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Nuclear Instruments and Methods in Physics Research B 230 (2005) 589-595 www.elsevier.com/locate/nimb

Comparative analysis of the energy dependences of the induced fission times for the Pb-like and U-like nuclei obtained by the crystal blocking technique
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, A. Uguzzoni c, O.A. Yuminov a
a

D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Vorobyevy gory, 119992 Moscow, Russia b ` Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Dipartimento di Fisica dell' Universita, 98166 Messina, Italy c ` Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Dipartimento di Fisica della Universita, 40126 Bologna, Italy

Abstract Comparative analysis of the experimental data on the induced fission lifetimes for the Pb-like and U-like nuclei produced in the 208Pb + 28Si and 238U + 28Si reactions obtained by the crystal blocking technique was performed. Analysis was produced within the dynamical approach based on Langevin equations taking into account light particle emission from the hot fissioning system. Description of the analyzed energy dependence of the time values for U-like nuclei allows us to obtain information on the magnitude of nuclear viscosity. ã 2004 Elsevier B.V. All rights reserved.
PACS: 21.10.Tg; 25.70.Gh; 25.70.Jj; 61.80.Mk; 25.85.Ðw Keywords: Nuclear reactions 232Th, 235U, 238U + p, d, 3He, a; 28Si + Induced fission lifetime; Neutron multiplicity; Nuclear viscosity
nat

Pt,

238

U+ 28Si and

208

Pb + 28Si; Crystal blocking technique;

More than 60 years after the discovery of nuclear fission in 1938 the dynamics of this complicated process is still one of the most interesting
* Corresponding author. Tel.: +7 095 939 2465; fax: +7 095 939 0896. E-mail address: platonov@p10-lnr.sinp.msu.ru (S.Yu. Platonov).

manifestations of collective flow of nuclear matter and an ideal example for the yet unsolved nuclear quantum many-body problem. The dissipation of collective energy into thermal excitation energy was introduced into nuclear physics already in 1940 by Kramers [1], who suggested for the case of nuclear fission viscosity might influence the fission dynamics by the reducing of the fission decay

0168-583X/$ - see front matter ã 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.12.106


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width and slowing down the dynamical motion of a fissioning nucleus on its way to the scission point. And though the dynamics of the induced fission process constitutes a complex interplay of the influence of potential energy surface peculiarities, dissipation phenomena, nuclear level densities and inertia tensors, nuclear shell effects, different approaches were developed in order to deduce the information on the nuclear dissipation from the fission process observables. The possibility to gain reliable information on the magnitude of nuclear matter viscosity, and on its probable energy and deformational dependencies, from the dynamics of the induced nuclear fission reaction has given rise to numerous experimental attempts devoted to the determination of the fission time scales (see, for example, the review [2]). Various experimental techniques can be used to measure the fission lifetimes. Among these methods the crystal blocking technique [3,4] is certainly more straightforward because it measures in a really model-independent way the recoil distance covered by the excited fissioning nucleus during the whole induced fission process from the instant at which the momentum is transferred from the beam particle to the target nucleus, and ending when the final fragment is formed. It is need to stress that another, more popular but indirect, methods (based on the measurement of the multiplicities of pre- and (or) post-scission evaporated particles [2] or of giant dipole resonance (GDR) c-rays [5]) also traditionally have been used to extract the information on the induced fission timescale. Unfortunately, very different absolute lifetime values are inferred with these experiments depending on the probe used (either neutrons, or light charged particles, or c-quanta), or even depending on assumptions made in the analysis [6]. Furthermore, the probabilities of the pre-scission neutron and GDR c-ray emission become very small at low excitation energies, which makes these methods very little sensitive. The application of the crystal blocking technique for the nuclear timescale measurements was proposed very soon after the channeling effects were discovered [3,4,7]. If excited compound nuclei are produced by nuclear interactions between the nuclei of lattice atoms in a single crystal

and projectiles, the decayed nuclear systems will recoil with a well-known velocity into the open space between the rows and planes of the lattice. If the charged nuclear reaction products are emitted promptly and thus the compound nucleus is still at the original lattice location, the emitted charged particles are shadowed towards the detector positioned in the direction of a lattice channel, they are blocked. If, however, the lifetime of compound nucleus 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 compound nucleus lifetime. At the present time the large set of experimental data on the induced fission times - sf, obtained by the crystal blocking technique, was accumulated. Among the data our own sf values for the 232Th, 235,238 U + p, d, 3He, a reactions [8], measured at the cyclotron U-120 of the Institute of Nuclear Physics, Moscow State University, at beam energies in the range from 4 MeV/nucleon to 7.8 MeV/nucleon. The experimental decay times, corresponding initial excitation energies between 5 and 30 MeV, fall in the range from 10Ð17 to 10Ð14 s, depending on the projectile energy. To obtain information for the excitation energies of initial U-like fissioning nuclei in the range from 50 to 70 MeV we measured sf values for the 28Si + natPt reaction at the silicon beam energies from 140 to 170 MeV [9]. This experiment was done with the Tandem-XTU accelerator of the LNL Laboratories (Padova, Italy) and provided experimental lifetimes ranging from 10Ð18 to 10Ð17 s. Recently in GANIL (France) sf values were measured for the U-like and Pb-like nuclei produced in the 238 U + 28Si and 208Pb + 28Si reactions at the Ubeam and Pb-beam energies of 24 and 29 MeV/nucleon, respectively [10]. The availability at GANIL of the 238U and 208Pb beams accelerated at so high energy makes it possible to study fission events induced in reverse kinematics. Therefore, it is the projectile-like nucleus, moving with a high velocity, which will undergo fission, and much shorter lifetimes (up to 3 Ç 10Ð19 s) than traditionally become then accessible. For the case of heavy U-like nuclei jointed analysis of our own experimental


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data and data obtained in GANIL allows us to reveal the existence of the smooth energy dependence of sf for nuclei with Z = 91-94 in the very wide range of the initial excitation energy from 50 to 250 MeV (see Fig. 1) [11]. For the case of lighter and much less fissile Pb-like nuclei the relative weights of the long lifetime component are smaller than for U-like nuclei [10]. The existence of this sf dependence for the Ulike excited nuclei constructed from the experimental data obtained for different nuclear reactions investigated both in direct and reverse kinematics demonstrates the exceptional ability of the crystal blocking technique for the nuclear lifetime measurements. At the same time the difference between U-like and Pb-like nuclei strongly requires respective explanations. In a general way, to describe correctly the observable duration of induced fission reactions it is necessary to analyze all the stages of this complex process which may contribute to the experimental fission lifetime measured by the crystal blocking technique: duration of the fusion process of bombarding particle with the nucleus in the single crystal target; time of equilibration in the initial stage of the compound nucleus formation; the lifetimes of the fissioning compound nuclei produced in the development of neutron emission cascade; the dynamical times to build up the fission flux at the saddle point of fission barrier; the time for

the fissioning system to move from the saddle to scission points; and also the de-excitation time of formed fission fragments. The first, from the above-listed, stage of induced fission process and also the thermodynamical equilibration time (and the influence of the pre-equilibrium processes on the reaction time, in a general sense) was analyzed in detail in [12]. It was demonstrated that these times ((10Ð20 s) does not manifest itself in the experimental lifetime values because they are shorter than the lowest sensitivity limit of the blocking technique. Phenomenon of the in-flight decay of the observed reaction products was described for the first time in [13,14]. It is based on the observation that the reaction products (fission fragments in our case) are themselves excited nuclei that can decay by particle emission during their flight within the crystal target. The recoil associated with in-flight decay produces a random perturbation on the fragment path that fills the blocking dip, simulating a compound nucleus having long lifetimes. This effect was taken into account during the extraction of sf values presented in Fig. 1 [10,12]. As was mentioned in [11], the experimental fission times are much longer than that expected from the standard statistical calculations of lifetimes of initial compound nuclei formed in the investigated reactions. Calculations in the framework of the rotating liquid drop model, taking into

10 10

-15 -16 -17 -18 -19 -20

, s

10 10 10 10

0

50

100

150

200

250

E*, MeV
Fig. 1. The induced fission times versus initial excitation energy. Filled symbols are experimental data: from the 232Th(p,xnf) - %, 232 Th(3He,xnf) - × and 232Th(a,xnf) - m reactions [8]; from the 28Si + natPt reaction - j [9]; and from the 238U + 28Si reaction - d [10]. Open symbols are the calculation results obtained for the case of 238U+ 28Si reaction at b = 2 Ç 1021 sÐ1 (h), b = 7 Ç 1021 sÐ1 (s) and b =12 Ç 1021 sÐ1 (Ö), respectively, and also for the case of 208Pb + 28Si reaction at b = 7 Ç 1021 sÐ1 (n) and b = 12 Ç 1021 sÐ1 (,), respectively.


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account only lifetimes of excited states under equilibrium deformation, underestimate the experimental data by approximately five-orders of magnitude at excitation energies $100 MeV. As is well known, the emission of neutrons from the fissioning nuclear system leads to the cooling of nuclei before fission and as a result to increasing the mean decay time in the fission channel. Considerations of all possible fission chances during the development of the neutron-emission cascade (each one weighted with its probabilities of occurP rence - sf = sfi Ö xi, where xi is the relative weight of the fission fragments from ith chance, and sfi is the corresponding decay time in the fission channel) improve the fit of the experimental data. But the large difference between theory and experiment (approximately three-orders of magnitude) still remains. It was demonstrated earlier [15], assuming the double-humped fission barrier model with allowance for the lifetimes of the both classes of excited nuclear states in the first and second potential wells make it possible to improve essentially the fit of sf in the excitation energy range below 60- 70 MeV. The reason is that the existence of an additional time delay in the fission channel (connected with the lifetime of the second well states) leads to a noticeable increasing of sf. But for higher initial excitation energies the influence of this additional time delay diminishes and finally disappears at energies above 70 MeV due to the damping of shell effects with increasing of nuclear temperature [9]. In this energy region the doublehumped structure of the fission barrier for heavy nuclei tends to transform into a single-humped one and only one class of excited nuclear states under equilibrium deformation survives. In order to account the above-mentioned effects and also the dynamical aspects of the nuclear fission process we performed analysis of the obtained energy dependence of the induced fission times for the U-like nuclei. We used the stochastic approach [16,17] based on the set of Langevin equations for the collective coordinate r (distance between the centers of mass of the formed fission fragments) and the corresponding momentum p. In the one-dimensional case, it can be represented as

dr p Ì ; d t m ?r î 2 dp 1p dm?rî dF ÌÐ Ð Ð b?rîp ? f ?tî: dt 2 m?rî dr dr

? 1î

? 2î

In Eq. (2) f(t) is a random delta-correlated force with the following properties: hf(t)i = 0, hf(t1)f(t2)i = 2Dd(t1 Ð t2); where D is expressed, through the Einstein relation, in terms of the nuclear temperature T and the nuclear viscosity coefficient c as D = Tc, b = c/m is the damping coefficient in the fission mode and m is the inertial parameter, which was calculated in the frames of the Werner-Wheeler approach. Assuming the main goal of this paper (to obtain information on the nuclear matter viscosity), the damping coefficient b was used as an adjustable parameter. The conservative forces are calculated by the free energy of the excited nuclear system, F(r, T, J)= V(r, T, J) Ð a(r)T2. The nuclear temperature is defined as T = (Eint/a(r))1/2 with Eint = E* Ð p2/ (2m) Ð V(r, T, J) Ð Erot (J), where E* is the total excitation energy, Erot(J) is the rotational energy. In this work, the level-density parameter was chosen in the form a(r)= a1A + a2A2/3Bs(r), where Bs(r) is the surface energy functional of the deformed nucleus, parameters a1 and a2 are taken from [18]. In order to reproduce the shell structure of fission barriers the potential energy was taken as V(r, T, J) = Vl.d.(r, J) + dVshell(r, T). The liquiddrop part of potential energy Vl.d.(r, J) was calculated within the rotating liquid-drop model with the Myers-Swiatecki parameters [19]. The shell correction part was used in the form taking into account the damping of shell effects with increasing of nuclear temperature dVshell(r, T) = Vshell(r, T = 0) Ö F(T), where Vshell(r, T = 0) was calculated by means of the method proposed in [20]. For the temperature dependence of shell structure we used the universal damping function of Fermi type F(T) = 1/(1 + exp((T Ð T0)/d)), where d = 0.2 MeV is the rate of washing out the shell effects with the temperature [21] and parameter T0 was chosen equal 1.75 MeV according [9] (see Fig. 2). Indeed an important property of the shell structure is that its influence on nuclear processes


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593

1 0.8 0.6 0.4 0.2 0 0 1 2 3

1

2

3

T (MeV)

Fig. 2. Different types of the shell correction damping functions discussed in the text. Dashed curves were taken from: 1 - [18]; 2 - [23]; 3 - [24]. Solid curve is the damping function of the Fermi type with d = 0.2 MeV and T0 = 1.75 MeV using in the present calculations.

diminishes in highly excited nuclei and finally disappears at a certain temperature which was found to be tÓ Ì X=2p Ì 1:5-2 MeV, where X is the h h inter-shell energy spacing [22]. Our damping function is very similar to the data of [23], where the dependence of shell effects on nuclear temperature was extracted from the experimental data on angular anisotropies of fission fragments and also [24], where a semi-empirical analysis of temperature and spin dependence of shell corrections was done. The initial values of p were generated for each Langevin sample under the assumption of the normal momentum distribution at r corresponding to the equilibrium deformation req: 1 p2 W ?r; pî Ì pffiffiffiffiffiffiffiffiffiffiffiffi exp Ð ? 3î d?r Ð req î: 2mT 2pmT Emission of light particles (neutrons, protons and a-particles) and c-quanta was simulated within the method that usually is used to calculate the multiplicity of pre-scission light particles in the frames of an approach based on the Langevin equations (see, for example [17,25]). The induced fission times were calculated by the following relation: h sf i Ì
Nf 1X sf i ; N f iÌ1

where Nf is the number of Langevin samples, which have fissioned, and sfi is the fission time for the ith Langevin sample. Another calculation details were described in [9]. Because of lack of the respective experimental information we used the HICOL code [26] to evaluate the dependence of the angular momentum of the initial fissioning U-like nuclei produced in the 238 U + 28Si reaction on its excitation energy and also for the Pb-like nuclei formed in the 208 Pb + 28Si reaction (see Fig. 3). As we can see, the J values are a monotonically increasing function of excitation energy up to 60-70 and are conh sistent with the peripherical mechanism of the reactions under study. These values are very similar to the experimental J values extracted in [27]. It must be emphasized that the fission barrier of investigated Pb-like and U-like nuclei disappears at so high J values. The best description of the investigated energy dependence of sf for U-like nuclei was achieved for b = 12 Ç 1021 sÐ1. Obtained value of the damping coefficient b falls into the range of estimations of other authors [2] and corresponds to the conception of the ``overdamped'' collective nuclear motion. Decreasing of b leads to the decreasing of the sf values due to the different reasons, among which are decreasing of partial fission width Cf and

F(T)

? 4î

Fig. 3. Calculated dependences of the angular momentum on excitation energy for the initial fissioning U-like (solid curve) and Pb-like (dashed curve) nuclei produced in the 208Pb + 28Si and 238U + 28Si reactions at the beam energies 29 and 24 MeV/ u, respectively.


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also decreasing of the dynamical time to build up the fission flux at the saddle point of fission barrier and the time for the fissioning system to move from the saddle to scission points. The visible sharp turn in the calculated dependences at excitation energy $75 MeV is connected with the damping of shell structure of fission barriers. It should be noted that at excitation energies below 50 MeV calculation results obtained for different b are very similar. It is connected with the fact that the dynamical effects begin to play the dominant role at excitation energy above 100 MeV [2]. Hence this range is more suitable to extract information about the nuclear dissipation. Moreover at so high excitation energies the influence of shell effects is washing out and the sensitivity of the calculation results to the used nuclear potential is very low. As one can see from Fig. 1 calculated energy dependences for the fissioning Pb-like nuclei lie significantly below than ones for the U-like nuclei and far beyond the low limit of the crystal blocking technique. It is connected with the different relation between fission barrier height Bf and neutron binding energy Bn for these nuclei. For the Ulike nuclei Bf % Bn that will produce the equality of the partial decay widths for the fission and neutron channels Cf % Cn. For the Pb-like nuclei large difference Bf ) Bn leads to the large difference at the decay widths Cf ( Cn. In this situation excited nuclei prefer to decay via neutron emission and weight of long-lifetime fissioning nuclei from high chance fission (having residual excitation energy very close to the fission barrier) becomes much smaller. This also clearly demonstrates the low sensitivity of the calculated sf values for Pb-like nuclei to the variations in the b values. A rise of sf values for Pb-like nuclei for the excitation energies from 175 MeV connected with increasing of the emission probability for the light charged particles from fissioning systems. In this case two correlated effects contribute to slow down fission process: fission barriers heights that become suddenly much higher and also more efficient cooling due to the high emission barriers that have to be overcome. In addition, we also calculated the pre-scission neutron multiplicity for the fissioning U-like nuclei

formed in the 238U + 28Si reaction for the obtained b values (see Fig. 4). As we can see from Fig. 4 our calculation results for different b values in the range from 2 Ç 1021 to 12 Ç 1021 sÐ1 diverge very slightly (1-3 neutrons). The opposite situation realized in the case of sf values where we have essentially large difference (one or two orders) for the same variations of b values. Therefore it is necessary to stress more high sensitivity of fission lifetime than neutron multiplicity to the nuclear matter viscosity. In conclusion, it is necessary to stress the unique sensitivity of the induced fission lifetime to the properties of the fissioning nuclear system, i.e. magnitude of nuclear matter viscosity, structure of the excited strongly deformed nuclear states and so on. Moreover, performed analysis allowed us to separate the excitation energy ranges in which the different kinds of experimental information can be extracted. At excitation energies below $30 MeV measuring fission time it is possible to obtain information on the structural properties of concrete nuclei (fission barrier parameters, level densities and so on). In the energy region around 70 MeV information on the energy damping of shell effects is accessible. And at excitation energies above $100 MeV the fission time is a very sensitive probe of the nuclear dissipation.

12
n

M

8 4 0
0 50 100
*

150

200

250

E , MeV
Fig. 4. The pre-scission neutron multiplicity versus initial excitation energy of the fissioning U-like nuclei produced in the 238U + 28Si reaction. Open symbols are the calculation results obtained for b =2 Ç 1021 sÐ1 (h), b = 7 Ç 1021 sÐ1 (s) and b = 12 Ç 1021 sÐ1 (Ö), respectively.


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Acknowledgements This work was supported in part by the Russian Foundation for Basic Research (02-02-17077-a) and the State Programme ``Russian Universities'' (UR.02.03.038). References
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