REACTIONS 11B+209BI AT ENERGIES ABOVE COULOMB BARRIER

Experimental data on production of radioactive residuals in 11B +209 Bi reaction a above-barrier projectile energy of 145.6 MeV are presented. The measurements and identification of reaction products were made using the method of induced activity. The residual nuclei in 24 ≤ A ≤ 211 mass range are considered as products of different interaction channels, occurring through evaporation at complete, incomplete fusion and the fission. The fragments in (60-160) atomic mass units range are regarded to the fission products and are confirmed with data from experiments with analogous fissile nuclei. The residual nuclei near target mass number can be presented as result of the different processes including emission of nucleons and light nuclei. Theoretical predictions within the frameworks of PACE-4 code simulation, allowing the predictions of formation, evaporation and fission of compound nuclei, were used for analyzing the measurement results. A substantial contribution to production of residual nuclei of the incomplete fusion and of additional mechanisms, proceeding at different impact parameters, were revealed at analysis of the experimental data.


Introduction
In previous low energy experiments [1][2][3][4] the complete fusion (CF) and particularly incomplete fusion (ICF) were considered as probable processes appearing in interactions at different impact parameters. In a number of papers [5][6][7][8] ICF was predicted to occur along with CF depending on the projectile energy and mass asymmetry in the entrance channel. It was shown that the fusion of a projectile with target (CF) occurs presumably at values of angular momentum lower than the critical one (l ≤ l crit ). At the critical value of angular momentum [9][10][11] and relatively large impact parameter the centrifugal forces increase, giving rise to peripheral collisions and direct interactions. The break up processes started to play an essential role also. The fusion with different light nuclei is localized in successive l-windows and can appear as a sequence of captures of different fragment mass by the target nuclei. The fraction of ICF accompanied by capture of separated fragments of the projectile became more probable, that are accompanied by building-up of the distribution of residual masses. The participation of break-up process in the nucleus -nucleus interactions are widely studied last years because in these experiments the structure properties of interacting nuclei are visually demonstrated. An understanding of the details of break-up and fusion processes may shed light on important questions pertaining to the isotope production in the universe also. Experimental studies with radioactive nuclei would be very informative in these cases, but in view of low beam intensity this kind the results of measurements are not always statistically provided. The reactions with weakly bound nuclei are also of interest because if one of colliding nuclei has sufficiently low binding energy, it can break into component parts. The weakly bound light elements give an opportunity of studying the interactions of this kind with good statistics. In the present experiment 11 B nuclei is assumed to be a weakly bound system with relatively low binding energy in comparison with the large incident projectile energy. The process of 11 B nucleus break-up may be proceed via the different channels: 11 B→ 4 He + 4 He, The total cross section of reaction is presented usually as a sum of (CF+ICF) and the decrement of CF probability corresponds to the contribution of ICF. The reaction channel via ICF is usually considered as a two step process: the break-up of projectile in the vicinity of the target and fusion of the projectile part with the target nucleus. This process is being discussed mainly above the Coulomb barrier for incident beam energies ≥ 5 MeV and is characterized by the transfer of only a part of the projectile energy and momentum to the target nucleus. The measurements of reaction yields at different energies below and above the fusion barrier permit the checking of theoretically predicted correlation of different processes in the energy dependence and of the properties of participating nuclei. Previously it was shown [2,3] that in reactions induced by weakly bound light nuclei the cross section of CF was suppressed at above?arrier energies in comparison with the prediction of single barrier penetration and the coupled channel models. At high energies and with increasing impact parameter the different processes take place that are accompanied by projectile break-up. In the yields of ICF the missing cross sections due to many possible parts are found. Additionally the pre-equilibrium emission of particles and light nuclei is followed by an excitation energy decreasing and by a changing of residual nuclei composition. In earlier works at energies near and above the barrier the total fusion was considered mainly as developing via xn-, pxn-and αxn -evaporation channels and fission processes [2,3]. At high energy the extension of the interaction channels and the addition of the different reaction products make the picture more complicate. The knowledge of the total composition of individual cross sections permits a detailed analysis of experimental data and sheds light on the role of different interaction mechanisms. In experiments using the activation methods the radioactive residual nuclei were measured as yields of definite channel reaction however the existence of the consistent chains of radioactive decays bring to mixing of the product yields. On the other side at high energy the products of different interaction channels are located in the same mass region that creates difficulties in understanding of a reaction mechanism and testing of model predictions.
In reaction ( 11 B+ 209 Bi) CF leads to the production of 220 Ra compound nucleus and as a results of ICF via the (1)-(3) channels are formed 216 Rn, 213 At, 217 Fr, 212 Pb composite nuclei.
In the present work the yields of radioactive residual nuclei are related to 24 ≤ A ≤ 211 amu. large mass region. The part of heavy residuals between compound nuclei and target masses ( A t ) were considered mainly as products of CF and ICF. The activation method in experiments of this kind give information mainly about a completely or partly isobar chains, including a final or intermediate measurable isotopes in α -and β ± -decay chains. The product mass range arranged approximately around A t /2 as usually relates to the location of fission fragments. The fission cross section was determined based on analyzing the charge and mass distributions of fragments taking into account the regularities observed in previous experiments and obtained by using some empiric predictions. The fission process is usually considered as a direct indication of compound nucleus formation in CF. It is expected, that increasing transfer excitation energy and angular momentum followed by a diminution of the fission barrier and growth of the fission cross section. In this way the fission process is considered as a main indication on existence of the complete fusion.
In the present paper the experimental data were analyzed versus the reactions, producing similar compound nuclei, as the decay of compound systems were independent of the formation way. Substantially the obtained results were considered as compared with the fission and evaporation products from reactions with an analogous nuclear systems produced in ( 12 C+ 208 Pb), ( 13 C+ 207 Pb), ( 22 Ne+ 198 Pt), ( 12 C+ 209 Bi) reactions [12][13][14][15][16]. It was shown in [12], that the excitation functions of both the fission and (xn)-evaporation processes induced by 12 C and 11 B on 208 Pb and 209 Bi-targets were similar at energies ≤ 94 MeV. For comparison with theoretical predictions the calculations in the framework of PACE-4 code were used. The previously published data on ( 11 B+ 209 Bi) reaction were reanalyzed using calculated results.

Experimental methods
The irradiation with 11 B beam to 17nA intensity was made on ACCULINA-1 separator on U-400 accelerator (JINR, Dubna, Russia) using the standard stacked foil technique for reducing the incident energy in combination with high resolution gamma-spectroscopy. The mean value of projectile energy in the target was equal to 145.6 MeV. Bi target, 0.64 mg/sm 2 thickness was produced by evaporation on 0.54 mg/sm 2 Al-foil. The exposition on beam was continued during 12 hours. The induced activities were measured using high energy resolution HpGe ?etectors ( ∼ 1.8 keV for 1330 keV line 60 Co) since the 3-rd hour after the irradiation up to two months. The energy and efficiency calibration of detectors was made by using a set of standard gamma sources ( 60 Co, 137 Cs, 154 Eu). The radioactive reaction products were identified based on spectroscopic characteristics from standard tabular data [17]. The cross sections of independent (I) and cumulative (C) reaction products are calculated using the general expressions for activation analysis, allowing for contributions of radioactive precursors [18]. The errors of cross section values were estimated using the following factors: the statistical significance of experimental results ( ∼ 2-5%), the accuracy in target thickness determination ( ∼ 10%), accuracy of tabular value of nuclear constant ( ∼ 3%) and errors in the detector efficiency determination with allowance for calculation of its energy dependence ( ∼ 10%). The obtained cross sections for residual nuclei are presented in Table 1 and Table  2.

Fission
In reaction ( 12 C+ 208 Pb) two asymmetric and one symmetric fission components were observed at the excitation energy E* ∼ 24 MeV [19]. The asymmetric fission shoulders disappeared practically at E* ∼ 53 MeV. In our experiment, according to PACE-4 code calculations, the excitation energy and angular momentum are E* ∼ 118 MeV and l ≤ 78h . These initial conditions suppose that the fission fragments are formed of a single symmetric component. The bell shaped distribution obtained in (60-160) atomic mass range (Figure 1) is considered as a binary mode of fission of 220 Ra compound nucleus. The fission cross section was calculated based generally on the assumption of Gaussian function form for the fragment charge and mass distributions [20,21]. The cross section of independently produced fission fragments σ (A, Z) can be presented as Gaussian Z-distribution curve at given A-value: where σ(A) is the total isobaric cross section for given A, Z p is the most probable charge and C is the parameter of the distribution width. In order to uniquely specify the variables σ(A) , Z p and C one needs to measure at least three independent cross sections for each isobar. The spectroscopic analysis of induced activity is not generally provided with data on several isobars required for determination of necessary parameters. As in previous publications [20,21], in the present work several assumptions on the basis of results of earlier measurements and the empiric applications were made. The first assumption relates to the slow dependence of the parameter of charge distribution widths (C) on the product charge number (Z) for the regions with close mass numbers.
Another assumption is that the charge distributions of the fission fragments are similar for the closed mass number and the corresponding parameters are depended mainly on the nuclear composition of fragments. The cross sections of a particular isotopes (in experiments like this) can be independent or cumulative (partly or completely) due to the presence and the decay of precursors. The betafeeding correction factors for the cumulative isobaric yield can be calculated once the centroid and width of the Gaussian are known. For obtaining the fitting parameters Z p and σ A the least-squares method was employed. In this way the measured cross sections were adjusted successively to remove the precursor feeding (where necessary) and a set of independent cross sections were generated. The mass-yield distribution was constructed (Figure 1) using the calculated values of σ A corresponding to the isobaric cross sections for a specific mass numbers. The total isobaric distribution was obtained by fitting the Gaussian form with certain values of the heightλ A , mean mass number -Ā and width parameter -Γ A : The fission cross section as obtained by summing all isobaric yields is equal to ∼ (1296.4 ±160 ) mb. The obtained experimental fission cross sections with data for 11 B + 209 Bi reaction [2], and data for ( 12 C+ 208 Pb) [13,23] reaction are presented in Figure 2 along with the calculation results by PACE-4 code. The data in Figure 2 show that the fission cross section increases near the barrier and then slows down up to reaching a plateau. The fission cross section is usually regarded to the complete fusion process. At lower energies ∼ 75MeV [2] the contribution of incomplete fusion with 4 He and 7 Li ions produced via the break-up of 11 B was approximately estimated to be ∼ 1%. Similarly, the fraction of ICF -fission at ∼ 13MeV/nucleon can be estimated as being no more than several percent taking into account the break-up and fission probabilities [24,25]. This value is within the accuracy of the present experiment. At high excitation energy and high angular momentum of the compound nucleus the decreasing of fission barrier leads to the prevalence of fission process. In a number of model predictions the ratio of fission cross section to the complete fusion cross section is assumed to be approximately equal to ∼ (0.7 ± 0.1) and weakly depend on the type of projectile. The total reaction cross section as estimated for this value of ratio is (2100 ± 300) mb. For comparison, in the frameworks of PACE-4 code the fission cross section was calculated to be ∼ 1540 mb and the total cross section of reaction ∼ 1910 mb. If the decrease in fission cross section is treated as the contribution of incomplete fusion [2], then an approximate estimate of the suppression of complete fusion via fission gives 121.8 %. This value is not at variance with previously obtained complete fusion suppression effect ( ∼ 7%) in ( 11 B+ 209 Bi) reaction at energy 75 MeV and can be considered as a consequence of ICF increasing with the energy of projectile.
At fitting of experimental data the values obtained for the centroid of mass distributions of fission fragments and for the width parameter were A=(104 ± 15) amu and C ∼ (12.9 ± 20) amu (FWHM ∼ 30.2 amu) respectively. The mass number of fissioning nucleus was determined as 208 amu and the total number of nucleons emitted before fission ∼ 12 (including the pre-and post-fission neutrons). At lower energies of 73.4 MeV and 84.2 MeV [25] the centroids of mass distributions in reaction ( 12 C+ 209 Bi) were obtained to be 107.7 amu and 107 and FWHM ∼ 24.8 and 25.4 amu respectively. These data agree with our results, taking into account increasing of the neutron evaporation with excitation energy and following enlargement of the fissioning nuclei number. The maximum of isobaric curve landing approximately at Z ∼ 44 (Z ∼ 88 -for fissioning nucleus) is explained by the preferential neutron emission before the fission.

Heavy reaction products
A number of residual nuclei formed approximately in the mass range between the compound 220 Ra nucleus and target ( ∆ A ∼ 20) are considered as products of CF and ICF followed with emission of nucleons and light nuclei. As was pointed out above, the initial conditions of the reaction-the excitation energy and angular momentum predicted by PACE-4 calculations, suppose an essential role of ICF [13,26] and decrease of CF, that are most probable at lower angular momenta. The composite nuclear states produced at high angular momentum preferentially undergo the fission decay. The presence of preequilibrium processes appears as the emission of neutrons, protons, α -particles and other fragments before statistical equilibration [28][29][30]. The heavy cluster emission from highly excited nuclear systems was considered in detail in [27] for ∆ Z ≤ 10 charge loss processes. In addition, the inelastic scattering of projectile on the target surface may lead to low energy transfer followed with emission of several nucleons. At subsequent α -and β -decays of heavier precursors are populated a number of lighter nuclei. Usually, CF reaction channel is revealed through a sum of the decays including xn-, α xn-, pxnemission from compound nucleus. In ( 22 Ne + 198 Pt)-reaction [14] these evaporation for the compound nucleus 220 Ra, excited up to (100-120) MeV, are measured in a mass spectrometer via the short lived α -active reaction products formed as a results of xn-evaporation. The obtained cross sections for (p8n-p9n)-reactions were ∼ 1 mb, for (p10n-p11n)reactions ∼ 2 mb and the same order of the cross sections of for emission of αparticles in ( α 10n), ( α 11n) reactions. The cross sections of Rn-isotopes formation proved to be significantly larger than those expected from α -decay of Ra parents, produced in xn?mission processes. CF yields were defined in [2,14] by comparing the measured cross sections for ( 12,13 C+ 208,207 Pb) and ( 10,11 B+ 209 Bi) reactions with statistical model calculations of ( 30 Si+ 186 Wi) fusion at above-barrier energy. The compound nucleus in the last 216 Ra case was considered as CF and the projectile 30 Si was considered as a normal, strongly bound, noncluster struc-ture nucleus. So, the statistical model describing the evaporation probability in ( 30 Si+ 186 Wi) reaction was used for reliable prediction of cross sections for similar processes in 10,11 B and 12,13 C induced reactions. The required extrapolation was made for a transfer from 216 Ra to 219,220 Ra compound nuclei and correction of the values of angular momentum and fission barrier. The calculated cross section for production of Ra isotopes through neutron evaporation from a compound nucleus is much smaller than the experimental values obtained for Rn yields assumed as products of α -decay of Ra. Nearly 80% of directly produced Fr and Rn isotopes was obtained to be due to ICF.
The method of induced gamma-activity in present work does not allow to obtain the yields short lived α -decaying Ra isotopes, populating Rn nuclei, which in its turn undergo via the α -decay and the consistent β + -conversion into Po, At isotopes. Fr-isotopes can be formed in (pxn) reactions and can be transformed through the α -decay also to At isotopes. On the other side, ( α xn) channel in ICF leads to the creation of Rn isotopes and via successive α , β + -decays to low lying elements. The reaction channels followed break up 11 B and incomplete fusion 7 Li and 4 He fragments are resulted to compound nuclei 216 Rn and 213 At and can participate in populating Rn, At, Po isotopes. A number of underlying elements can be formed via particles emission and radioactive decay processes. The experimental data of the present work give large yields of Rn, Po and At isotopes, that is indicative of aforementioned significant contribution of ICF. The production of Bi-isotopes can find out as an inelastic scattering leading to the transfer of insignificant excitation energy to the target nucleus and emission of small number of neutrons [31]. Due to such a mixing it turns impossible to extract separate interaction channel without prior chemical separation. The isobars with measurable spectroscopic characteristics may provide a partial or full summary effect. The mass distributions of such residuals give a complicated picture including all processes to occur.
Calculations in frames of PACE-4 code give the cross sections of evaporation products produced via neutrons, protons and α -particles evaporation using statistical model for reaction representation [32]. The calculation cross sections of the individual reaction products can? compare with experimental data directly because the measurements relates mainly to the cumulative yields.
For comparison the calculation results can be summed including the products of consecutive decay channels. We think that in this way one can obtain the estimates of CF contribution in the measurements data. In Figure 3 are presented the calculation and measurement results. The experimental data are seen to sufficiently exceed the calculation results and shifted to lower mass range. This excess may be due to the contribution of ICF. As was shown in [14], ∼ 80% part of Rn isotope cross sections can be attributed to increasing contribution of ICF processes. The displacement of distribution to lower masses can be explained as due to increased excitation energy and involvement of additional interaction channels. The high cross sections, observed for products near the target mass number, can be explained by the contribution of inelastic scattering and transfer processes following small number transmission nucleons.
The independent cross sections of several isotopes in 160 ≤ A ≤ 190 mass range (Au, Hg, Re) and residuals in A ≤ 50 range seemingly result from binary processes with heavy fragment emission considered in detail in [27] for ion in- duced reactions. The high probability for formation of 198m Au and 196m Au isomer states ( 12 − ) may be an indication of high spin value of preceding intermediate composite nucleus. The transition of this kind appears more probable as the first fast step of the interaction with emission of the accompanying fragment. There are different opinions on the formation probability of an intermediate mass fragment: in [32][33][34][35][36] the fragment formation was ascribed to the coalescence of nucleons during the nucleon-nucleon interaction cascade started as soon as two nuclei come into contact; in [17] the authors developed a method for calculation of the probability of heavy fragment emission from excited nucleus with simultaneous evaporation of nucleons. The other probable way for formation of residuals of this kind can be the asymmetric decay of highly excited nuclei.

Conclusions
The study of ( 11 B+ 209 Bi) interaction at energy 145.6 MeV showed the mixing of different interaction channels occurring at the residuals distribution. The fission cross section of (1296.4 ± 190) mb obtained at analyzing the distribution of fission fragments proved lower than the model predictions using PACE-4 code (1540 mb). Assuming the fission process as the most probable channel of compound nuclei decay in CF at given energy, one can regard the decrease in fission cross section as an estimate of (12 ± 1.8)% suppression of this CF channel. Characteristics of the charge and mass distributions of fission fragments well agree with data from reactions with similar fissioned nuclei under near energy conditions. The transfer of excitation energy to the compound nuclei became apparent in case of 12 emitted nucleons in the fission channel (including pre-and postfission neutrons). The main part of heavy reaction products are created in ICF followed with evaporation of nucleons and a sequence of radioactive transformations. The yields of intermediate mass fragments and several heavy isotopes may be explained by supposing the contribution of possible asymmetric decay or emission of heavy fragments at high excitation energy.