Measurements of the 234U(n,f) Reaction with a Frisch-Grid Ionization Chamber up to En=5 MeV

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(1)Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1002. Measurements of the 234U(n,f) Reaction with a Frisch-Grid Ionization Chamber up to En=5 MeV ALI AL-ADILI. ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2013. ISSN 1651-6214 ISBN 978-91-554-8554-2 urn:nbn:se:uu:diva-185306.

(2) Dissertation presented at Uppsala University to be publicly examined in Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, January 18, 2013 at 10:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Abstract Al-Adili, A. 2013. Measurements of the 234U(n,f) Reaction with a Frisch-Grid Ionization Chamber up to En=5 MeV. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1002. 109 pp. Uppsala. ISBN 978-91-554-8554-2. This study on the neutron-induced fission of 234U was carried out at the 7 MV Van de Graaff accelerator of IRMM in Belgium. A Twin Frisch-Grid Ionization Chamber (TFGIC) was used to study 234U(n,f) between En = 0.2 and 5.0 MeV. The reaction is important for fission modelling of the second-chance fission in 235U(n,f). The fission fragment (FF) angular-, energy and mass distributions were determined using the 2E-method highlighting especially the region of the vibrational resonance at En = 0.77 MeV. The experiment used both conventional analogue and modern digital acquisition systems in parallel. Several advantages were found in the digital case, especially a successful pile-up correction. The shielding limitations of the Frisch-grid, called "grid-inefficiency", result in an angular-dependent energy signal. The correction of this effect has been a long-standing debate and a solution was recently proposed using the Ramo-Shockley theorem. Theoretical predictions from the latter were tested and verified in this work using two different grids. Also the neutronemission corrections as a function of excitation energy were investigated. Neutron corrections are crucial for the determination of FF masses. Recent theoretical considerations attribute the enhancement of neutron emission to the heavier fragments exclusively, contrary to the average increase assumed earlier. Both methods were compared and the impact of the neutron multiplicities was assessed. The effects found are significant and highlight the importance of further experimental and theoretical investigation. In this work, the strong angular anisotropy of 234U(n,f ) was confirmed. In addition, and quite surprisingly, the mass distribution was found to be angular-dependent and correlated to the vibrational resonances. The anisotropy found in the mass distribution was consistent with an anisotropy in the total kinetic energy (TKE), also correlated to the resonances. The experimental data were parametrized assuming fission modes based on the Multi-Modal Random NeckRupture model. The resonance showed an increased yield from the Standard-1 fission mode and a consistent increased TKE. The discovered correlation between the vibrational resonances and the angular-dependent mass distributions for the asymmetric fission modes may imply different outer fission-barrier heights for the two standard modes. Keywords: Fission, U-234, Neutron, Uranium, Resonance, Ionization Chamber, Frisch-grid Ali Al-Adili, Uppsala University, Department of Physics and Astronomy, Applied Nuclear Physics, Box 516, SE-751 20 Uppsala, Sweden. © Ali Al-Adili 2013 ISSN 1651-6214 ISBN 978-91-554-8554-2 urn:nbn:se:uu:diva-185306 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-185306).

(3) To Sheima and Josef.

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(5) List of papers. This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I. A. Al-Adili, F.-J. Hambsch, S. Oberstedt, S. Pomp and S. Zeynalov. "Comparison of digital and analogue data acquisition systems for nuclear spectroscopy", Nucl. Inst. and Meth. A624 (2010) p684-690.. II. A. Al-Adili, F.-J. Hambsch, R. Bencardino, S. Oberstedt and S. Pomp. "Ambiguities in the grid-inefficiency correction for Frisch-Grid Ionization Chambers", Nucl. Inst. and Meth. A673 (2012) p116-121.. III. A. Al-Adili, F.-J. Hambsch, R. Bencardino, S. Pomp, S. Oberstedt and S. Zeynalov. "On the Frisch-Grid signal in ionization chambers", Nucl. Inst. and Meth. A671 (2012) p103-107.. IV. A. Al-Adili, F.-J. Hambsch, S. Pomp and S. Oberstedt. "Impact of prompt-neutron corrections on final fission-fragment distributions". Phys. Rev. C86 054601 (2012).. V. A. Al-Adili, F.-J. Hambsch, S. Pomp and S. Oberstedt. "Indication of anisotropic TKE and mass emission in 234 U (n, f )". GAMMA-1 Emission of Prompt Gamma-Rays in Fission and Related Topics, Novi Sad, (Republic of Serbia) 22-24 November 2011. Physics Procedia 31 (2012) p158-164.. VI. A. Al-Adili, F.-J. Hambsch, S. Pomp and S. Oberstedt. "First evidence of correlation between vibrational resonances and anisotropy in fission mass distribution". In manuscript.. VII. A. Al-Adili, F.-J. Hambsch, S. Pomp and S. Oberstedt. "Fragment mass-, kinetic energy- and angular distributions for 234 U (n, f ) at incident neutron energies from En = 0.2 to 5.0 MeV". In manuscript.. Reprints were made with permission from the publishers..

(6) Other papers not included in this Thesis. List of papers related to this Thesis, but not included in the comprehensive summary. I am first author or co-author of all listed papers.. 1. A. Al-Adili, F.-J. Hambsch, S. Pomp and S. Oberstedt. "Angular dependent TKE and Mass emission in 234 U (n, f )", 13th International Conference on Nuclear Reaction Mechanisms, Varenna (Italy), June 11-15 (2012). To be published in CERN-Proceedings. 2. A. Al-Adili, F.-J. Hambsch, S. Oberstedt and S. Pomp. "Investigation of 234 U (n, f ) as a function of incident neutron energy", Seminar on fission VII, Ghent (Belgium), May 17-20, 2010, World Scientific Pub Co Inc, (2010) p99-105, ISBN=978-981-4322-73-7. 3. F.-J. Hambsch, S. Oberstedt, A. Al-Adili, R. Borcea, A. Oberstedt, A. Tudora and Sh. Zeynalov. "Investigation of the Fission Process at IRMM", International Conference on Nuclear Data for Science and Technology (2010) J. Korean Phys. Soc. 59, p1654-1659. 4. F.-J. Hambsch, S. Oberstedt, Sh. Zeynalov, N. Kornilov, I. Fabry, R. Borcea and A. Al-Adili. "Fission Research at IRMM", CNR*09 - Second International Workshop on Compound Nuclear Reactions and Related Topics, EPJ Web of Conferences, Bordeaux, France, October 0508, (2009), ISBN:978-2-7598-0521-1. 5. P.-A. Söderström, F. Recchia, J. Nyberg, A. Al-Adili, et al. "Interaction position resolution simulations and in-beam measurements of the AGATA HPGe detectors", Nucl. Inst. and Meth. A638 (2011) p96-109.. vi.

(7) Contents. Page List of Figures. ix. 1 Introduction. 12. 2 Theoretical background 2.1 Introduction to fission . . . . . . . . . . . . . . 2.2 Fission modelling . . . . . . . . . . . . . . . . 2.3 The Multi-Modal Random-Neck Rupture model 2.3.1 Formalism . . . . . . . . . . . . . . . . 2.3.2 Mode fits to experimental data . . . . . . 2.4 Energy release and time scales . . . . . . . . . . 2.5 Anisotropy in nuclear fission . . . . . . . . . . 2.6 Prompt-neutron emission . . . . . . . . . . . .. 15 15 17 18 20 22 23 24 26. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. 3 Experiments 3.1 The Van de Graaff accelerator . . . . . . . . . . . . . . . . . . 3.2 The ionization chamber . . . . . . . . . . . . . . . . . . . . . 3.3 The 234,235 U targets . . . . . . . . . . . . . . . . . . . . . . . 3.4 Data-acquisition systems . . . . . . . . . . . . . . . . . . . . . 3.5 Grid inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Additive approach . . . . . . . . . . . . . . . . . . . . 3.5.2 Subtractive approach . . . . . . . . . . . . . . . . . . . 3.5.3 Ramo-Shockley theorem . . . . . . . . . . . . . . . . . 3.5.4 Experimental investigation of the grid-inefficiency ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Results from the grid-inefficiency experiment . . . . . . 3.6 Emission-angle extraction . . . . . . . . . . . . . . . . . . . . 3.6.1 Grid and summing methods . . . . . . . . . . . . . . . 3.6.2 Drift-time method . . . . . . . . . . . . . . . . . . . .. 30 30 32 34 35 37 37 38 38 39 40 42 42 43. 4 Analysis 4.1 Digital-signal treatment . . . . . . . . . . . . . . . . . . . . . 4.1.1 Pile-up correction . . . . . . . . . . . . . . . . . . . . 4.1.2 CR-RC 4filtering . . . . . . . . . . . . . . . . . . . . .. 44 44 44 45.

(8) 4.2 Angle determination . . . . . . . . . . . . . . 4.3 Energy-loss correction . . . . . . . . . . . . . 4.3.1 Individual and collective corrections . . 4.3.2 The impact of the α pile-up correction 4.4 Pulse-height defect . . . . . . . . . . . . . . . 4.5 Prompt-neutron multiplicity corrections . . . . 4.6 Fragment-mass determination . . . . . . . . . 4.7 Calculating the angular anisotropy . . . . . . .. . . . . . . . .. 46 48 49 50 51 51 54 54. 5 Results and discussions 5.1 Angular anisotropy . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Mass and energy distributions . . . . . . . . . . . . . . . . . . 5.3 Yield comparison to simulations . . . . . . . . . . . . . . . . . 5.4 Energy dependencies in mass and energy distributions . . . . . 5.5 Parametrization of experimental data in terms of fission modes 5.6 Anisotropy in TKE and mass emission . . . . . . . . . . . . . 5.6.1 Experimental evidence . . . . . . . . . . . . . . . . . . 5.6.2 Details of the analysis on mass and TKE anisotropy . . 5.6.3 Link to the fission barrier . . . . . . . . . . . . . . . . 5.7 Impact of neutron-multiplicity shapes . . . . . . . . . . . . . . 5.7.1 The impact of both methods . . . . . . . . . . . . . . . 5.7.2 Conversion between the methods . . . . . . . . . . . . 5.7.3 Objectives from the neutron-emission study . . . . . . .. 57 58 61 63 65 72 78 78 82 83 85 85 86 90. 6 Summary 6.1 Fission observables of 234 U (n, f ) . . . . . . . . . . . . . . . . 6.2 Impact of the neutron-multiplicity corrections on yield distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Digital and analogue data-acquisition systems . . . . . . . . . 6.4 Grid inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91 91. 7 Summary in Swedish. 96. 8 Acknowledgements. 99. Appendix A: Kinematics. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. ................................................................................ Appendix B: Uncertainty estimation Bibliography. . . . . . . . .. ............................................................. 93 93 94 94. 101 104 107.

(9) List of Figures. 1.1 The fission cross section of 234 U (n, f ). . . . . . . . . . . . . . 2.1 The fission barrier for a typical actinide. . . . . . . . . . . . . 2.2 Example of the fit of a Gaussian function to the fission yield distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The separation of fission mode paths along the barrier. . . . . . 2.4 Generalized Lawrence representation of a fissioning nucleus. . 2.5 The flat-neck representation of a fissioning nucleus. . . . . . . 2.6 The fission modal fit on the yield of mass and TKE. . . . . . . 2.7 The share of TKE and TXE in the fission process. . . . . . . . 2.8 Angular distribution of a fissioning nucleus. . . . . . . . . . . 2.9 Neutron-multiplicity as a function of mass. . . . . . . . . . . . 2.10 ν (A) from 237 Np (n, f ) at two different excitation energies. . . 3.1 Schematic view of the Van de Graaff accelerator. . . . . . . . . 3.2 The neutron fluxes . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The ionization chamber. . . . . . . . . . . . . . . . . . . . . . 3.4 Schematic view of the Twin Frisch-Grid Ionization Chamber . 3.5 The electronic scheme used for the experiment . . . . . . . . . 3.6 The chamber used for the grid-inefficiency experiment. . . . . 3.7 GI affected signal and experimental determination of σ . . . . . 3.8 The original anode PH from the GI experiment. . . . . . . . . . 3.9 The corrected anode PH from the GI experiment. . . . . . . . . 3.10 The PH of the grid signal, before and after GI correction. . . . 4.1 Digital traces from the chamber and the α pile-up. . . . . . . . 4.2 The grid PH plotted vs. the anode PH to extract θ . . . . . . . . 4.3 The energy-loss correction. . . . . . . . . . . . . . . . . . . . 4.4 The PH from sample and backing sides with the energy losses as a function of En . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Effect of α pile-up correction on the energy-loss correction. . . 4.6 The pulse-height defect as a function of fragment mass. . . . . 4.7 Neutron multiplicity as a function of mass, TKE and En . . . . . 4.8 Neutron-emission distribution as a function of excitation energy, using the heavy (HE) and average (AV) methods. . . . . . 4.9 Legendre fits on the experimental data. . . . . . . . . . . . . . 5.1 A scheme of the outomces of this thesis. . . . . . . . . . . . .. 13 16 19 20 21 21 23 24 25 28 28 31 31 32 33 36 39 40 41 41 42 45 47 48 49 50 51 53 53 56 57 ix.

(10) 5.2 The angular distributions of 234 U (n, f ). . . . . . . . . . . . . . 5.3 The full Legendre fits for the angular distributions. . . . . . . . 5.4 Example of Legendre fits. . . . . . . . . . . . . . . . . . . . . 5.5 The angular anisotropy in terms of W (0◦ ) /W (90◦ ). . . . . . . 5.6 Values of W (0◦ ) /W (90◦ ) for Legendre P2 and P4 . . . . . . . . 5.7 Yield and TKE of 235 U (nth , f ). . . . . . . . . . . . . . . . . . 5.8 Mass yield of 234 U at E n = 2.0 MeV. . . . . . . . . . . . . . . 5.9 Y (A, TKE) and Y (A, Ekin ) for E n = 2.0 MeV. . . . . . . . . . . 5.10 TKE and σTKE as a function of pre-neutron emission FF mass. . 5.11 Comparison to yield simulations using GEF and TALYS. . . . 5.12 Absolute mass differences for all measurements. . . . . . . . . 5.13 Cont. absolute mass differences for all measurements. . . . . . 5.14 The differences in TKE as a function of FF mass. . . . . . . . . 5.15 Cont. the differences in TKE as a function of FF mass. . . . . . 5.16 Changes in the TKE as a function of En . . . . . . . . . . . . . 5.17 Average heavy fragment mass and σTKE as a function of En . . . 5.18 E kin and σE as a function of En . . . . . . . . . . . . . . . . . . 5.19 Individual contributions of TKE and mass to TKE. . . . . . . . 5.20 Two dimensional MM-RNR fit. . . . . . . . . . . . . . . . . . 5.21 Data parameterization with fission modes. . . . . . . . . . . . 5.22 TKE and σTKE of fission modes. . . . . . . . . . . . . . . . . . 5.23 The fission mode weights. . . . . . . . . . . . . . . . . . . . . 5.24 The mode weights after fixing A2 . . . . . . . . . . . . . . . . 5.25 TKE and σA of the fission modes. . . . . . . . . . . . . . . . . 5.26 Individual contributions of modal TKE and mass to TKE. . . . 5.27 A schematic view of the solid angle coverage. . . . . . . . . . 5.28 TKE as a function of cos (θ ). . . . . . . . . . . . . . . . . . . 5.29 Anisotropy in TKE as a function of En . . . . . . . . . . . . . . 5.30 Three dimensional plot of mass as a function of cos (θ ). . . . . 5.31 Anisotropy in mass as a function of En . . . . . . . . . . . . . . 5.32 Mass and TKE anisotropies fitted for 0.5 ≤ cos (θ ) ≤ 0.9◦ . . . 5.33 A demonstration of the mass anisotropy . . . . . . . . . . . . . 5.34 The difference in energy release for the (AV) and (HE) methods. 5.35 The yield difference between (AV) and (HE), for En = 5.0 MeV. 5.36 The absolute mass difference of the (AV) and (HE) methods . . 5.37 The relative mass change between the (AV) and (HE) methods. 5.38 The ν impact on TKE and AH . . . . . . . . . . . . . . . . . . A.1 A schematic view of the reaction kinematics before the fission process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 A schematic view of the reaction kinematics after the fragments have been separated. . . . . . . . . . . . . . . . . . . . . . . .. 58 59 59 60 60 61 62 62 63 64 66 67 68 69 70 70 71 71 74 74 75 75 76 76 77 78 80 80 81 81 82 84 87 87 88 88 89 102 102.

(11) List of acronyms. . AA = Analogue Acquisition ADC = Analogue to Digital Converter AV = Average method (neutron-emission correction) BF = Ballistic Free CFD = Constant Fraction Discrimination CM = Center of Mass frame DA = Digital Acquisition DG = Delay Generator DSP = Digital Signal Processing GI = Grid Inefficiency FWHM = Full Width at Half Maximum HE = Heavy method (neutron-emission correction) HV = High Voltage IRMM = Institute for Reference Materials and Measurements LAB = Laboratory frame LE = Leading Edge LFIFO = Linear Fan In Fan Out LDM = Liquid Drop Model MM-RNR = Multi Modal Random Neck Rupture model NIM = Nuclear Instrumentation Module PA = Pre-Amplifier PH = Pulse Height QFA = Quad Fast Amplifier SA = Spectroscopic Amplifier sf = spontaneous fission TAC = Time to Amplitude Converter TFA = Timing Filter Amplifier TFGIC = Twin Frisch-Grid Ionization Chamber TKE = Total Kinetic Energy TXE = Total Excitation Energy VdG = Van de Graaff accelerator. 11.

(12) 1. Introduction. "There is not the slightest indication that nuclear energy will ever be obtainable. It would mean that the atom would have to be shattered at will." (Albert Einstein). Less than 75 years ago, the study of nuclear fission was pioneered and it changed the history of mankind dramatically. The impact of this new acquired knowledge on the energy industry was very hard to imagine in these early days. The bare idea of humans controlling nuclear energy was obviously hard to grasp, even to the greatest revolutionaries of physics. In 1938, fission was discovered after irradiating Uranium with neutrons and revealing a remarkable and unexpected transformation into a pair of much lighter elements [1]. This new and exotic reaction became the center of attention for many years. Particularly to the uranium isotopes, countless studies were devoted. The significance of this element is far beyond any other actinide especially for what nuclear reactor technology is concerned. But despite the numerous experimental works on uranium, detailed nuclear data exist only for the main fissioning systems 236 U∗ and 239 U∗ . The third uranium isotope naturally abundant in very small amounts is 234 U and it has been much less explored. This isotope has a very small chemical abundance and similarly to 238 U, it is fertile. The nuclear data libraries lack fission-fragment (FF) data from 234 U (n, f ) especially on yield and energy distributions. One main goal of this work was to answer some of these data needs and to continue the accurate investigation campaign of the various actinides, carried out by the Joint Research Centre (Institute for Reference Materials and Measurement) of the European Commission.. Motivation for the experiment The main motivation for doing this study is that 234 U+n is the compound nucleus at second chance fission of 235 U (n, f ). If the energy of the fissioninducing neutron is above 6 MeV, the formed compound nucleus, 236 U∗ , has enough excitation energy to emit a neutron before fissioning. The present experiment is very important for the theoretical modelling of 235 U (n, f ) as only few data exist at higher excitation energies. 234 U (n, f ) is also relevant for the Th-U cycle [2]. More accurately measured observables (mass and kinetic energies) on 234 U (n, f ) are needed for next reactor generations as well as for nuclear waste management. Besides the contribution to nuclear industry application, this reaction exhibits interesting fission properties in terms of 12.

(13) . JEFF 3.1 ENDFB VII. σF (barn). 1.5 1.3. 1.0. 1.2. 0.5. 0.0. 1.1 0.6 0.7 0.8 0.9 1.0 1.1 1.2. 0. 1. 2. 3. 4. 5.

(14) . Figure 1.1. The fission cross section of 234 U (n, f ) with the vibrational resonance focused in the inset. All measurements are highlighted with arrows together with the uncertainty in neutron energy.. angular- and kinetic-energy distributions. Figure 1.1 shows the fission cross section of 234 U (n, f ). Large fluctuations of the distributions were reported, in the vicinity of the vibrational resonances in the barrier region below E n = 1 MeV [3, 4, 5, 6]. Increased knowledge, especially of the mass distributions, may contribute to an improved modelling of the fission process. In this work 234 U (n, f ) was studied at 14 different incident-neutron energies, E , ranging n from 0.2 MeV to 5.0 MeV. The investigation focused on the angular-, massand energy distributions. The experimental data were also parametrized based on the Multi-Modal Random-Neck Rupture model [7] to search for fissionmode fluctuations. The results on the properties of 234 U (n, f ) are presented in papers V, VI and VII. In order to study 234 U (n, f ), developments were performed on the acquisition system and analysis. The main problem encountered was the high α pile-up rate which could be properly treated if one considers the advancement of new digital techniques. New modern digital instruments and methods are entering almost all branches of science substituting conventional analogue techniques. Through the last decades, digital techniques proved to be superior in countless areas of physics. In this work, both digital and analogue acquisition systems were employed in parallel. The aim was to perform a benchmark experiment in which a direct comparison can show the consistency and superiority of the digital techniques. The comparison is presented in paper I 13.

(15) and further digital developments on the emission-angle determination can be found in paper III. The detector used in this work, namely an ionization chamber, is a wellstudied versatile instrument. It has been applied in nuclear spectroscopy already by Frisch to detect the first fission-fragment pulses [8]. Despite its simplicity, this detector is still employed in nuclear measurement, in the 21 century. However some issues in the operation are still being discussed. For instance, the so called "grid inefficiency" (GI) effect, first described in Ref. [9]. The Frisch-grid is used in the ionization chamber to remove the angle dependency from the energy signal. Due to a shielding inefficiency, a correction is needed before the energy signal can be used in calculations. There has been an ambiguity concerning the nature of this correction and two contradicting methods were applied by the community. Recently a theoretical investigation was performed to understand the GI dilemma, based on the Ramo-Shockley theorem [10]. To test the predictions of the new theoretical study and to verify the proper method of correction, a dedicated experiment on 252 Cf (sf) was planned and performed in this work. The experimental test and evidence on the validity of the new approach, is presented in paper II for the anode signal and in paper III for the grid signal. At last, a hot topic in today’s fission theory concerns the prompt-neutron emission which is relevant to the analysis of this work. The dependency of the neutron multiplicity on the incident-neutron energy is well known. The average total neutron emission increases when the excitation energy becomes higher. However, less is known on how the extra neutron emission is distributed among the fission fragments. Some few measurements have shown that the heavy fragment emits the extra neutrons [11, 12, 13, 14, 15]. An exciting theoretical discussion is ongoing, trying to explain these experimental findings [16, 17, 18]. It is still in debate, whether the excess in neutron emission is on average equally higher or higher only for heavy fragments. These two methods of prompt-neutron correction have an impact on measurements such as this one, performed with the 2-E technique. To estimate this effect, a study is presented in paper IV. The impact is assessed on the final mass and energy distributions by applying the two different methods. As will be seen, the impact found was significant and emphasizes the vital need to solve this enquiry both theoretically and experimentally.. 14.

(16) 2. Theoretical background. "Erwin with his psi can do calculations quite a few. but one thing has not been seen: just what does psi really mean? " (Erich Hückel). 2.1 Introduction to fission Right after the experimental discovery of nuclear fission by Hahn and Strassmann, a quantitative explanation was introduced by Meitner and Frisch based on the liquid drop model (LDM) [1, 19]. The same year, the theoretical description was extended by N. Bohr and J. A. Wheeler [20]. The basis of the early LDM is understood from the semi-empirical and phenomenological mass equation of Bethe-Weizsäcker [21], which describes the nuclear binding energy as: B = av A − as A2/3 − ac Z (Z − 1) A−1/3 − asym A−1 (A − 2Z)2 + ap A−1/2 . (2.1) The first term in Eq. (2.1) is the volume term describing the increase of binding energy with the number of nucleons (A). The second term is the surface term which reflects that not all nucleons have equal number of neighbouring nucleons, thus lowering the binding energy. The third term is due to the Coulomb repulsion between the protons which strives to break the nucleus apart. The fourth term, sometimes refereed to as the "Pauli term" is present since neutrons and protons are fermions and thus have to obey Pauli’s exclusion principle. The binding energy is affected by the asymmetry in the number of protons and neutrons. The last term is due to the paring effect which is related to the spin states of the nucleons. The strong nuclear force is dominant at small scales so the binding energy is governed mostly by av A. However if the nucleus deforms considerably, the Coulomb repulsion might overcome the strong nuclear force due to its short range. In neutron-induced fission, a neutron enters a uranium nucleus and adds excitation energy to the compound nucleus leading to shape deformations and hence potential-energy changes. As the nuclear deformation increases, the potential energy increases above the ground state level [see Fig. 2.1]. The fission barrier which the nucleus has to overcome in order to fission, has a maximum which is refereed to as the "saddle point". If the excitation energy 15.

(17) .

(18) . . 6.

(19) . . . 4 2. LDM LDM + shell corr..

(20) Saddle point . Deformation Figure 2.1. The fission barrier for a typical actinide. Classically the LDM model predicts a single humped barrier, but with corrections for shell effects it becomes double humped.. exceeds the level of the barrier height, nothing prevents the two fission fragments from separating, after a long-standing marriage once formed in heavystellar super-novas. The amount of excitation energy inserted by the added neutron is dependent on the target nucleus. For even-mass target nuclei such as 234,236,238 U, the extra neutron will give less energy than required to fission, because the extra nucleon will be not paired. These nuclei are thus fertile and show a threshold in the fission cross section. However for the odd-mass nuclei, for instance, 233,235 U, the extra neutron will pair with another nucleon and the excitation energy increases to above the fission-barrier height. The incident neutron does not need to have any kinetic energy in order to induce fission in these fissile elements. More specifically, for the case of 234 U (n, f ) the energy added to the system, when a neutron enters a 234 U nucleus can be calculated by adding the masses as: U∗ = mn + m 234 U ≈ (1.00866 u + 234.04095 u) ≈ 235.04961 u . (2.2) 235 235 The mass of a U nucleus is m U ≈ 235.04393 u. Thus, by using u = 931.502 MeV the excitation energy after neutron absorption is: Eex = m 235 U∗ − m 235 U ≈ 5.30MeV. (2.3) . m. 235. Eex is lower than the fission barrier height which is roughly 6.6 MeV, relative to the ground state. Therefore more energy is needed from the incident neutron. However, in the case of 235 U (n, f ), Eex = 6.54 MeV and the barrier height is 16.

(21) approximately 6.2 MeV. Thus, already by adding the mass of a neutron, fission is energetically possible.. 2.2 Fission modelling Despite the success of the LDM in describing the fission process, it has clear limitations to explain experimental results. Isomeric fission is a phenomenon not possible to describe within the predicted single-humped fission-barrier. Another obvious limitation is that the LDM fails to explain the asymmetric mass division in fission. The model also does not describe the unique shape of the prompt-neutron emission. All these effects were attributed later to shell effects, which were introduced to the LDM by Strutinsky [22]. With the new corrections, the barrier transformed from a single- to a double humped one, as demonstrated in Fig. 2.1. The ground state lies in the first minimum of the barrier and the uranium nucleus is deformed already in this state. Inside the barrier wells discrete excited states exist and they are referred to as class-I and class-II states. Considering the single-particle model, if the nucleus is excited, a nucleon is occupying one of these levels and the nucleus could de-excite by γ-ray emission, for instance. The levels in the wells are well defined but they become less resolved, the higher the excitation is. Eventually, it becomes practically impossible to distinguish the levels and one treats "level densities" rather than discrete levels. On the saddle points there are excited states which are refereed to as "transition states" and they have their characteristic spin and parity. Resonance fission is when different states couple to each other, enhancing the fission cross section. One main observable to be affected by the coupling of the transition states is the angular distribution as will be discussed in Sect. 2.5. The state coupling may correlate strongly to the fission fragments (FF) angular distribution, resulting in an angular anisotropy. Up to date, the search for the ultimate fission model is still ongoing. Due to the complexity of the fission reaction mechanism, it remains still difficult to explain various experimental observations. Different models were developed during the years. In page 228 of Ref. [23], fission models are divided into microscopic, stochastic and deterministic models. Microscopic models (and stochastic models to some extent), are usually too complicated and need to include approximations. The wave function of each nucleon has to be calculated but usually the Hartree-Fock method is used to simplify the calculations. Historically the calculations were limited by computation power but with the fast developing technology nowadays, these calculation-heavy models are becoming feasible. Deterministic codes are more practical and have proven to be closer to experimental observations. They treat the fissioning nucleus with macroscopic+microscopic descriptions. One successful example among the deterministic models is the scission-point model. It calculates the potential energy with respect to two deformation parameters. It uses the LDM (macro17.

(22) scopic treatment) with nuclear shell corrections (microscopic treatment). The model manages to explain a few experimental observations. However the calculated mass distributions are not very compatible with experiments. Another criticism to the model concerns the assumption of statistical balance between the collective excitation and intrinsic excitation at the moment of scission [24]. Another deterministic model which has proven to be among the more promising models is the Multi-Modal Random-Neck Rupture model (MM-RNR), developed by Brosa et al. [7]. This model links the fission mass and energy distributions to the potential-energy landscape and defines different paths through which fission may occur. The model was rather successful to describe the experimental fission observables from 213 At to 258 Fm. As the model is relevant for this work, it will be further discussed in the next section.. 2.3 The Multi-Modal Random-Neck Rupture model The first part of the model, (MM), concerns the fission-mode interpretation. The basis for this mode idea was early implemented by Turkevich and Niday for the mass distribution of 232 Th [25]. In order to explain the symmetric and asymmetric mass yields, they proposed two different channels through which fission occurs. At a certain moment individual Gaussian functions were used to fit the mass distribution. Formerly, one Gaussian function was fitted to the symmetric part of the yield distribution and one to the asymmetric part, respectively. However it turned out later that one Gaussian function is not sufficient to describe the asymmetric region of the mass distribution, instead two Gaussian functions were included. Figs. 2.2(a) and (b) demonstrate the improvement in fitting with two Gaussian functions. At least three modes were needed for some actinides e.g. 235 U [26]. Knitter et al. were the first who successfully used the mode picture on the fissioning system 236 U∗ for mass and TKE distributions and could explain the dip of about 22 MeV in TKE [27]. According to the MM-RNR model, in order for the nucleus to rupture, it may follow different paths through the fission-barrier landscape. These assumed paths through the potential energy landscape yield different mass- and energy distributions. The Gaussian functions which were fitted to the experimental data were now interpreted as representing the corresponding paths through the potential-energy landscape. The fission mode assigned for the symmetric fission is denoted as the "Super-Long" (SL) mode. It is assumed to have a higher outer fission barrier than asymmetric fission since it is has a very low yield. The SL mode is also attributed with a relatively large distance between the charge centres of the fragments, which has as a consequence a lower average fragment kinetic energy of roughly 20 MeV. The "standard" modes are responsible for more than 98% of the fission yield at low excitation energies. The Standard-1 (S1) mode represents the pre-scission shape with the 18.

(23) . 6. th

(24)

(25). 235. (a). 4. th

(26)

(27). 235. (b). 4 2. 2 0. 6. 130. 140. Apre (u). 150. 160. 0. 130. 140. Apre (u). 150. 160. Figure 2.2. A demonstration of the fit of a Gaussian function to the mass distribution of 235 U (nth , f ). The single Gaussian function fitted to the asymmetric mass peak was too simplistic (a), at least two Gaussian distributions are required (b).. shortest distance between the fragment charge centres. Therefore these fission events have high TKE compared to the Standard-2 (S2) mode. The S2 mode is usually the dominant path and is responsible for the more asymmetric fragment mass divisions. The position of S1 and S2 in the mass yield distribution is attributed to the doubly magic closed spherical shell (Z = 50, N = 82) and the deformed shell (N ≈ 88), respectively [28]. For some nuclei more than two asymmetric modes might be needed for instance in 237 Np (n, f ) [29]. The second part of the model (RNR) introduces a random behaviour into the rupture. The main reason for this is to explain the experimentally observed width of the mass distribution. Without this part, the mass yield would peak at the most probable mass ratio. It is also this part which gives the variation in TKE when the neck properties vary. The neutron emission is also connected to the fission modes and the neck length. The highest average neutron emission is found for the SL mode, followed by the S2 mode and finally by the S1 mode. Fig. 2.3 depicts the evolution of all modes. There is a wide agreement that the asymmetric and symmetric modes start to deviate already after the second minimum. Less is understood about the asymmetric fission modes split. In terms of the original MM-RNR model, the S1 and S2 were assumed to separate after the second saddle point, hence have the same outer fission barrier [30]. However this was revised in later theoretical calculations based on the MM-RNR model [29, 31]. As will be discussed, the angular anisotropy is closely linked to the fission barrier. Therefore one test for an individual S1/S2 outer barrier heights would be the observation of a mass-dependent angular distribution. 19.

(28) S1 S2 SL. Saddle GS. Potential energy (MeV). ?. Deformation Figure 2.3. Schematic view of the mode paths through the barrier. Asymmetric and symmetric fission paths separate already after the second minimum. It is still questioned whether the asymmetric fission modes (S1 and S2) separate before or after the second saddle point.. 2.3.1 Formalism In the MM-RNR model, the nuclear shape is represented with a generalized Lawrence shape [32] in a five-dimensional potential-energy landscape, as demonstrated in Fig. 2.4. The parameters in the figure are: the full length of the pre-scission shape (2l), the asymmetry (z), the neck curvature (c), neck radius (r) and the system center of gravity (s). The shape is described by Eq. (2.4) in the cylindrical coordinates ρ and ζ : N ρ 2 (ζ ) = l 2 − ζ 2 ∑ an (ζ − z)2 .. (2.4). n=0. The calculations based on the Lawrence shape do however not yield a mass distribution similar to what we know from experiment. The neck has some curvature and in order to reproduced the experimental yield distribution, the neck is sought to be flat. Therefore the Lawrence parametrization is transformed to a flat-neck representation as demonstrated in Fig. 2.5. In view of the new representation it is useful to express the two nascent fragments as two embedded spheroids at contact just before scission. The embedded spheroids, seen in the bottom part of Fig. 2.5 are used to calculate the fragment energies in terms of the electromagnetic proton-proton repulsion. One criticism to the original MM-RNR model was the non-physical sudden transformation from the Lawrence shape to the flat-neck representation. Such change results in a lower distance between the fragment which gives a higher TKE compared to experiment [31]. To calculate modes within the potential-energy landscape, relation (2.5) between the neck length and radius is used. This condition was a key element of 20.

(29) ρ 1/c. r. ζ z. s 2l. Figure 2.4. Generalized Lawrence representation. The figure was adapted from Ref. [7].. ρ/fm 2l-r1-r2. 10.

(30). 5. r1. ζ /fm. r. -5 -5. a110. ζ1 5. b1. 15 a. 2. ζ2. 35 35. 25. ζ /fm. b2. ρ/fm. Figure 2.5. Upper part: The flat-neck representation. spheroids. The figure was adapted from Ref. [7].. Lower part: embedded. 21.

(31) the recipe to determine modes. For ζ = 0, one obtains the Rayleigh criterion [33], which introduces a minimum required thin neck for rupture at random places of the neck. The neck may rupture when the total pre-scission shape length (2l) is larger than 11 times the neck radius (r): ζ 11 r− − ζ , ζ = −2, ..., 3. (2.5) l= 2 2. 2.3.2 Mode fits to experimental data Based on the fact that at least three Gaussian distributions are needed to fit the mass distribution, those functions are interpreted based on the MM-RNR model as representing the theoretically predicted fission modes. In the original work of Brosa et al. a parametrization was proposed which can be used to fit the two-dimensional mass versus TKE distribution [7]. The mass distribution is assumed to be described by Gaussian functions whereas the TKE distribution is assumed to be skewed semi-Gaussian distributions, in order to respect the Q-value limit:. (A − A)2 w exp − Y (A, TKE) = 2σA2 2πσA2 (2.6). L (dmax − dmin )2 200 2 2 (dmax − dmin ) . exp − − × TKE ddec ddec Lddec The height of the Gaussian is related to by w, A is the mean fragment mass and σA is the width of the Gaussian distribution. The parameter d is the distance between the fragment centres. The parameter dmax gives the distance at highest fission yield probability (around the mass distribution peaks) and dmin is the minimum distance between the fragment charge centres. The parameter ddec describes the exponential decrease of the yield when d is increasing. The term L is given by: L = d − dmin =. ZL ZH e2 AL AH (ZCN /ACN )2 e2 − dmin ≈ − dmin TKE TKE. .. (2.7). The approximated distance between the fragment centres, d, is given by the pure coulomb interaction. The approximation in Eq. (2.7) is justified because the charges ZL and ZH are not measured in this experiment so one has to assume a uniform charge distribution. Then it follows that ZL /AL ≈ ZH /AH ≈ ZCN /ACN . Six parameters are needed to fit one fission mode to the two dimensional distribution. At least three fission modes are theoretically predicted hence three of these distributions are used to obtain a decent fit to the experimental data. Fig. 2.6 shows a fit example with the fission modes (S1, S2 and SL) superimposed onto the experimental data. 22.

(32) Figure 2.6. The experimental yield in a three-dimensional TKE versus mass plot. The data are fitted with three modes as illustrated here. One S1, one S2 and one SL mode were used to parametrize the data, using Eq. (2.6). Note that the three fission modes have to be mirrored to fit the other side of the mass distribution, with identical parameters, except for A.. 2.4 Energy release and time scales The enormous energy released in nuclear fission reflects the strength of the Coulomb interaction, once the nucleus is allowed to rupture. The energy is divided between the fragments and the secondary fission particles. The lion’s share (about 80 %) is given to the kinetic energy of the FF. The rest of the energy appears in prompt-neutron emission and prompt γ-ray emission and later delayed neutrons and β emission from the neutron-rich fragments. The share of energies can be studied in Fig. 2.7 which was adapted from Ref. [17]. The fission energy is divided between the fragments total kinetic energies (TKE) and a total excitation energy (TXE). The TXE is a sum of an intrinsic excitation (single-particle like), a deformation excitation and collective excitations (e.g. rotations) [17]. Primarily, the prompt-neutron emission, ν¯ (A), is a measure of the deformation energy in the nascent fragments and secondary on their excitation energy. The TKE release may be estimated using the systematics of Unik [34]: TKE = (0.13323). Z2 − (11.64) MeV, A1/3. (2.8) 23.

(33) .

(34)

(35) . 180 160. scission. 140 120 100. TXE.

(36) . TKE. . 200. 10. 20. 30. 40. 50. F

(37) . 60. Figure 2.7. The share of TKE and TXE in the fission process where the latter can either be deformation, excitation or collective excitation (e.g. rotation). Fig. adapted from Ref. [17].. which results in roughly 170 MeV on average, for a typical uranium fission. The conservation of momentum requires that A1 × v1 = A2 × v2 . Neglecting effects like momentum transfer and neutron emission, the ratio of the fragment velocities v1 and v2 , is then approximately given by the ratio of the fragment masses A1 and A2 . Since A2 /A1 ≈ v1 /v2 it follows that the light fragments end up with higher average kinetic energy compared to the heavy fragments. The time scale for the entire fission process is relatively long as described in page 499 of Ref. [23]. The time from the saddle point to the nuclear scission is estimated to 10−20 s. Within 10−19 s the kinetic energies are shared by the fragments. The prompt neutrons are emitted by the fragments within 10−17 s, followed by the prompt γ-ray emission which happens after 10−13 s and by β decay of the fragments starting after 10−6 s. Finally, the delayed neutron emission range in decay times from 0.2 to 60 seconds depending on the delayed-neutron group.. 2.5 Anisotropy in nuclear fission Angular anisotropy in nuclear fission is well documented for various reactions, from photo-fission to charged-particle induced fission and neutron-induced fission. It is truly fascinating how the fragments may drastically change their spatial emission, within a range of a few hundreds of keV difference in inci24.

(38) dent particle energy. The first explanation of angular anisotropy was given by A. Bohr [35]. He proposed that FF angular distributions are closely related to the fission barrier and that the quantum states at the saddle points determine the angular distribution. Different quantum numbers are used to describe the fissioning system and are illustrated in Fig. 2.8. The total angular momentum (J), its projection on the symmetry axis (K), the projection on the beam axis (M) and finally the state parity π. The neutron beam is defined parallel to the space-fixed z axis and the x is defined as the nuclear symmetry axis. An assumption of the Bohr theory is that K is a good quantum number, i.e. it remains conserved during scission. The second ansatz for his theory is that the nucleus fissions along the symmetry axis. In the case of 234 U (n, f ) results were reported in Ref. [4, 5] suggesting the existence of four different states. The different fission states are (K,π) = 12 +, 32 −, 12 − and 32 +. These open fission states give rise to four partial cross sections which all superimposed give the total cross section in the barrier region. The theoretically calculated angular anisotropy is peaked at 0◦ for K = 12 and for K = 32 it peaks at 90◦ . Further details can be found in Ref. [5]. The partial fission cross section based on the K = 32 states dominates at the first vibrational resonance, En ≈ 0.5 MeV. At the second vibrational resonance, En ≈ 0.77 MeV, the K = 21 states dominate and give hence rise to an anisotropy in the beam direction. ^. z. ^x. J K. M. n Figure 2.8. The fissioning nucleus with the quantum numbers J, K, π and M [see text for details]. In the descriptive view, z is a space-fixed axis normally along the incident neutron beam and x is the nuclear symmetry axis. The trajectory of the fissioninducing neutron is also shown.. Fragment mass anisotropy Another aspect of fission anisotropy is far less evident and may sound controversial, namely the anisotropy in mass emission. A few experimental studies reported a mass anisotropy e.g. in 235,236,238 U (n, f ) and 232 Th (n, f ) [36, 37, 25.

(39) 38, 39, 40]. Some of these observations were attributed to effects connected with multi-chance fission as discussed in page 209 of Ref. [41]. Another set of experimental works did not find any mass anisotropy [42, 43, 44, 45]. Classical fission models do not consider such anisotropic mass behaviour as discussed in Ref. [41]. As mentioned earlier, the fission barrier was supposed to determine the FF angular distribution. Because the barrier is assumed to be the same for most asymmetric fission events, it is natural to expect equal angular anisotropy regardless of the fragment mass. However, if one changes the theoretical frame, one may explain a possible experimental observation of a mass-dependent anisotropy. More specifically, the MM-RNR model adopted the idea of an anisotropic mass emission where each fission mode may theoretically have its own angular distribution. The fission modes represent different fission asymmetry, therefore the angular anisotropies could change for different parts of the mass distribution, which is discussed in page 494 of Ref. [23]. Eq. (2.9) represents the angular distribution, W (A, TKE, Θ), as dependent on each fission mode (m). The Wm (Θ) distribution is independent on the mass and TKE, however when multiplied with the mass and TKE yields for a given mode (m), Ym (A, TKE), it becomes mass dependent. W (A, TKE, Θ) =. n. ∑ Wm (Θ) ×Ym (A, TKE). (2.9). m=1. An interesting idea emerges if one combines the classical Bohr theory of angular distributions with the revised MM-RNR model. If the fission barrier is to determine the angular distribution, and that different angular distributions are found for the S1 and S2 modes, the two modes could actually have different outer barriers as indicated by Fig. 2.3. As stressed in Sect. 2.3 the original MM-RNR model predicts the same barrier heights for S1 and S2. However in the revised versions of the model, different outer barriers were expected for the different modes. For example, based on the calculations performed for 238 U (n, f ) in Refs. [29] and [31]. Since each fission mode has different pre-scission shapes, with respective different FF characteristics, this may be observed on the angular distributions. One evidence on the presence of the fission modes would in fact be in a mode-dependent angular distribution.. 2.6 Prompt-neutron emission The neutron multiplicity, ν, is an important gateway to understand fission dynamics. The neutron emission depends on the pre-scission shape and the deformation energies of the nascent fragments. It reflects nuclear shell effects and also relates to the energy release in fission as well as the excitation energy. 26.

(40) Mass and TKE dependencies The mass dependency in ν¯ (A) is dominated by nuclear shell effects, which gives the typical "saw-tooth" like structure of ν¯ (A) seen in Fig. 2.9. The presented data for 233,235 U (nth , f ) and 239 Pu (nth , f ) were taken from Ref. [46]. The 234,238 U neutron-multiplicity shapes were parametrized from the two neighbouring uranium isotopes. The special "saw-tooth" trend is described by the characteristic deformation energies stored in the nascent fragments at the scission point [47]. For masses A ∼ 130 u, a dip is prominent, which is the result of nearly spherical fragment shapes due to doubly magic nuclear closed shell configurations (N = 82, Z = 50). On the contrary, the neutron emission is high for fragment masses around 105-115 u for the light fragment and around 150-160 u for the heavy fragment because of a much more deformed shape. The deformation energy, responsible for the higher neutron emission, can be estimated from the total excitation energy (TXE) which is defined as: TXE = EL∗ + EH∗ = Q − TKE,. (2.10). where Q denotes the reaction Q-value, EL∗ and EH∗ are the excitation energies of the fragments. The neutron multiplicity is also TKE dependent. It follows from Eq. (2.10) that the TXE increases as TKE decreases. Therefore, ν¯ (TKE) is inverse proportional to the TKE. Dependency on excitation energy Naturally, the internal excitation energy of the compound nucleus increases for higher incident neutron energies. As a result, it enhances the neutron emission which has been confirmed experimentally in different measurements on the total neutron-emission, ν¯ tot . However, an interesting debate is ongoing, on the share of extra excitation energy by the two fragments. It was assumed in the majority of earlier studies that the neutron emission is enhanced on average equally for the heavy and light fragments. Some few experimental studies have shown on the contrary, that the heavy fragments emit the extra neutrons exclusively [11, 12, 13, 14, 15]. Fig. 2.10 shows the most prominent example from Ref. [11], performed for 237 Np (n, f ) at En = 0.8 and En = 5.55 MeV. By using the 2E-2v method, the neutron emission was indirectly measured. These observations were recently discussed in theoretical investigations attempting to explain this behaviour [16, 17, 18]. One promising hypothesis originates from thermodynamical arguments and is presented in Refs. [16, 17]. It is based on the assumption of a constant-nuclear temperature, up to excitation energies of 20 MeV [48, 49]. The level densities ρ (E ∗ ) are within good approximation described by: ρ (E ∗ ) ∝ exp (E ∗ /T ). ,. (2.11). where T is the temperature parameter. The nuclear temperature seems to stay constant even if the excitation energy increases which is owed to pairing cor27.

(41) 3. U-235 U-238 Pu-239. U-233 U-234. ν (A). 2. 1. 0. mass distr. 80. 100. 120. Mass (u). 140. 160. Figure 2.9. Neutron-multiplicity distributions for 233,235 U (n, f ) and 239 Pu (n, f ) from Ref. [46]. The data for 234,238 U (n, f ) are deduced as described later in Sect. 4.5. The mass yield distribution is from 234 U (n, f ).. 4. Np(n,f). En= 0.8 MeV En= 5.55 MeV. 237. ν (A). 3 2 1 0. 80. 100. 120. Mass (u). 140. Figure 2.10. The neutron-multiplicity shape from 237 Np (n, f ) at two different excitation energies, from the measurements of Ref. [11]. The neutron emission increases only for the heavy fragments.. 28.

(42) relations [16]. According to Ref. [48] the energy-independent fragment temperature T is related to the fragment mass by: T∝. 1 A2/3. .. (2.12). As a consequence from Eq. (2.12), the hotter fragment is always the lighter one. The nascent fragments are assumed to be in thermal contact before the scission point. Similar to heat transfer processes, the excess energy located in the light fragment will be distributed to the heavy fragment. This proposed "energy-sorting" ensures that the nucleus strives to reach equilibrium before splitting. However due to the constant-temperature behaviour, the equilibrium is never reached and all energy is transferred to the heavy fragment. The extra excitation energy will now be in the heavy fragments, allowing for a higher neutron multiplicity, as the incident neutron energy increases. Note that despite the experimental data favouring the pre-dominate heavy¯ up to date the debate is still ongoing. The shares of fragment increase of ν, excitation energies is not fully understood and too few experiments exist on ν¯ (A) as a function of excitation energy. Therefore, various works still assume an average increase of ν¯ (A) e.g. Refs. [50, 51, 52, 53, 54].. 29.

(43) 3. Experiments. "I can prove anything by statistics, except the truth." (George Canning). The measurements of the reaction 234 U (n, f ) are summarized in Tab. 3.1. The absolute energy calibration was done using 235 U (n, f ) at thermal neutron energy. Table 3.1. Experiment statistics Incident neutron energy (MeV) 0.200 ± 0.066 0.350 ± 0.057 0.500 ± 0.052 (0.039) 0.640 ± 0.035 0.770 ± 0.033 0.835 ± 0.034 0.900 ± 0.032(0.033) 1.000 ± 0.111 1.500 ± 0.093 (0.094) (0.103) 2.000 ± 0.081 (0.082) (0.089) 2.500 ± 0.067 (0.072) 3.000 ± 0.065 4.000 ± 0.309 5.000 ± 0.177 235 U (n , f ) th. Target 7 LiF(p, n) 7 LiF(p, n) 7 LiF(p, n) 7 LiF(p, n) 7 LiF(p, n) 7 LiF(p, n) 7 LiF(p, n). TiT(p, n) TiT(p, n) TiT(p, n) TiT(p, n) TiT(p, n) D(d, n) D(d, n) TiT(p, n). Thickness μg/cm2 830 830 830 (619) 596 596 619 596 (619) 1936 1930 (1936) (2130) 1930 (1936) (2130) 1930 (1936) 1936 1902 1902 1936 (2130). Statistics ×103 17 20 161 444 182 92 73 155 406 895 711 359 81 141 2 914. 3.1 The Van de Graaff accelerator The basis for doing accurate fission studies is a stable and precise neutron beam. An excellent candidate is the quasi-monoenergetic beam from the Van de Graaff accelerator (MONNET) of the IRMM in Geel, Belgium. The accelerator is vertical, single ended and can reach up to 7 MV high voltage. A schematic view of the accelerator is given in Fig. 3.1. The accelerator operates by electrostatic charging of the dome through the belt. An ion source is located in the top of the machine at high voltage, from which protons and deuterons can be extracted. The ion beam is accelerated via the voltage difference and is steered and focused with quadrupole magnets. An analysing 30.

(44) + + + +. . +. +. +. +. . + + +. + + +.

(45) .

(46) . -. TFGIC.

(47)

(48)

(49) .

(50) . Φn ×106 (n/s/cm2). Figure 3.1. Schematic view of the Van de Graaff accelerator. The charged ions are accelerated in the tube, bent in the analysing magnet and focused with quadrupole magnets. The neutron production is done via several nuclear reactions. The inset picture shows the open VdG with the dome of the high voltage terminal.. 1 30.

(51) . 2. 3. 4. ). 5. 15. Ti(p,n) 1930 g / cm. 2. (a). 2. 3. 4. 5. 6. 7. Li(p,n) 619 g / cm2. (b). 10. 20. 5. 10 0 0.

(52). 1. 2. 3. 4.

(53) . 5. 0 0. 1. 2. 3. 4.

(54) . 5. Figure 3.2. The neutron fluxes (Φn ) from the two main reactions used for neutron production in this work; T (p, n) (a) and 7 Li (p, n) (b). The calculations were done with the Energyset code [55]. The proton energies are also given.. 31.

(55) Figure 3.3. Left (a): The experimental setup showing the end of the beam-line where the (p, n) and (d, n) reactions produce neutrons. The TFGIC is placed close to the neutron production target and the chamber signals are read out by charge-sensitive preamplifiers. Right (b): The interior of the ionization chamber with the five electrode plates.. magnet bends and selects ions based on the desired energy. The neutrons are produced using three different reactions which are listed in Tab. 3.1. For En ≤ 0.9 MeV the 7 Li (p, n) reaction was used. Because of the relatively thin target a good precision in neutron energy was obtained, however at the price of a reduced neutron flux. For 1.0 ≤ En ≤ 3.0 MeV, T (p, n) provided higher neutron flux due to the thicker targets, but with a larger spread in neutron energy. The typical neutron fluxes from these reactions can be seen in Fig. 3.2 and were calculated by the Energyset code [55]. Finally, D (d, n) was used for the En = 4.0 MeV and 5.0 MeV runs. On average, the neutron beam current was ranging between 5 and 15 μA. In order not to destroy the neutron-producing targets due to the beam-energy deposition, water cooling was used to cool the target. The water used for the cooling does moderate the neutrons to lower energies, but the moderation is negligible and affects only the neutron tail [56].. 3.2 The ionization chamber The FF were detected by means of a Twin Frisch-Grid Ionization Chamber (TFGIC). The main advantages of the TFGIC are its radiation hardness, versatility and nearly 4π solid angle. The chamber is shown in Fig. 3.3 and schematically drawn in Fig. 3.4(a). It consists of two anodes, two Frisch-grids and one common cathode, with the Uranium sample mounted in the center of the cathode. High voltage was applied to the electrodes, 1.0 kV on the anodes, -1.5 kV on the cathode and the grids were grounded. The sample side faced the impinging neutrons. The chamber dimensions along with the Frisch-grid properties are given in Tab. 3.2. The choice on electrode high voltage was based on the requirement from Ref. [9] to minimize the electron losses on the 32.

(56) Table 3.2. Dimensions of the chamber and Frisch-grid properties. Parameter Grid-cathode distance (D) Anode-grid distance (d) Grid wire spacing (a) Grid wire radius (r). Value (mm) 31 6 1 0.05. Frisch-grid: p + pρ + 0.5 · r ρ 2 − 4 · ln ρ VA −VG ≥ VG −VC a − aρ − 0.5 · r (ρ 2 − 4 · ln ρ). ,. (3.1). where ρ = 2πr · d −1 . The values of the parameters required for the calculation are given in Tab. 3.2. The reduced field strength in the anode-grid region should roughly be three times stronger than the grid-cathode field strength. The chosen high voltages fulfil the relation (3.1) and give a field strength ratio between anode-grid and grid-cathode which is larger than 3. Note that VA /0.6 cm = 1667 V × cm−1 and −VC /3 cm = 500 V × cm−1 . The chamber was operated with a P-10 counting gas (90% Ar+10% CH4 ) at a gas pressure of 1.05 × 105 Pa and a gas flow of 0.1 l/min. The choice on counting gas is mainly based on the electron-drift velocity. A fast drift velocity is desired and typical values of 5 cm/μsec are reached with P-10 gas [45]. Signal generation The best way to address the principle of signal generation is to consider the Ramo-Shockley theorem, as pointed out by Ref. [57]. As the fission fragment enters the counting gas, it ionizes the atoms and electrons are liberated. The ionized electrons are proportional to the deposited fragment energy. Due. 0V.

(57) - 1.5 kV 0V. + 1.0 kV. FF2. . U. 234. n. θ. _ FF1. . . d. Backing. 90o 0o Cathode. (b). D. X. n. +n0e. Q(t). (a) + 1.0 kV. 0o 90o. o. 90 0. D -n e 0 . . d.

(58). Grid. o. 0. 1. Anode. (). 2. Figure 3.4. (a): Schematic view of the TFGIC (D and d are given in Tab. 3.2). (b): A demonstration of the signals generated by the TFGIC for different FF emission angles. The time-scale is approximated.. 33.

(59) to the applied voltage the electrons drift towards the anodes. Because of the three orders of magnitude difference in weight, the positive ions are practically motionless in the short time-scale of electron collection on the anode. The electron cloud drifts along the electric field between the electrodes and it induces charge signals on anode, grid and cathode. According to the RamoShockley theorem, the charge induction is due to the motion of the electrons rather than the actual collection. One can also explain the charge signals in terms of the total charge collection and the positive ion position, based on the mirror-charge theorem as in Ref. [9]. Both approaches yield the same expressions for charge induction. A demonstration of the signals is shown in Fig. 3.4(b), for two emission angles. In the ideal case, the anodes do not detect the electrons before they pass the grid plate. After passing the grid, all electrons travel the same distance on their way to the anode (d). The result is that the charges induced on the anodes are independent on the emission angle and are the sum of the total number of electron-ion pairs, n0 : (3.2) QA = −n0 e . The cathode signal, QC , is not shielded and is thus angular dependent: X QC = n0 e 1 − cos (θ ) , D. (3.3). where X is the center-of-gravity of the electron-cloud distribution and D is the grid-cathode distance. The grid signal is more complex, showing a bipolar shape. The shape results from the fact that the electrons drift towards the grid first, then away from it. After the atoms have been ionized, the first liberated electrons drift and thus induce a signal on the grid, opposite in sign to the cathode signal. But after they pass the grid they induce a signal, opposite to the anode instead. The full bipolar grid signal holds information on the emission angle. Following Gauss’s flux theorem, the total induction is zero due to the conservation of charge and energy: QA + QC + QG = 0. .. (3.4). Combining this information with Eqs. (3.2) and (3.3) leads to the grid signal in the ideal case: X (3.5) QG = n0 e cos (θ ) . D. 3.3 The 234,235 U targets. The 234 UF4 target 92.133 ± 0.455 μgU/cm2 was used for neutron irradiation. It was produced at IRMM, through vacuum evaporation on a polymide 34.

(60) foil 32 ± 1.5 μg/cm2 covered with Au 50 μg/cm2 and fixed on aluminium rings. The Au coating ensures a good conductivity of the sample mounted in the cathode, which is important in order to shield the two chamber sides from each other. The isotopic composition of the sample (measured 237 U, 0.08 % 235 U and 0.06 % 236 U. A in 1977) was 99.08 % 234 U, 0.79 % 235 UF sample 45 ± 2 μgU/cm2 , was used for absolute energy calibration 4 and was prepared in the same way. α activity of 234 U The main decay mode of 234 U is α emission (231.3 MBq/g). The target mass is roughly 0.65 mg and the half-life of 234 U is T1/2 = 245500 years. Using the radioactive decay law: −. dN = λ N0 e−λ t = λ N, dt. (3.6). one can estimate the α activity to 1.5×105 α/s. Due to the relatively high activity, the isotopic composition of the sample changes. However this effect is negligible, since from 1977 (time of isotopic analysis) it produced only 0.01 % of 230 Th in the sample.. 3.4 Data-acquisition systems Five signals were extracted from the chamber. The two anode signals give the pulse-height information, two grid signals which hold the angular information and one cathode signal as signal trigger. The signals were fed into charge-sensitive pre-amplifiers. Two parallel acquisition systems were used, conventional analogue and modern digital data-acquisition systems. The full electronic scheme of a single chamber side is shown in Fig. 3.5. A precision pulse generator was fed into the anodes and cathode to monitor signal drifts. In both systems, the cathode signal was triggering the acquisition by using a Constant-Fraction Discriminator (CFD). Analogue systems In the analogue case, three Analogue to Digital Converter modules (ADC) were used for each chamber side. The anode signal was splitted in a Linear Fan In Fan Out (LFIFO). To read the energy dependent anode pulse height it was fed into a Spectroscopic Amplifier (SA) with shaping time of 2 μs and stored after treatment in ADC2. The summation of anode and grid signals was used for the angle determination and was stored in a similar manner after passing through ADC3. The drift-time method, which is an alternative method to extract the angle, was used when storing the electron drift-time using ADC1. The anode signal was fed into a Timing Filter Amplifier (TFA) and later into a Leading Edge (LE). A Time to Amplitude Converter (TAC) registered the 35.

(61) PA.

(62) G PA. C. PA.

(63) . . . . ANALOGUE. . ADC.

(64). . . . . .

(65) . DIGITAL. MPA Delta BOX. A. . . PC. Figure 3.5. The electronic scheme used for the experiment, both for the digital and analogue acquisition systems. Explanation to the abbreviations can be found in the list of abbreviations. ADC1 stored the drift-time signal, ADC2 the anode pulse height and ADC3 the summation signal.. stop from the delayed cathode signal, by a Delay Generator (DG). Due to the drawbacks of the AA data compared to the DA, the final fission-fragment analysis and results are only performed with the DA data. The AA measurements served as benchmark to the consistency and superiority of the digital techniques. The main findings on this comparison are discussed in Sect. 4 as well as in paper I.. Digital systems For the digital acquisition system, much less electronic modules are needed. The charge signals (cathode, both anodes and both grids) were digitized in 100 MHz waveform digitizers and stored on a hard disc for off-line analysis. The functionality of the NIM-electronics needed in the analogue case, had to be implemented software-wise in the digital-signal processing (DSP). The digitizers were set to store 256 pre-trigger sampling channels and a total of 1024 channels. The sampling rate was 10 ns per channel, thus each stored fission track was roughly 10 μs long. Large amount of data (roughly 0.5 Terra Byte) were stored compared to the analogue case. This is because for each fission event, 1024 numbers had to be stored in case of DA and 1 number for AA. 36.

(66) 3.5 Grid inefficiency Because of the imperfections in the shielding efficiency of the grid, the charge signal on the anode is slightly angular dependent as first discussed in Ref. [9]. This happens since the anode detects the motion of the electrons already before they pass the grid. As the anode signal, the grid signal is affected by the Grid Inefficiency (GI), and needs also to be corrected. The amount of inefficiency is measured in term of the factor σ for a parallel-wired grid. It depends on the anode-grid distance (d), the grid wire radius (r) and the distance between grid wires (a) and was derived in Ref. [9]: . d σ (d, r, a) = 1 + 2 2 −2 a/2π ((π r · a ) − ln (2πr · a−1 )). −1. .. (3.7). In the presented setup σ = 0.03, based on the grid properties listed in Tab. 3.2.. 3.5.1 Additive approach The first historical correction applied to the grid inefficiency is based on Ref. [58]. It is referred to as the "additive approach" and took into account the induction from the positive ions, after the electrons have been collected. Based on this, the detected anode signal is: X ∗ . (3.8) QA = −n0 e 1 − σ cos (θ ) D The correction method was to add the angular-dependent part missing from the signal, due to the positive ion contribution. The pulse heights PA and PC are obtained from the charge signals QA and QC and they are corrected by applying the following formula: (3.9) PA = PA∗ + σ · (PA∗ − PC ) , where PA is the GI corrected signal height and PA∗ is the detected anode signal height. Note that this correction type is an approximation in the framework of the additive approach with the defined charge signals QA , Q∗A and QC . Following Eq. (3.9), the l.h.s. is: PA = n0 e. .. (3.10). However the r.h.s. is: PA∗ + σ · (PA∗ − PC ) = X X X n0 e 1 − σ cos (θ ) + σ n0 e 1 − σ cos (θ ) − σ n0 e 1 − cos (θ ) = D D D X . n0 e 1 − σ 2 cos (θ ) D (3.11) . . 37.

(67) The term with σ 2 is very small and justifies the use of this GI correction based on the additive approach.. 3.5.2 Subtractive approach The additive-approach correction was revised when the first digitizer systems were adapted in fission experiments. The new possibilities of studying the digital traces in offline-mode gave new insights. It was observed that the anode signals already exhibit a linear rise due to the GI which is be expressed as: Q∗A = −σ QC. ,. (3.12). which is valid as long as the electrons drift in the cathode-grid region. The interpretation of this rise was to consider it as an offset to the total charge. As a consequence it was subtracted from the total charge induced as done in Ref. [59]. The following correction was proposed in the "subtractive approach": PA = PA∗ − σ · PC. .. (3.13). As a consequence, two different methods were used amongst the community. One adding, one subtracting the angle-dependent part from the pulse height.. 3.5.3 Ramo-Shockley theorem Recently, the Ramo-Shockley theorem was applied to solve the pending ambiguity [10]. The basis for this new approach was to consider moving charges, calculating weighting potentials and to solve the Laplace equation. It was found that the original additive approach was the valid method and that the detected anode signal is in fact given exactly by Eq. (3.8). Despite this, the correction given in Eq. (3.9) is an approximation since PA inside the brackets on the right hand side, still holds an angle dependency. The proper correction is to first subtract the angle-dependent linear rise of the anode signal (before electrons pass the grid), as described by −σ QC . Then to add σ QA , where QA is the ideal anode signal as given in Eq. (3.2). The last step is done by dividing with (1 − σ ). The new exact formula correcting for the grid inefficiency is thus: (3.14) QA = (Q∗A + σ QC ) (1 − σ )−1 , keeping in mind that QC and Q∗A have opposite signs. The grid signal, is also affected by the grid inefficiency. By applying Gauss law, given in Eq. (3.4), but on the non-ideal (detected) chamber signals, the grid signal becomes: Q∗G = n0 e (1 − σ ). X cos (θ ) , D. so by dividing with (1 − σ ) it is properly corrected for the GI effect. 38. (3.15).

(68) Table 3.3. Two Frisch-grids used on the sample side.. .

(69) . 2. Cf. 252.  = 0.9.

(70) . -1.5 kV. 2. d. . 0.0 V 1.0 kV. d. Ni-backing . 0.0 V 1.0 kV. 1. _θ X. D. d. . . Ni-backing. 1.0 kV 0.0 V.

(71) . (b). D. Cf. 252.  = 0.3. 1. _θ X. D. . -1.5 kV. 1.0 kV 0.0 V. . (a). σcalc Eq. (3.7) 0.03 0.09. Wire spacing (a) (mm) 1.0 2.0.

(72) . d. Wire radius (r) (mm) 0.05 0.05. D. Grid type Grid I Grid II. Figure 3.6. (a): The IC chamber used for the first grid-inefficiency experiment with Frisch-grid I, used on the sample side, with 1 mm wire spacing. (b): The IC chamber used for the second grid-inefficiency experiment with Frisch-grid II, used on the sample side, with 2 mm wire spacing as listed in Tab. 3.3.. 3.5.4 Experimental investigation of the grid-inefficiency ambiguity The long-standing debate on the proper correction method for the GI was discussed above. There was still a need for an experimental verification of both additive and subtractive methods based on traditional FF spectroscopy. For this purpose an experimental set-up was planned and prepared in the framework of this thesis work, to determine the proper GI correction method. A dedicated measurement was performed on 252 Cf (sf) with the same operation conditions as the uranium experiment (dimensions, gas type and pressure and electrode voltages etc). Two measurements were done, utilizing two different Frisch-grids as listed in Tab. 3.3. The only allowed change was the grid wire spacing on the sample side, a = 1 and 2 mm, respectively. All other settings were unchanged during the two measurements. The setup is illustrated in Figs. 3.6(a) and 3.6(b). By changing the grid-wire on the sample side the GI was expected to be more than double, which eventually could be studied on the raw FF pulse-height spectrum. A larger σ leads to a higher pulse height according to the subtractive method. On the contrary it leads to a lower pulse height according to the additive method. The data acquisition was based on digital data acquisition techniques. On the backing side, a mesh grid was used (pitch of 0.48 mm and wire diameter of 0.028 mm). The backing side was used as signal quality check to monitor for drifts. 39.

(73) QA. . . . . (. 400. 1.5. - QC -QC. 800 . = 0.083). TC. TG. TA. (b). mesh. . = 0.011± 0.006. . grid I 1 mm grid II 2 mm. 1.0. TCOG.  =0.031 ± 0.003   .  . 0.5. . . 0. = 0.083 ± 0.003 . (a). 240. 320. 400.

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