⁵⁰Cr,²⁰Ne(E _lab=146MeV)+⁵⁴Cr and²⁰Ne(E _lab=146MeV)+⁹²Mo,¹⁰⁰Mo. The kinetic energy, angular and charge distributions have been observed for those products. The yields of symmetric-mass-splitting products for²⁰Ne+⁵⁰Cr were found about three times larger than those for²⁰Ne+⁵⁴Cr. There was also observed a similar difference in the cross sections of the symmetric-mass-splitting products between²⁰Ne+⁹²Mo and²⁰Ne+¹⁰⁰Mo reactions. In order to explain the bombarding energy dependence of the cross sections of symmetric-mass-splitting products by the transport theory, it was found necessary to assume that the mean life of the composite nucleus was dependent on the bombarding energy. However, the target isotope dependence of the cross sections could not be explained by such an assumption. They could be partly explained by fission calculations.     

Forward peaking of near Coulomb energy protons in (n,p) reactions at 14.1 MeV

We apply a modified statistical model of compound nucleus reactions to analyse low energy proton angular distributions from the ⁹³Nb(n, p), ^natAg(n, p) and ^natIn(n, p) reactions at E_n=14.1 MeV. The forward peaking at the maximum of the proton evaporation spectrum at E _p = 6–8 MeV is reproduced and interpreted as an indication of the decay of thermalized-nonequilibrated nuclear states.     

Statistical analysis of the (d,p) and (d,d) reactions on 40Ca

Excitation functions of the ⁴⁰Ca(d, p)⁴¹Ca and ⁴⁰Ca(d, d)⁴⁰Ca reactions have been measured at 45°, 90°, 135° and 170° from E_d = 4.50 to 5.43 MeV in 10 keV steps. Angular distributions of these reactions have been taken at E_d = 4.70, 5.00 and 5.30 MeV from 25° to 170° in 5° steps. Transitions were observed to the excited states for the range 0.0 ≦ E_x ≦ 3.74 MeV in ⁴¹Ca. Rapid fluctuations in the excitation functions and strong variations of the angular distributions with the incident energy were observed, suggesting that the contribution from compound nucleus processes is very large. Various quantities extracted from the experimental data were compared to the predictions of the statistical theories combined with the DWBA theory for the calculation of the direct reaction amplitudes. The results of the present analysis are consistent with the predictions of the standard statistical theories based on the neglect of the channel-channel correlation.