ЯДЕРНАЯ ФИЗИКА, 2009, том 72, № 6, с. 982-989
= ЯДРА ^^
FISSION-TO-SPALLATION RATIO AND FISSION DYNAMICS
MANIFESTATION
© 2009 S. A. Karamian*
Joint Institute for Nuclear Research, Dubna, Russia Received June 27, 2008; in final form, December 15, 2008
Fission of highly excited nuclei is affected by the viscous character of the system motion in deformation coordinates as is reported for very heavy nuclei with Z > 90. The long-time-scale fission was proved for such systems formed in heavy-ion-induced reactions. The overdamped diabatic motion may influence also fission of the spallation-residue products in reactions with protons at intermediate energy. In the present work, the experimental results on fission-to-spallation ratio are analyzed and the evidences for the long-time-scale fission are found in the fission excitation functions for medium-mass targets with Z = 70-75.
PACS:24.75.+i, 25.40.Sc
1. INTRODUCTION
Traditionally, the intermediate energy of protons is defined as corresponding to the range of 100 < Ep < < 1000 MeV, where the mechanisms of pre- and nonequilibrium emission of nucleons are switched on and become competitive to the statistical evaporation mechanism. Near 100—200 MeV, it would not be easy to isolate clearly the dominance of one of the mentioned mechanisms. We may assume that at 100 MeV the equilibrium and nonequilibrium mechanisms make comparable contributions, in abundance. Then, this energy can be taken as a start point for the analysis of the fissile-nucleus properties changing at higher energies, Ep > 100 MeV. The characteristic neutron-evaporation time for nuclei near 181 Ta at the excitation energy of 100 MeV is as short as of about 10"20 s, according to the standard statistical model estimates with the Fermi-gas level density. This is still by two orders of magnitude longer than the time of nucleon passage across the nucleus. Therefore, fast intranuclear cascade may happen prior to the evaporation being isolated on time scale. For simplicity, we will join pre- and nonequilibrium processes under common term of the fast-reaction mechanism.
In the series of experiments carried out [1—3] at Dubna synchrocyclotron, the yields of products have been systematically measured in reactions of protons with the Hf, Ta, W, and Re targets at Ep = = 100—650 MeV. Main objective was to study the production of high-spin Lu and Hf isomers in the spallation reactions. Along the course of these works,
E-mail: karamian@nrmail.jinr.ru
the fission products have also been observed, and fission-to-spallation ratio is finally deduced for many targets at different proton energies. Despite the fact that data has appeared as by-product, it should be analyzed because the fission mechanisms are still under discussion in modern publications.
Unexpected manifestation of the long-time-scale fission for strongly excited nuclei has been established [4—6] in experiments applying the crystal-blocking and atomic-clock methods. Prefission particle-emission experiments [7, 8] had stimulated the explanations of long time as a manifestation of the reduced excitation energy for fission past emission of many neutrons and other particles. Statistical-model calculations were undertaken to quantify the "neutron-clock" approach and to deduce the characteristic fission time. However, recent blocking experiments [4, 5] bring evidences for inherent origin of the fission time scale, while particle emission does accompany the evolution of a system to fission, being not a main reason for time delay. This conclusion follows from the experiment [4] on fission of the W crystal target induced with 32S, 48Ti, and 58Ni ions, and from measurements [5] of the fission time for superheavy composite systems formed in reactions of 238U with the Si, Ni, and Ge crystal targets. In the latter cases, long times could not arise due to emission of many neutrons, because this contradicts low cross sections for the evaporation residues detected in experiments on a new element production.
The over-damped viscous motion was attracted for explanation of the long-time evolution of the fissile system, more details see below in Section 3. It would be interesting to find this effect's manifestation
not only in heavy-ion-induced fission but also in other reactions, in particular, in the case of fission of the spallation residue. In the present work, results on the fission probability of medium-weight nuclei near Z = 70 [1 —3] are analyzed at proton energies from 100 to 250 MeV. Within the selected energy range, statistical model calculations should be still applicable, and a comparison to the fission time-scale experiments [4—6] must be possible. Correlation between results of different-style experiments may be established past the analysis.
At much higher energies, near and above 1 GeV/u, the fragmentation reactions have been recently studied with new results. In particular, the dynamical evolution time, as long as about 10_20 s, is deduced and is interpreted as a manifestation of the transient time in fission width [9]. Our analysis corresponds to the domain of much lower energies, and other conclusions are possible.
2. FISSION OF THE SPALLATION RESIDUE
Nuclear reactions induced by proton at intermediate energy are schematically described as a consequence of fast and slow stages. Each of them may be a multistep process, as well. The fast intranuclear cascade releases nucleons due to the direct impact when the proton crosses a nucleus, and then the preequilibrium emission takes place. The nucleus remains excited after fast stages, and the residue undergoes the slow statistically equilibrated evolution with evaporation of particles, mostly neutrons. Final steps are similar to the well-known scenario of the compound-nucleus deexcitation. The fission events will appear due to the stage of residual evolution, and this-stage entrance parameters make significance for the fission-probability estimates. Within traditional schemes, the major problem arises in simulation of Z, A, and excitation-energy E* distributions for the residual nucleus past intranuclear cascade. The sophisticated computer codes are created for that and applied up to the GeV proton energies. However, at Ep lower than 200 MeV, the compound-nucleus-decay codes were used in some cases, for instance, the GNASH code [10] was specially developed to follow up the angular-momentum evolution in the statistical decay of excited nucleus. At the same time, some encounter coordinates are achievable basing on the measured mass distributions of the spallation products.
In experiments, Z and A numbers of the detected products are reached after ending of both stages of the reaction. Mass distributions measured in [1—3] show that a mean number of emitted nucleons does not exceed 8 particles at Ep = 100 MeV, and 15 ones at 200 MeV. During the fast stage, neutrons and protons
are emerged with almost equal probability without specific selectivity, unlike the statistical evaporation of mostly neutrons. Thus, the preformation product remains near the ^-stability line past the fast stage of the reaction if the ^-stable nucleus is used as a target. Mean mass number of this residue can be estimated, assuming that only half of the total number of nucleons is released at the fast reaction. Each nucleon, struck out from nucleus at the fast stage, should leave the nucleus excited to E* that may be enough for evaporation of one neutron more at the slow stage. Such consequence of the processes is supported within the widely used "percolation" mechanism of the proton—nucleus interaction. Percolation means the creation of a vacancy in the deep nuclear orbital. Then, after relaxation, the excitation energy comparable to the neutron binding energy may arise.
Parameters of the preformation residual nucleus are estimated using the assumptions above, and then the statistical calculations might be productive for the fission probability prediction. Certainly, the described approach looks schematic, but in restricted range of the proton energies from 100 to 200 MeV, the accuracy of estimates must be acceptable. The experimental results [1—3] on the fission-to-spallation ratio dependent on the proton energy for Hf to Re targets are presented in Fig. 1. Relatively flat function is manifested, contradicting the predictions by the advanced computer code LAHET [11], as is clear from Fig. 1. Thus, some model should be attracted for understanding of the unusual fission-probability function. In addition to the LAHET simulations, the simplified scheme is developed here mostly to verify that physical essence of the reaction mechanism is not screened by the mathematical and program complications. The conclusions made from the experiment-to-theory comparison would be more reliable if they are similar in two different schemes of calculations. Quantitative details of the present calculations are given below.
The fission probability is calculated for the 174Yb nucleus, which can serve as a typical example of the spallation residue in interaction of protons with the Hf and Ta targets at energies Ep ^ 200 MeV. In statistical model, the probability depends on E* and is expressed as a ratio of decay widths: wf (E*) = = rf (E*)/rt(E*), where rt is a total width containing all partial widths of the open decay channels with emission of neutrons, protons, gammas, alphas, and other particles: rt = rf + rn + rp + T7 + ...
At moderate E* values, main contribution corresponds to the neutron emission, and wf & rf/(rn + + Tf). In numerical calculations, the level-density p(E*) function was taken by the Gilbert—Cameron
+ G f
10-2r
10-
10-
/
natRe
A natTa
10-
O 179Hf • natHf
200
400
600
Ep, MeV
Fig. 1. Fission-to-spallation ratio displayed as a function of the proton energy: (a) for targets of Ta to Re according to measurements [1, 2], and (b) for179Hf and natHf targets [3]. Solid curves are the guide lines, dashed and dash-dotted curv
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