elements up to uranium (see Figure 1.15 left panel). Only ions showing a full energy deposition in both detectors were chosen for further analysis, thus rejecting ions with different charge states in both MUSIC detectors or reaction products created in the material of the detector. In the second step a distribution of the reconstructed nuclear charge as a function of the energy loss of the ions in the degrader located at the central focal plane was created. This allowed to determine the ionic charge state of a fragment within the FRS by the measuring the energy loss in the degrader, as described in in Section 1.4.1. Unambiguous identification of the transmitted nuclei required additional selection based on the analysis of the position of the fragments at the final focal plane. Figure 3.4 shows the selected isotopes of Hf for the magnetic setting of the FRS centered on 180
Uranium ssion fragments produced and separated at the FRS were for the rst time injected into the ESR. The energy of a ssion fragment is dened by ssion kinematics, i.e. the recoil energy and the angle between fragment and primary beam. If they are parallel the energy reaches a maximum, if they are antiparallel it has a minimum. In these two cases the nal direction of the fragment is identical with the primary beam direction. The direction of the recoil products is spatially isotropic. This peculiarity of the ssion kinematics is used in order to separate eciently the most neutron-richisotopes produced by the ssion process and to suppress undesired isotopes intensively produced by the projectile fragmentation. The kinetic energy as a function of the horizontal angle for 135 Sn
These values are not yet final. Improving them would, e.g., require studying and in detail absorption effects of QFS nucleons in the nucleus and including them into the event generator which is used for deriving the detector response of the Crystal Ball. Comparing the final results with the ones obtained in a recent experiment on 12 C, as well as with those for the neutron-richisotopes, which are also under analysis at the moment, could enhance the understanding of the phenomenon of quenching significantly. The measured momentum distributions for the fragments of these three reactions show good agreement with DWIA-calculations for a p-shell knockout. The analysis of the γ-energy spectra measured in coin- cidence with 11 C(p,pn) 10 C and 11 C(p,2p) 10 B reveals a strong population of the low-lying excited states in both cases, indicating a strong contribution of particle-hole states to the ground state of 11 C. Also, the low-lying unbound states are populated with a large cross section in both 10 C and 11 C. No indication of knockout from the s-shell, expected to occur at excitation energies E ∗ ¦ 20 MeV has been observed in the present analyis. However, these invariant mass analysis employed suffers from acceptance cuts for both the fragments and the protons and assumptions about the proton velocity. A more detailed analysis using similar tracking for the protons as for the fragments as well as simulations of the detector response of both the fragment and the proton arm could lead to a better undestanding of these reactions.
The first of these interactions, the USD [Bro88] developed by the Michigan group, allows the valence protons and neutrons to move in the full sd shell. It was developed around 1985 and is based on experimental data from stable and close-to-stable nuclei available at that time. USD was updated to USD-05 in 2005 to include new experimental results collected since 1985. The predictions of the energies of different levels in 29,31 Mg for the 2005 version are very close to the ones of the original USD interaction [Bro06], but there are so far no g-factor predictions and, furthermore, the updated interaction is not yet available publicly. Therefore, in this thesis, only results of calculations using the original USD will be presented. The SDPF.SM interaction, known also as iokin.spdf.si35 [Ret97], [Cau02] by the Madrid- Strasbourg groups, extends over the full sd shell for the valence protons and the full sd and pf shells for the neutrons, since it is aimed to study the very neutron-richisotopes with Z < 20. It includes the USD interaction for the sd shell (see above), a modified Kuo-Brown interaction [Pov81] for the pf shell (obtained from the renormalisation of the G-matrix), as well as the G-matrix of Lee, Kahana, and Scott [Kah69] for the cross-shell part.
These parametrizations can be then used to calculate the total photoabsorption cross section 1 for the selected multipolarity and, also, it has been observed that using them in conjunction with a Lorentzian curve will provide a good fit of the corresponding giant resonances. This latter approach, though, it is not suited to the energies examined in this work: in this region, in fact, the nucleus will have distinct energy levels and will not respond with a continuous spectrum; these, though, can be influenced in their density and relative strength by the so- called tail of the giant resonances that may extend also to energies well below the neutron separation threshold.
For a more precise description of collective and single particle excitation in nuclei, more advanced models and potentials have been developed. Potentials have been de- signed from first principles, for example the (pionless) effective field theory [SH00], or phenomenological interactions such as the Gogny-force [BGG91]. For the models the shell model is an example, in which the excitation energies and states are calculated. Also on the experimental side modes of excitation have been discovered and are stud- ied, e.g., collective modes. One of these is the Giant Dipole Resonance (GDR). This excitation mode splits into an isovector and isoscalar part and is located well above the particle separation energy. These modes can be pictured as a vibration of the protons and neutrons out-of-phase and in-phase, respectively, see for exam- ple [AN13, PVKC07a]. On the low-energy tail located between excitation energy of 5 and 11 MeV, another excitation mode was discovered, see for example [SAZ13], the low-energy dipole excitation, also referred to as soft-dipole mode or as pygmy dipole resonance. This mode appears for nuclei with an asymmetric proton-to-neutron ratio and its nature is still under debate. Nevertheless, to understand this mode, its isoscalar and isovector nature is explored. Many efforts are undertaken to investigate this mode with different probes as a function of the asymmetric proton-to-neutron ratio, see chap- ter 2. As such, the tin isotopes have been selected as they provide 10 stable isotopes and have a closed proton shell 1 (Z = 50).
of light need less than 1 µs to pass the FRS. Thus, it is safe to assume, that even 9 C 1 , the shortest lived of the investigated isotopes passes the fragment separator without major losses due to decay. Therefore, reaction studies utilizing inverse kinematics are a strong tool to investigate exotic isotopes. Knockout ex- periments in inverse kinematics at relativistic energies may be described within the sudden and eikonal approximations to model the reaction process. Detailed descriptions of the eikonal model can be found in [18–20]. Calculations using the sudden and eikonal approximations describe the removal of a nucleon assuming the projectile core to be separated into two geometrical regions. As indicated in Figure 2.1 the projectile has a region overlapping with the target nucleus and within the approximations only the nu- cleon to be removed is assumed to occupy this overlapping region. The removal reactions studies within the framework of this dissertation were carried out at energies above 1600 MeV/nucl. and consequently the nuclei’s high velocity led to highly forwarded angles of the residues due to the lorentz boost. The time scales of the interaction can be assumed to be very short (sudden approximation), so that no in- teraction between the projectile core and the target nuclei is to be expected. Consequently the reaction mechanism only depends on the state of the removed nucleon. The relative momentum distribution of the remaining reaction residue originates from the intrinsic momentum distribution of the removed nucleon.
The determination of the atomic, nuclear and chemical properties of elements beyond fer- mium (Fm, Z = 100) is one of the most interesting and challenging fields of study [ 1 , 2 , 3 , 4 ]. Such elements do not exist in nature and can be produced only in minute quantities, some- times at the rate of one atom per week, via fusion evaporation reactions at accelerator facili- ties. The liquid drop model predicts these elements to instantaneously undergo spontaneous fission. The repulsive Coulomb force of the positively charged protons is high enough to overcome the attractive short range interaction of the strong nuclear force. However, the existence of heavier elements suggests enhanced stability not covered by this simple model. Thus, the heaviest elements owe their existence to nuclear shell effects, which can be con- sidered analogous to the electron shells. The proton and neutron shell formation counteracts the repulsive Coulomb interaction between the protons, thus preventing the immediate fis- sioning of the nuclei. This stabilization effect in very- and super-heavy nuclei allows probing the underlying forces in the nucleus at the extremes of nuclear existence. This general interest in this region of the nuclear chart has triggered investigations of the production of elements up to oganesson (Og, Z = 118) [ 5 ], decay and in-beam spectroscopy probing the underlying nuclear structure [ 6 , 7 ], mass measurements determining the binding energy of the nuclear ground state [ 8 , 9 , 10 , 11 ] and also investigations to study the atomic and chemical behaviour of the heaviest elements [ 1 , 4 ].
1.1. MOTIVATION 3 The formation of elements heavier than iron cannot be explained by fusion reactions in stars, since the binding energy per nucleon is lower for heavier nuclei. There are, nevertheless, models to describe heavy-element nucleosynthesis. One of these is the rapid neutron-capture process (r- process) [ 18 ]. It occurs in extremely dense neutron-rich environments like core-collapse supernovae or neutron-star mergers. An initial seed nucleus from the iron region rapidly captures neutrons from its surroundings and then β decays into nuclei with higher atomic number. This process of rapid neutron capture and β decay repeats many times until the nucleus either undergoes fission or decays to heavy stable nuclides. For a theoretical description of the r-process and accurate calculations of nucleosynthesis yields precise knowledge about neutron-rich nuclei along the r-process path is key. In particular, accurate half-lives and ground-state energies are needed for r-process simulations. The experimental access to these neutron-rich nuclei is very challenging. Neutron-rich nuclei have extremely short lifetimes and their production is difficult. At present, experimental facilities are lim- ited in neutron excess, see, e.g., the recent measurements along the calcium isotopic chain [ 19 , 20 ]. However, there exist many facilities under construction worldwide (e.g., FAIR at the GSI Helmholtz Centre in Darmstadt, or FRIB at the Michigan State University in East Lansing, USA) which will access a great extent of the neutron-rich regime of the nuclear chart but will not reach the neutron drip line of heavy elements.
The angle of the dipole magnet with respect to the zero-degree line was calculated from the depicted measurement, too. As the outcome, ALADiN is rotated by 6.0 ◦ with respect to the x-axis. Usually, this rotation is set to 7.0 ◦ . However, an earlier measurement by a specialised company confirms the former value and excludes the latter . In table B.1, the position of ALADiN refers to the so-called centre of the dipole. The magnet is attributed to this coordinate in a simplified treatment of its geometry in the tracker software. All active detector volumes from the photogrammetric position measurement are presented in figure B.8, showing the setup relevant for projectile (pink), fragment (pink) and neutron (green) detection of Coulomb-dissociation reactions. The target is located at the centre of the XB, whose left hemisphere is cut for illustration purpose. ALADiN is indicated by its frame and opening windows. The inset is a zoom on the detectors for projectile identification and the target area. A scale is given in addition, because the presented data refers to the measured detector positions and their real active volumes.
In Figure 4.1 proton and neutron densities of a Slater determinant are shown. The parameters of the Slater determinant were minimized without any projection. In all plots of intrinsic densities the nucleus is aligned such, that the largest prin- cipal moment of inertia of the nucleus is the z axis and the second largest is the y axis. The axes are always scaled from −9 to 9 fm. The densities are indicated by contour lines and the intensity of the color in the background. From the densities shown in Figure 4.1 it can be seen that the mean-field state is not an eigenstate of parity or angular momentum. The intrinsic energy of this state is −54.5 MeV. If projected on angular momentum the energy expectation values of this state be- comes −42.1 MeV and −58.0 MeV, for the J π = 1/2 + and J π = 1/2 − , respectively.
Für einen formalen Usability Test müssen die Prototypen zwingend digital sein. Papier- Prototypen eignen sich aufgrund ihrer fehlenden inhärenten Interaktivität nicht für eine selbstständige Anwendung durch den Benutzer. Ein mit Axure erstellter Prototyp generiert zwar einen klickbaren HTML Output, dieser kann aber nur mit Vorbehalten für einen Usability Test einer Rich Internet Anwendung verwendet werden. Wie bereits besprochen, mussten für einige Interaktionsmuster Alternativlösungen erarbeitet werden, welche nicht dem mentalen Modell des Benutzers entsprachen. Dies führte bei den Tests vereinzelt zu unüberwindbaren Problemen und erforderte teilweise die Hilfe des Moderators. Die Durchführung eines Usability Tests setzt also zwangsmässig auch ein realistisches