Università degli Studi di Napoli Federico II

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1 Università degli Studi di Napoli Federico II Scuola Politecnica e delle Scienze di Base Area Didattica di Scienze Matematiche Fisiche e Naturali Dipartimento di Fisica Tesi di Laurea Magistrale Discrete gamma-rays as probe of fission and quasi-fission dynamics in the reaction 32 S Au near the Coulomb barrier Relatori Prof. Emanuele Vardaci Dott. Daniele Quero Candidato Alessandro Pulcini N94/223 Anno Accademico 2015/2016

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3 I Content Abstract III Chapter Reaction mechanism classification Fusion and fission Quasi-fission Dynamical description of competition between fusion and QF Observables Fission Quasi-fission Gamma ray probe Performed experiment Aim of the Thesis 23 Chapter 2: Experimental Setup The Time-Of-Flight Spectrometer CORSET CORSET geometry Gamma rays detection Gamma interaction with matter Solid state detectors Compton suppression ORGAM detector ORGAM geometry PARIS detector Electronics and trigger 37 Chapter 3: Data Analysis and Results ORGAM calibration Energy calibration Efficiency calibration Fragments velocities Masses and energies Gamma rays energies and Doppler correction Gamma rays data analysis 48

4 II Conclusions and Perspectives 57 References 58

5 III Abstract Nowadays many nuclei around the super heavy elements region have been synthesized in fusion reactions of heavy nuclei. The existence of these nuclei is completely determined by the existence of proton and neutron closed shells at Z = and N = 184, the island of stability. Due to the high fissility of heavy and super heavy elements caused by the relatively small fission barrier, only a minor part of the fusion cross section is expected to fall into the evaporation residue channel. The excited compound nucleus formed in fusion reaction mainly undergoes fission. The study of the fission of heavy and super heavy nuclei gives important information about the cross section of compound nucleus formation, the fission barriers and survival probabilities of these nuclei. The mechanism of fusion of massive nuclei is significantly different from the formation of a compound nucleus in the case of light projectiles because of the substantial increase of the Coulomb repulsion between the interacting nuclei. After capture, indeed, the complete fusion of two massive nuclei, at energies around the Coulomb barrier, has to face a strong counteracting binary process, the quasi-fission. Quasi-fission is a transitional mechanism between deep-inelastic collisions and complete fusion, in which the composite system separates into two main fragments without forming a compound nucleus. Quasi-fission happens to be the most important mechanism that prevents the formation of super heavy nuclei. Due to the low production rate of super heavy elements, experiments on synthesis of new elements last many months. Therefore, one of the main challenges is to search for initial condition that favor the production of super heavy elements. Such a search could be pursued experimentally by detecting evaporation residues, but it might be time-consuming and not always feasible. An alternative way is to study in detail those processes that act against the compound nucleus formation, like quasi-fission, and gain insight on their occurrence and properties. Compound nucleus fission and quasi-fission are both binary decay channels characterized by large nucleon exchange and energy dissipation. These common properties make the experimental separation between them difficult. Several techniques have been developed to decompose all fission-like fragments into the two components, by the measurement of mass, energy and angular distributions and the comparison with experimental fission systematics, or with theoretical predictions in the frame of a chosen

6 IV model. Nevertheless an un-ambiguous disentanglement of the two processes has not been achieved yet. This means that these observables are not a complete set for the correct disentanglement of the two processes. The differences between these two processes mark the path towards the identification of better observables for their disentanglement. On one side there is fusion-fission, a slow process passing through an equilibrium stage. On the other side there is quasi-fission, a faster process with less mass transfer and less energy dissipation, strongly governed by shell effects. It is reasonable to think that for the slower process the whole orbital angular momentum is transferred into internal degrees of freedom of the compound nucleus and so the two fragments after fission have a higher spin than the fission-like fragments produced by quasi-fission. A possible way to probe the angular momentum of the two fragments is to use gamma rays. Gamma rays have many possible advantages with respect to other probes; as an example, by measuring discrete gamma transitions it is possible to identify the fragments charge numbers instead of only the mass numbers and, by gating on high or low angular momentum gamma transitions, disentangle fusion-fission and quasi-fission paths. As a case study, the reaction 32 S Au at E lab = 166 MeV was proposed by an international collaboration and performed at the Tandem ALTO facility at IPN ORSAY (Institut de Physique Nucléaire d'orsay, France) to test the concept above. ORGAM and PARIS, two different gamma detectors arrays, are coupled with the CORSET fission-like fragments detector, which is a two arm time-of-flight spectrometer based on micro-channel plates. CORSET gives access to the two products in coincidence with a mass resolution of 3-4 u, a kinetic energy resolution of a few MeV and an angular resolution around 0.3. Thus, several relevant signatures of the reaction dynamics are accessible with sufficient resolution for the present physics objectives. These observables are to be correlated to the prompt gamma rays measured with ORGAM and PARIS detectors; ORGAM is an array of high-resolution Ge detectors surrounded by BGO anti- Compton shields, PARIS is a high efficiency array detector composed by LaBr3 (Ce)- NaI(Tl) phoswich base units. It shall be emphasized that the velocity vector of the reaction products being measured with CORSET, the gamma ray spectrum can be properly corrected for Doppler effects. The aim of this thesis is to extract gamma energy spectra from the ORGAM detectors in coincidence with the fragments of two-body reactions due to the quasi-elastic channel

7 V and the fusion-fission channel, and to perform the appropriate corrections. The first chapter starts with a brief overview on reaction mechanisms, with a more specific description of fusion-fission and quasi-fission, their competition and the most used observables for the decomposition of the two processes. Then the advantages of the gamma ray probe as a discriminant between the two processes are described. In the second chapter the experimental setup and its characteristics are described, with particular focus on gamma rays detection aspects and the ORGAM array. The third chapter illustrates the steps of the data analysis.

8 1 Chapter Reaction mechanism classification Heavy ion reactions are those induced by incident ions with mass number A 4. For a nuclear reaction to take place, the energy of the incident ion must be at least comparable with that of the Coulomb barrier, EB = Z1Z2Ee 2 /r, where r is the separation of the centers of the two ions. At such energies heavy ions typically have De Broglie wavelengths much smaller than their radii, so that in some respects their motion is similar to that of a classical particle. De Broglie wavelength is given by λ = h μv [1.1] where μ is the reduced mass and v is the relative asymptotic velocity. On this basis, the overall features of heavy ion interactions can be described in terms of the impact parameter b, as shown in Figure 1.1. Four different b windows can be identified: Fig 1.1 Reaction mechanisms as a function of the impact parameter b. [Hod78]

9 2 a) Distant collisions: b gr < b b) Grazing collisions: b dir < b < b gr c) Close collisions: b fus < b < b dir d) Central collisions: b < b fus In case a) the impact parameter is bigger than the sum of the radii of the ions. The two ions can only interact through the Coulomb field and this results in Rutherford scattering and possibly Coulomb excitation. b gr is defined as the grazing impact parameter and it is equal to the sum of the radii of the two ions. It can be determined experimentally. As the impact parameter decreases, the increasing superposition of nuclear matter opens the way to new reaction channels. In case b) the impact parameter value decrease up to b dir, where deep inelastic reactions show up. In this window nuclear forces are no longer negligible and the trajectories after collision are defined by the competition between Coulomb and nuclear forces. These reactions come with some loss of relative motion energy, hence are called quasi elastic reactions. In case c), with impact parameter reduced still further, the ions begin to interact very strongly. This happens quite sharply because the nuclear density rise very rapidly in the surface region and the interaction change from those in which a few nucleons are transferred from one ion to the other, with little energy loss, to the deep inelastic reactions in which the ions lose a substantial fraction of their energy. In this window of reactions, fragments are produced in high excitation states and with masses similar to the projectile one and to the target one. In case d), if the energy is high enough to overcome the Coulomb potential, the fusion channel is opened. In complete fusion reaction there is a complete superposition of the nuclear matter; the two ions lose their individuality and form a compound nucleus (CN) that reaches thermodynamic equilibrium. In this kind of process all the relative motion energy is dissipated in the formation of the compound system in an excited state. A discussion in term of the impact parameter is equivalent to a discussion in term of the angular momentum, being lħ = μv b = kħb [1.2] where k is wavenumber associated to the relative motion and μ is the reduced mass. The total cross section for these processes σ R may be estimated with angular momentum as

10 3 σ R = π k 2 l=0 (2l + 1)T l [1.3] where T l is the reaction probability in the collision between a projectile with angular momentum l and the target nucleus. In the strong absorption model, it is usually used the sharp cut-off approximation for T l T l =1 l<l gr T l =0 l>l gr [1.4] where l gr is the angular momentum corresponding to the grazing impact parameter. For a generic l < l gr one has that σ = π (l + 1)2 k2 [1.5] and, deriving with respect to l, one obtain dσ R dl = 2π k 2 l [1.6] Fig 1.2 Reaction mechanisms as a function of the angular momentum l. [Hod78]

11 4 From this formula, it is possible to identify three different windows of angular momentum limited by different values of l:, as shown in Figure 1.2: 0 l fus in which we have mostly fusion reaction; l fus l dir in which we have mostly inelastic reactions; l dir l gr in which we have mostly direct reactions. The first window can be further divided in two different windows. In the first one, the excited compound nucleus has high probability to deexcite with the emission of light particle; this leads to the formation of the so-called evaporation residue. For higher values of l the fission barrier of the exit channel decreases and the fission become more probable; in this window there is mostly production of fission fragments. Reaction mechanisms can also be categorized according to the interaction time. Typical value extracted with systematics are: Quasi elastic reactions: τ int < s Dissipative reactions: s < τ int < s Complete fusion reaction: τ int > s It has to be said that the sharp distinction amongst mechanisms is somewhat blurred by a full quantum-mechanical treatment. The character of the interaction depends on the masses and charges of the two ions and on their relative energy. Furthermore there are particular phenomena that occur in special circumstances. Fig 1.3 Effective potential for the system 16 O+ 120 Sn as a function of the radial distance of the center of the two nuclei. Different curves are for different values of the angular momentum. [Ba80]

12 5 Semi-classical models describing heavy ions reactions are based on an effective potential made by three terms [Hod78]: the repulsive electrostatic Coulomb potential, equal to Z1Z2e 2 /r outside the ions and rather less inside, the strongly attractive nuclear potential that essentially acts only within the volume occupied by the ions and falls off exponentially outside and the repulsive centrifugal potential l(l+1)/r 2 that accounts for the increasing difficulty for ions with higher momentum to approach each other. The sum of these three terms gives a series of potentials that depend on l and on the radial distance r as shown in Figure 1.3 for the case of 18 O+ 120 Sn. The value of l fus is one of the most important quantities predicted by these models, because it allows to determinate the fusion cross section. In fact classically, in order for an incident ions with angular momentum l to cross the potential barrier, the relative kinetic energy should be higher than the value V(l, R lfus ). Fusion can occur only if potential has a pocket and dissipative forces are strong enough to deexcite the system in to a bound state. These dissipative forces represent a schematization of energy transfer from the relative motions to intrinsic excitation. As l increases, the centrifugal potential increases and this means that the relative minimum of the potential will be less pronounced up to the disappearance of the pocket. As a consequence fusion does not occur for angular momentum higher than a critical value l crit. Consequently, given the value of the energy of the relative motion in the center of mass reference frame E CM, the maximum value of the angular momentum that allows the fusion to occur, the one identified before as l fus, can be obtained imposing E CM equal to the potential barrier V(l fus, R lfus ). l fus is limited by the l crit value beyond which fusion cannot occur anymore. In sharp cut off approximation, according to [1.5], the fusion cross section is σ fus = π k 2 (l fus + 1) 2 [1.7] 1.2 Fusion and fission Reactions with low impact parameter, low angular momentum and enough kinetic energy to overcome the Coulomb barrier can lead to the complete fusion of the two ions. A composite system is created, called compound nucleus. During the interaction, all the relative motion energy get distributed to the intrinsic degree of freedom through a series of nucleon-nucleon interaction leaving the CN in an highly excited state. Due to

13 6 the relatively long interaction time, τ int > s, the system reaches thermodynamic equilibrium before the decay. The energy of the system is the energy of the relative motion in the center of mass reference frame plus the reaction Q-value; the angular momentum is the vector sum of the orbital angular momentum and the spins of the two nuclei. Nuclear fission is the process in which the CN decays by splitting into two fragments. A model that describes the main features of the fission process is the Rotating Liquid Drop Model (RLDM). According to RLDM the CN behaves like an incompressible rotating liquid drop, with uniform charge distribution, that deforms in an elongated shape up to the separation of the two fragments. The nucleus shape is determined by the action of the attractive nuclear force, that acts like a surface tension, and repulsive Coulomb and centrifugal forces. So a potential energy is defined as a function of deformation and of angular momentum. This potential has a maximum (saddle point) as shown in Figure 1.4 after which the nucleus has high chances to fission. At the scission point, the elongated nucleus breaks into separate pieces and the two heavy fragments are called primary fragments. Primary fragments have usually high excitation energy and cool down predominantly by neutron evaporation. Fragments which no longer emit neutrons and deexcite by gamma rays emission are called secondary fragments. Unstable ground states of secondary fragments decay by β emission until a stable nucleus is reached. This is illustrated schematically in Figure 1.5. Fig 1.4 Potential energy as a function of the nuclear deformation.

14 7 Fig 1.5 Schematic drawing showing the formation of fragments in the fission of 248 Cm. Primary and secondary fragments, as used in the text, are defined in this figure. [Ahm95] Fig 1.6 Schematic drawing showing entry points into a secondary fission fragment after neutron evaporation from a primary fragment. The contours, spaced roughly at intervals successively decreasing by factor of two, show the region of excitation energy and spin from which the secondary fragments deexcite by emission of statistical gamma rays to discrete yrast or near-yrast levels. [Ahm95]

15 8 Gamma rays from the secondary fragments arise from a broad range of excitation energy corresponding to the spread in energies of the neutrons emitted from the primary fragment. They also arise from levels with a large spread of spins corresponding to the spread in the primary fragments introduced by fission mechanism. There are also many gamma ray paths to the ground state from any point in this entry region. A variable number of statistical gamma rays, with essentially continuous energy distribution and relatively high energies of an MeV or greater, takes the secondary fragments from the initial chaotic entry region down to a more ordered regime in which there are rather few yrast or near-yrast levels. An yrast level is the state of a nucleus with the minimum excitation energy for a given angular momentum. This is illustrated schematically in Figure 1.6. The number of statistical gamma rays depends partly on the initial excitation energy of the primary fragment. This is higher for fission of high excited system but typically gamma ray deexcitation from the entry region involves one to three statistical gamma rays per fragment [Ahm95]. Decay from the relative few levels populated in the yrast region are observed as discrete gamma rays. Within the RLDM, a useful parameter is the fissility parameter that is related to the probability of the nucleus to decay by fission. Fissility parameter is defined as: χ = E (0) C (0) 2E = Z2 A ( 2a S a C ){1 k[(n Z) A] 2 } S [1.8] where E C (0) and ES (0) represent respectively the Coulomb and the surface energy of the non-deformed nucleus, a C and a S are respectively the parameters related to E C (0) and E S (0) and k is the surface asymmetry constant. 1.3 Quasi-fission In heavy-ion collisions at energy around the Coulomb barrier, the complete fusion process has to face a strong counteracting binary process, the quasi-fission (QF). QF is a transitional mechanism between deep-inelastic collisions and complete fusion, in which the composite system separates in two main excited fragments without forming a CN due to the action of the repulsive Coulomb force. Despite the QF process is strongly connected with the reaction entrance channel, a

16 9 clear picture of what are the most important characteristics that either enhance or hinder QF is still matter of discussion. Three criteria are widely used to identify the reaction mechanism (fusion or QF): The reaction Coulomb factor Z 1 Z 2, the charge product of reaction partners. This parameter relates to the Coulomb energy in the entrance channel. It has been identified a threshold value of Z 1 Z 2 = 1600 for the appearance of QF. Entrance channel mass asymmetry α 0 = (A p A t ) (A p + A t ) [1.9] where A p in the mass number of the projectile and A t the mass number of the target. With decreasing mass asymmetry, the cross section for QF increase. Effective fissility parameter χ eff connected with repulsive and attractive forces in the entrance channel. Recently, a mean fissility parameter was proposed, given by χ m = 0.75χ eff χ CN, where χ CN is the one identified by the [1.8]. From analysis of a large data set it has been found that QF take place for reaction with χ m > Those criteria, however, are not universal. For instance, they do not take into account the shapes of the interacting nuclei. The relative orientation of deformed nuclei changes the Coulomb barrier and the distance between the centers of the colliding nuclei and this leads to a change in the balance between repulsive and attractive forces. The interaction energy is also a very important parameter for QF. The relative contribution of QF process decreases when the interaction energy increases. The question about the influence of angular momentum on the QF process is furthermore still open and additional experimental data together with gamma ray emission are needed to shed light on this point. The interpretation of what happens during QF is that, after the capture by nuclear attraction, the intermediate di-nuclear system re-separate due to Coulomb repulsion before achieving complete amalgamation into a CN. This interpretation implies a dynamical view of the interaction. A dynamical treatment, necessary for the description of fusion and QF processes and their competition, is discussed in the next section.

17 Dynamical description of competition between fusion and QF A dynamical description of a nuclear reaction cannot follow all the single particle degrees of freedom. Instead, it becomes important to identify some bulk degrees of freedom which can provide a realistic picture of collective behavior. All the remaining degrees of freedom (unknown) are treated as a heat bath. The energy transfer between the chosen degrees of freedom and the heat bath is schematized whit the presence of dissipative forces. This dissipation is treated with a friction term and a stochastic term to introduce fluctuations. The equations that couple these degrees of freedom describe the time evolution of the reaction in terms of the chosen variables and their conjugate momenta. The choice of the proper degrees of freedom is crucial to describe transfer reactions and provide an estimate of cross sections. On one side, the number of degrees of freedom must not be too large in order to have a limited set of coupled differential equations to solve. On the other side, too few variables would not allow the simultaneous description of several competitive mechanisms such as fusion and QF. Fig 1.7 Degrees of freedom used in the model [Zag08] In the stochastic model of Zagrebaev and Greiner [Zag08], the chosen degrees of freedom are the following: the distance R between nuclear centers or elongation of mono-nucleus; the quadrupole deformation of the two nuclei, β 1,2 ; the mass asymmetry as defined by [1.9]; the angle of rotation of nuclei in the reaction plane, φ 1,2 ;

18 11 the angle between beam axis and the line connecting nuclear centers, θ. The equation are in the form of Langevin type: μq = V q γq + γtγ(t) [1.10] where : q is a generic degree of freedom; V is the potential energy plus the centrifugal barrier; γ is the friction coefficient associated to q; T = E a is the nuclear temperature, E = E CM E kin V the excitation energy, a the nuclear level density; Γ(t), aleatory function with Gaussian distribution (zero mean value, takes into account stochastic diffusion). The friction and the stochastic terms are responsible of the dissipation and are used to describe the mechanism of energy loss during mass transfer. The time evolution of the system represented by the chosen coordinates is represented by trajectories in the phase space. One of the key ingredient of this type of models is clearly the choice of the potential once the degrees of freedom are chosen. The choice of the multidimensional potential determines the driving potential on which the trajectories of the solutions of the Langevin equations describe the possible reaction channels. As instance in Figure 1.8 is shown the driving potential energy surface (PES) as a function of elongation and mass asymmetry for the nuclear system formed in 48 Ca Cm collision. After just overcoming the Coulomb barrier and reaching the contact point, the intermediate system can follow different trajectories, due to the stochastic term in the Langevin equations, some of which may end up in the same binary channel with or without forming a CN. Solid lines show (without fluctuations) the QF trajectories for symmetric and asymmetric mass split. Dashed curves correspond to fusion (CN formation) and fission processes with the same symmetric mass split of QF. The entrance channel is also a key element for the competition between CN fission and QF, as previously said. In Figure 1.9 is shown the potential energy landscape for the nucleus 216 Ra as a function of mass asymmetry of the entrance channel, elongation and deformation. The mass distributions for two reactions, leading to the same composite system, are shown in the bottom-right corner. It is possible to see that for the more

19 12 asymmetric entrance channel QF is practically absent. For the less asymmetric reaction, 168 Er + 48 Ca, the entry point of the reaction is near the forking between QF and CN fission so part of the events follows the QF trajectory and another part follows the CN fission one. The QF trajectory is given by the presence of the doubly magic 132 Sn. For the 204 Pb + 12 C reaction, the system has to walk through a longer path before the forking. In doing so, there is more time for complete amalgamation of the two nuclei into a CN and this dynamic factor greatly hinder the QF exit channel. CN fission and QF are both binary decay channels characterized by large nucleon exchange and energy dissipation. These common properties make the experimental separation between them difficult, especially in the case were both process result in symmetric mass split, like in Figure 1.8. In order to achieve this separation, several techniques have been developed based on the analysis of different experimental observables of fission-like fragments. Fig 1.8 Example of a driving potential energy surface as a function of elongation and mass asymmetry for the nuclear system formed in 48 Ca Cm collision. The solid lines with arrows show schematically (without fluctuations) the quasi-fission trajectories going to the lead and tin valleys. The dashed curves correspond to fusion (CN formation) and fission processes.

20 13 Fig 1.9 Example of potential energy landscape as a function of mass-asymmetry of the entrance channels, elongation and deformation for 216 Ra. The lines with arrows show schematically (without fluctuations) the possible trajectories for the reactions. Different entrance channels imply different paths along there trajectories and this can either enhance or hinder one of the two process. 1.5 Observables In most of the experiments held by now, the most used observables of fission-like fragments were [Itk15] angular distribution, mass distributions and total kinetic energy distribution. Total kinetic energy (TKE) is the sum of the kinetic energies of the two fragments in the center of mass reference frame: (1) (2) TKE = E CM + ECM [1.11] The main idea used for decomposing all fission-like fragments into CN fission and QF is to compare the experimental properties of fission-like fragments for reaction leading to the formation of the same composite system but having different entrance channel properties, either with experimental systematics or with theoretical predictions in the frame of a chosen model. In the lack of a comprehensive theoretical model it is

21 14 necessary to proceed empirically by searching for correlations between observables and extrapolating the systematics to unknown regions. One of the real doubts in these extrapolation is that nuclear properties in the region of heavy and super-heavy nuclei may change unexpectedly quite dramatically just by adding few nucleons because of the sharp change of the shell effects Fission At high excitation energy (~ 50 MeV) the influence of shell effects is negligible and the fission process is well described by the liquid drop model LDM. According to LDM the fission into two symmetrical nuclei is energetically favorable. It is well known that in the fission of heated nuclei the mass distribution of fragments is one-dumped and close to a Gaussian shape whose variance σ M 2 increase approximately proportionally to the temperature of the fissioning nucleus. In Figure 1.10 the mass-tke distribution of fission fragments of 216 Ra * formed in the reaction 12 C+ 204 Pb at CN excitation energy of 40 MeV is presented as an example of a classic case of LDM fission. The solid curves are the mass distribution, average TKE and its dispersion expected according to LDM with parameters set from the systematics. In the framework of LDM, the average TKE for a given nucleus undergoing fission has a parabolic dependence on the fragment mass and does not depend on its excitation energy and angular momentum. The average TKE is expected to increase with the ratio (Z CN ) 2 (A CN ) 1 3, as confirmed by a large systematics known as Viola systematics [Vio85]. Fig 1.10 In the first column, from top to bottom: mass-tke distribution of fission fragments of 216 Ra*; mass distribution of fission fragments. In the second column, from top to bottom: average TKE distribution; TKE dispersion.

22 15 Spontaneous and low energy fission have a completely different behavior. It is known that, at low excitation energy, an asymmetric fission mode is observed in mass- TKE distribution of fission fragments for all nuclei from A 200 u up to A 256 u. For nuclei with A < ( ) u the LDM symmetric mode prevails, with a small contribution ( < 0.5%) of the asymmetric component. For actinide nuclei with Z = and A = u the asymmetric mode prevails in spontaneous fission as well as in induced fission at excitation energies up to MeV. For transitional cases like nuclei in the region of Ra or Ac, the mass distributions at low energy fission are a superposition of symmetric and asymmetric modes with comparable contributions. The above properties of the fission fragments mass distributions have been understood qualitatively, and in some case quantitatively on the basis of the concept of multimodal nuclear fission, whose foundation arises from the valley structure in the PES in the multimodal deformation space of the fissioning nucleus. In a frame of a two-center shell model, the PES exhibits a sequence of pronounced valleys as the consequence of the shell structure of the formed fragments. Four main fission modes have been distinguished in theoretical calculations as well as experimentally: symmetric mode; standard I mode, caused by the influence of proton Z = 50 and neutron N = 82 shells; standard II mode determined by deformed nuclear shells with Z and N 86; supershort mode, manifesting itself only when light and heavy fragments are close in their nucleon composition to the double magic tin with A 132. Empirically, the multimodality is supported by the reproduction of measured mass and energy spectra of fission fragments as a sum of several Gaussian curves representing each fission mode. The average TKE of fission fragments is determined by the Coulomb repulsion of the primary fragments at scission point which, in turn, depends on the shape of the two fragments. The different TKE values of the different fission modes could be explained by considering different paths in the PES. One path reaches the scission point in a stretched neck configuration, as the one predicted by the LDM; the other reaches the scission point in a touching sphere configuration and therefore higher TKE than the other path. The same PES concept can also explain the widths of the mass and TKE distributions. According to the shape of the PES, the distribution width grows with the valley width: the wider the valley the larger the width. Therefore, even if two paths result in symmetric mass distributions, the higher TKE valley is narrower than the lower TKE valley. This explains the differences in the widths of the mass and TKE

23 16 distributions of the different modes. In Figure 1.11 are shown the mass distributions, the average TKE and its variance as a function of the mass of the binary product of the 18 O PB reaction for different excitation energy of the CN. The mass distributions are reproduced summing the contributions of symmetrical fission mode (the filled areas) and asymmetrical fission modes standard I and standard II (hatched areas). In the average TKE distributions it is possible to notice that for asymmetric fission modes the TKE has higher value than for symmetric fission. Fig 1.11 Mass-TKE distributions of binary product of the 18 O Pb reaction at different excitation energies. From top to bottom: mass yields, average TKE and its variance as a function of mass. Filled areas in the mass distributions are associated to symmetric mode, hatched are associated with the sum of standard I and standard II asymmetric modes Quasi-fission Typical pattern of the mass-tke distribution which elucidate the onset of the QF are summarized in Figure All reactions lead to the formation of Hs composite system but entrance channels are vastly different. These reaction were chosen as a case study to provide a prompt view of some of the most important characteristic features of QF. From left to right, the entrance channel mass symmetry increases and the two reaction in the middle are expected to form the same CN from a different entrance channel. Furthermore the Coulomb factor increases from left to right.

24 17 Fig 1.12 Mass-TKE distributions of binary product at energy above the Coulomb barrier. From left to right the entrance channel mass asymmetry decreases and the Coulomb factor Z 1 Z 2 increases. Solid curves in the average TKE and its variance are the expectation for CN fission. Figure 1.12 gives a clear progression of the mass-tke distribution shape with decreasing entrance mass asymmetry and increasing Coulomb repulsion. The area between the expected quasi-elastic region and the symmetric mass split region, typical of CN fission, gets filled with further binary products. In the case of the reaction 22 Ne Cf, the mass distribution shows a Gaussian shape with an evidence for asymmetric fission. In the reaction 26 Mg Cm the mass distribution is nearly Gaussian with the appearance of two slight shoulders. These two reactions show mass-tke distributions features that can be ascribed to the expectation of the LDM fission and therefore can be considered mainly originated by a CN fission process. From reaction 36 S U the mass distributions of the fragments change quite remarkably. At energies below the Coulomb barrier the mass distributions of fission-like fragments formed in this reaction are dominantly asymmetric. A symmetric peak appears with growing intensity as the interaction energy is increased. Supported by the orientation effect on the QF we attribute the asymmetric component of mass distribution to the QF process. In the case of 36 S U two asymmetric QF shoulders become more pronounced in comparison with 26 Mg Cm and for 56 Fe Pb the mass distribution becomes a pot-shaped. Also quite striking is the difference in the shapes of the mass- TKE distribution in the case in which the same composite system 274 Hs is populated.

25 18 The progression in the mass-tke distribution, which makes one to invoke QF mechanism, is also reflected in the other two observables, the average TKE and the variance of the TKE distributions for a fixed mass split. Both these observables deviate from the expectation of the systematics based on the CN fission. In particular, the deviation observed in the reaction 56 Fe Pb make us suspect that this QF process is dominant with respect to CN fission in the full mass range and result in more cold fragment being the average TKE higher. The above mentioned properties of the entrance channel are reported to play a primary role in the rising of QF. However, microscopic features, such as shell closures, have quite a striking impact on the mass-tke distribution which is the main playground where to probe our knowledge of the shell effects. Moreover, microscopic features offer a key to interpret the competition between QF and CN fission and a way to estimate their relative contribution. Figure 1.9 shows the effect of the shell closure on the QF process. With the relative minimum of the potential energy landscape in correspondence with the doubly magic 132 Sn, the QF channel that leads to 132 Sn and 84 Sr is greatly enhanced. The importance of the shell effects still holds when heavier system are considered. It is known that in superheavy composite system QF mainly leads to the formation of asymmetric fragments with mass asymmetry ~ 0.4. This type of QF process, the socalled asymmetric quasi-fission (QF asym ), is characterized by asymmetric angular distributions in the center of mass system and thus fast reaction times (~ s). The TKE for these fragments is observed to be higher than that for CN fission and hence this process is colder. Due to this reason shell effect in QF asym are more pronounced. It is possible to disentangle QF asym and asymmetric fission modes thanks to the different natures of this two mechanism. The first one is a reaction mechanism and changes with the entrance channel of the reaction. The second one is a decay mode typical of the CN, so it should be independent of the way that CN was created, e.g. from a fusion reaction, from decay of heavier nuclei, et cetera. Therefore once the possible fission modes of a CN are known it is possible to comprehend, in a reaction with possible formation of that CN, whether the reaction passed through a CN system or not by observing the presence of the mass distribution typical of that CN fission modes. In Figure is shown 1.13 the overlap of the mass distribution from the reactions 26 Mg Cm and 36 S U expected to lead to the CN 274 Hf at the excitation energy of 35 MeV. The average position of the heavy asymmetric peaks due to QF changes in the two reactions, from 200 u for 36 S U to 185 u for 26 Mg Cm. The shift towards the

26 19 more symmetric masses in QF process with increasing entrance channel mass asymmetry has also been observed for other reactions. This change is in contrast with the expectation of the multimodal fission where the position of each mode determined by the nuclear shells is constant for a specific compound nucleus and only the relative contribution of each mode varies with excitation energy. This is a strong argument supporting the thesis that the asymmetric part of those distributions is due to a QF asym process that does not go through the formation of a CN. Fig 1.13 Mass distributions for fission-like fragments formed in the reactions 26 Mg Cm and 36 S U at energy below the Coulomb barrier. Red curves are fusion fission components estimated from TKE analysis, thick curves are QF components. Besides the asymmetric component, the symmetric component may be affected by the presence of the QF process. Consequently, the question of whether the symmetric fragments originate from CN fission or QF process (QF sym ) arises. Furthermore, the angular distribution for all these mass-symmetric fragments in symmetric with respect to 90 in the center of mass system and the estimated reaction time is ~ s, typical for CN fission process. The overlap of CN fission and QF in the symmetric mass region constitutes an inescapable problem when CN fission cross section has to be estimated. That said, it appears clear that a disentanglement of fission and QF processes is very hard to achieve. This is possible only for the asymmetric part of the mass distribution and only if the other reaction processes are completely known or if it is possible to compare the experimental results with different reactions with some common elements (e.g. the same composite system, same mass symmetry in the entrance channels, et

27 20 cetera). Furthermore most of the analysis are based on the decomposition of mass and TKE distributions with the help of models predictions, so the experimental results are greatly model dependent. Mass, TKE and angular distributions with their variances are not a good set of observable for the correct disentanglement of the two processes and there isn t still a complete picture on what are the factors which determine the QF process. 1.6 Gamma ray probe The differences between these two processes mark the path towards the identification of better observables for their disentanglement. On one side there is fusion-fission, a process in which two nuclei form a CN with the dissipation of all the relative motion energy, passing through an equilibrium stage, with the successive decay; typical times are about τ ~ s. On the other side there is QF, a faster process with less mass transfer, less energy transfer and less energy dissipation; typical times are about τ ~ s. It is reasonable to think that for the slower process all the orbital angular momentum is transferred into internal degree of freedom of the CN and so the two fragments after the fission have an higher spin than the fission-like fragments produced by QF. The possible ways to probe angular momentum of the two fragments are neutrons and gamma rays. Neutrons have higher detection efficiency than gammas but to extract information on the angular momentum transported by neutrons it is necessary to use the statistical model. This imply model dependent analysis. Furthermore neutron detection systems are less common than gamma detector systems. Gamma rays have many possible advantages: disentangle fusion-fission and QF path by gating on high or low angular momentum gamma transitions, identify the fragments charge numbers instead of only the mass numbers, directly investigate shell effects, the physics of the scission point (excitation energy and angular momentum), the connection between fission modes and feeding of the fragments. Information about angular momentum can be extracted from discrete gamma transitions as well as from gamma multiplicity, M γ, that is the average number of gamma emitted per event. Recent studies were performed using modern gamma ray detector arrays and spontaneous fission sources on thick backings to stop the recoiling fission fragments. The advantage of this method is that the Doppler broadening is absent if the recoiling fission fragments stop before emitting gamma rays. The resulting energy resolution is

28 21 close to the intrinsic resolution of Ge detectors providing the maximum resolving power for the very dense spectra of gamma ray transitions from hundreds of nuclear species. The disadvantage of this approach is that simplification of the complex gamma ray spectrum cannot be made because the origin of the gamma ray from either fission fragment cannot easily be established without having mass or energy measurement of the fission fragments. In addition, only states with lifetimes longer than the stopping time for the recoiling fission fragments can be studied because of large Doppler broadening effects. Moreover from the gamma rays alone is not possible to reconstruct the whole mass distribution. This is shown in Figure The masses of the secondary fragments are reconstructed with characteristic gamma rays in triple coincidence (black square) and compared with the distributions measured in two different experiments. Although the distribution shape is similar, the spectrum presents many holes due to detection efficiency. The drawback of the thick-target technique can be overcome by the fragment-gamma coincident technique, which adds mass selectivity as well as identification from which fission fragment the gamma ray originates. It significantly improves the sensitivity for the study of neutron-rich nuclei. The measurements arising from this technique are affected by gamma rays energy shift and peak broadening, both due to Doppler effect, that will briefly discussed later on. Fig 1.14 Yields of correlated fragment pairs in the reaction 208 Pb( 18 O,f) obtained in γ-γ-γ coincidence method [Bog07]

29 22 Therefore, gating on high angular momentum gamma rays in coincidence with masses and TKE, it should be possible to see that some fragments are more populated in the fission region than in others and this could lead to a separation of CN fission and QF products even in the symmetric split region. Spin distributions could be a key element for disentangling the two processes. 1.7 Performed experiment This method of correlating the high angular momentum population with the time scale of a reaction channel can be tested first by using the quasi-elastic (QE) channel. As shown in Fig.1.12, fragments from the quasi-elastic channel, namely for the faster process, are also present in the Mass-TKE matrix and are located in the mass region around the mass of the target and projectile nuclei. Their TKE is also about equal to the entrance channel relative motion energy, being the Q-value of the reaction about zero. If the hypothesis that a higher angular momentum population corresponds to a large interaction time is valid, the gamma transitions measured in coincidence with the quasielastic component should come from nuclei populated to lower angular momentum regions than the one in coincidence with the fragments in the symmetric mass region. This would prove the concept and would open the road to experiments to distinguish between QF and CN fission in the symmetric region by employing an additional probe. To explore this concept, the reaction 32 S Au, at the energy near the Coulomb barrier, E lab ( 32 S) = 166 MeV, was proposed and performed at the Tandem ALTO accelerator at IPN Orsay (France). This reaction is characterized by a large fusionfission cross section, and a negligible contribution from the QF. The Mass-TKE distribution is therefore characterized by a dominating component from fusion-fission process, and the population of high angular momentum regions of the nuclei detected in coincidence with the mass symmetric fragments would therefore be not polluted with components from processes of nearby time scale. Consequently, the comparison between the gamma transitions in the quasi-elastic channel and the fusion-fission channel would provide the best conditions to evaluate the concept described above.

30 23 In this experiment, the time-of-flight spectrometer CORSET was used to detect two fragments in coincidence, and a section of the ORGAM array was used in coincidence with CORSET to detect gamma rays. In this way, the Mass-TKE and the gamma rays in coincidence can be extracted. 1.8 Aim of the Thesis The aim of this thesis is to extract gamma energy spectra in coincidence with the fragments of two-body reactions due to the quasi-elastic channel and the fusion-fission channel, and to perform the appropriate corrections. The candidate has taken part to the experiment, from the preparation to the run, and was directly in charge of the ORGAM array, taking care of the mounting, electronics, energy calibration and efficiency measurements. In this experiment also the PARIS array of LaBr + NaI crystals was used to measure the average gamma multiplicity distributions from FF and QE channels in coincidence with CORSET. A complementary type of information can be extracted with this detector. In the following chapter, the detectors principles and setup will be discussed in some detail.

31 24 Chapter 2: Experimental Setup 2.1 The Time-Of-Flight Spectrometer CORSET Binary reaction products are detected in coincidence by the two-arm time-of-flight (TOF) spectrometer CORSET (Correlation Setup). Each arm of the spectrometer consists of a compact START detector and a position-sensitive STOP detector, both based on microchannel plates. Depending on the reaction under investigation, the arms can be positioned at different angles to the beam axis. The distance between the START and STOP detectors of each arm (the fight path) usually ranges from 10 to 25 cm and the distance from the start detector to the target is typically around 3 to 6 cm. The START detector is composed of a conversion foil, an accelerating grid, an electrostatic mirror and a chevron MCP assembly. A schematic diagram of a START detector is shown in Figure 2.1 and a picture of it is shown in Figure 2.2. When passing through the conversion foil of the detector, a charged particle (from protons to heavy ions) knocks out electrons, which are accelerated in the electric field between the foil Fig 2.1 Schematic diagram of the start detector. [Koz08]

32 25 Fig 2.2 Picture of the start detector. and the accelerating grid to an energy of ~3 kev. The grids of the electrostatic mirror deflect the electrons by 90, and then hit the chevron MCP assembly. Wherever a particle hits the entrance foil, the electron ranges have the same length; therefore the output timing signal is position-independent. The detector design has been optimized in order to obtain the maximum active area for a minimum detector size. Mylar films with a thickness of μg/cm 2 are used as the entrance foil. Gold or aluminum layers μg/cm 2 thick are sputtered onto the films to raise the secondary yield of electrons. A particle passes through all electrostatic fields generated by the grids without being deflected from its primary direction and practically without changing its initial velocity. Nevertheless, one must take into account the energy lost by a particle in its passage through the conversion foil. For fission fragments, these losses in the foils that we use are a few MeV (2 5% of the initial energy of a particle). The change in the particle direction due to collisions with atoms of the foil appears to be negligible. The STOP detector consists of a conversion entrance foil, an assembly of two MCPs and coordinate system and a printed circuit board with fast amplifiers for one timing signal and two coordinate signals. A schematic diagram of a STOP detector is shown in Figure 2.3. The coordinate system consists of two mutually perpendicular delay line wires. Each coordinate is composed of two independent delay lines shifted by 0.5 mm with respect to each other. The potentials applied to the delay lines are selected so that electrons escaping from the MCP are collected on only one of them. The other delay line (which does not collect electrons) is used to compensate for the interference of the fast timing signal from the exit surface of the MCP. The coordinate of a particle s hit

33 26 Fig 2.3 Schematic diagram of the position-sensitive stop detector. [Koz08] point at the detector is determined from the difference in the arrival time of the timing signal (the STOP signal) and the signal from the relevant delay line. The angular resolution of the stop detectors is about 0.3. In order to monitor the quality of the beam and its position at the target and to normalize event numbers to cross section, four surface-barrier detectors, the so-called beam monitors, are placed into the reaction chamber. Knowing the counting rates of elastically scattered ions for each of the four detectors and comparing them to the values calculated from the Rutherford elastic scattering, one can find the average point of incidence of the beam onto the target. The time resolution, taken as the full width half maximum (FWHM), of both TOF arms is 150 ps. The mass resolution is 3 u. The high time and angular resolutions of the spectrometers permit the setting of minimum TOF distance (up to 10 cm) without significant deterioration of the mass resolution. This provides a means for reducing the overall dimensions of the reaction chamber and using the spectrometer as a convenient trigger of fission fragments in correlation measurements of neutrons and gamma rays. The geometrical efficiency of CORSET spectrometer is about 3% CORSET geometry The two arms of CORSET were placed at 68 and 66.5 from the beam axis. The START detectors for both arms were at 60 mm from the target and the STOP detectors at 210 mm from the START. Beam monitors were at 18 from the beam axis and at 40 mm from it. The four monitors are placed at angles of 90 with respect to each other. Figure 2.4 illustrates the geometry of the CORSET setup for the present experiment.

34 27 Fig 2.4 Geometry for the CORSET setup for the present experiment. In the bottom right corner are illustrated the characteristic of the target and of the start and stop foils. 2.2 Gamma rays detection Gamma interaction with matter The detection of gamma rays is critically dependent on the interaction that transfers all or part of the photon energy to an electron in the absorbing material. Because the primary gamma-ray photons are "invisible" to the detector, it is only the fast electrons created in gamma-ray interactions that provide any clue to the nature of the incident gamma rays. These electrons have a maximum energy equal to the energy of the incident gamma-ray photon and will slow down and lose their energy through ionization and excitation of atoms within the absorber material and through bremsstrahlung emission. In order for a detector to serve as a gamma ray spectrometer, it must carry out two distinct functions. First, it must act as a conversion medium in which incident gamma rays have a reasonable probability of interacting to yield one or more fast electrons; second, it must function as a conventional detector for these secondary electrons. Typical detectors used in gamma ray spectroscopy are solid state Ge detectors, like

35 28 ORGAM, and scintillator detectors, like PARIS. Of the various ways gamma rays can interact in matter, only three interaction mechanisms have any real significance in gamma-ray spectroscopy: photoelectric absorption, Compton scattering, and pair production. Figure 2.5 shows the linear attenuation coefficient of gamma rays in germanium and its component parts. Photoelectric absorption is an interaction in which the incident gamma-ray photon disappears. In its place, an electron is released from one of the electron shells of the absorber atom with a kinetic energy given by the incident photon energy hν minus the binding energy of the electron in its original shell. For typical gamma-ray energies, the electron is most likely to emerge from the K shell, for which typical binding energies range from a few kev for low-z materials to tens of kev for materials with higher atomic number. Conservation of momentum requires that the atom recoils in this process, but its recoil energy is very small and usually can be neglected. Thus, the effect of photoelectric absorption is the liberation of an electron, which carries off most of the gamma ray energy, together with one or more low-energy electrons corresponding to absorption of the original binding energy of the photoelectron. If nothing escapes from the detector, then the sum of the kinetic energies of the electrons that are created must equal the original energy of the gamma ray photon. Photoelectric absorption is therefore an ideal process if one is interested in measuring the energy of the original gamma ray. The cross section for photoelectric absorption is proportional to the n-th power of the Z of the detector material, where n is within the range 3 to 5 depending on the radiation energy. The result of a Compton scattering interaction is the creation of a recoil electron and scattered gamma-ray photon, with the sharing of energy between the two. The energy of the scattered gamma ray hν is a function of the scattering angle θ. Two extreme cases can be identified: A grazing angle scattering, or one in which θ 0. In this extreme, the recoil Compton electron has very little energy and the scattered gamma ray has nearly the same energy as the incident gamma ray A head-on collision in which θ = π. In this extreme, the incident gamma ray is backscattered, whereas the electron recoils along the direction of incidence. This extreme represents the maximum energy that can be transferred to an electron in a single Compton interaction, that is less than the total energy of the gamma ray hν.

36 29 Fig 2.5 The linear attenuation coefficient of germanium and its component parts. [Gil08] Fig 2.6 Spectra for monochromatic gamma rays. The sum effect of the three interaction mechanisms are shown. Compton continuum and multiple Compton events create a background for the spectrum. Fullenergy peak collects all the events in which all the gamma rays energy is released inside the detector. If the energy of the gamma ray is at least 1.02 MeV, pair production interactions create the single and double escape peak, in which one annihilation photon or both of them leave the detector without further interaction. [Kno79]

37 30 The third significant gamma-ray interaction is pair production. The process occurs in the intense electric field near the nuclei of the absorbing material and corresponds to the creation of an electron-positron pair at the point of complete disappearance of the incident gamma-ray photon. Because an energy of 2m 0 c 2 is required to create the electron-positron pair, a minimum gamma-ray energy of 1.02 MeV is required to make the process energetically possible. If the incident gamma-ray energy exceeds this value, the excess energy appears in the form of kinetic energy shared by the electron-positron pair. For typical energies, both the electron and positron travel a few millimeters at most before losing all their kinetic energy to the absorbing medium. The pair production process is complicated by the fact that the positron, once its kinetic energy becomes very low (comparable to the thermal energy of normal electrons in the absorbing material), annihilates. At this point both an electron and the positron disappear, and they are replaced by two annihilation photons of energy m 0 c 2 (0.511 MeV) each. The time required for the positron to slow down and annihilate is small, so that the annihilation radiation appears in virtual coincidence with the original pair production interaction. The combination of these three interaction mechanisms for monochromatic gamma rays gives the spectrum shown in Figure 2.6. Single Compton scatterings contribute with a continuum from the energy for a grazing collision up to the energy for the gamma ray backscatter, the Compton edge. Multiple Compton events partially fill in the gap between the Compton edge and the full-energy peak. In the full-energy peak are collected all the events in which gamma rays release all their energy in the detector. Photoelectric absorption is the main component of the peak, often called photopeak, but multiple Compton scatter and events of pair production can also contribute to the fullenergy peak. If the gamma rays are enough energetic for the pair production, it can happen that one or both the positron annihilation gamma rays escape from the detector. Single and double escape peak are so visible at m 0 c 2 (0.511 MeV) and 2m 0 c 2 (1.02 MeV) below the full-energy peak Solid state detectors In a semiconductor, the valence band is full and the next available energy states are in a higher band, the conduction band, separated by a forbidden region. The energy gap between the two region is of the order of 1 ev. Under normal conditions there will always be a small population of electrons in the conduction band, depending on the temperature, and the material will exhibit a limited degree of conductivity. Cooling the

38 31 material will reduce the number of electrons in the conduction band, thereby reducing the background current (leakage current) and make it much easier to detect the extra excitation due to the gamma-ray interactions. When an electron is promoted to the conduction band, a vacancy is left behind. This vacancy is effectively positively charged and is referred to as a hole. Holes are also mobile. An electron within the valence band may replace that lost from the vacancy, thus filling the hole. That will leave, in turn, another vacancy. In the presence of an external electric field, the hole can appear to move towards the cathode. Since both electrons and holes carry charge, both will contribute to the conductivity of the material. The interaction of a gamma ray with the semiconductor material will produce secondary electrons with energies considerably greater than thermal energies. Interaction of these can produce a cascade of electron hole pairs for each secondary electron interaction. Under normal circumstances, the extra excited electrons in the conduction band might be expected to eventually deexcite and return to the valence band. In the presence of an electric field, they will instead migrate up (electrons) or down (holes) the field gradient. The number of electron hole pairs produced is directly related to the energy that the gamma-ray release inside the detector. In an absolutely pure semiconductor material, thermal excitation would promote a certain number of electrons from the valence band to the conduction band, leaving behind an equal number of positively charged holes. A material of this kind containing equal numbers of electrons and holes is described as an intrinsic semiconductor. It is, of course, not possible to prepare any material completely free of impurities. In semiconductors, these can have a significant effect upon the conductivity. Replacing one of the lattice atom with another atom of a different valence, there will be one electron too few or too much to maintain the overall electronic configuration. Impurities with valence lower than the semiconductor are referred to as acceptor impurities. Semiconductors with this type of impurity would be called p-type. Impurities with valence higher than the semiconductor are referred to as donor impurities. Semiconductors with this type of impurity would be called n-type. The semiconductor gamma-ray detector depends upon the electronic redistribution which takes place when masses of dissimilar semiconductor types are placed in contact with each other. The p-type material has an excess of holes and the n-type an excess of electrons. As these diffuse under thermal influence, holes may stray from the p side to the n side of the junction and electrons from the n side to the p side. Excess holes meeting excess electrons will combine together, mutually annihilating. The result will

39 32 be a region around the physical junction of the two types of material where the excess charge carriers have cancelled each other out. This is called a depletion region and is the active element of the detector. This region is very thin, but if a positive voltage is connected to the n side of the junction, i.e. if reverse bias is applied, the width of the depletion layer increases as the electrons are withdrawn from the material. The secondary electrons passing through the depletion area will create a certain number of electron-hole pairs, most of which will migrate up to the electrodes due to the electric field. Collecting all these electron and holes will create a current proportional to the number of charge carrier collected and so proportional to the energy released by the gamma ray into the semiconductor material. Germanium is by far the most common gamma ray detector material. Its higher atomic number than silicon makes it practicable to use it for the detection of gamma radiation, due to the increased photoelectric absorption cross section. Moreover germanium has the highest electron and hole mobility and the lower band gap amongst most used semiconductor materials. Lower band gap means more electron hole pairs produced for the same incident particle energy and so a higher energy resolution. Germanium gamma ray detectors are not constructed by placing differing types of semiconductor materials in contact but by conversion of one face of a block of germanium to the opposite semiconductor type by evaporation and diffusion or by ion implantation. If the concentration of impurities on either side of the junction is different, the space charge distribution will not be symmetrical about the junction: the width of the depletion region is greater on the side of lower impurity concentration. It follows that if a layer with high p dopant concentration (p+) is created on one face of a block of suitably high purity n-type germanium, applying a reverse bias to the detector will create a depletion layer throughout the n-type material Compton suppression The Compton continuum in gamma-ray spectra is generated primarily by gamma rays that undergo one or more scatterings in the detector followed by escape of the scattered photon from the active volume. In contrast, the full-energy absorption events result in no escaping photons. Therefore, coincident detection of the escaping photons in a surrounding annular detector can serve as a means to reject preferentially those events that only add to the continuum, without affecting the full-energy events. The rejection is carried out by passing the pulses from the germanium detector through an electronic

40 33 gate that is closed if a coincident pulse is detected from the surrounding detector (called anticoincidence mode). To be effective, the surrounding detector must be large enough to intercept most of the escaping photons and should have a good efficiency for their detection. Large scintillation detectors most readily meet these requirements, and both NaI(Tl) and BGO have been used for this purpose. BGO has the strong advantage that its high density and atomic number allow a more compact configuration compared with a sodium iodide detector of the same detection efficiency. Because they also result in some coincident events in both detectors, pair production interactions of the incident gamma rays followed by escape of one or both of the annihilation photons are also suppressed by these systems. Single and double escape peaks in the recorded spectrum are therefore less prominent than in the original spectrum from the germanium detector. One potential disadvantage of Compton suppression systems becomes apparent if a radioisotope source with a complex decay scheme is being measured. Many gamma rays can then be emitted in coincidence, and it is possible for independent gamma rays from the same disintegration to interact in both detectors. These events are therefore rejected, leading to unwanted suppression of some full-energy peaks. The reduction in the Compton continuum from the ORGAM germanium detectors by operating them and the BGO detectors in anticoincidence mode is illustrated in Figure 2.7. Fig 2.7 Pulse height spectra from a double 137 Cs 60 Co gamma ray source. a) Normal spectrum recorded from the central germanium detectors. b) Spectrum recorded in anticoincidence with the scintillation BGO detectors, showing the suppression of the Compton continuum. The full-energy peak areas were unaffected to within 1%.

41 ORGAM detector The ORsay GAMma Array (ORGAM) has been installed and running at IPN Orsay/France since It is dedicated to gamma ray spectroscopy using stable beams accelerated by a 15 MV MP-Tandem Accelerator. It is permanently installed in IPN s room 420 where stable beams can be provided. ORGAM is a packed array of high-resolution germanium (Ge) detectors surrounded by bismuth germanate (BGO) scintillators. Figure 2.8 gives a schematic diagram of a single detector. The Ge detectors are large, coaxial, hyper pure n-type crystals, ~ 70 mm in diameter and ~ 75 mm in length. The liquid nitrogen cryostat keep the detector at operative temperature. Every Ge detector has a Compton suppression shield composed of ten optically isolated BGO scintillators, each with a photomultiplier readout. Individual BGO have a resolution (for 662 kev gamma rays) of 18 22% when the source is placed in the germanium detector position. The detectors are tapered over the front 3 cm out of their lengths to allow closer packing when in the array. The array can host up to 45 unit detector. Figure 2.9 shows a picture of the detector used for our experiment. Fig 2.8 Schematic diagram of a single ORGAM element. [Nol94]

42 35 Fig 2.9 Picture of ORGAM detectors used for this experiment ORGAM geometry In our experiment, 10 ORGAM detector were used. Figure 2.10 shows the structure of the support frame. The numbers from 1 to 10 mark the position of the used detectors. Table 2.1 shows the position of the used detectors in term of the angle θ and φ with respect to the target. θ is the angle between the detector and the beam axis, φ is the angle between the vertical axis and the detector in the plane perpendicular to the beam axis. Every detector has an angular opening of 20. The target is positioned 181 mm from the front of the Ge crystals.

43 36 Fig 2.10 Illustration of the support frame. The number from 1 to 10 mark the position of the used detectors. Detector θ ( ) φ ( ) Detector θ ( ) φ ( ) Tab. 2.1 Position of the used detectors in term of the angle θ and φ. 2.4 PARIS detector PARIS (Photon Array for the studies with Radioactive Ion and Stable beams) is a high efficiency gamma-calorimeter array detector composed by LaBr 3 (Ce)-NaI(Tl) phoswich base units. A phoswich, literally phosphor sandwich, is a scintillation detection system consisting of two or more different scintillators, with dissimilar pulse shape characteristic, optically coupled to each other and to a common photomultiplier tube. The primary crystal is thick enough to absorb the radiation of interest, while the secondary one, which is thicker, acts as an Compton suppression shield. The individual phoswich detector element consists of a front LaBr 3 (Ce) cubic crystal (2 2 2 ) optically coupled to a NaI(Tl) crystal (2 2 6 ) at the back. Every detector is coupled with a cylindrical photomultiplier tube (PMT), which collects the light outputs generated in both phosphor components. The phoswich is then hermetically sealed in a single aluminum, coupled through a glass window to the PMT. The final array will consist of multiple clusters, each made by 9 phoswich elements arranged in a 3x3 square matrix, as shown in Figure 2.11 [Spo16].

44 37 Fig 2.11 On the left, a PARIS cluster. On the right, a single phoswitch detector element. 2.5 Electronics and trigger The circuit diagram of the double-arm TOF spectrometer is shown in Figure The timing and coordinate signals from the START and STOP detectors (St1, St2, Sp1, Sp2, X1, Y1, X2, and Y2) are fed into constant-fraction discriminators (CFDs). Then, signals St1, St2, Sp1, and Sp2 arrive at the logic modules, which generate an output signal (a trigger) if there are two stop signals and at least one start signal. The start and stop signals go to time-to-amplitude converters (TACs) and then to analog-to-digital converters (ADCs). These converters are used to measure the following time intervals: Fig 2.12 Block diagram of the double-arm TOF spectrometer. [Koz08]

45 38 ToF1 between the arrival of signals St1 and Sp1, ToF2 between the arrival of signals St2 and Sp2, ToFL1 between the arrival of signals St2 and Sp1, ToFL2 between the arrival of signals St1 and Sp2, ΔT St between the arrival of signals St1 and St2, ΔT Sp between the arrival of signals Sp1 and Sp2. The start and stop signals, as well as the coordinate signals, are independently transmitted via delay lines to a time-to-digital converter (TDC). The trigger signal acts as the start signal for the TDC. The TDC is used to measure the time intervals between the trigger and all the other signals. The coordinate signals are extracted from the difference between two time intervals: the interval between that coordinate signal and the trigger; the interval between the stop signal and the trigger. The photon energy signals from ORGAM and PARIS detectors are transmitted to ADCs for the spectroscopic information only if a trigger occurs. In other words, PARIS and ORGAM are treated as slave detector. Signals from the Compton suppression shield are fed into CFDs together with energy signals and come to TDCs. This gives the time information for the Compton anticoincidence. Figure 2.13 shows a general block diagram for the electronics used in this experiment. During the processing of a signal the ADCs and TDCs prevent the electronics to accept new trigger with a busy signal used as a veto for further trigger. The dead time, defined as the number of refused triggers to the number of total trigger ratio, is returned by the electronics.

46 Fig 2.13 Block diagram of the used electronics. 39

47 40 Chapter 3: Data Analysis and Results 3.1 ORGAM calibration Energy calibration ORGAM Ge detectors were calibrated with a 152 Eu source Eu gamma ray peaks have been used for the energy calibration. Figure 3.1 shows the spectrum for the detector number 1. The used peaks are marked with a number representing their energy in kev. Figure 3.2 shows, as example, the calibration curve for detector number 1. A linear regression produces the calibration parameter. Table 3.1 shows the parameters of calibration curves for every detector. Parameters are in the form Energy = a + b channel. Energy resolution, taken as the FWHM, for detector 1 to 9 is ~ 4 kev for 1408 kev gamma rays. Detector 10 has a really poor energy resolution of 8 kev for 1408 kev gamma rays. Figure 3.3 shows a comparison between the 1408 kev peak from the detector 1 spectrum and from detector 10 spectrum. Fig 3.1 Calibration spectrum got with an ORGAM Ge detector. The eleven peaks used for the calibration are labelled with their energy in kev.

48 41 Fig 3.2 Calibration curve for the detector number 1. Fig 3.3 Comparison between the 1408 kev peaks in the spectra from the detector number 1 and the detector number 10. Detector number 10 has poor energy resolution.

49 42 Detector a b Detector a b Tab. 3.1 Parameters of the calibration curves for the ORGAM Ge detectors. Parameters are in the form Energy = a + b channel Efficiency calibration The detector counting efficiency ε relates the amount of radiation emitted by a radioactive source to the amount measured in the detector for a given energy as following: ε(e) = N det (E) N tot (E) [3.1] where N det (E) is the number of detected events in the full energy peak and N tot (E) the total number of photons emitted by the source. The same 152 Eu source was used for the efficiency calibration. Nominal activity of the source is kbq, at 12/07/2011 (12 UTC), with a half-life t 1 2 = years. Depending on the detector energy resolution and efficiency, up to 18 peaks have been used. The list of the gamma rays energies for each peak and their emission probability P(γ E ) is shown in Table 3.2. Energy (kev) P(γ E ) (%) Energy (kev) P(γ E ) (%) 121,8 28,58 688,7 0, ,7 7, ,9 12, ,9 0, ,4 4, ,3 26,5 964,1 14, ,8 0, ,9 10, ,1 2, ,1 13, ,9 3, ,9 1, ,9 0, ,1 1, ,3 0, ,005 Tab. 3.2 Energy of the gamma rays used for efficiency calibration and their probability.

50 43 To obtain the efficiency calibration spectra, the source was placed in front of each detector for about 10 minutes. The number of events for each full energy peak, N peak, has been obtained by Gaussian fit, cutting the background. N det is obtained by N peak and the dead time D through the following relation: N det = N peak (1 D) [3.2] To obtain N tot it is necessary to estimate the activity of the source at the time of the measurements. The activity of the source has been estimated as kbq, according to exponential decay law: A(t) = A(t )e λ(t t ) [3.3] where t is the reference time of the activity and λ is the decay constant related to the half-life through the relation λ = ln (2) t 1 2 [3.4] Thus N tot can be obtained by N tot = A(t)P(γ E ) t [3.5] where t is the duration of the measurements. The errors on the efficiency has been estimated through the statistical errors on N peak and D. The errors on N peak include the errors on the cut of the background. To obtain the efficiency curves, a polynomial fit in ln (E) has been used [Kis98]: ln(ε) = i=0,5 a i (ln E) i [3.6] Figure 3.4 shows, as example, the efficiency curve for detector number 1.

51 44 Fig 3.4 Efficiency curve for the detector number Fragments velocities In order to obtain the velocity of each fragment flying in CORSET arms 1 and 2 it is necessary to compute the flight path of the fragments from the START to the STOP detectors. Position-sensitive detectors provide the velocity vector and the trajectory length of the fragments in a reference frame in which the target is at the origin and the beam lies on the z axis. The x axis coincides with the vertical one and the y axis is set to obtain a right-handed reference frame. In Tab. 3.3 are listed the main parameters used to obtain, event by event, the position of the point hit on the detectors, the flight paths and the velocity vectors. The position of the hit point on each stop MCP is given by the following equations: { x sp = mcp y y sp = PY + mcp x cos(θ) z sp = PY + mcp x sin(θ) [3.7] where mcp x and mcp y are the coordinates (calibrated) of the fragment onto the detecting surface; mcp y is the vertical position of the fragment on the MCP, mcp y is the orizontal one.

52 45 Start foil target distance D 60 mm Stop MCP target distance L 270 mm Arm 1 angular position θ 1 68 Arm 2 angular position θ Arm START MCP center coordinates (TX, TY, TZ) (0, D sinθ i, D cosθ i ) Arm STOP MCP center coordinates (PX, PY, PZ) (0, L sinθ i, L cosθ i ) Tab. 3.3 Main parameters used to calculate flight paths.. Writing the equation of the line between the center of the target and the hit point, and finding the intersection with the start detector plane it is possible to determinate the coordinates of the hit point on the start detector: { x st = y st = z st = TX 2 + TY 2 TX x sp + TYy sp x sp TX 2 + TY 2 TX x sp + TYy sp y sp TX 2 + TY 2 TX x sp + TYy sp z sp [3.8] The flight path of the fragment is the distance: L = (x sp x st ) 2 + (y sp y st ) 2 + (z sp z st ) 2 [3.9] The polar and azimutal angles defining the direction are: θ = acos (z sp L) [3.10] φ = atan (y sp x sp ) [3.11] The velocity module of the fragment is immediately given by V = L tof [3.12] where tof is the time of flight given by CORSET. The velocity so obtained will be used for the Doppler correction of the gamma rays energies.

53 Masses and energies In a full momentum transfer (FMT) binary reaction, the masses of the two reaction products can be obtained using the momentum conservation law, projected onto beam axis and an axis orthogonal to the beam and the mass conservation law: M proj V proj = M 1 V 1 cosθ 1 + M 2 V 2 cosθ 2 [3.13] 0 = M 1 V 1 sinθ 1 M 2 V 2 sinθ 2 [3.14] M proj + M tar = M = M 1 + M 2 [3.15] where M 1 and M 2 are the masses of the two products. Solving the system of [3.13] and [3.14] knowing V i and θ i from the previous calculations, the masses and energies of the fragments are: M 1 = MV 2 senθ 2 V 1 sinθ 1 + V 2 sinθ 2 [3.16] M 2 = M M 1 [3.17] E i = M i V i (MeV) [3.18] From the energies, TKE is obtained as following: TKE = E 1 + E 2 E proj M proj M proj + M tar [3.19] Masses and energies so obtained need to be corrected due to the energy loss of the fragments along their path towards the detectors: each fragment has to exit from the target and cross the start detector foil. This means that the measured velocities do not correspond to the velocities of the two fragments just after the scission or when they emit the measured gamma rays. This will obviously affect the mass-tke distributions and the Doppler correction of the gamma rays energies. However, the correction of these parameters will be done in a later stage of the analysis.

54 Gamma rays energies and Doppler correction Gamma ray data are recorded event by event in coincidence with the two fission-like fragments. Germanium detectors and BGO are operated in anticoincidence mode, so if the time signal of the Ge-BGO coincidence is bigger than 0, the event is rejected. To reveal the true energies connecting nuclear levels of a given nuclide from gamma rays emitted in flight, the measured gamma ray spectrum has to be corrected for Doppler effect, which is the change in frequency (and energy) of electromagnetic radiation caused by the relative motion of the source and the observer. The Doppler shifted energy E γ of a gamma ray of energy E γ 0 is given to the first order in β = v c by: E γ (θ) = E γ 0 (1 + β cos(θ)) [3.20] where θ is the emission angle of the gamma ray with respect to the nucleus velocity vector. This equation shows that the observed energy depends on the projection of the source velocity on the gamma ray direction. A forward emitted gamma ray has the maximum energy; a backward emitted one has the minimum energy; the one emitted at θ = 90 is not affected by the energy shift. The fluctuations on β and θ lead to a fluctuation on the measured Doppler shift which broadens the gamma ray line in the spectra E γ (θ) = E γ 0 (cos(θ) β + β sin(θ) θ) [3.21] The Doppler broadening depends on experimental conditions. Due to the finite opening of the Ge detectors, for a given direction of the nucleus velocity vector, a detector can detect gamma rays with different emission angles θ within its opening θ. 0 A given transition energy E γ is observed with different energies ranging from E γ (θ min ) to E γ (θ max ). Moreover the straggling in the target of the fragment after the emission leads to an incorrect measurement of the velocity vector and this produces fluctuations on both β and θ. Since either fragment is an emitter candidate, multiple possible correction have to be applied. Within two-fold gamma ray coincidences, 4 different corrections have to be applied for the two gamma rays emitted by the fragment reaching CORSET arm 1 or 2. Given the gamma ray and the fragment couple, the corrected energy is given by the

55 48 inverse of [3.20]: E γ 0 = E γ /(1 + β cos(θ)) [3.22] cos(θ) is estimated by the angles θ p and φ p of the particle, given by CORSET analysis, and θ Ge and φ Ge of the Ge detector as following: cos(θ) = sin(θ Ge ) sin(θ p ) cos(φ Ge φ p ) cos(θ Ge ) cos(θ p ) [3.23] 3.5 Gamma rays data analysis The ultimate goal for this experiment is to investigate potential differences in the gamma ray properties depending on the reaction mechanism: fusion-fission or QF. These properties are connected to angular momentum and excitation energy population and so to the population and feeding of a specific isotope in different mechanisms. This kind of study does not require a sorting of the data according to fragment masses and TKE, but widely profits from mass gating. Indeed, hundreds of different isotopes are populated in a fission reaction, so that the integral gamma ray spectrum is very crowded and selectivity is essential to study specific nuclides. That can be done using either many-fold gamma ray coincidences, or identifying the fragment in a heavyion spectrometer. The latter option has the advantage of preserving as much as possible gamma ray detection efficiency. In this first stage of the analysis, the goal is to check if it is possible to identify fission-like fragments by their deexcitation gamma rays from the spectra, gating on masses and gamma rays two-fold coincidences, and verify that higher angular momenta are populated in the FF region of masses. The total spectrum without any gate, but recorded in coincidence with any fragment, is shown in Figure 3.5. Detector number 10 has been excluded due to his poor energy resolution.

56 49 Fig 3.5 The total spectrum recorded by ORGAM Ge detectors. Fig 3.6 Mass-TKE matrix. The two lateral parts of the distribution corresponds to elastic and quasi elastic events; the central part is mostly symmetric fusion-fission.

57 50 From the mass-tke matrix, shown in Figure 3.6, it is possible to distinguish the typical loci for a fusion-fission process: the two lateral parts are elastic and quasi elastic events, the central part is mostly fusion-fission with different modes of fission. From a first gate on the central part of the distribution, gamma energy lines corresponding to target and projectile levels should disappear. This is shown in Figure 3.7. The yellow curve represent the total spectrum while the green one represent the spectrum obtained with gating the fusion-fission of the mass-tke distribution. The most visible peaks of the total spectrum disappear almost completely in the gated spectrum. This suggest that these peaks are related to 32 S or 197 Au transitions. From a comparison with the data on levels and transitions of the two nuclei, it has been possible to identify the peaks as 197 Au transitions plus the 511 kev peak of positron annihilation. Fig. 3.8 shows the gamma transitions that were identified in 197 Au. Fig 3.7 The total spectrum recorded by ORGAM Ge detectors, yellow, compared with the spectrum relative to the central part of the mass-tke distribution, green. The 197 Au transitions identified are marked with their energy and angular momentum.

58 51 Fig 3.8 Gamma transitions (in red) identified in 197 Au. Excluding most of the elastic transitions, it is possible to gate on single masses, within the sensitivity of CORSET, for a more targeted search. As example, a gate on masses from 100 to 105 u on the arm 1 of CORSET has been made. Furthermore, a gate has been made on a more prominent peak, with energy of 96 ± 5 kev, in the spectrum with the Doppler correction for arm 1. With the assumption that fission-like fragments have an A to Z ratio similar to the one of the composite system 229 Am, the obtained spectrum has been compared to gamma transitions of nuclei with atomic number around Rh has been identified as a possible candidate, with a level at 97.1 kev with spin-parity 2 +. The gamma ray energy corresponds to the transition to the ground state on the nucleus, with spin-parity 1 +. In the spectra, more transitions attributable to the same nucleus have been searched for. Four transitions, all feeding the 2 + level, have been found. In Figure 3.9 is shown the spectra with the described above gates. The identified transitions are marked with their energy and the angular momentum of involved levels. Table 3.4 shows the levels of 104 Rh with their spin-parity, transition energy and probability, and the final levels for the different transitions. The spectrum corrected for arm 2 has been analyzed in search for transition of the fission partner of 104 Rh. Starting from a mass number of = 125, level and transition scheme of the Sn has been compared with the peaks in the spectrum. Due to neutron evaporation from primary fragments, 125 Sn and 124 Sn have not been found in the spectrum, but other isotopes has been identified. Figures 3.10 and 3.11 show the spectra with Doppler correction for arm 2. Some isotopes of tin have been identified as possible candidates for the peaks marked with transition energies and mass number of the nucleus. Tables show the levels of the identified Sn isotopes with their spinparity, transition energy and probability, and the final levels for the different transitions.

59 52 Fig 3.9 The spectrum obtained with gating on mass numbers from 100 to 105 and energies from 93 to 99 kev for one of the two gamma rays in coincidence. Energies have Doppler correction for arm 1 of CORSET. Possible transitions of 104 Rh are marked with transition energies and spin-parity. Tab 3.4 Energy levels of 104 Rh with their spin-parity and transitions.

60 53 Fig 3.10 The spectrum obtained with gating on mass numbers from 100 to 105 and energies from 93 to 99 kev for one of the two gamma rays in coincidence. Energies have Doppler correction for arm 2 of CORSET. Possible transitions of tin isotopes are marked with transition energies. Fig 3.11 The spectrum obtained with gating on mass numbers from 100 to 105 and energies from 93 to 99 kev for one of the two gamma rays in coincidence. Energies have Doppler correction for arm 2 of CORSET. Possible transitions of tin isotopes are marked with transition energies.

61 54 Tab 3.5 Energy levels of 119 Sn with their spin-parity and transitions. Tab 3.6 Energy levels of 120 Sn with their spin-parity and transitions. Tab 3.7 Energy levels of 121 Sn with their spin-parity and transitions. Tab 3.8 Energy levels of 122 Sn with their spin-parity and transitions. Tab 3.9 Energy levels of 123 Sn with their spin-parity and transitions.

62 55 From the preliminary analysis above it appears evident that the identification of nuclei is a long process. Furthermore, the mass-tke matrix needs to be further corrected for the energy loss of the fragments in the many passive absorbers and for this reason the mass resolution is not yet optimal. This makes the selection within mass ranges still very uncertain. Nevertheless, remembering that the main goal of this analysis is to search for nuclei, in the FF region, that decay from level with angular momentum higher than the ones in the QE, the search has continued for those transitions. As an example we show here the case of 129 La for which we find the entire set of gamma transitions from the level at 39/2 (Fig. 3.12). Fig 3.12 Some high angular momentum transition gamma rays of 129 La. This findings have two main direct consequences. The first one is that we can confirm the expectation that in the FF process higher angular momentum levels can be produced. Consequently, we can support the idea that processes with longer time scales can convert much more orbital angular momentum into the fragments. The different regions of angular momentum populated in FF and QE, at least for the ions selected so far, confirms this conclusion. On the same foot, we can reasonably expect the same effect also in QF and FF. Hence, this results confirms our initial expectations. The second one is that 129 La is a proton rich nucleus, and thus the partner must be the neutron rich nucleus 100 Sr whose level scheme is only fairly known. This means that