Документ взят из кэша поисковой машины. Адрес оригинального документа : http://danp.sinp.msu.ru/Tulinov_85/NIMB193(2002)846-AFT.pdf
Дата изменения: Tue Mar 9 20:44:11 2010
Дата индексирования: Mon Oct 1 22:24:47 2012
Кодировка:

Nuclear Instruments and Methods in Physics Research B 193 (2002) 846851 www.elsevier.com/locate/nimb

Crystal blocking measurements of the induced fission time in the 232Th Ч p and 232Th Ч 3He reactions
V.A. Drozdov a, D.O. Eremenko a, O.V. Fotina a, G. Giardina b, F. Malaguti c, S.Yu. Platonov a, A.F. Tulinov a, O.A. Yuminov a,*
b

D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Vorobyevy gory, Moscow 119992, Russia Instituto Nazionale di Fisica Nucleare, Sezione di Catania, Dipartimento di Fisica dell' Universita, Messina, Italy c Instituto Nazionale di Fisica Nucleare, Dipartimento di Fisica della Universita, Bologna, Italy

a

Abstract The crystal blocking technique has been used to measure the induced fission lifetimes for the 232;233 Pa and 232 U nuclei produced in the 232 Th Ч p and 232 Th Ч 3 He reactions at bombarding energies of protons and 3 He included in the 6.87.8 MeV and 20.823.4 MeV ranges, respectively. The experimental fission lifetimes observed in these reactions vary from 10ю16 to 10ю14 s, depending on the projectile energy. Experimental data have been compared with the statistical model calculations that take into account the existence of both classes of excited states of fissioning nucleus, realized in the first and second potential wells of the double-humped fission barrier. By the analysis of the measured decay times it is possible to determine the absolute values of the level density in the second well, type of shape symmetry in the second well, and also the unknown early values of the shell correction for the investigated fissioning nuclei at the deformation corresponding to the second potential well. с 2002 Elsevier Science B.V. All rights reserved.
PACS: 21.10.Tg; 25.70.Gh; 25.70.Jj; 61.80.Mk; 25.85.)w Keywords: Nuclear reactions 232 Th Ч p and 232 Th Ч 3 He; Ep ј 6:87.8 MeV and E3 He ј 20:823.4 MeV; Crystal blocking technique; Induced fission lifetime; Level density in the second well; Shell effects; Statistical theory

The second minimum in the potential energy surface of heavy fissionable nuclei was established by Strutinsky's shell-correction method in [1]. Therefore, two classes of quasistationary excited states exist for heavy fissionable nuclei. Such two classes differ in the value of the deformation of

* Corresponding author. Tel.: +7-095-939-50-92; fax: +7-095939-08-96. E-mail address: yuminov@p5-lnr.npi.msu.su (O.A. Yuminov).

fissioning nuclei, and the fission barrier is doublehumped with a deep second potential well. The existence of an additional class of transitional excited states for a fissioning nucleus is reflected in different time dependencies of the yields for different decay channels [2,3]. It is directly observed as a distinctive additional time delay of the fission process with respect to the decay of the excited nucleus through any other channel [3,4]. This time delay is due to the fact that when the excited heavy nucleus decays via the fission channel, the first- and second-well states are successively

0168-583X/02/$ - see front matter с 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 9 1 4 - X

V.A. Drozdov et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 846851

847

populated. Consequently, the time of the induced fission process (sf ) is determined by the lifetimes of both classes of excited nuclear states, sf ' h h Ч; C1 C2 П 1ч

232

where C1 and C2 are the total decay widths of the first and second-well excited states, respectively. The de-excitation times of the compound nucleus through any other decay channel involving light particles and neutron emission are determined practically by the lifetimes of the nuclear states under the equilibrium deformation, si ' h ; C1 П 2ч

because after transition to the second-well excited states the fissioning nucleus has cooled considerably, and the corresponding decay probabilities are strongly suppressed. The additional time delay (Ds) in the induced fission decay channel in the framework of the BohrWheeler statistical theory of nuclear reactions is h q Ds ј sf ю si ' ј 2 p 2 ; h C2 N2 П 3ч

ThП3 He; xnf ч reactions, respectively. The experiments were performed with the cyclotron U-120 of the Nuclear Physics Institute, Moscow State University at the bombarding energies of protons and 3 He ions in the 6.87.8 MeV and 20.8 23.4 MeV ranges, respectively. In these experiments, thick natural ThO2 single crystals, prepared by the radiochemical gas-transport technique, were used as targets. We explored the conventional scheme of crystal blocking measurements (see, for example [3,9]). Angular distributions of the outgoing fission fragments were measured by means of glass track detectors placed in the direction of the h11 1i crystallographic axis, which forms an angle of 160° with respect to the beam direction. The detectors were placed at the distance of 23 cm from the target. In order to extract information on the fission lifetime we used a blocking dip parameter vmin , i.e. the relative intensity of the detected fission fragments at the minimum of the angular distribution. The quantitative characteristic of the lifetime effect is Dv, Dv ј v
min

юv

ref min

;

П4ч

where q2 is the level density in the second potential well and N2 is the effective number of open decay channels of the second-well states. Eq. (3) shows that the additional fission time delay is directly related to the lifetime of the excited second-well states. The experimental determination of this value allow us to obtain an unknown earlier information on characteristics of the nucleus in the strongly deformed excited states (i.e. level densities [5], shell effects [6] and so on) and parameters of the double-humped fission barrier [3,7], in contrast to the traditional nuclear reaction characteristics such as cross sections, fission probabilities and angular distributions of the decay products, which are insensitive to the structure of the second-well states in the excitation energy region above the fission barrier. In the present work, an experimental crystal blocking technique [8,9] was used to measure the fission lifetime of the excited 232;233 Pa and 232 U nuclei produced in the 232 ThПp; xnf ч and

where vref is the parameter of the ``reference'' min blocking dip unaffected by the displacement of the nucleus from the lattice site. The knowledge of Dv permits one to extract the fission lifetime values using the relations connecting the change in the blocking dip with the mean displacement of a nuclear system from the lattice site. These relations for the thick ThO2 single crystal were obtained on the basis of multi-string model, and the Fokker Planck equation was used to take the multiple scattering of the fission fragments into account. The relative yield of fission fragments at the minimum of the reference blocking dip vref , was min determined from the experiments with 232 Th fission by a-particles of 30.5 MeV. As was demonstrated in [3,4], at this energy of bombarding a-particles fissioning nuclei 236;235;234 U produced in the neutron-emission cascade have mean excitation energies Eц > 12 MeV and mean fission lifetimes sf < 10ю17 s. For the values of momentum transfer to the compound nucleus produced in the 232 Th Ч a reaction the displacements of these fissioning nuclei from the lattice sites over their

848

V.A. Drozdov et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 846851

lifetimes are smaller than the radius of screening of the nuclear Coulomb field by atomic electrons that is, this displacement is smaller than the lower sensitivity limit of the blocking technique for this nuclear reaction. The mean excitation energy of 233 U nuclei produced at subsequent stages of the neutron-emission cascade is about 4 MeV, that considerably lower than the fission barrier. The contribution of these nuclei to the observed yield of fission fragments does not exceed 1%. To a reasonably high degree of precision, the value of vmin at energy Ea ј 31:2 MeV can be regarded as a reference one. During the irradiation of the target, the control on the radiation damage of the single crystal was made according to the procedure described in [9]. So it should be noted that the vref min was determined repeatedly in a run of measurements to detect a possible change in vref due to a min rise of the radiation damage. Figs. 1 and 2 show the experimental data of Dv as a function of beam energy for the 232 ThПp; xnf ч and 232 ThП3 He; xnf ч reactions, respectively. It is seen from Figs. 1 and 2 that it is possible to extract the contribution of the fissioning nucleus which is responsible for the lifetime effect in a certain range of incident beam energies. For the 232 ThПp; xnf ч

Fig. 2. As Fig. 1, but for the

232

ThП3 He; xnf ч reaction.

reaction at Ep ј 6:8 MeV this nucleus is 233 Pa, because of the mean excitation energy of 232 Pa nuclei produced at subsequent stage of the neutron-emission cascade is about 4 MeV, that considerably lower than the fission barrier. At Ep ј 7:3 and 7.8 MeV the 232 Pa nucleus, formed after the emission of one neutron from the compound nuclear system, is responsible for the observed lifetime effect. In this case the lifetime of the initial 233 Pa nucleus with high excitation energies (Eц > 12 MeV) is very short (sf $ 10ю19 s) and outside the sensitivity of the method. The same situation occurs for the 232 ThП3 He; xnf ч reaction, for which 232 U nuclei produce the observed lifetime effect. As we can see from Fig. 2, the yields of another nuclei produced in the reaction under study are negligible. So the observed dependence of Dv (Ebeam ) reflects, on the one hand, the change in the Dv contributions provided by the fissioning nuclei produced in the neutron emission cascade and, on the other hand, the changes in the lifetime of each nucleus with excitation energy. The contribution of every nucleus produced in the neutron-emission cascade to Dvexp , may be presented as D vi ј Dvexp ; bi П 5ч

Fig. 1. The parameter Dv versus the incident beam energy for the 232 ThПp; xnf ч reaction. The dots are the experimental values. The solid line (1) represents the Dv values calculated with inclusion of the lifetime of the excited states in the second potential well (s2 ). The solid line (2) shows the results of the calculations neglecting s2 . The broken lines demonstrate the partial contributions of the fissioning nuclei formed in the neutronemission cascade for the last case.

where Dvi is a contribution of the ith nucleus of the cascade, bi ј X
E ;J

P

rf ПE; J ч i n f iј1 ri ПE;

Jч

;

П 6ч

V.A. Drozdov et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 846851

849

Fig. 3. Mean lifetimes of 232 Pa as a function of the excitation energy. Points are sf experimental data: circles are the data from the 232 ThПp; xnf ч reaction, and squares are the data from the 232 ThПd; xnf ч reaction obtained by us earlier [7]. Solid line (1) represents the calculated induced fission decay time with a nonzero s2 , dashed line is the fission decay time calculated without s2 , and solid line (2) is the lifetime with respect to the neutron emission decay channel for the same parameters as in the case of the line (1).

Fig. 4. As Fig 3, but for the

233

Pa compound nucleus.

and rf is a fission cross section for ith nucleus of i the neutron-emission cascade. Figs. 3 and 4 represent the experimental sf values for the 232;233 Pa isotopes respectively, the results of the theoretical calculations of the fission

lifetimes and the decay times for the neutron emission channel. Fig. 5 shows the obtained fission decay times versus initial excitation energies of the uranium-like nuclei. Our experimental fission decay times range from 10ю16 to 10ю14 s, depending on the projectile energy, and are in a good agreement with the data of [10]; only the sf -values obtained in the 232 Th Ч 3 He reaction are in excess. Probably such excess is connected with the influence of the cold nuclei produced in the direct channels (3 He; df ) and (3 He; af ) of the reaction under study. It is

Fig. 5. The fission decay times of uranium-like nuclei versus initial excitation energy. Points are sf experimental data: open circle and triangle are our data from the 232 ThПp; xnf ч and 232 ThП3 He; xnf ч reactions respectively (present work); open squares are our data from the 232 ThПa; xnf ч reaction [4]; black squares are our data from the 28 Si Ч nat Pt reaction [6]; and black circles are the data from the 238 U Ч 28 Si reaction [10].

850

V.A. Drozdov et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 846851

need to stress that all presented fission decay times are much longer than what expected from trivial statistical calculations for the lifetimes of initial compound nuclei produced in the investigated reactions. Analysis of the experimental data was performed within the statistical theory of nuclear reactions. Parameters of the double-humped fission barriers for the nuclei under study were taken from systematics [11] except the unknown values of the second-well depth for the 232;233 Pa nuclei. These values were treated as an adjustable parameter and determined in the present study. The level density was calculated within the framework of Ignatyuk's phenomenological model with inclusion of the collective excitation contributions, the correlation effects of the superconducting type and the shell effects [12]. In the calculation we used different assumptions on the symmetry type of the nuclear shape in the second well allowing to determine such symmetry. It should be noted that the use of two adjustable parameters is justified because in this study, we analyzed the experimental energy dependences of sf . As it is seen from Figs. 14 to describe the experimental Dv and sf satisfactorily, it is necessary to take the lifetime of the second-well states into account. Our analysis of experimental data revealed that the second-well depths of the 232 Pa and 233 Pa nuclei are (3:5 ф 0:5) MeV and (2:0 ф 0:5) MeV respectively, and the investigated nuclei have neither mirror nor axial shape symmetry in the secondwell states. This conclusion is in line with the information that Figs. 6 and 7 show, where the experimental values of the level densities in the second potential well (derived from the Ds values according to the Eq. (3)) are compared with the calculation results obtained under different assumptions on the symmetry type of the nuclear shape in the second well. In conclusion, we measured the fission decay times for the excited 232;233 Pa and 232 U nuclei produced in the 232 ThПp; xnf ч and 232 ThП3 He; xnf ч reactions respectively, at Ep ј 6:87.8 MeV and E3 He ј 20:823.4 MeV by means of the blocking technique. The analysis of the obtained experimental data within the statistical theory of nuclear

Fig. 6. Level densities in the second potential well for the 232 Pa compound nucleus as a function of the internal excitation energy. Points are experimental data: circle is for the 232 ThПp; xnf ч reaction, and squares are the data from 232 ThПd; xnf ч reaction obtained by us earlier [7]. The lines represent the calculated level densities under various assumption on nuclear shape symmetry: (1) mirror and axial symmetry, (2) mirror asymmetry and axial symmetry, (3) ellipsoidal symmetry, (4) axial asymmetry and mirror symmetry and (5) no symmetry.

Fig. 7. As in Fig. 6, but for the

233

Pa compound nucleus.

reactions was performed, and the invoked doublehumped structure of fission barrier allows us to extract previously unknown information on the

V.A. Drozdov et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 846851

851

fission barrier parameters, namely the absolute values of the level density in the second well and the symmetry type of the nuclear shape in the second-well states.

Acknowledgements This work was supported in part by the Russian Foundation for Basic Research (grant no. 02-0217077-a) and the State Program Russian Universities. References
[1] V.M. Strutinsky, Nucl. Phys. A 95 (1967) 420. [2] O.A. Yuminov, S.Yu. Platonov, O.V. Fotina, D.O. Eremenko, F. Malaguti, G. Giardina, A. Lamberto, J. Phys. G 21 (1995) 1243. [3] D.O. Eremenko, S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, Phys. At. Nucl. 61 (1998) 695.

[4] D.O. Eremenko, V.A. Drozdov, O.V. Fotina, S.Yu. Platonov, A.F. Tulinov, O.A. Yuminov, Nucl. Instr. and Meth. B 164165 (2000) 965. [5] S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, Nucl. Phys. A 503 (1989) 461. [6] O.A. Yuminov, S.Yu. Platonov, D.O. Eremenko, O.V. Fotina, E. Fuschini, F. Malaguti, G. Giardina, R. Ruggeri, R. Sturiale, A. Moroni, E. Fioretto, R.A. Ricci, L. Vannucci, G. Vannini, Nucl. Instr. and Meth. B 164165 (2000) 960. [7] D.O. Eremenko, V.O. Kordyukevich, S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, G. Giardina, F. Malaguti, G. Vannini, Nucl. Phys. A 589 (1995) 395. [8] A.F. Tulinov, Dokl. Akad. Nauk SSSR 162 (1965) 546. [9] D.O. Eremenko, V.O. Kordyukevich, S.Yu. Platonov, A.F. Tulinov, O.V. Fotina, O.A. Yuminov, Phys. At. Nucl. 60 (1997) 149. [10] F. Goldenbaum, M. Morjean, J. Galin, E. Lienard, B. Lott, Y. P erier, M. Chevallier, D. Dauvergne, R. Kirsch, e J.C. Poizat, J. R emillieux, C. Cohen, A. L'Hoir, G. Pr e evot, e D. Schmaus, J. Dural, M. Toulemonde, D. Jacquet, Phys. Rev. Lett. 82 (1999) 5012. [11] J.E. Lynn, S. BjЬrnholm, Rev. Mod. Phys. 52 (1980) 725. [12] A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Yad. Fiz. 21 (1975) 485; Sov. J. Nucl. Phys. 21 (1975) 255.