Dynamical deformation of nuclei in deep-inelastic collisions: A gamma coincidence study of 130Te + 275 MeV 64Ni and 208Pb + 345 MeV 58Ni heavy ion reactions

Nuclear Physics A 832 (2010) 170–197 www.elsevier.com/locate/nuclphysa

Dynamical deformation of nuclei in deep-inelastic collisions: A gamma coincidence study of 130 Te + 275 MeV 64 Ni and 208 Pb + 345 MeV 58 Ni heavy ion reactions W. Królas a,∗ , R. Broda a , B. Fornal a , T. Pawłat a , J. Wrzesi´nski a , D. Bazzacco b , G. de Angelis c , S. Lunardi b , R. Menegazzo b , D.R. Napoli c , C. Rossi Alvarez b a H. Niewodnicza´nski Institute of Nuclear Physics PAN, Radzikowskiego 152, 31-342 Kraków, Poland b Istituto Nazionale di Fisica Nucleare, Sezione di Padova, and Universitá di Padova, I-35131 Padova, Italy c Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, I-35020 Legnaro (PD), Italy

Received 24 June 2009; received in revised form 16 October 2009; accepted 16 October 2009 Available online 29 October 2009

Abstract Products of 130 Te + 275 MeV 64 Ni and 208 Pb + 345 MeV 58 Ni collisions at energies slightly above the Coulomb barrier have been studied in two gamma spectroscopy thick target experiments. The product yield distributions have been established from the γ –γ coincidence analysis supplemented by target radioactivity measurements. Neutron evaporation from excited primary products has been estimated to determine the pre-emission maps of fragments. The transfer of protons and neutrons between the colliding ions is discussed in terms of the N/Z ratio equilibration. The discussion of experimental N/Z values compared with expectations based on potential energy minimizations leads to conclusion that the involved nuclei are dynamically deformed during the crucial interaction time. These results are discussed in connection with the earlier published study of the 208 Pb + 350 MeV 64 Ni system [1]. The present and perspective use of deep-inelastic reactions for spectroscopic studies of exotic neutronrich nuclei in experiments with stable and radioactive beams is outlined. © 2009 Elsevier B.V. All rights reserved.

* Corresponding author.

E-mail address: [email protected] (W. Królas). 0375-9474/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2009.10.159

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Keywords: N UCLEAR REACTIONS 130 Te(64 Ni, X), E = 275 MeV; 208 Pb(58 Ni, X), E = 345 MeV; 208 Pb(64 Ni, X), E = 350 MeV; measured Eγ , Iγ , γ γ -coin using the GASP array in both on- and off-line modes; deduced fragment production σ , reaction mechanism features; analysed fragment N/Z ratios. 208 Pb(64 Ni, X), E = 350 MeV; analysed fragment production σ

1. Introduction For nearly two decades deep-inelastic heavy ion reactions have been used in gamma spectroscopy studies of nuclei that cannot be accessed in standard fusion–evaporation reactions [2]. Within this research line many thick target γ –γ coincidence experiments have been performed and the accumulated data provide continuous flow of new spectroscopic information. In the analyses the excellent resolving power of Germanium multi-detector arrays is used to select discrete gamma transitions of a specific nucleus from an extremely complex spectrum of gamma rays associated with a large number of collision products. The advanced inspection of multifold prompt and delayed gamma coincidence data allowed to establish yrast structures in many nuclei located in the hitherto poorly studied neutron-rich sections of the chart of nuclides often reaching to large neutron excess and extending to high-spin and high excitation energy ranges (see e.g. [3–11]). The planning of these spectroscopic experiments was initially guided by general understanding of the reaction mechanism of deep-inelastic heavy ion collisions acquired in earlier investigations which employed various charged particle and fragment detection techniques (see e.g. [12–14] and references therein). However, it was early recognized that the knowledge of kinematics and dynamics of the colliding systems coming from the broad studies covering many target and projectile combinations was not satisfactory for practical application of deep-inelastic reactions for nuclear spectroscopy. In particular, it was not straightforward to predict yields of populated fragments in order to select optimal experimental conditions. Moreover, the trend to equilibrate the N/Z ratio of two colliding nuclei, which is one of the most important features determining the access to exotic, neutron-rich nuclei, was known only in general terms [15–18]. Therefore, parallel to spectroscopic studies, we performed a detailed analysis of the complete set of experimental data collected for three selected colliding systems, with the aim to clarify points important for spectroscopic applications. Such analysis was done already earlier for the 106 Cd + 54 Fe collisions of two neutron-deficient nuclei [19]. It demonstrated that the combination of in-beam gamma coincidence and radioactive decay data can provide a very complete information on the distribution of production yields including also a measure of the nucleon evaporation process from the excited primary fragments. It was also shown that such results provide important information on the N/Z equilibration process which governs the directed flow of neutrons and protons between the colliding initial nuclei with different neutron-to-proton ratios. The effort to analyze in a similar way reactions involving neutron-rich nuclei appeared to be necessary in view of the increasing interest in spectroscopic applications. Three colliding systems selected for such analysis in the present study represent cases suitable to look at the N/Z equilibration process from the perspectives of gamma spectroscopy. This selection was also aimed to shed a new light on the reaction mechanism of deep-inelastic heavy ion reactions, possibly supplementing the earlier knowledge. The 208 Pb + 350 MeV 64 Ni and 208 Pb + 345 MeV 58 Ni reactions and beam energies were chosen as systems for which the fusion process is practically absent and the neutron-to-proton ratios for the incident ions are dramatically different. The third, more symmetric system, 130 Te + 275 MeV 64 Ni, involves

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two neutron-rich nuclei for which the fusion–evaporation and fusion–fission reactions compete strongly with deep-inelastic reaction channels and therefore might affect the observed N/Z equilibration in mass regions where the distribution of products from the two processes overlaps. Similar thick target gamma coincidence studies of the population of exotic heavy nuclei by multi-nucleon transfer have been performed for collisions of 56 Fe, 86 Kr and 136 Xe incident ions with 232 Th targets [20–23]. The authors used in- and off-beam γ –γ coincidence analysis to reproduce partial yield distributions and discussed the role of the mass and charge equilibration process in the population of fragments arising in large nucleon transfer. However, for 232 Th target experiments, the fission of the excited target constituted the main component of the product distribution. The presence of those fission products which often could not be separated experimentally from deep-inelastic collision products affected the discussion of the N/Z equilibration process. In particular, the authors observed that the N/Z values of the populated fragments naturally come close to that of the composite system [20]. In one of the initial considerations of the neutron-to-proton ratio equilibration process an equilibration formula was derived from the minimization of the potential energy of two tangent spherical final fragments [15]. More sophisticated dynamical descriptions of the equilibration effect were based on diffusion and transport calculations. Results of several experiments in which final fragments were detected and the kinetic energy loss was determined event-by-event were used to draw contradictory conclusions. Whereas some of the authors claimed that the neutronto-proton ratio equilibration is a “fast” degree of freedom in comparison to the mass asymmetry degree of freedom [24–27], others argued that the N/Z equilibration is a continuous process that is not completed until full energy damping is achieved [28–30]. In our experiments all variables related to the reaction dynamics are integrated and only average features can be extracted from the data. Nevertheless, we anticipated that such analysis may be complementary to the previously used methods for the following reasons: the perfect A and Z identification, based on the observation of the characteristic gamma radiation, allows to determine production yields for all nuclei, including also the heavy fragments. The observed coincidences between gamma rays from two fragments arising in the exit channel allow to identify fully the reaction and thereby enable to account for the secondary particle evaporation in reconstruction of the primary fragment distribution. Finally, the full integration of kinematics by which important variables are lost, may also be of some advantage, since it automatically includes fragments scattered to forward angles, which are typically inaccessible in particle detection experiments. In the previously published paper we presented a full report on results obtained for the first of three studied systems, the 208 Pb + 350 MeV 64 Ni reaction [1]. The emphasis was placed on detailed description of all techniques used in the analysis i.e. quantitative analysis of in-beam and off-beam gamma coincidences, analysis of cross-coincidences between gamma rays emitted from two fragments in the exit channel as well as determination of yields from radioactivity measurements. The procedure used to obtain the primary fragments distribution was also discussed and observed features of the N/Z equilibration were initially interpreted. In this paper we shall present results obtained in a similar way for the other two systems referring to the earlier described methodology. The discussion of the obtained N/Z equilibration results will summarize the study of all three reactions and provide conclusions and guidance for nuclear spectroscopy application of deep-inelastic heavy ion reactions. Some results of this study were already presented as part of a Ph.D. Thesis [31] and briefly outlined in [32].

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2. Experiment and analysis 2.1. Experimental procedure Both 130 Te + 64 Ni and 208 Pb + 58 Ni experiments were performed at Laboratori Nazionali di Legnaro (INFN) using the GASP multi-detector Germanium array as the principal device for gamma coincidence measurements. For the 130 Te run the 275 MeV 64 Ni beam the beam delivered by the XTU Tandem accelerator impinged on a 1.2 mg/cm2 thick 99% enriched 130 Te target evaporated on a 14 mg/cm2 208 Pb backing. The beam energy at the surface of the target corresponded to a collision at 13% above the Coulomb barrier. In case of the second experiment, the 58 Ni beam from the Tandem was post-accelerated by the ALPI superconductive accelerator [33] to an energy of 345 MeV. This experiment was one of the commissioning runs of the ALPI accelerator. The beam was focused on a very thick 200 mg/cm2 99% enriched 208 Pb target. The collision energy was about 12% above the Coulomb barrier. In both experiments the beam was pulsed with a 200 ns pulse repetition rate to allow for a clean separation of in- and off-beam events. The gamma-ray energies and time signals with respect to the beam pulse were collected for each of the 40 Germanium detectors of the GASP array [34] in configuration I which provided the total photo-peak gamma detection efficiency of about 3% (for 1332 keV gammas). The reaction products were stopped inside the target or backing material. Discrete gamma transitions not broadened by the Doppler effect were observed for deexcitation of states with half-life and/or feeding time longer than a few picoseconds. The 130 Te + 64 Ni experiment was followed by offline short- and long-lived radioactivity measurements. Additionally, the short-lived isotopes were identified and their production yields were determined from a measurement in which the beam pulsing was extended to 14 ms (1 ms beam-on and 13 ms beam-off periods) [35] and the GASP array was set to collect single gamma events in the off-beam time range. This data allowed for identification of isomeric and radioactive decays with half-lives longer than a few milliseconds. 2.2. Analysis of the product distribution The main goal of the analysis was to reconstruct detailed and complete distributions of isotopes produced in the collisions. We were able to obtain those by combining results from the analysis of the off- and in-beam γ –γ coincidence data, and, for the 130 Te + 64 Ni system, by measurements of radioactive decay of isotopes produced and stopped in the target. The procedure was similar to that applied to the 208 Pb + 64 Ni system, described in [1]. In the analysis of complex radioactive decay spectra relative activity of each produced isotope was established using known decay intensities from the Reus–Westmaier tables [36]. The direct production yields were then calculated taking into account the time of irradiation and, in more complex cases, the contribution from sequential decays. In all, production yields for 44 radioactive isotopes produced in 130 Te + 64 Ni collisions were established from the combined short- and long-lived radioactivity analysis. In both reported experiments the conditions were suitable for clean separation of off-beam γ –γ coincidence events from the prompt events. The obtained off-beam coincidence spectra were practically background free. By measuring off-beam coincidences one can in principle observe all decays in which at least two gammas are emitted in coincidence. The beam pulsing cycle of 200 ns allowed for identification of 120 radioactive and isomeric decays for the 130 Te + 64 Ni

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system and about 170 decays for the 208 Pb + 58 Ni reaction. The life-times of the identified decaying states range from a few hours down to tenths of nanoseconds. We were also able to set upper intensity limits for a number of radioactive decays which could not observed. The analysis which converted the measured coincidence intensity into the production yields was based on the most recent Nuclear Data Sheets compilations. Examples of the off-beam gamma coincidence spectra used for production yield analysis for the earlier discussed 208 Pb + 64 Ni reaction were published in Refs. [1,31]. The determination of yields from the in-beam γ –γ coincidence analysis was more difficult and, as a consequence, provided less accurate results. One of the difficulties is the complexity and relatively high background present in the in-beam gamma coincidence data. Moreover, the interpretation of the obtained results requires a knowledge of the population of individual states and their deexcitation cascades in a given reaction product. In other words, one needs to estimate how much of the total production yield is represented by the observed coincidence intensity of two specific transitions. For deep-inelastic reaction products which arise in collisions involving massive transfer of nucleons it turned out the population of excited states is predominantly yrast. Thus, for even–even fragments, the intensity of the lowest 4+ → 2+ → 0+ yrast cascade usually represents the bulk of the production yield. Obvious difficulties arise in odd products, which have more complicated patterns of yrast excitations. In case of many odd isotopes a complete analysis of all possible coincidence cascades was not possible. Instead, the production yield was estimated based on the values firmly established for neighboring isotopes and/or element chains. Also, the presence of isomeric states in some of the populated nuclei required dedicated analysis. The population of the isomeric states extracted from the off-beam data was added to the observed in-beam population. To summarize, the analysis of the in-beam coincidence data was used for cases not suitable for radioactivity and off-beam coincidence analysis, especially for stable isotopes. The difficulties outlined above are reflected by typically larger errors. A number of well established values obtained for the same isotopes from the in-beam and off-beam analysis as well as from the radioactive decay spectra were used to normalize all production yields to common relative units which were later converted to absolute cross-section values. 2.3. Absolute cross-section normalization The obtained product yield distributions include about 220 isotopes for the 130 Te + 64 Ni collisions and over 260 isotopes for the 208 Pb + 58 Ni system. For those nuclei relative production yields have been established with 10 to 40% accuracy taking into account all possible sources of errors. In order to convert these results into an absolute cross-section scale we compared our results with the cross-section values reported previously for similar colliding systems. Such a cross-section determination is not very accurate (we estimate it to be correct within a 50% error margin), yet it allows us to present the production yield results in absolute units to give a direct sense of the population intensity. For the 130 Te + 275 MeV 64 Ni reaction, apart from dominating binary processes, an abundant fusion–evaporation channel is present. The fusion–evaporation populates mainly Hg isotopes which arise after a few neutron evaporation from the 194 Hg compound system. From the gamma coincidence data we firmly established the relative production yield of those products and compared our results with the systematics of evaporation residue cross-sections measured for the 64 Ni + 124 Sn system by Lesko et al. [37]. Both 124 Sn and 130 Te are the most neutron-rich stable isotopes of the respective Z = 50 and 52 elements which allows for a direct comparison. More-

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Table 1 Cross-sections of one and two neutron transfer processes induced on 58 Ni projectiles in bombardments of 208 Pb target. Reaction (58 Ni, 57 Ni) (58 Ni, 59 Ni) (58 Ni, 60 Ni)

208 Pb + 375 MeV 58 Ni Ref. [38] (mb)*

208 Pb + 345 MeV 58 Ni

11 265 61

6.6 (10) 253 (30) 61 (7)

this work (mb)

* No errors given.

over, in [37] the energy dependence of the cross-section for energies close to the Coulomb barrier has been determined. Based on those results we adopted a total fusion–evaporation cross-section of 160 mb for a center-of-mass collision energy of 184 MeV, i.e. at the energy of our experiment. We assume a 50% systematic error which is due to the transformation from 64 Ni + 124 Sn to 130 Te + 64 Ni system and to the spread in the experimental collision energy caused by slowing down of the projectile within the 1.2 mg/cm2 thick 130 Te target. For the 208 Pb + 345 MeV 58 Ni system we compared the total measured reaction cross-section with the 58 Ni + 1215 MeV 208 Pb inverse kinematics measurement reported by Sapotta et al. [27]. The total reaction cross-section of 1035(45) mb given in [27] was used to normalize the production yields obtained in our measurement. The two reactions converted into the center-of-mass reference system have very similar collision energies of ECM = 270 and 265 MeV, respectively. It is to be noted, that in the thick target experiment the beam energy was degraded throughout the target material down to Coulomb barrier and consequently our production yield results relate to an integrated cross-section. To account for this effect we adopt a conservative estimate of 50% uncertainty for the absolute cross-section scale. To confirm this production yield normalization we compared cross-sections for population of specific nuclei obtained from our study with those reported by other authors. In particular, the transfer of one and two nucleons from/to medium mass projectiles bombarding a 208 Pb target has been investigated [38]. In Table 1 we compare the cross-sections for (58 Ni, 57 Ni), (58 Ni ,59 Ni) and (58 Ni, 60 Ni) transfers induced on 208 Pb reported previously and obtained in this work at a similar collision energy. A reasonable agreement of cross-sections with the listed values supports our absolute cross-section normalization. It should be noted that the main purpose of our estimates of absolute cross-sections is to provide guidelines useful for spectroscopic applications. It turns out that isotopes produced in deep-inelastic reactions with cross-sections as low as tens of microbarns can be studied by selective gamma coincidence analysis. 2.4. Gamma cross-coincidence analysis The good quality of the experimental data allowed us to observe and analyze the crosscoincidence relations between gammas emitted from the excited nuclei that appeared as partners in the binary reaction exit channel. In such analysis both final reaction products are recognized by characteristic gamma-ray energies, which provides full identification of the reaction, including direct information on the number of nucleons evaporated from the primary collision products. An example of a cross-coincidence spectrum is shown in Fig. 1. In the 130 Te + 64 Ni reaction data the gate was set on the 1425 keV 2+ → 0+ transition in 66 Ni. The coincidence spectrum shows predominantly other lines from 66 Ni, but includes also gamma transitions that belong to Te isotopes – target-like fragments complementary to 66 Ni. The observed gamma transitions from several Te isotopes ranging from 128 Te to 124 Te identify processes in which up to 4 neutrons are

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Fig. 1. In-beam coincidence spectrum gated on 1425 keV 2+ → 0+ transition in 66 Ni (130 Te + 64 Ni experiment). Strong lines from 66 Ni and from 124–128 Te partner nuclei are identified and labelled.

evaporated from the primary fragments. Such cross-coincidence analysis could be performed in a number of favorable cases yielding direct experimental information on the neutron evaporation process. It was crucial for the reconstruction of the primary fragments distribution as will be described in Section 4. 3. Distributions of reaction products 3.1. Products of 130 Te + 275 MeV 64 Ni collisions The complete list of final reaction products established for the 130 Te + 275 MeV 64 Ni collisions is given in Table 2. The cross-section values are in microbarn units. The errors reflect the uncertainty of the experimental procedure of relative yield determination but does not include the uncertainty of the absolute cross-section normalization. Yield values correspond to direct production of each nucleus. If determined from radioactive decay data the yield corresponds to the sum of all decay branches with the population from the preceding decay chain subtracted. The method of analysis used for yield determination of specific isotope is given in the last column of Table 2, using the following symbols: a. – yield established from radioactivity measurements, af. – yield established from radioactivity measurements and confirmed by the off-beam gamma coincidence analysis, f. – from off-beam gamma coincidence data, i. – from in-beam coincidence data, fi. – from both off- and in-beam coincidences. For some nuclei the experimental yield determination was very difficult or impossible due to the lack of spectroscopic information. In such cases the production yield was interpolated basing on firm results obtained for two neighboring

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nuclei – such values are marked in the tables by an e. – “estimated” note. The adopted errors for such estimated values are large enough to allow for possible odd-even staggering effects. For regions of lowest cross-sections only scattered results are available for isotopes with decays most favorable for gamma coincidence observation. The distribution of binary reaction products in the N − Z plane is displayed in Fig. 2. The size of each black square is proportional to the production yield of a given isotope. The isobar projected mass distribution of products is shown in Fig. 3. Both Figs. 2 and 3 do not show the fusion–evaporation residues (Hg isotopes) which are included in Table 2. The established total reaction cross-section is dominated by binary processes amounting to about 1240(180) mb for the combined contribution of fusion–fission, deep-inelastic and quasielastic processes and 162(9) mb for the fusion–evaporation channel. The distribution of Fig. 3 shows products of quasielastic and deep-inelastic reactions located within prominent broad peaks around the target and projectile mass. The deep-inelastic reaction Table 2 Products of the 130 Te + 275 MeV 64 Ni reaction. See text for details. Isotope

σ (µb)

53 V

< 450 650 (80) 900 (300)

54 V 55 V 52 Cr 53 Cr 54 Cr 55 Cr 56 Cr 57 Cr 55 Mn 56 Mn 57 Mn 58 Mn 59 Mn 60 Mn 61 Mn 62 Mn 58 Fe 59 Fe 60 Fe 61 Fe 62 Fe 63 Fe 64 Fe 59 Co 61 Co 62 Co 63 Co 64 Co 65 Co 66 Co

a. f. af.

< 60 < 150 500 (250) 1000 (500) 1500 (250) 4000 (740)

i. i. i. i. i. f.

300 (150) 1000 (500) 2200 (800) 2850 (250) 5000 (500) 1800 (250) 1000 (500) 250 (30)

i. f. a. af. f. af. e. f.

200 (100) 1200 (600) 7400 (1000) 18 500 (1500) 26 000 (2500) 26 500 (2500) < 5000

i. a. i. af. a. af. e.

< 500 18 000 (10 000) 12 500 (2500) 16 000 (5000) 7000 (5000) 2500 (2000) 280 (30)

i. a. af. f. af. e. af.

Isotope

σ (µb)

60 Ni

125 (25) 330 (150) 8000 (1000) 36 000 (10 000) 720 000 (70 000) 130 000 (15 000) 56 000 (4000) 7500 (1500) 1000 (150) 180 (40)

i. i. i. i. i. af. a. f. fi. f.

72 Ga 1700 (500) 73 Ga 2000 (700)

< 180 750 (150) 1500 (500) 2700 (500) 9000 (2000) 3600 (1000) 3300 (800) 1050 (150) 250 (200)

i. fi. e. fi. a. f. f. f. e.

79 Ge

1500 (250) 1400 (200) 1600 (200) 1800 (300) 2200 (200) 1600 (150) 1700 (300) < 600

i. f. i. e. i. f. a. f.

81 Se

100 (50) 550 (100) 600 (200) 1000 (500)

f. i. i. e.

61 Ni 62 Ni 63 Ni 64 Ni 65 Ni 66 Ni 67 Ni 68 Ni 69 Ni 63 Cu 64 Cu 65 Cu 66 Cu 67 Cu 68 Cu 69 Cu 70 Cu 71 Cu 66 Zn 67 Zn 68 Zn 69 Zn 70 Zn 71 Zn 72 Zn 73 Zn 68 Ga 69 Ga 70 Ga 71 Ga

Isotope

74 Ga 1850 (200) 75 Ga 500 (150) 76 Ga

310 (80)

74 Ge 1700 (500) 75 Ge 1700 (500) 76 Ge 1650 (250) 77 Ge 1050 (200) 78 Ge

Isotope

σ (µb)

900 (200) < 200

85 Kr

89 Kr

3500 (500) 3600 (400) 2250 (250) 700 (150) < 350

i. e. i. f. i. f.

84 Rb

420 (80)

76 As 1500 (1000) f. 77 As 2500 (1500) f. 78 As 2700 (400) 79 As 1500 (500) 80 As 1400 (200) 78 Se 79 Se 80 Se 82 Se 83 Se 81 Br 82 Br 83 Br 84 Br 85 Br 86 Br 82 Kr

σ (µb)

f. f. f. f. f.

f. f. f.

550 (100) 1000 (500) 3000 (500) 2500 (500) 1700 (200) 800 (100)

i. i. i. e. i. f.

1500 (250) 3900 (400) 3700 (400) 3400 (400) 1700 (500) 350 (40)

f. a. fi. f. f. f.

300 (150) i. 83 Kr 1500 (1000) e. 84 Kr 3600 (600) fi.

86 Kr 87 Kr 88 Kr

e. i. f. f. f.

a. i. a. 87 Rb 3300 (400) i. 88 Rb 3500 (1000) f. 89 Rb 3700 (300) f. 90 Rb 1850 (250) f. 91 Rb < 1500 f. 85 Rb 1500 (750) 86 Rb 2800 (500)

86 Sr 87 Sr 88 Sr 89 Sr 90 Sr 91 Sr 92 Sr 93 Sr 94 Sr 88 Y 89 Y 90 Y 91 Y 92 Y 93 Y 94 Y 95 Y 96 Y

200 (100) 1000 (400) 2000 (500) 3000 (750) 4000 (500) 2500 (750) 2800 (400) 1650 (250) < 1000

fi. i. i. i. i. f. f. f. f.

850 (150) 1250 (500) 2000 (400) 3500 (1000) 4700 (1500) 4700 (700) 3000 (500) 2300 (300) 350 (50)

a. i. f. e. f. f. f. f. f.

(continued on next page)

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Table 2 (Continued) Isotope 90 Zr 91 Zr 92 Zr 93 Zr 94 Zr 95 Zr 96 Zr 97 Zr 98 Zr 99 Zr

σ (µb) 300 (150) 1000 (500) 2000 (400) 2500 (500) 3000 (500) 3000 (500) 3100 (300) 1500 (500) 800 (250) 400 (100)

95 Nb

Isotope a. e. i. e. i. a. i. f. i. f.

2100 (600) 3000 (750) 97 Nb 3500 (800) 98 Nb 4200 (700) 99 Nb 4000 (800) 100 Nb 3700 (500) 101 Nb 2000 (1000) 102 Nb 400 (100)

a. f. e. f. e. f. e. f.

92 Mo

180 (50) 200 (50) 500 (500) 500 (500) 1150 (250) 2500 (1000) 3700 (400) 6800 (1500) 6150 (600) 3300 (1000) 1700 (250) 500 (500)

fi. fi. e. e. i. e. i. a. i. f. i. e.

106 Tc

150 (50) 500 (500) 1000 (1000) 1000 (500) 2100 (250) 3000 (1000) 4650 (350) 5600 (1000) 3600 (400) 1250 (500) 500 (150)

a. e. e. e. f. e. f. f. f. f. f.

97 Ru

320 (40)

a.

96 Nb

93 Mo 94 Mo 95 Mo 96 Mo 97 Mo 98 Mo 99 Mo 100 Mo 101 Mo 102 Mo 103 Mo 96 Tc 97 Tc 98 Tc 99 Tc 100 Tc 101 Tc 102 Tc 103 Tc 104 Tc 105 Tc

98 Ru 99 Ru 100 Ru 101 Ru 102 Ru 103 Ru 104 Ru 105 Ru 106 Ru 107 Ru 108 Ru 104 Rh 105 Rh 106 Rh 107 Rh 108 Rh 109 Rh 110 Rh 106 Pd 107 Pd 108 Pd 109 Pd 110 Pd 111 Pd 112 Pd 113 Pd 114 Pd

σ (µb)

σ (µb)

Isotope

σ (µb)

500 (500) 1350 (200) 1300 (500) 1750 (250) 1500 (300) 1150 (300) 350 (200)

e. f. f. f. e. f. f.

127 I

25 (15) 500 (100) 1000 (250) 1400 (400) 1750 (300) 1750 (300) 1750 (250) 1200 (400) 750 (150) 500 (250) 300 (150)

f. a. f. e. fi. e. fi. e. fi. e. fi.

5000 (2000) 8500 (1500) 12 500 (2500) 17 000 (3000) 38 000 (5000) 6800 (500) 5500 (1500) 650 (150)

e. f. e. a. a. f. af. f.

650 (100) 3000 (800) 8500 (1000) 15 500 (4000) 28 000 (4000) 22 000 (6000) 4300 (500) < 400 50 (25)

i. e. i. a. fi. a. fi. e. f.

250 (50) 800 (500) 2150 (250) 2300 (300) 2350 (250) 2400 (400) 2250 (600) 2800 (250) 900 (150) 850 (100) 150 (70)

a. e. a. e. a. e. af. a. f. f. f.

1000 (1000) 2500 (1000) 4700 (700) 2000 (1000) 500 (80)

e. i. a. f. a.

138 Ba

350 (150) 750 (250) 1150 (250) 1100 (300) 1100 (150) 700 (300) 250 (50)

i. e. fi. e. fi. e. f.

i. e. i. i. i. e. i. af. fi. af. a. f.

135 La

200 (100)

i.

136 Ce

142 Ce

50 (50) 100 (70) 100 (50) 100 (70) 200 (25) 100 (100) < 50

i. e. f. f. f. e. i.

142 Nd

15 (15)

i.

133 Te

< 200 800 (500) 2000 (300) 4000 (1500) 10 000 (1000) 20 000 (7000) 46 000 (5000) 140 000 (15 000) 600 000 (50 000) 34 000 (3000) 9000 (800) < 150

189 Hg

5000 (500)

a.

126 I

1500 (500)

a.

Isotope 115 In

500 (200) 300 (300) 230 (200) 800 (800) 1700 (300) 2800 (700) 5000 (500) 4800 (800) 3300 (500) 2300 (400) 200 (150)

i. e. i. e. i. fi. i. f. i. f. i.

500 (500) 1500 (1000) 2600 (250) 3300 (800) 3200 (500) 1850 (350) 1000 (400)

e. e. f. f. f. f. f.

120 Sn

300 (100) 1000 (500) 1800 (300) 2500 (500) 3000 (400) 2200 (500) 1400 (250) 500 (500) < 100

i. e. i. e. i. e. i. e. i.

120 Sb

116 In 117 In 118 In 119 In 120 In 121 In 116 Sn 117 Sn 118 Sn 119 Sn 121 Sn 122 Sn 123 Sn 124 Sn 125 Sn 126 Sn 121 Sb 122 Sb 123 Sb 124 Sb 125 Sb 126 Sb 127 Sb 128 Sb

500 (500)

129 Sb

110 Ag 1500 (750) 111 Ag 1500 (750)

122 Te

109 Ag

e. e. e. 112 Ag 2400 (600) f. 113 Ag 3400 (1000) f. 114 Ag 1000 (1000) e. 110 Cd 111 Cd 112 Cd 113 Cd 114 Cd 115 Cd 116 Cd 117 Cd 118 Cd

550 (100) 650 (200) 750 (150) 1500 (500) 2150 (300) 2000 (400) 1650 (250) 1000 (500) 250 (100)

i. e. i. e. i. e. i. e. i.

130 Sb 123 Te 124 Te 125 Te 126 Te 127 Te 128 Te 129 Te 130 Te 131 Te 132 Te

128 I 129 I 130 I 131 I 132 I 133 I 134 I 128 Xe 129 Xe 130 Xe 131 Xe 132 Xe 133 Xe 134 Xe 135 Xe 136 Xe 132 Cs 133 Cs 134 Cs 135 Cs 136 Cs 132 Ba 133 Ba 134 Ba 135 Ba 136 Ba 137 Ba

137 Ce 138 Ce 139 Ce 140 Ce 141 Ce

190 Hg 100 000 (5000) af. 191 Hg 53 000 (3000) af. 192 Hg

3700 (500)

i.

products extend over a wide range of masses corresponding to increasing transfer of nucleons. Tails of this distribution overlap with products of fusion–fission process which fill the central part of the plot. The general trend to equilibrate the mass asymmetry can be clearly seen by asymmetry of peaks in the vicinity of the target and projectile. As in the previously reported

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Fig. 2. Distribution of the binary products of 130 Te + 275 MeV 64 Ni collisions. The size of each black square is proportional to the production yield of an isotope.

Fig. 3. Mass distribution of the binary products of 130 Te + 275 MeV 64 Ni collisions.

180

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208 Pb + 64 Ni

reaction [1] very neutron rich Ni isotopes are populated in processes which involve neutron pick-up by the 64 Ni projectile up to 69 Ni.

3.2. Products of 208 Pb + 345 MeV 58 Ni collisions The identified final reaction products of the 208 Pb + 345 MeV 58 Ni collisions are listed in Tables 3 (mass range 40 < A < 140) and 4 (mass range 170 < A < 220). The same notes and explanations as those given in Table 2 apply to Tables 3 and 4. The distribution of reaction products on the N–Z plane is displayed in Figs. 4 and 5 and the mass distribution is shown in Fig. 6. The product distribution for the 208 Pb + 58 Ni colliding system is less complete than for the previously discussed reactions since in this case the off line radioactivity was not measured. Instead, whenever possible, off-beam coincidence analysis was used to extract production yield information for longer lived radioactive isotopes with appropriate corrections accounting for production time. For many isotopic chains the only information available comes from in-beam gamma coincidence analysis of yrast cascades. The results obtained for the 208 Pb + 58 Ni system can be compared with those of the 208 Pb + 64 Ni measurement [1]. In Fig. 7 the distribution of heavy fragments of the 64 Ni induced reaction is presented, with the mass distribution shown in the inset. One notices that the population of most heavy target-like fragments for 58 Ni induced collisions is reduced, their distribution does not extend as far as for the 64 Ni induced reaction. Another striking feature is the appearance of a broad “island” of intermediate mass nuclei in the 80 < A < 130 mass range – compare Fig. 6 and the mass distribution inset in Fig. 7. The nuclei located within this “island” are produced in fission of excited heavy target-like fragments arising in deep-inelastic collisions. The center of mass of the observed “island” corresponds well to the 1/2 of the average mass of heavy fragments above 208 Pb for which fission is expected to appear. It is worthwhile to note that for both systems involving 58 Ni and 64 Ni collisions on 208 Pb the used beam energies were significantly below the threshold needed for complete fusion and correspondingly only traces of products are observed in the region expected for the symmetric fission of the compound system. The explanation of the strong enhancement of the discussed mass 80 < A < 130 “island” of products in the 58 Ni case compared to the 64 Ni is related to N/Z equilibration process in deep-inelastic reactions. The more intense flow of protons from the small N/Z 58 Ni to the 208 Pb target populates heavy fragments with higher Z than for the 64 Ni projectile which therefore are more susceptible to undergo fission. This N/Z equilibration effect can be directly seen comparing heavy fragment distributions obtained for 58 Ni (Fig. 5) and 64 Ni projectiles (Fig. 7). Unlike for the 208 Pb + 64 Ni system, the formation of isotopes of Z < 82 elements such as Tl, Hg, Au and Pt is less favored in the 208 Pb + 58 Ni system. Instead, higher production yields are found for isotopes of Z > 82 elements: Bi, Po, At, Rn and even Fr and Ra. The flow of neutrons between the target and projectile is directed in the opposite way. One notes that in 58 Ni induced reactions no isotopes with neutron number N > 126 are created, except for 212 Pb which can be populated in quasielastic alpha particle transfer. At the same time one observes abundant population of isotopes with N < 126. Combined with the effect of neutron evaporation from excited fragments it results in population of such light Pb isotopes as 194 Pb – 14 neutrons away from the target. In the projectile-like fragment distribution, the strong absorption of neutrons by the projectile is demonstrated by the extended population of Ni isotopes, which ranges from 58 Ni to 67 Ni – up to 9 neutrons are transferred. This dramatic N/Z equilibration effect for the 208 Pb + 58 Ni system is illustrated by gamma coincidence spectra of Fig. 8. Using the in-beam coincidence data with gates set on the most intense 2+ → 0+

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Table 3 Light and medium-mass fragments produced in 208 Pb + 345 MeV 58 Ni collisions. See text for details. Isotope 48 Sc 50 Sc 51 Sc 44 Ti

Isotope

σ (µb) 370 (150) 110 (15) < 100

f. f. f.

50 Ti

< 200 720 (200) 740 (200) 570 (150)

i. i. i. i.

54 V

1250 (150)

f.

46 Ti 48 Ti

50 Cr 51 Cr 52 Cr 53 Cr 54 Cr 55 Cr 50 Mn 51 Mn 52 Mn 53 Mn 54 Mn 55 Mn 56 Mn 57 Mn 58 Mn 59 Mn 60 Mn 53 Fe 54 Fe 55 Fe 56 Fe 57 Fe 58 Fe 59 Fe 60 Fe 61 Fe 62 Fe 54 Co 55 Co

··· 62 Co 63 Co 64 Co 56 Ni

63 Ni 64 Ni 65 Ni 66 Ni 67 Ni 68 Ni 58 Cu

i. i. i. i. i. i.

30 (20) 500 (200) 2300 (300) 2500 (500) 3000 (300) 10 000 (5000) 16 600 (1600) 10 000 (4000) 4100 (400) 2000 (1000) 240 (60)

f. i. f. e. i. e. f. e. f. e. f.

65 Cu

300 (100) 1300 (200) 4000 (2000) 41 000 (5000) 20 000 (8000) 9600 (1000) 6000 (2000) 3500 (500) 1320 (150) 300 (100)

f. fi. e. i. e. i. e. i. f. i.

71 Zn

100 (50) 1000 (200)

f. f.

900 (400) 6600 (1000) 58 Ni 730 000 (60 000) 59 Ni 253 000 (30 000) 60 Ni 61 000 (7000) 57 Ni

61 Ni 10 000 (4000) i. 62 Ni 4800 (1000) i.

800 (200) 900 (300) 1200 (300) 2100 (400) 2700 (500) 500 (200)

8600 (700) 4000 (2000) 700 (250)

f. e. f. f. f. i. i. i.

Isotope

σ (µb)

59 Cu 60 Cu 61 Cu 62 Cu 63 Cu 64 Cu 66 Cu 67 Cu 68 Cu 69 Cu 70 Cu 66 Zn 67 Zn 68 Zn 69 Zn 70 Zn 72 Zn 69 Ga 70 Ga 71 Ga 72 Ga 73 Ga 74 Ga 70 Ge 72 Ge 74 Ge 77 Ge 77 As 78 As 76 Se 78 Se 80 Se 82 Br 84 Br 86 Br

3500 (1000) 2000 (500) 2900 (900) 680 (150) 255 (50) < 15

e. i. f. i. f. f.

230 (100) 7000 (1500) 5200 (300) 9400 (1500) 9000 (4000) 6000 (3000) 3500 (1000) 3200 (700) 2800 (600) 1800 (600) 900 (200) 500 (300) 120 (30)

f. f. f. f. e. e. f. i. f. e. f. f. f.

2600 (400) 2300 (400) 1900 (400) 1400 (400) 1000 (200) 450 (50) 150 (100)

i. e. i. e. i. f. i.

1500 (1500) 3000 (500) 2200 (600) 1500 (200) 1000 (400) 390 (50)

e. fi. e. f. e. f.

2350 (300) 2030 (300) 1200 (300) 120 (60)

i. i. i. f.

1040 (200) 1000 (300)

f. f.

1100 (300) 800 (300) 400 (300)

i. i. i.

1260 (300) 340 (50) 150 (80)

f. f. f.

84 Kr 86 Kr 87 Kr 88 Kr 89 Rb 90 Rb 84 Sr 86 Sr 88 Sr 90 Sr 86 Y 90 Y 92 Y 93 Y 94 Y 95 Y 96 Y 88 Zr 90 Zr 92 Zr 94 Zr 96 Zr 97 Zr 98 Zr 99 Zr 96 Nb 98 Nb 100 Nb 92 Mo 93 Mo 94 Mo 96 Mo 98 Mo 100 Mo 102 Mo 104 Mo 96 Tc

σ (µb) 360 (150) 500 (150) 200 (100) 280 (150)

Isotope i. i. f. f.

450 (70) f. 350 (100) f. 230 (50) 980 (150) 640 (100) 500 (150)

i. fi. i. i.

100 (80) 740 (90) 1000 (500) 500 (200) 650 (150) 600 (300) 120 (40)

f. f. f. f. f. f. f.

240 (50) 600 (100) 720 (150) 530 (150) 400 (100) 400 (100) 400 (200) 180 (60)

f. f. i. i. i. f. i. f.

870 (130) f. 970 (80) f. 720 (80) f. 80 (40) 120 (60) 160 (40) 350 (80) 430 (60) 790 (120) 530 (70) 120 (40)

f. f. fi. i. i. i. i. i.

70 (30)

f.

100 Tc 1500 (300) f. 102 Tc 1100 (200) f. 104 Tc 106 Tc 98 Ru

700 (100) f. 40 (40) f.

300 (150) 300 (200) 102 Ru 400 (100) 104 Ru 600 (150) 105 Ru 1000 (500) 100 Ru

i. i. i. i. f.

σ (µb)

106 Ru 660 (100) i. 107 Ru 800 (400) f. 108 Ru 360 (90)

i.

106 Rh 480 (150) f. 108 Rh 760 (70) f. 109 Rh 900 (300) f. 110 Rh 700 (150) f. 102 Pd

< 80

i.

104 Pd 430 (200) i. 105 Pd 400 (100) f. 108 Pd 400 (100) i. 110 Pd 410 (100) i. 112 Pd 220 (70)

i.

102 Ag

f.

60 (30)

105 Ag 140 (60) f. 112 Ag 900 (300) f. 110 Cd 270 (80) i. 112 Cd 660 (200) i. 114 Cd 300 (100) i. 116 Cd 290 (80) i. 117 Cd 300 (90) 118 Cd < 70

f. i.

116 In 700 (100) f. 117 In 500 (120) f. 118 In 360 (70) 120 In < 100

f. f.

114 Sn 100 (20) 116 Sn 330 (50)

f. f. 118 Sn 320 (60) f. 120 Sn 300 (100) f. 122 Sn 105 (25) f. 120 Te

< 120

i.

122 Te 360 (80) i. 124 Te 590 (120) i. 126 Te 120 (60)

i.

122 Xe

i. i. i.

40 (40)

124 Xe 200 (60) 126 Xe 120 (60) 128 Ba

80 (50) 80 (60) 130 Ba 240 (80) 132 Ba 50 (30)

i. f. i. i.

130 La

f.

129 Ba

< 50

132 La 200 (100) f.

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Table 4 Heavy fragments produced in 208 Pb + 345 MeV 58 Ni collisions. See text for details. Isotope

σ (µb)

178 Hf

140 (40)

f.

178 W

< 100 100 (80) 200 (80) < 70

i. i. i. i.

180 W 182 W 184 W 178 Os

Isotope

σ (µb)

Isotope

σ (µb)

190 Tl

300 (150) 2150 (400) 5600 (700) 6400 (800) 3800 (700) 2500 (500) 1600 (300) 1500 (300) 620 (80) 270 (100) 200 (50) 100 (50) < 50

f. f. f. f. f. f. f. f. f. f. f. f. f.

210 Pb

< 100

f.

198 Bi

1500 (1000) 2500 (700) 3400 (1500) 5400 (1000) 7300 (1500) 7500 (2000) 7500 (1500) 7900 (800) 10 000 (2000) 12 600 (1300) > 50 000

f. f. f. f. f. f. fi. fi. f. fi. f.

< 60 450 (100) 1500 (400) 2300 (400) 5800 (1000) 5200 (1000) 4500 (1000) 5800 (1000) 6000 (1500) 5800 (800) 7000 (1500) 9800 (1000) 18 700 (2500) 124 000 (15 000) 290 000 (40 000) 120 000 (15 000)

f. f. f. f. f. fi. f. fi. f. fi. f. fi. f. fi. fi. fi.

200 Po

450 (150) 1260 (200) 2700 (200) 4700 (600) 7700 (900) 9500 (1000) 14 900 (1500) 14 300 (2000) 14 000 (2000) 15 400 (2100) 13 700 (1800) 14 400 (2000) 300 (100)

f. fi. fi. fi. f. f. f. fi. f. fi. fi. fi. fi.

700 (300) 3800 (800) 7600 (800) 9300 (1000)

i. f. f. f.

192 Tl 194 Tl 196 Tl 197 Tl 198 Tl

186 Os

260 (70) 460 (80) 1020 (180) 1500 (500) 690 (140) 200 (100)

i. i. i. f. i. i.

184 Ir

1500 (400)

f.

207 Tl

184 Pt

600 (150) 2070 (300) 1660 (260) 1100 (300) 540 (150) 300 (100) 80 (40)

i. i. i. i. i. i. i.

192 Pb

190 Au 3000 (1000) f. 191 Au 1900 (500) f.

200 Pb

180 Os 182 Os 183 Os 184 Os

186 Pt 188 Pt 190 Pt 192 Pt 194 Pt 196 Pt

192 Au 1100 (400) 188 Hg 190 Hg 192 Hg 194 Hg 196 Hg 198 Hg 200 Hg

100 (100) 900 (200) 2100 (300) 1600 (350) 540 (200) 380 (100) 100 (100)

f. i. i. i. i. i. i. i.

199 Tl 200 Tl 201 Tl 202 Tl 204 Tl 206 Tl

194 Pb 195 Pb 196 Pb 197 Pb 198 Pb 199 Pb 201 Pb 202 Pb 203 Pb 204 Pb 205 Pb 206 Pb 207 Pb 208 Pb

199 Bi 200 Bi 201 Bi 202 Bi 203 Bi 204 Bi 205 Bi 206 Bi 207 Bi 209 Bi 199 Po 201 Po 202 Po 203 Po 204 Po 205 Po 206 Po 207 Po 208 Po 209 Po 210 Po 212 Po 203 At 204 At 205 At 206 At

Isotope

σ (µb)

207 At 10 500 (1500) f. 208 At 8600 (1500) f. 209 At

4900 (700) 5000 (800) 1700 (300)

f. fi. fi.

330 (100) 1230 (200) 3500 (800) 5800 (800) 5700 (800) 4300 (600) 3000 (500) 1100 (300) < 70

f. fi. f. fi. f. f. fi. f. f.

500 (300) 1840 (300) 2400 (400) 600 (100)

f. fi. f. f.

214 Ra

390 (60) 570 (80) 430 (80)

f. f. f.

215 Ac

70 (15)

f.

210 At 211 At 205 Rn 206 Rn 207 Rn 208 Rn 209 Rn 210 Rn 211 Rn 212 Rn 213 Rn 210 Fr 211 Fr 212 Fr 213 Fr 212 Ra 213 Ra

transitions the corresponding spectra document the production of subsequent even Ni isotopes with 2, 4, 6 and 8 neutron transfer. The off-beam gate was used to show the presence of the 67 Ni 9/2+ isomer arising in the 9 neutron transfer reaction. 3.3. Primary product distributions The reaction product yields discussed in the previous section refer to secondary, final products created after evaporation of particles, mainly neutrons, from the excited primary fragments. We will now discuss two procedures, which we combined and applied to the experimental data, to transform the secondary, post-evaporation product map into the primary, pre-emission one. Most of the fragments observed in the discussed reactions, with the exception of those in the vicinity of the 58 Ni projectile, are stable or neutron-rich nuclei. Therefore in the analysis, we assumed that only neutrons are evaporated from the excited primary fragments. In fact we did not observe any γ –γ cross-coincidences that would involve two fragments arising in processes in which protons or alpha particles are evaporated. Whereas some proton evaporation may take

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183

Fig. 4. Distribution of light and medium-mass fragments produces in 208 Pb + 345 MeV 58 Ni collisions. The size of each black square is proportional to the production yield of an isotope.

Fig. 5. Distribution of heavy fragments produced in 208 Pb + 345 MeV 58 Ni collisions. The size of each black square is proportional to the production yield of an isotope.

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Fig. 6. Mass distribution of fragments produced in 208 Pb + 345 MeV 58 Ni collisions.

Fig. 7. Distribution of heavy fragments produced in 208 Pb + 350 MeV 64 Ni collisions (from [1]). The size of each black square is proportional to the production yield of an isotope. The full mass distribution of the reaction products is shown in the inset.

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place from excited fragments located close to 58 Ni projectile of the 208 Pb + 58 Ni reaction, the further analysis of this case focuses on heavy fragment part where neutron evaporation dominates. Following this assumption one observes that the total charge of the target and projectile is preserved throughout the collision and equal to the total charge of the target-like and projectile-like final fragments. This means that final fragments are always complementary, with ZPLF + ZTLF = ZBEAM + ZTARGET . The procedure involved calculating the average mass for isotopes of each element. The established production rates were used as weights. As a result, for each combination of complementary elements the average total mass of the final fragments was obtained. By subtracting it from the mass of the incident ions we obtained the average number of evaporated neutrons. The results of this “missing-mass” analysis for the 130 Te + 64 Ni colliding system are summarized in Table 5. In order to reproduce the pre-emission distribution of products the calculated average number of evaporated neutrons was divided between the heavy and light complementary fragment proportionally to their masses. The primary product distribution was then obtained by shifting the secondary distribution of isotopes of each elements towards the more neutron-rich species by the obtained number of evaporated neutrons. For nuclei in the vicinity of the target and projectile this Z-dependent but isotope-independent procedure cannot be applied. This is due to the dominating contribution of quasielastic processes which do not involve large excitations of the fragments. Thus, an isotope-dependent, differential correction has to be used. The analysis of γ –γ cross coincidences described in Section 2.4 provided experimental data for the isotope-dependent mass shift procedure. The importance of such differential correction decreases at larger mass distances from the target and projectile. In Fig. 9 we show results of a systematic cross-coincidence analysis for the Te–Ni combination of elements, the complementary products of the 130 Te + 64 Ni collisions. Gates set on most intense Table 5 Average masses for isotopes of complementary elements populated in 130 Te + 275 MeV 64 Ni collisions. Each line represent a given proton transfer channel with Z1 + Z2 = ZTARGET + ZBEAM = 80. Average number of evaporated neutrons is calculated for each combination of elements. Errors reflect the uncertainty of the weighted average masses. Z1

A1 

Z2

A2 

p transfer

A1 + A2 

n evaporated

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

54.6 56.3 58.5 61.8 62.4 64.2 67.3 69.3 72.5 75.5 77.9 80.7 83.1 85.2 87.6 90.2 92.2 94.5

57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40

135.0 134.9 133.9 131.7 130.2 129.6 124.7 121.0 117.9 114.2 111.9 109.7 107.2 104.1 102.0 99.0 98.0 94.5

−5 −4 −3 −2 −1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12

189.6(16) 191.2(4) 192.4(4) 193.5(4) 192.6(4) 193.8(2) 192.0(2) 190.3(3) 190.4(3) 189.7(4) 189.8(5) 190.4(3) 190.3(3) 189.3(4) 189.6(4) 189.2(4) 190.2(3) 189.0(4)

4.4(16) 2.8(4) 1.6(4) 0.5(4) 1.4(4) 0.2(2) 2.0(2) 3.7(3) 3.6(3) 4.3(4) 4.2(5) 3.6(3) 3.7(3) 4.7(4) 4.4(4) 4.8(4) 3.8(3) 5.0(4)

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Fig. 8. Gamma coincidence spectra illustrating the population of Ni isotopes from 60 Ni to 67 Ni in 208 Pb + 345 MeV 58 Ni collisions. Gates set on the most intense 2+ → 0+ transitions show the production of subsequent even Ni isotopes. The off-beam gate was used to show the population of the 67 Ni 9/2+ isomer.

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Fig. 9. Results of the cross-coincidence analysis for Ni and Te isotopes produced in 130 Te + 64 Ni collisions. Gates were set on most intense transitions in 64–68 Ni isotopes. Data points indicate relative yields of Te partners observed in coincidence.

transitions in Ni isotopes displayed gamma lines from several corresponding Te reaction partners. The extracted intensities were used to estimate their probability of being populated in coincidence with the selected Ni isotope. By weighting each partner mass with the cross coincidence yield we deduced the average number of neutrons evaporated in processes that contribute to the production of a given Ni isotope. For the 130 Te + 64 Ni collisions, this procedure was performed for Ni–Te, Co–I, Fe–Xe and Cu–Sb pairs of complementary elements. It has to be noted that even such sophisticated analysis does not distinguish which of the two partners emitted neutrons. Thus, the obtained total number of evaporated neutrons had to be divided between the heavy and light partner proportionally to their mass. The scheme of reconstruction of the target-like primary products of 130 Te + 64 Ni collisions from the observed final products is shown in Fig. 10. Results of a similar analysis for the 208 Pb + 58 Ni system are presented in Fig. 11. In the right panels of Figs. 10 and 11 the average number of neutrons evaporated from isotopes of each element is shown as established from the “missing-mass” analysis. 4. Equilibration of the N/Z ratio To investigate the equilibration of the neutron-to-proton ratio we calculated from the primary product distributions the average N/Z value for isobars of each mass. In Fig. 12 we show the evolution of the neutron-to-proton ratio for all three of the studied systems, including the 208 Pb +

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Fig. 10. Reconstruction of the primary distribution of target-like products of the 130 Te + 64 Ni reaction from cross coincidence analysis. For each isotope the average number of neutrons evaporated in all processes that contributed to its formation is given. The average numbers of neutrons evaporated from isotopes of a specific element are listed on the right.

Fig. 11. Reconstruction of the primary distribution of target-like products of the 208 Pb + 58 Ni reaction from cross coincidence analysis. For each isotope the average number of neutrons evaporated in all processes that contributed to its formation is given. The average numbers of neutrons evaporated from isotopes of a specific element are listed on the right. 64 Ni results [1]. For the 208 Pb + 58 Ni system, N/Z

values only for heavy reaction products could be established, as the light product distribution is affected by the “island” of fission products at mass 80 < A < 130.

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Fig. 12. Experimental N/Z values for products of three studied reactions: (a) 130 Te + 275 MeV 64 Ni, (b) 208 Pb + 350 MeV 64 Ni [1] and (c) 208 Pb + 345 MeV 58 Ni (heavy products only). Dashed lines are drawn to indicate the N/Z ratios of the target, projectile and the compound system.

In all cases only in the closest vicinity of projectile and target the N/Z of products remains near the initial N/Z values marked by dashed lines. As soon as one departs from these mass numbers experimental values show a distinct trend to equilibrate N/Z ratios towards the full equilibration represented by compound system values. It is obvious that peripheral collisions involving mostly quasi-elastic processes dominate production yields for products located close

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to the projectile and target nuclei. Here the direction of small mass and charge transfer is governed rather by Q-optimum and only small part of yields come from deep-inelastic reactions. With larger mass transfer the increasing contribution of deep-inelastic processes is reflected by growing effect of the N/Z equilibration. Already about 5 mass units away from the initial values the N/Z equilibration process appears to be well advanced and saturates N/Z values at a constant level which however, is different from the full equilibration line. As pointed out earlier the 130 Te + 64 Ni system is the only case where the compound nucleus is formed with subsequent neutron evaporation or fission decay. The N/Z results displayed for this case in Fig. 12(a) clearly reflect this feature. For fragment masses of 80 < A < 110 which correspond to an almost symmetric fusion–fission mechanism the N/Z ratio equilibration appears to be complete. In binary product mass ranges where both deep-inelastic and fusion–fission reactions compete and cannot be separated the N/Z saturation level corresponding to deep-inelastic part cannot be as clearly established. Nevertheless, it appears that the full equilibration of the compound system is reproduced in the central fusion–fission part and deep-inelastic reaction products show incomplete N/Z equilibration. Another interesting feature that can be observed in Fig. 12 is that for all three studied systems the N/Z values determined for products corresponding to an increased mass asymmetry, i.e. with masses larger than the target and smaller than the projectile, the N/Z equilibration process appears to be even less effective. For these products the N/Z ratios are distinctly closer to the initial values than the saturation level observed for products arising in reactions in which the mass asymmetry is reduced. In the following we shall discuss a simple approach to interpret the observed features of the N/Z equilibration. In particular we shall try to understand why the equilibration trend saturates at an observed level of incomplete equilibration. We discussed some general concepts of the neutron-to-proton ratio equilibration in Refs. [1,2]. Following a historical approach of Swiatecki [15] we adapted a formula for the optimum N/Z value of fragments of a given mass, obtained by minimization of the liquid drop energy of two touching spherical nuclei. The N/Z equilibration results obtained in our work prompted Swiatecki to suggest a more general approach that involves a possible configuration of distant, non-touching nuclei at the scission point [39]. The motivation for this was the idea that during the collision both nuclei might attain strongly deformed shapes. Such deformation effects can be simulated by assuming a system of distant spheres, where the varying distance will reduce in a controlled way the Coulomb repulsion which is the most significant part of the minimized energy. In the lower panel of Fig. 13 the experimental N/Z results for the 130 Te + 64 Ni system are compared to the equilibration formula calculation (discussed in detail in Ref. [31]). The dashed line is drawn for a configuration of two touching spheres, representing the incident nuclei, the distance between their centers being d = 11 fm. The line indicates a very effective N/Z equilibration for all products and clearly does not follow the experimental points, except for the expected complete equilibration in the fusion–fission 95 < A < 115 mass range. The solid line which reproduces the experimental data much better shows the most probable N/Z value for a system of two spheres at a distance between the centers of d = 22 fm, thus separated by about 11 fm. It suggests that the equilibration formula properly describes the N/Z evolution trend for deep-inelastic reactions when an artificial increase of the distance between the two interacting nuclei is introduced. This distance parameter serves to simulate the effect of a possible deformation of colliding nuclei in the critical moment of interaction when the neutron and proton redistribution takes place.

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Fig. 13. Equilibration of the N/Z ratio for heavy fragments produced in 130 Te + 64 Ni collisions. In the lower panel the lines follow the equilibration formula for d = 11 fm touching spheres configuration (dashed line) and for d = 22 fm distant spheres configuration (solid line). In the upper panel the solid line shows results of the total energy minimization for d = 22 fm optimum distance. See text for details.

Since the liquid drop mass formula describes the average properties of nuclei, also the equilibration formula based on it accounts only for the general trend of the N/Z ratio evolution. In particular, any observed fluctuations of the experimental N/Z cannot be reproduced. We therefore tried an analogous procedure of total energy (reaction Q-value and Coulomb interaction) minimization which takes into account experimental nuclear masses [40]. The Coulomb repulsion term was calculated for a deformed system of two spheres connected by tangent cones [31]. In the upper panel of Fig. 13 results of such total energy minimization are compared with the experimental values. From the fit to the data the value of the separation distance parameter of d = 22 fm was obtained, implying a configuration of strongly deformed colliding nuclei. This corresponds with the value of d = 22 fm obtained from the equilibration formula fit to the data. However, the total energy minimization fit with experimental masses does not reproduce the data any better than the general equilibration formula. The agreement with some of the fluctuations of the N/Z data points seems to be accidental. In Fig. 14 we show experimental N/Z values for the target like fragments produced in the 208 Pb + 58 Ni collisions along with predictions of the equilibration formula (lower panel) and the energy minimization with experimental masses (upper panel). In this case none of the two curves calculated with the equilibration formula reproduce the experimental data correctly. The d = 12 fm touching spheres calculation (dashed line) is well below the data points, whereas the d = 21 fm distant spheres calculation (solid line) accounts only for the average trend with particular deviation observed for masses A > 210. In contrast, the experimental data are much better reproduced by the total energy minimization results presented in the upper part of Fig. 14. The agreement extends over a broad mass range, except for products in the vicinity of the target

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Fig. 14. Equilibration of the N/Z ratio for heavy fragments produced in 208 Pb + 58 Ni collisions. In the lower panel the lines follow the equilibration formula for d = 12 fm touching spheres configuration (dashed line) and for d = 21 fm distant spheres configuration (solid line). In the upper panel the solid line shows results of the total energy minimization for d = 21 fm optimum distance. See text for details.

and heavier. The discrepancy in the A ≈ 208 region is explained by strong contribution from quasielastic processes that are governed by other mechanisms and do not involve N/Z ratio equilibration. The discrepancy observed for the A > 210 fragments deserves some explanation. The probable reason for it is the fission of some excited target-like fragments in this mass range, discussed in Section 3.2. It changes the observed experimental N/Z values which refer only to the heavy fragments surviving fission. Fission of isotopes with a larger neutron excess is less likely and so the observed N/Z values are likely to be larger. The 208 Pb + 58 Ni system is probably best suited to study the charge and mass equilibration since it provides the largest space for the N/Z variation. Furthermore, fragments in the mass range below the A = 208 target mass are produced only via the deep-inelastic processes as the fusion–fission does not happen at the selected beam energy. The observed agreement suggests that the approach based on realistic (i.e. using experimental nuclear masses) energy minimization procedure accounts well for the equilibration effects. The proton and neutron redistribution results discussed in this work cannot be easily related to similar experimental studies based on fragment and particle detection. A qualitative comparison can be made with two such experiments in which 58 Ni and 64 Ni incident ions were used [27,30]. In both of them, the evolution of the neutron-to-proton ratio was measured as a function of the total kinetic energy loss during the collision. This quantity could not be observed in our experiment, since the established product distributions result from integration over all possible reaction dynamics. The only parameter which within a crude approximation can be related to the total energy loss is the mass transfer. Within this assumption one may conclude that results obtained in this work agree with previously observed features. Even at a relatively small mass transfer

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between two colliding nuclei a partial N/Z equilibration is achieved and the effect gradually increases at larger mass transfers corresponding to larger total kinetic energy losses. In some of the more recent studies population of nuclei far from stability via multinucleon transfer has been studied for similar target-projectile combinations with fragment spectrometers (see e.g. [41–43]). For the 208 Pb + 58 Ni system we could compare the cross-sections for proton stripping channels shown in [42] with our results. They agree reasonably well, for instance for 56 Fe, the (−2p) channel the values are 41(5) mb and 20 mb (this work and Ref. [42], respectively), for the (−3p) channel: 10(5) mb and 9 mb, respectively, and for the (−4p) channel: 2.7(5) mb and 4 mb, respectively. The cross-sections of Ref. [42] were established at a lower collision energy of 328 MeV and required an integration of the measured angular distributions to obtain total cross-section values. For the 208 Pb + 58 Ni system [42] the authors considered the correlations of number of stripped protons with the number of picked-up neutrons which are the prevailing direction of proton and neutron transfer between those colliding nuclei. They concluded that apparently the accompanying secondary neutron evaporation contributes more strongly as the number of stripped protons increases. The conditions of our thick target and integrated kinematics experiments do not allow for a direct comparison with these observations. However, from our results it is clear that besides the decisive role of the N/Z equilibration trend governing the transfer one observes enhanced neutron evaporation for products that involve larger mass transfer. It seems to be a natural consequence of the increased dissipation of energy for processes involving larger exchange of nucleons in any transfer direction. There are also some experimental characteristics of both methods – gamma coincidence measurements and particle and fragment detection experiments – that make them complementary. The mass and charge resolution in experiments based on the detection of fragments is much better for the light fragments than for the heavy ones. Consequently, the authors of such studies, usually discuss the evolution of the N/Z ratio for light reaction fragments only. In contrast to this, our method of analysis produces complete distributions of all products, independent on the considered mass range. The N/Z results derived from these distributions are even more complete and reliable for the heavy fragments. In this way the mass regions explored by both methods do not overlap but rather complement each other. Another complementary feature of present results comes from the full integration of reaction kinematics that cannot be avoided in thick target experiments. This prevents any model based extrapolations of the experimental data to include forward angles that are usually inaccessible in experiments based on direct fragment detection. 5. Conclusions on spectroscopic applications In the introductory part of the present work a number of references were given to display specific spectroscopic applications of deep-inelastic reactions to study nuclei that are not accessible in standard fusion–evaporation reactions. It was emphasized that the development of large gamma multi-detector arrays paved the way to use these complex reactions for yrast spectroscopy study of hard-to-reach nuclei in particular those located on the neutron-rich side of the stability valley. One of the important aims of this work was to investigate in a more systematic way how far one can reach with the neutron excess using the relatively simple thick target experiments. The conclusion drawn from the studied N/Z equilibration process shows some limitations in reaching very exotic neutron-rich nuclei. The full N/Z equilibration practically does not happen even for a very large mass transfer between the colliding ions. It has been observed for all of the studied systems, including the early result obtained for the neutron-deficient 106 Cd + 54 Fe sys-

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Fig. 15. Yield distributions for isobars of selected masses produced in the 208 Pb + 350 MeV 64 Ni reaction [1]. Lines are drawn to guide the eye.

tem [19], that the most probable N/Z of fragments arising in deep-inelastic reactions saturates at a level which is clearly different from the full equilibration value. In our considerations the mechanism responsible for the reduced ability to fully equalize the N/Z ratio is related to the strong dynamical deformation of nuclei in the critical moment of collision. In spite of this limitation a surprisingly broad range of hitherto unknown structures of neutron-rich nuclei could be studied when most neutron-rich stable isotopes are selected as initial colliding nuclei. At present the use of the 238 U target having largest N/Z ratio provides the best way to study neutron-rich nuclei located in regions close to the used projectile isotopes, preferably also neutron-rich (e.g. 48 Ca, 64 Ni, 76 Ge). However, in future the availability of appropriate radioactive beams may open new areas of neutron excess. The hitherto considered most probable N/Z ratios of final nuclei produced in deep-inelastic reactions define only the most easily accessible neutron richness. The real access range is determined by the experimental detection limit and depends on the variation of reaction yields for isobars around the maximum N/Z value. In Fig. 15 we show yield distributions for isobars of selected masses produced in the 208 Pb + 350 MeV 64 Ni reaction. A typical isobar yield distribution is rather narrow and limited to 3–4 isobars. It is also symmetrical, with the exception of isotopes close to the target and projectile – see the marked yield peak for 66 Ni production in the A = 66 isobars plot. In Fig. 16 we show distributions of reaction yields for isotopes of selected elements produced in the same colliding system. The isotopic distributions stretch over 8 to 10 mass units. For fragments produced in processes in which larger numbers of protons are transferred, i.e. going from Z = 30 (Zn) to Z = 32 (Ge) and Z = 34 (Se) isotopes, the distributions become increasingly flat. On the other hand, for Z = 26 (Fe) isotopes produced in processes in which 2 protons are removed from the Ni projectile, one notices a distinct asymmetry. Light Fe isotopes are produced with much lower yields, probably mostly by secondary neutron evaporation from more neutron-rich Fe isotopes. The actual ranges of observed isotopic or isobaric distributions are determined by the experimental detection limit if the corresponding information on gamma transitions is available. In spectroscopic applications, especially for exotic neutron-rich nuclei, such information is often not available and the study requires unambiguous identification and association of gamma rays with a given nucleus. In many cases the analysis of gamma cross-coincidences described in Section 2.4 serves this purpose. However, the cross-coincidence procedure can be applied only to partners produced with high enough intensities. For low yield exotic species one needs an inde-

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Fig. 16. Yield distributions for isotopes of selected elements produced in the 208 Pb + 350 MeV 64 Ni reaction [1]. Lines are drawn to guide the eye.

pendent way to identify few crucial gamma rays to provide the starting point for the thick target experimental data analysis. Present experiments use fragment spectrometer techniques employing separators designed specifically for the identification of fragments produced in deep-inelastic collisions and coupled to gamma arrays, such as the PRISMA-CLARA setup [44,45]. Problems related to spectroscopic identification of exotic neutron-rich isotopes are described in detail in Ref. [2]. Recently, new results were obtained on neutron-rich isotopes in the 48 Ca region by combining identifications of new gamma rays made with the PRISMA-CLARA setup with earlier thick target experiments data [46–48]. 6. Summary Three heavy ion systems 64 Ni + 208 Pb, 58 Ni + 208 Pb and 64 Ni + 130 Te colliding at energies approximately 12% above the Coulomb barrier were studied in thick target gamma coincidence experiments. Complex gamma ray spectroscopy analysis established complete product distributions which could be converted to primary product distributions by accounting for secondary neutron evaporation. Following the detailed description of the method used in the analysis for the 64 Ni + 208 Pb system [1], the experimental results obtained for two other systems were now presented and the complete set of data was discussed in terms of the deep-inelastic reaction mechanism. Specifically the N/Z equilibration process was considered with the aim to provide guidance for spectroscopic applications of deep-inelastic reactions to study neutron-rich nuclei. The comparison of the observed N/Z equilibration effect with simple calculations based on a model of two separated spheres led to conclusion that in the critical moment of reaction when the massive transfer of nucleons takes place both colliding nuclei are dynamically deformed. As a consequence the N/Z equilibration process is significantly less effective than one would expect for two touching nuclei. This poses some restrictions on access with spectroscopic study

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to exotic, very neutron-rich nuclei. To complete the picture of potential use of deep-inelastic reactions to spectroscopic application some typical isotope and isobar distributions were shown and a number of examples of nuclei studied with this technique were quoted. The brief outline of future perspectives was given with the emphasis on the progress achieved in identification of new nuclei with fragment separators combined with the analysis of gamma coincidence data from thick target experiments. The present results prepare the way for further extension of the neutron-rich region accessible for nuclear structure study with radioactive beams which will be available for this type of experiments. Acknowledgements The interpretation of the observed N/Z equilibration patterns was inspired by discussions with W.J. Swiatecki and J. Błocki. This work was supported by Polish Ministry of Science under contract No. NN202103333. References [1] W. Królas, R. Broda, B. Fornal, T. Pawłat, H. Grawe, K.H. Maier, M. Schramm, R. Schubart, Nucl. Phys. A 724 (2003) 289. [2] R. Broda, J. Phys. G: Nucl. Part. Phys. G 32 (2006) 151. [3] R. Broda, B. Fornal, W. Królas, T. Pawłat, D. Bazzacco, S. Lunardi, C. Rossi Alvarez, R. Menegazzo, G. de Angelis, P. Bednarczyk, J. Rico, D. De Acuña, P.J. Daly, R.H. Mayer, M. Sferrazza, H. Grawe, K.H. Maier, R. Schubart, Phys. Rev. Lett. 74 (1995) 868. [4] B. Fornal, R. Broda, W. Królas, T. Pawłat, J. Wrzesi´nski, D. Bazzacco, D. Fabris, S. Lunardi, C. Rossi Alvarez, G. Viesti, G. de Angelis, M. Cinausero, D.R. Napoli, Z.W. Grabowski, Phys. Rev. C 55 (1997) 762. [5] C.W. Beausang, A.N. Wilson, N. Amzal, D.E. Appelbe, S. Asztalos, P.A. Butler, R.M. Clark, P. Fallon, A.O. Macchiavelli, Acta Phys. Hung. N.S. 6 (1997) 295. [6] C.T. Zhang, P. Bhattacharyya, P.J. Daly, Z.W. Grabowski, R.H. Mayer, M. Sferrazza, R. Broda, B. Fornal, W. Krolas, T. Pawlat, D. Bazzacco, S. Lunardi, C. Rossi Alvarez, G. de Angelis, Nucl. Phys. A 628 (1998) 386. [7] S.J. Asztalos, et al., Phys. Rev. C 60 (1999) 044307. [8] B. Fornal, R. Broda, W. Królas, T. Pawłat, J. Wrzesi´nski, D. Bazzacco, S. Lunardi, C. Rossi Alvarez, G. Viesti, G. de Angelis, M. Cinausero, D.R. Napoli, J. Gerl, E. Caurier, F. Nowacki, Eur. Phys. J. A 7 (2000) 147. [9] T. Ishii, M. Asai, A. Makishima, I. Hossain, P. Kleinheinz, M. Ogawa, M. Matsuda, S. Ichikawa, Eur. Phys. J. A 13 (2002) 15. [10] R.V.F. Janssens, et al., Phys. Lett. B 546 (2002) 55. [11] B. Fornal, et al., Phys. Rev. C 70 (2004) 064304. [12] R. Bock (Ed.), Heavy Ion Collisions, North-Holland Publishing Company, Amsterdam, 1980. [13] D.A. Bromley (Ed.), Treatise of Heavy Ion Science, Plenum Press, New York, 1984. [14] A. Gobbi, W. Nörenberg, in: R. Bock (Ed.), Dissipative Collisions in Heavy Ion Collisions, North-Holland Publishing Company, Amsterdam, 1980. [15] W.J. Swiatecki, J. Phys. Colloq. C5 33 (1972) 45. [16] W. Nörenberg, J. Phys. Colloq. C5 37 (1976) 141. [17] W.U. Schröder, J.R. Huizenga, in: D.A. Bromley (Ed.), Damped Nuclear Collisions in Treaties of Heavy Ion Science, vol. 2, Plenum Press, New York, 1984. [18] H. Freiesleben, J.V. Kratz, Phys. Rep. 106 (1984) 1. [19] R. Broda, C.T. Zhang, P. Kleinheinz, R. Menegazzo, K.H. Maier, H. Grawe, M. Schramm, R. Schubart, M. Lach, S. Hofmann, Phys. Rev. C 49 (1994) 575. [20] J.F.C. Cocks, D.J. Blumenthal, R. Broda, P.A. Butler, K.J. Cann, B. Crowell, B. Fornal, R.V.F. Janssens, G.D. Jones, P.M. Jones, R. Julin, S. Juutinen, T.L. Khoo, T. Lauritsen, D. Muller, D. Nisius, M. Piiparinen, A. Savelius, J.F. Smith, Acta Phys. Pol. B 27 (1996) 213. [21] J.F.C. Cocks, P.A. Butler, Acta Phys. Pol. B 28 (1997) 75. [22] P.A. Butler, J.F.C. Cocks, P.T. Greenlees, in: J.H. Hamilton, W.R. Phillips, H.K Carter (Eds.), Proceeding of the 2nd International Conference on Fission and Properties of Neutron-Rich Nuclei, St. Andrews, Scotland, June 28–July 3, 1999, World Scientific, Singapore, 2000, p. 28.

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