- Email: [email protected]
Fission time for the 235U + α reaction measured by the crystal blocking technique
Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Fission time for the
235
U + a reaction measured by the crystal blocking technique
O.A. Yuminov a,*, A.M. Borisov a, V.A. Drozdov a, D.O. Eremenko a, O.V. Fotina a, F. Malaguti b, P. Olivo c, S.Yu. Platonov a, V. Togo b, A.F. Tulinov a a
D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Vorobyevy Gory, Moscow 119991, Russia Istituto Nazionale di Fisica Nucleare – Sezione di Bologna, Dipartimento di Fisica dell’Università, Via Irnerio 46, Bologna, Italy c Dipartimento Matemates, Universita’ di Bologna, Via Irnerio 46, Bologna, Italy b
a r t i c l e
i n f o
Article history: Available online 23 May 2009 PACS: 21.10.Tg 25.70.Gh 25.70.Jj 61.80.Mk 25.85.w
a b s t r a c t The crystal blocking technique has been used to measure the total time of the induced fission process for the 235U + a reaction in the energy range of bombarding a-particles from 25.9 to 31.2 MeV. Experimental fission times observed in this reaction vary from 1017 to 1016 s, depending on the projectile energy. Together with the corresponding experimental data on angular anisotropy in the same reaction they were analyzed within the dynamic-statistical approach with allowance for the nuclear dissipation phenomenon and the double-humped fission barrier model. It was demonstrated that the time of induced fission at low excitation energies is sensitive to the nuclear dissipation magnitude. Ó 2009 Published by Elsevier B.V.
Keywords: Nuclear reaction 235U + a Ea = 25.9–31.2 MeV Crystal blocking technique Total time of induced fission process Double-humped fission barrier model Nuclear dissipation
1. Introduction In recent years, several different approaches have been proposed to extract, from the observables of induced fission, information on nuclear dissipation and on its dependence on energy and deformation parameters. In particular, great attention has been paid to the fission time scales because of their strong connection with the dynamics of the fission process (see, for example, the review [1]). Many different experimental techniques have been adopted to measure the induced fission times sf. Among them, crystal blocking [2,3] is certainly the most straightforward one because it is sensitive, in a really model-independent way, to the recoil distance covered by the excited fissioning nuclear system during the whole process, from the instant at which the momentum is transferred from the projectile to the target nucleus, up to the emission of the final fragment. In [4] we analyzed a large set of experimental data on sf, obtained by the crystal blocking technique in a very wide range of excitation of the fissioning nucleus from 5 to 250 MeV. It was demonstrated that at excitation energies above 100 MeV the induced * Corresponding author. Tel.: +7 495 939 50 92; fax: +7 495 939 08 96. E-mail address: [email protected] (O.A. Yuminov). 0168-583X/$ - see front matter Ó 2009 Published by Elsevier B.V. doi:10.1016/j.nimb.2009.05.018
fission time is a very sensitive probe of nuclear dissipation. This sensitivity is higher than that corresponding to the analysis of multiplicity of pre-scission evaporated neutrons, also traditionally used to extract information on the nuclear dissipation. In this context, a further interest in the potentialities of experiments with the crystal blocking technique has arisen. The present paper is devoted to studying the ability of the crystal blocking technique for investigation of dynamical and statistical aspects of the nuclear fission process at low excitation energies. The main attention will be devoted to the nuclear dissipation phenomenon and the temperature dependence of shell effects. 2. Experimental procedure In the present work, the crystal blocking technique was used to measure the total induced fission time for the 235U + a reaction. The application of the crystal blocking technique to nuclear lifetime measurements was proposed very soon after the discovery of channeling effects [2,5]. If excited compound nuclei are produced by nuclear interactions between the nuclei of the lattice atoms in a single crystal and projectiles, the decaying nuclear system will recoil with a well-known velocity into the open space between the atomic rows and planes of the crystal. If the charged reaction
2593
O.A. Yuminov et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595
products are emitted promptly and thus the compound nuclear system is still at its original location, the emitted charged particles are shadowed towards a detector positioned in the direction of a lattice channel, and are blocked. As a result their angular distributions display minima at the crystallographic axis and plane directions, the so called ‘‘blocking dips”. If, however, the decay time is long enough that the nucleus has moved sufficiently into the channel then the blocking of the charged products is reduced. This reduction can be converted to a flight distance inside the lattice channel and, together with the recoil velocity, into a nuclear system lifetime. The present measurements were performed with the 120-cm cyclotron of the Nuclear Physics Institute, Moscow State University, in the energy range of bombarding a-particles from 25.9 to 31.2 MeV. The target was a thick enriched (90%) 235UO2 single crystal produced by the electrolytic growing method at the Moscow State University [6]. We exploit the conventional scheme of crystal blocking measurements (see, for example, [7]). Angular distributions of the outgoing fission fragments were measured by means of glass track detectors placed in the direction of the h1 1 1i crystallographic axis, forming an angle of 120° with respect to the beam direction. The glass detectors can register fission fragments with energy from 20 MeV and higher (see, for example, [8]) and allow one effectively to discriminate the fission fragments from the substantial background of backscattered a-particles, unregistered by the glass detectors. The detectors were placed in the reaction chamber at 23 cm distance from the target. In our case the linear size of the blocking dips on the glass detector surface is approximately 3 mm. After irradiation, the glass track detectors were etched by a 5% solution of HF acid at room temperature for 15 min. As a result the size of the fission tracks was (3–10) micrometers. The scanning and measurement of the fission tracks were performed with the Elbek image analyzer system [9], that allows the registration, on an event-by-event basis, of various geometrical characteristics of the tracks, like, such as their Cartesian coordinates on the detector, their area, their perimeter, their central brightness, the major and minor axes and so on. An autofocus system allows a fully automatic and quick reading over large detector areas. The system is able to read over 104 tracks per hour. The typical distribution over the track areas is displayed in Fig. 1 for Ea = 25.9 MeV. In this figure the dashed lines mark out the part of the distribution which was used to construct the blocking dip.
In order to extract information on the induced fission time we used the blocking dip parameter X, i.e. the ‘‘volume” of the blocking dip. The quantitative characteristic of the lifetime effect is R = X/Xref, where Xref is the parameter of the ‘‘reference” blocking dip unaffected by the displacement of the fissioning nucleus from the lattice site. The advantage of using parameter R lies in the fact that it is approximately independent of multiple-scattering within the crystal, that over large traversed distances in the crystal, spoils the blocking dips reducing their volumes X, which sometimes may simulate a non-existent time delay. Using R has the disadvantage of its being extremely sensitive to the choice of the ‘‘random yield” I, that has, therefore, to be determined with high accuracy. But recent developments [10] demonstrate that a precise measurement of I is now possible. The knowledge of R permits one to extract the induced fission lifetime values using the relations connecting the change in the blocking dips with the mean displacement of the nuclear system from the lattice site. These relations for a thick 235UO2 single crystal were obtained on the basis of a Monte Carlo code allowing the simulation of the charged-particle motion within crystal [10]. The volume of the ‘‘reference” blocking dip Xref = (606 ± 30) microsterad, was determined from the fission fragments produced in the experiment with a-particles of 29.6 MeV on 235U. As it was demonstrated in [11], at this energy of bombarding a-particles, fissioning nuclei 239,238,237Pu produced in the neutron-emission cascade have mean excitation energies E* > 12 MeV and mean fission lifetimes sf 6 1017 s. For the values of momentum transfer to the compound nucleus produced in the 235U + a reaction the displacements of these fissioning nuclei from the lattice sites over their lifetimes are comparable with the radius of screening of the nuclear Coulomb field by atomic electrons. The mean excitation energy of 236Pu nuclei produced at subsequent stages of the neutron-emission cascade is about 4 MeV, 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 X at energy Ea = 29.6 MeV can be regarded as a reference one. As a confirmation of these theoretical considerations, the experimental value of X at energy Ea = 29.6 MeV is maximal in the investigated beam energy range. Fig. 2 is a comparison of experimental blocking dips, the prompt one and the delayed observed at 25.9 MeV, to show the delay time effect on the shape of the dip. Fig. 3 shows the obtained experimental data of sf as a function of beam energy for the 235U(a, xnf) reaction investigated in the
25000
1.2 1.0
15000
normalized yield
Number of tracks
20000
10000
0.8 0.6 0.4
5000
25.9 MeV 29.6 MeV
0.2
0
0.0
0
20
40
60
80
100
120
Area, μm2
140
160
180
200
Fig. 1. Example of the distribution over the track areas (Ea = 25.9 MeV). The dashed lines mark out the part of the distribution which was used to construct the blocking dip.
0
10
20
30
40
50
60
angle (mrad) Fig. 2. Comparison between ‘‘prompt” (Ea = 29.6 MeV) and ‘‘delayed” (Ea = 25.9 MeV) blocking dips. The time delay effect is clearly visible: the prompt dip is larger and deeper.
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O.A. Yuminov et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595 -
1
10 15
τf , sec
-
10 16
0.1 -
10 17
Δχ -
10 18
20
24
28
32
0.01
Eα , MeV Fig. 3. Fission time for the 235U + a reaction: experimental data of this study (}) and from [11] (d), the curve is a result of theoretical calculations. The experimental uncertainties in the data of the present study are comparable with the symbol size.
0.001 19
3. Theoretical analysis As is well-known, heavy nuclei possess a double-humped structure of fission barriers, caused by the influence of nuclear shells on the potential energy of the deformed nuclei. With the nuclear temperature rise the shell structure of fission barrier is washed out [4,7]. Analysis of the present experimental data was performed within the theoretical model [12] which takes into account the nuclear dissipation phenomenon, the double-humped structure of the fission barrier and temperature dependence of the shell correction. It allows one to extract information on the nuclear dissipation from experimental sf data at low excitation energies (<15–20 MeV). This model is based on combined dynamical and statistical Monte Carlo calculations for making a decision on the decay channel of the excited nucleus. The probabilities of the different decay channels were given by the ratios between the corresponding decay widths, which were calculated within the Hauser-Feshbach formalism in the case of the emission of light particles (n, p and a) and c-quanta. The decay widths for the fission channel (for the double-humped fission barrier, these are the widths associated with passage through the inner and outer barriers) were calculated by the Bohr-Wheeler relations with allowance for Kramer’s correction [13]. In the case of the double-humped fission barrier, further evolution of a nucleus that has passed into the second potential well was simulated using a set of the stochastic Langevin equations. Level densities were calculated by a phenomenological model with mutually consistent account taken for collective coherent
23
25
27
29
31
Eα , MeV Fig. 4. Parameter Dv versus the incident beam energy for the 235U + a reaction. The dots are the experimental values from [11]. The curves are the results of theoretical calculations produced for different values of the damping coefficient b = 0.5 1021 s1 (solid line); 1.5 1021 s1 (dotted-dashed line) and 3.0 1021 s1 (dashed line).
excitations (rotational and vibrational), superconducting-type correlation effects and shell effects [14]. In our calculations we used the damping coefficient b (which is characterized by the rate of the dissipation of the nuclear collective energy into internal excitations) as a free parameter. A best fit of our experimental data on sf (Fig. 3), and also of another corresponding set of experimental data on the Dv parameter [11] (Fig. 4) was achieved for the value b = 1.5 1021 s1. Fig. 4 displays the experimental values of the parameter Dv = vminvminref (where vminref is corresponding parameter for the ‘‘reference” blocking dip) versus the incident beam energy for the 235U + a reaction [11] and the results of theoretical calculations produced for the different values of the damping coefficient in the range from 0.5 1021 s1 to 3.0 1021 s1. The absence of a local minimum in the calculation results near Ea = 29.6 MeV (the energy of the reference blocking dip) is probably connected with the underestimating of the fission fragment yield from 236Pu. Unfortunately, for this nucleus information on the level density and fission barrier parameters is absent. As was demonstrated in [15,16], the angular anisotropy of the fission fragment yield is also sensitive to the nuclear dissipation. So we try to test the obtained damping coefficient in an analysis of experimental data on angular distributions of fission fragments for the investigated reaction [17]. The angular anisotropy of the fis-
1.5 W(174°) / W(90°)
present work, together with the respective experimental sf values measured for this reaction in [11] earlier. Our experimental fission times observed for this reaction, range from 1017 to 1016 s, depending on the projectile energy. It is necessary to pay attention to the fact that in [11] sf values were extracted from the blocking dip parameter vmin, i.e. the relative intensity of the detected fission fragments at the minimum of the angular distribution. Here, it should be noted that in [11] for the ‘‘reference” blocking dip, one was used at Ea = 29.6 MeV for the h1 1 1i crystallographic axis, forming an angle of 170o with respect to the beam direction. Use of the same angle for the reference blocking dip in the case of X is not correct for the lifetime extractions. The reason lies in the dependence of X on both the lifetime magnitude and on the kinetic energies of fission fragments. The kinetic energy depends on the yield angle in the laboratory system. Nevertheless, we have a reasonable agreement between the different experimental sf values obtained using vmin and X, except for the points at Ea = 25.9 MeV. Apparently, the difference at Ea = 25.9 MeV is connected with the statistical precision of the experiment. So, one may support the ability of the crystal blocking technique for nuclear time measurements.
21
1.4 1.3 1.2 1.1 1.0 20
24
28
32
Eα , MeV Fig. 5. Angular anisotropy of the fission fragment yield in the 235U + a reaction. Symbols: (d) are the experimental data from [15]; () and (}) are the calculation results obtained with allowance for the characteristics of the fissioning nucleus at only the first or second saddle points of the double-humped fission barrier, respectively. Symbols (+) are the calculation results within the approach proposed in [16]. All calculations were performed with b and other parameters obtained in the analysis of vmin and X.
O.A. Yuminov et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595
sion fragment yield (Fig. 5) was calculated within the HalpernStrutisky approach [18] generalized to the case of a doublehumped fission barrier [15,16]. As shown in [15,16] fission fragment angular distribution is determined by the spectrum of fission channels (which are characterized by the projection K of the total angular momentum onto the fission axis) at an effective transition point. The position of this point essentially depends on the relation between the lifetime of an excited nucleus in the second potential well and the relaxation time for the K-mode (sK). The value of sK was chosen as 8 1021 s according to [15]. As one can see from Fig. 5, the experimental data cannot be described by choosing the fission channels only in the first or second saddle points. And statistical model parameters and the damping coefficient, obtained here from the analysis of Dv and sf, allow a good description of experimental data. Here, it should be noted that the total measured lifetime effect is an integral characteristic over the all fission branches: Dvtotal = Rixi Dvi. Here, Dvi is the modification of the ‘‘depth” of blocking pattern connected with the fission time of the i-th component of the neutron-emission cascade and xi is the weight of the i-th fission branch in the total yield of fission fragments. The existence of the different fission branches leads to non-monotonic energy dependences of Dv and sf (see Figs. 3 and 4). It is well-known that the angular distributions of fission fragments are anisotropic. However the anisotropy of the fission fragment distribution does not by itself affect the blocking dip at the registration angle since the dip extends over a very small angular range. Nevertheless xi depends on the angle of fragment emission. It is necessary to stress that although the total angular anisotropy of the fission fragment yield for the investigated 235U(a, xnf) reaction is well known [15], data on the angular anisotropy of the fission fragments for each fission chance are absent. Because the angular anisotropy of the fission fragments is strongly dependent on the nuclear temperature at the transition point, the yields of each concrete fissioning nucleus component of the neutron-emission cascade can be different. The above-mentioned theoretical approach allows us to calculate the angular anisotropy of the fission fragments for each fission chance [15]. All theoretical curves in
2595
Fig. 4 were calculated taking into account the influence of the angular anisotropy of the fission fragments. 4. Conclusion Our analysis demonstrates the high sensitivity of the induced fission time at low excitation energies to the magnitude of the damping coefficient. The obtained value of the damping coefficient b is consistent with the predictions of the linear response theory at the nuclear temperatures under study [19]. So we may state that the crystal blocking technique provides a way to study the nuclear dissipation phenomenon at low excitation energies (<15–20 MeV). References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19]
D. Hilsher, H. Rossner, Ann. Phys. (Paris) 17 (1992) 471. A.F. Tulinov, Dokl. Akad. Nauk SSSR 162 (1965) 546. W.M. Gibson, Ann. Rev. Nucl. Sci. 25 (1975) 465. V.A. Drozdov, D.O. Eremenko, O.V. Fotina, G. Giardina, F. Malaguti, S.Yu. Platonov, A.F. Tulinov, A. Uguzzoni, O.A. Yuminov, Nucl. Instr. and Meth. B 230 (2005) 589. D.S. Gemmell, R.E. Holland, Phys. Rev. Lett. 14 (1965) 945. V.O. Kordyukevich, V.I. Kuznetsov, Yu.D. Otstavnov, N.N. Smirnov, At. Energ. 42 (1977) 131. D.O. Eremenko, S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, Phys. At. Nucl. 61 (1998) 695. C. Fulmer, Phys. Rev. 108 (1957) 1113. A. Noll et al., Nucl. Tracks Rad. Meas. 15 (1988) 265. F. Malaguti, Nucl. Instr. and Meth. B 34 (1988) 157. and work to be published. O.V. Grusha, V.O. Kordyukevich, Yu.V. Melikov, L.N. Syutkina, A.F. Tulinov, O.A. Yuminov, Nucl. Phys. A 429 (1984) 313. M.H. Eslamizadeh, V.A. Drozdov, D.O. Eremenko, O.V. Fotina, S.Yu. Platonov, O.A. Yuminov, Moscow Univ. Phys. Bull. 63 (1) (2008) 24. Y. Abe, S. Ayik, P.-G. Reinhard, E. Suraud, Phys. Rep. 275 (1996) 49. (a) A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Yad. Fiz, Sov. J. Nucl. Phys. 21 (1975) 485; (b) A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Yad. Fiz, Sov. J. Nucl. Phys. 21 (1975) 255. D.O. Eremenko, V.A. Drozdov, S.Yu. Platonov, O.V. Fotina, M.H. Eslamizadeh, O.A. Yuminov, Moscow Univ. Phys. Bull. 63 (2) (2008) 118. D.O. Eremenko, B. Mellado, S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, G. Giardina, G. Rappazzo, F. Malaguti, J. Phys. G: Nucl. Part. Phys. 22 (1996) 1077. R.B. Leachman et al., Phys. Rev. 137 (1965) 814. R. Vandenbosh, J.R. Huzenga, Nuclear Fission, Academic, New York, 1973. H. Hofmann, Phys. Rep. 284 (1997) 137.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Fission time for the
235
U + a reaction measured by the crystal blocking technique
O.A. Yuminov a,*, A.M. Borisov a, V.A. Drozdov a, D.O. Eremenko a, O.V. Fotina a, F. Malaguti b, P. Olivo c, S.Yu. Platonov a, V. Togo b, A.F. Tulinov a a
D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Vorobyevy Gory, Moscow 119991, Russia Istituto Nazionale di Fisica Nucleare – Sezione di Bologna, Dipartimento di Fisica dell’Università, Via Irnerio 46, Bologna, Italy c Dipartimento Matemates, Universita’ di Bologna, Via Irnerio 46, Bologna, Italy b
a r t i c l e
i n f o
Article history: Available online 23 May 2009 PACS: 21.10.Tg 25.70.Gh 25.70.Jj 61.80.Mk 25.85.w
a b s t r a c t The crystal blocking technique has been used to measure the total time of the induced fission process for the 235U + a reaction in the energy range of bombarding a-particles from 25.9 to 31.2 MeV. Experimental fission times observed in this reaction vary from 1017 to 1016 s, depending on the projectile energy. Together with the corresponding experimental data on angular anisotropy in the same reaction they were analyzed within the dynamic-statistical approach with allowance for the nuclear dissipation phenomenon and the double-humped fission barrier model. It was demonstrated that the time of induced fission at low excitation energies is sensitive to the nuclear dissipation magnitude. Ó 2009 Published by Elsevier B.V.
Keywords: Nuclear reaction 235U + a Ea = 25.9–31.2 MeV Crystal blocking technique Total time of induced fission process Double-humped fission barrier model Nuclear dissipation
1. Introduction In recent years, several different approaches have been proposed to extract, from the observables of induced fission, information on nuclear dissipation and on its dependence on energy and deformation parameters. In particular, great attention has been paid to the fission time scales because of their strong connection with the dynamics of the fission process (see, for example, the review [1]). Many different experimental techniques have been adopted to measure the induced fission times sf. Among them, crystal blocking [2,3] is certainly the most straightforward one because it is sensitive, in a really model-independent way, to the recoil distance covered by the excited fissioning nuclear system during the whole process, from the instant at which the momentum is transferred from the projectile to the target nucleus, up to the emission of the final fragment. In [4] we analyzed a large set of experimental data on sf, obtained by the crystal blocking technique in a very wide range of excitation of the fissioning nucleus from 5 to 250 MeV. It was demonstrated that at excitation energies above 100 MeV the induced * Corresponding author. Tel.: +7 495 939 50 92; fax: +7 495 939 08 96. E-mail address: [email protected] (O.A. Yuminov). 0168-583X/$ - see front matter Ó 2009 Published by Elsevier B.V. doi:10.1016/j.nimb.2009.05.018
fission time is a very sensitive probe of nuclear dissipation. This sensitivity is higher than that corresponding to the analysis of multiplicity of pre-scission evaporated neutrons, also traditionally used to extract information on the nuclear dissipation. In this context, a further interest in the potentialities of experiments with the crystal blocking technique has arisen. The present paper is devoted to studying the ability of the crystal blocking technique for investigation of dynamical and statistical aspects of the nuclear fission process at low excitation energies. The main attention will be devoted to the nuclear dissipation phenomenon and the temperature dependence of shell effects. 2. Experimental procedure In the present work, the crystal blocking technique was used to measure the total induced fission time for the 235U + a reaction. The application of the crystal blocking technique to nuclear lifetime measurements was proposed very soon after the discovery of channeling effects [2,5]. If excited compound nuclei are produced by nuclear interactions between the nuclei of the lattice atoms in a single crystal and projectiles, the decaying nuclear system will recoil with a well-known velocity into the open space between the atomic rows and planes of the crystal. If the charged reaction
2593
O.A. Yuminov et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595
products are emitted promptly and thus the compound nuclear system is still at its original location, the emitted charged particles are shadowed towards a detector positioned in the direction of a lattice channel, and are blocked. As a result their angular distributions display minima at the crystallographic axis and plane directions, the so called ‘‘blocking dips”. If, however, the decay time is long enough that the nucleus has moved sufficiently into the channel then the blocking of the charged products is reduced. This reduction can be converted to a flight distance inside the lattice channel and, together with the recoil velocity, into a nuclear system lifetime. The present measurements were performed with the 120-cm cyclotron of the Nuclear Physics Institute, Moscow State University, in the energy range of bombarding a-particles from 25.9 to 31.2 MeV. The target was a thick enriched (90%) 235UO2 single crystal produced by the electrolytic growing method at the Moscow State University [6]. We exploit the conventional scheme of crystal blocking measurements (see, for example, [7]). Angular distributions of the outgoing fission fragments were measured by means of glass track detectors placed in the direction of the h1 1 1i crystallographic axis, forming an angle of 120° with respect to the beam direction. The glass detectors can register fission fragments with energy from 20 MeV and higher (see, for example, [8]) and allow one effectively to discriminate the fission fragments from the substantial background of backscattered a-particles, unregistered by the glass detectors. The detectors were placed in the reaction chamber at 23 cm distance from the target. In our case the linear size of the blocking dips on the glass detector surface is approximately 3 mm. After irradiation, the glass track detectors were etched by a 5% solution of HF acid at room temperature for 15 min. As a result the size of the fission tracks was (3–10) micrometers. The scanning and measurement of the fission tracks were performed with the Elbek image analyzer system [9], that allows the registration, on an event-by-event basis, of various geometrical characteristics of the tracks, like, such as their Cartesian coordinates on the detector, their area, their perimeter, their central brightness, the major and minor axes and so on. An autofocus system allows a fully automatic and quick reading over large detector areas. The system is able to read over 104 tracks per hour. The typical distribution over the track areas is displayed in Fig. 1 for Ea = 25.9 MeV. In this figure the dashed lines mark out the part of the distribution which was used to construct the blocking dip.
In order to extract information on the induced fission time we used the blocking dip parameter X, i.e. the ‘‘volume” of the blocking dip. The quantitative characteristic of the lifetime effect is R = X/Xref, where Xref is the parameter of the ‘‘reference” blocking dip unaffected by the displacement of the fissioning nucleus from the lattice site. The advantage of using parameter R lies in the fact that it is approximately independent of multiple-scattering within the crystal, that over large traversed distances in the crystal, spoils the blocking dips reducing their volumes X, which sometimes may simulate a non-existent time delay. Using R has the disadvantage of its being extremely sensitive to the choice of the ‘‘random yield” I, that has, therefore, to be determined with high accuracy. But recent developments [10] demonstrate that a precise measurement of I is now possible. The knowledge of R permits one to extract the induced fission lifetime values using the relations connecting the change in the blocking dips with the mean displacement of the nuclear system from the lattice site. These relations for a thick 235UO2 single crystal were obtained on the basis of a Monte Carlo code allowing the simulation of the charged-particle motion within crystal [10]. The volume of the ‘‘reference” blocking dip Xref = (606 ± 30) microsterad, was determined from the fission fragments produced in the experiment with a-particles of 29.6 MeV on 235U. As it was demonstrated in [11], at this energy of bombarding a-particles, fissioning nuclei 239,238,237Pu produced in the neutron-emission cascade have mean excitation energies E* > 12 MeV and mean fission lifetimes sf 6 1017 s. For the values of momentum transfer to the compound nucleus produced in the 235U + a reaction the displacements of these fissioning nuclei from the lattice sites over their lifetimes are comparable with the radius of screening of the nuclear Coulomb field by atomic electrons. The mean excitation energy of 236Pu nuclei produced at subsequent stages of the neutron-emission cascade is about 4 MeV, 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 X at energy Ea = 29.6 MeV can be regarded as a reference one. As a confirmation of these theoretical considerations, the experimental value of X at energy Ea = 29.6 MeV is maximal in the investigated beam energy range. Fig. 2 is a comparison of experimental blocking dips, the prompt one and the delayed observed at 25.9 MeV, to show the delay time effect on the shape of the dip. Fig. 3 shows the obtained experimental data of sf as a function of beam energy for the 235U(a, xnf) reaction investigated in the
25000
1.2 1.0
15000
normalized yield
Number of tracks
20000
10000
0.8 0.6 0.4
5000
25.9 MeV 29.6 MeV
0.2
0
0.0
0
20
40
60
80
100
120
Area, μm2
140
160
180
200
Fig. 1. Example of the distribution over the track areas (Ea = 25.9 MeV). The dashed lines mark out the part of the distribution which was used to construct the blocking dip.
0
10
20
30
40
50
60
angle (mrad) Fig. 2. Comparison between ‘‘prompt” (Ea = 29.6 MeV) and ‘‘delayed” (Ea = 25.9 MeV) blocking dips. The time delay effect is clearly visible: the prompt dip is larger and deeper.
2594
O.A. Yuminov et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595 -
1
10 15
τf , sec
-
10 16
0.1 -
10 17
Δχ -
10 18
20
24
28
32
0.01
Eα , MeV Fig. 3. Fission time for the 235U + a reaction: experimental data of this study (}) and from [11] (d), the curve is a result of theoretical calculations. The experimental uncertainties in the data of the present study are comparable with the symbol size.
0.001 19
3. Theoretical analysis As is well-known, heavy nuclei possess a double-humped structure of fission barriers, caused by the influence of nuclear shells on the potential energy of the deformed nuclei. With the nuclear temperature rise the shell structure of fission barrier is washed out [4,7]. Analysis of the present experimental data was performed within the theoretical model [12] which takes into account the nuclear dissipation phenomenon, the double-humped structure of the fission barrier and temperature dependence of the shell correction. It allows one to extract information on the nuclear dissipation from experimental sf data at low excitation energies (<15–20 MeV). This model is based on combined dynamical and statistical Monte Carlo calculations for making a decision on the decay channel of the excited nucleus. The probabilities of the different decay channels were given by the ratios between the corresponding decay widths, which were calculated within the Hauser-Feshbach formalism in the case of the emission of light particles (n, p and a) and c-quanta. The decay widths for the fission channel (for the double-humped fission barrier, these are the widths associated with passage through the inner and outer barriers) were calculated by the Bohr-Wheeler relations with allowance for Kramer’s correction [13]. In the case of the double-humped fission barrier, further evolution of a nucleus that has passed into the second potential well was simulated using a set of the stochastic Langevin equations. Level densities were calculated by a phenomenological model with mutually consistent account taken for collective coherent
23
25
27
29
31
Eα , MeV Fig. 4. Parameter Dv versus the incident beam energy for the 235U + a reaction. The dots are the experimental values from [11]. The curves are the results of theoretical calculations produced for different values of the damping coefficient b = 0.5 1021 s1 (solid line); 1.5 1021 s1 (dotted-dashed line) and 3.0 1021 s1 (dashed line).
excitations (rotational and vibrational), superconducting-type correlation effects and shell effects [14]. In our calculations we used the damping coefficient b (which is characterized by the rate of the dissipation of the nuclear collective energy into internal excitations) as a free parameter. A best fit of our experimental data on sf (Fig. 3), and also of another corresponding set of experimental data on the Dv parameter [11] (Fig. 4) was achieved for the value b = 1.5 1021 s1. Fig. 4 displays the experimental values of the parameter Dv = vminvminref (where vminref is corresponding parameter for the ‘‘reference” blocking dip) versus the incident beam energy for the 235U + a reaction [11] and the results of theoretical calculations produced for the different values of the damping coefficient in the range from 0.5 1021 s1 to 3.0 1021 s1. The absence of a local minimum in the calculation results near Ea = 29.6 MeV (the energy of the reference blocking dip) is probably connected with the underestimating of the fission fragment yield from 236Pu. Unfortunately, for this nucleus information on the level density and fission barrier parameters is absent. As was demonstrated in [15,16], the angular anisotropy of the fission fragment yield is also sensitive to the nuclear dissipation. So we try to test the obtained damping coefficient in an analysis of experimental data on angular distributions of fission fragments for the investigated reaction [17]. The angular anisotropy of the fis-
1.5 W(174°) / W(90°)
present work, together with the respective experimental sf values measured for this reaction in [11] earlier. Our experimental fission times observed for this reaction, range from 1017 to 1016 s, depending on the projectile energy. It is necessary to pay attention to the fact that in [11] sf values were extracted from the blocking dip parameter vmin, i.e. the relative intensity of the detected fission fragments at the minimum of the angular distribution. Here, it should be noted that in [11] for the ‘‘reference” blocking dip, one was used at Ea = 29.6 MeV for the h1 1 1i crystallographic axis, forming an angle of 170o with respect to the beam direction. Use of the same angle for the reference blocking dip in the case of X is not correct for the lifetime extractions. The reason lies in the dependence of X on both the lifetime magnitude and on the kinetic energies of fission fragments. The kinetic energy depends on the yield angle in the laboratory system. Nevertheless, we have a reasonable agreement between the different experimental sf values obtained using vmin and X, except for the points at Ea = 25.9 MeV. Apparently, the difference at Ea = 25.9 MeV is connected with the statistical precision of the experiment. So, one may support the ability of the crystal blocking technique for nuclear time measurements.
21
1.4 1.3 1.2 1.1 1.0 20
24
28
32
Eα , MeV Fig. 5. Angular anisotropy of the fission fragment yield in the 235U + a reaction. Symbols: (d) are the experimental data from [15]; () and (}) are the calculation results obtained with allowance for the characteristics of the fissioning nucleus at only the first or second saddle points of the double-humped fission barrier, respectively. Symbols (+) are the calculation results within the approach proposed in [16]. All calculations were performed with b and other parameters obtained in the analysis of vmin and X.
O.A. Yuminov et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 2592–2595
sion fragment yield (Fig. 5) was calculated within the HalpernStrutisky approach [18] generalized to the case of a doublehumped fission barrier [15,16]. As shown in [15,16] fission fragment angular distribution is determined by the spectrum of fission channels (which are characterized by the projection K of the total angular momentum onto the fission axis) at an effective transition point. The position of this point essentially depends on the relation between the lifetime of an excited nucleus in the second potential well and the relaxation time for the K-mode (sK). The value of sK was chosen as 8 1021 s according to [15]. As one can see from Fig. 5, the experimental data cannot be described by choosing the fission channels only in the first or second saddle points. And statistical model parameters and the damping coefficient, obtained here from the analysis of Dv and sf, allow a good description of experimental data. Here, it should be noted that the total measured lifetime effect is an integral characteristic over the all fission branches: Dvtotal = Rixi Dvi. Here, Dvi is the modification of the ‘‘depth” of blocking pattern connected with the fission time of the i-th component of the neutron-emission cascade and xi is the weight of the i-th fission branch in the total yield of fission fragments. The existence of the different fission branches leads to non-monotonic energy dependences of Dv and sf (see Figs. 3 and 4). It is well-known that the angular distributions of fission fragments are anisotropic. However the anisotropy of the fission fragment distribution does not by itself affect the blocking dip at the registration angle since the dip extends over a very small angular range. Nevertheless xi depends on the angle of fragment emission. It is necessary to stress that although the total angular anisotropy of the fission fragment yield for the investigated 235U(a, xnf) reaction is well known [15], data on the angular anisotropy of the fission fragments for each fission chance are absent. Because the angular anisotropy of the fission fragments is strongly dependent on the nuclear temperature at the transition point, the yields of each concrete fissioning nucleus component of the neutron-emission cascade can be different. The above-mentioned theoretical approach allows us to calculate the angular anisotropy of the fission fragments for each fission chance [15]. All theoretical curves in
2595
Fig. 4 were calculated taking into account the influence of the angular anisotropy of the fission fragments. 4. Conclusion Our analysis demonstrates the high sensitivity of the induced fission time at low excitation energies to the magnitude of the damping coefficient. The obtained value of the damping coefficient b is consistent with the predictions of the linear response theory at the nuclear temperatures under study [19]. So we may state that the crystal blocking technique provides a way to study the nuclear dissipation phenomenon at low excitation energies (<15–20 MeV). References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19]
D. Hilsher, H. Rossner, Ann. Phys. (Paris) 17 (1992) 471. A.F. Tulinov, Dokl. Akad. Nauk SSSR 162 (1965) 546. W.M. Gibson, Ann. Rev. Nucl. Sci. 25 (1975) 465. V.A. Drozdov, D.O. Eremenko, O.V. Fotina, G. Giardina, F. Malaguti, S.Yu. Platonov, A.F. Tulinov, A. Uguzzoni, O.A. Yuminov, Nucl. Instr. and Meth. B 230 (2005) 589. D.S. Gemmell, R.E. Holland, Phys. Rev. Lett. 14 (1965) 945. V.O. Kordyukevich, V.I. Kuznetsov, Yu.D. Otstavnov, N.N. Smirnov, At. Energ. 42 (1977) 131. D.O. Eremenko, S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, Phys. At. Nucl. 61 (1998) 695. C. Fulmer, Phys. Rev. 108 (1957) 1113. A. Noll et al., Nucl. Tracks Rad. Meas. 15 (1988) 265. F. Malaguti, Nucl. Instr. and Meth. B 34 (1988) 157. and work to be published. O.V. Grusha, V.O. Kordyukevich, Yu.V. Melikov, L.N. Syutkina, A.F. Tulinov, O.A. Yuminov, Nucl. Phys. A 429 (1984) 313. M.H. Eslamizadeh, V.A. Drozdov, D.O. Eremenko, O.V. Fotina, S.Yu. Platonov, O.A. Yuminov, Moscow Univ. Phys. Bull. 63 (1) (2008) 24. Y. Abe, S. Ayik, P.-G. Reinhard, E. Suraud, Phys. Rep. 275 (1996) 49. (a) A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Yad. Fiz, Sov. J. Nucl. Phys. 21 (1975) 485; (b) A.V. Ignatyuk, G.N. Smirenkin, A.S. Tishin, Yad. Fiz, Sov. J. Nucl. Phys. 21 (1975) 255. D.O. Eremenko, V.A. Drozdov, S.Yu. Platonov, O.V. Fotina, M.H. Eslamizadeh, O.A. Yuminov, Moscow Univ. Phys. Bull. 63 (2) (2008) 118. D.O. Eremenko, B. Mellado, S.Yu. Platonov, O.V. Fotina, O.A. Yuminov, G. Giardina, G. Rappazzo, F. Malaguti, J. Phys. G: Nucl. Part. Phys. 22 (1996) 1077. R.B. Leachman et al., Phys. Rev. 137 (1965) 814. R. Vandenbosh, J.R. Huzenga, Nuclear Fission, Academic, New York, 1973. H. Hofmann, Phys. Rep. 284 (1997) 137.