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The present article reports new data on the $^{48}$Ti($^{18}$O,$^{17}$O)$^{49}$Ti reaction at 275 MeV incident energy as part of the systematic research pursued within the NUMEN project. Supplementary measurements of the same reaction on $^{16}$O and $^{27}$Al targets were also performed in order to estimate the background arising from the use of a composite target (TiO$_{2}$ + $^{27}$Al). These data were analyzed under the same theoretical framework as those obtained with the titanium target in order to reinforce the conclusions of our analysis. Differential cross-section angular distribution measurements for the $^{17}$O$^{8+}$ ejectiles were performed in a wide angular range by using the MAGNEX large acceptance magnetic spectrometer. The experimental results were analyzed within the distorted-wave and coupled-channels Born Approximation frameworks. The optical potentials at the entrance and exit channels were calculated in a double folding approach adopting the S\~ao Paulo potential, and the spectroscopic amplitudes for the projectile and target overlaps were obtained from large-scale shell model calculations. The differential cross-sections are well-described by the theoretical calculations, where a weak coupling to collective excitations of projectile and target is inferred. The sensitivity of transfer cross-sections on different model spaces adopted in nuclear structure calculations, is also discussed.

Purpose: We want to analyze transitions to low-lying excited states of the residual and ejectile nuclei in the 76Se(18O, 17O) 77Se one-neutron stripping reaction at 275-MeV incident energy and determine the role of single-particle and core excitation in the description of the measured cross sections. In addition, we explore the sensitivity of the calculated cross section to different nuclear structure models. Methods: The excitation energy spectrum and the differential cross-section angular distributions are measured using the MAGNEX large acceptance magnetic spectrometer for the detection of the ejectiles and the missing mass technique for the reconstruction of the reaction kinematics. The data are compared with calculations based on distorted-wave Born approximation, coupled-channels Born approximation, and coupled reaction channels adopting spectroscopic amplitudes for the projectile and target overlaps derived by large-scale shell-model calculations and interacting boson-fermion model. Results: Peaks in the energy spectra corresponding to groups of unresolved transitions to 77Se and 17O are identified. The experimental cross sections are extracted and compared to theoretical calculations. A remarkable agreement is found, without using any scaling factors, demonstrating that the adopted models for nuclear structure and reaction take into account the relevant aspects of the studied processes. The main transitions which contribute to the cross section of each peak are identified., Comment: 15 pages, 4 figures

Charge exchange (CE) reactions offer a major opportunity to excite nuclear isovector modes, providing clues about the nuclear interaction in the medium. Moreover, double charge exchange (DCE) reactions are proving to be a tempting tool to access nuclear transition matrix elements (NME) related to double beta-decay processes. Through a multi-channel experimental analysis and a consistent theoretical approach of the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In single charge exchange (SCE) reaction at 306 MeV, we aim at disentangling from the experimental cross section the contribution of the competing mechanisms, associated with second or higher order sequential transfer and inelastic processes. We measured excitation energy spectra and absolute cross sections for elastic + inelastic, one-proton transfer and SCE channels, using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. For the first two channels, we also extracted the experimental cross section angular distributions. The experimental data are compared with theoretical predictions obtained by performing two-step distorted wave Born approximation and coupled reaction channel calculations. We employ spectroscopic amplitudes for single-particle transitions derived within a large-scale shell model approach and different optical potentials for modeling the initial and the final state interactions. The present study significantly mitigates the possible model dependence existing in the description of these complex reaction mechanisms, thanks to the reproduction of several channels at once. In particular, our work demonstrates that the two-step transfer mechanisms produce a non negligible contribution to the total cross section of the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In reaction channel, although a relevant fraction is still missing, being ascribable to the direct SCE mechanism, which is not addressed here., Comment: 21 pages, 11 figures

The MAGNEX magnetic spectrometer is used in the experimental measurements of Double Charge Exchange and Multi-Nucleon Transfer reactions induced by heavy ions within the NUMEN project. These processes are characterized by small cross sections under a large background due to other reaction channels. Therefore an accurate control of the signal to background ratio is mandatory. In this article, the determination of the MAGNEX spectrometer background contribution on cross section measurements is presented by applying a suitable analysis to quantify the limits of the adopted particle identification technique. The method is discussed considering the 116Cd(20Ne,20O)116Sn Double Charge Exchange reaction data, however it can be applied to any other reaction channel of interest.

Single-nucleon transfer reactions are processes that selectively probe single-particle components of the populated many-body nuclear states. In this context, recent efforts have been made to build a unified description of the rich nuclear spectroscopy accessible in heavy-ion collisions. An example of this multichannel approach is the study of the competition between successive nucleon transfer and charge exchange reactions, the latter being of particular interest in the context of single and double beta decay studies. To this extent, the one-proton pickup reaction $^{48}$Ti($^{18}$O,$^{19}$F)$^{47}$Sc at 275 MeV was measured for the first time, under the NUMEN experimental campaign. Differential cross-section angular distribution measurements for the $^{19}$F ejectiles were performed at INFN-LNS in Catania by using the MAGNEX large acceptance magnetic spectrometer. The data were analyzed within the distorted-wave and coupled-channels Born approximation frameworks. The initial and final-state interactions were described adopting the S\~ao Paulo potential, whereas the spectroscopic amplitudes for the projectile and target overlaps were derived from shell-model calculations. The theoretical cross sections are found to be in very good agreement with the experimental data, suggesting the validity of the optical potentials and the shell-model description of the involved nuclear states within the adopted model space.

Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-beta decay. In this framework, the exploration of two-nucleon transfer reactions in the 20Ne+116Cd collision at energies above the Coulomb barrier is particularly relevant since the 116Cd nucleus is a candidate for the double-beta decay. Methods: We measured the excitation energy spectra and absolute cross sections for the two reactions using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. We performed direct coupled reaction channels and sequential distorted wave Born approximation calculations using the double folding S\~ao Paulo potential to model the initial and final state interactions. The spectroscopic amplitudes for two- and singleparticle transitions were derived by different nuclear structure approaches: microscopic large-scale shell model, interacting boson model-2 and quasiparticle random phase approximation. Results: The calculations are able to reproduce the experimental cross sections for both two-neutron and twoproton transfer reactions. The role of couplings with the inelastic channels are found to be important in the two-proton transfer case. A competition between the direct and the sequential process is found in the reaction mechanism. For the two-proton transfer case, the inclusion of the 1g7/2 and 2d5/2 orbitals in the model space is crucial.

Background: The influence of halo structure of $^6$He, $^8$B, $^{11}$Be and $^{11}$Li nuclei in several mechanisms such as direct reactions and fusion is already established, although not completely understood. The influence of the $^{10}$C Brunnian structure is less known. Purpose: To investigate the influence of the cluster configuration of $^{10}$C on the elastic scattering at an energy close to the Coulomb barrier. Methods: We present experimental data for the elastic scattering of the $^{10}$C+$^{208}$Pb system at $E_{\rm lab}$ = 66 MeV. The data are compared to the three- and the four-body continuum-discretized coupled-channels calculations assuming $^9$B+$p$, $^6$Be+$\alpha$ and $^8$Be+$p$+$p$ configurations. Results: The experimental angular distribution of the cross sections shows the suppression of the Fresnel peak that is reasonably well reproduced by the continuum-discretized coupled-channels calculations. However, the calculations underestimate the cross sections at backward angles. Couplings to continuum states represent a small effect. Conclusions: The cluster configurations of $^{10}$C assumed in the present work are able to describe some of the features of the data. In order to explain the data at backward angles, experimental data for the breakup and an extension of theoretical formalism towards a four-body cluster seem to be in need to reproduce the measured angular distribution., Comment: 26 pages, 9 figures

We consider the classical 3-body system with $d$ degrees of freedom $(d>1)$ at zero total angular momentum. The study is restricted to potentials $V$ that depend solely on relative (mutual) distances $r_{ij}=\mid {\bf r}_i - {\bf r}_j\mid$ between bodies. Following the proposal by J. L. Lagrange, in the center-of-mass frame we introduce the relative distances (complemented by angles) as generalized coordinates and show that the kinetic energy does not depend on $d$, confirming results by Murnaghan (1936) at $d=2$ and van Kampen-Wintner (1937) at $d=3$, where it corresponds to a 3D solid body. Realizing $\mathbb{Z}_2$-symmetry $(r_{ij} \rightarrow -r_{ij})$ we introduce new variables $\rho_{ij}=r_{ij}^2$, which allows us to make the tensor of inertia non-singular for binary collisions. In these variables the kinetic energy is a polynomial function in the $\rho$-phase space. The 3 body positions form a triangle (of interaction) and the kinetic energy is $\mathcal{S}_3$-permutationally invariant wrt interchange of body positions and masses (as well as wrt interchange of edges of the triangle and masses). For equal masses, we use lowest order symmetric polynomial invariants of $\mathbb{Z}_2^{\otimes3} \oplus \mathcal{S}_3$ to define new generalized coordinates, they are called the {\it geometrical variables}. Two of them of the lowest order (sum of squares of sides of triangle and square of the area) are called {\it volume variables}. We study three examples in some detail: (I) 3-body Newton gravity in $d=3$, (II) 3-body choreography in $d=2$ on the algebraic lemniscate by Fujiwara et al where the problem becomes one-dimensional in the geometrical variables, and (III) the (an)harmonic oscillator., Comment: 32 pages, 2 figures

A study is presented of superintegrable quantum systems in two-dimensional Euclidean space $E_2$ allowing the separation of variables in Cartesian coordinates. In addition to the Hamiltonian $H$ and the second order integral of motion $X$, responsible for the separation of variables, they allow a third integral that is a polynomial of order $N\, (N\geq3)$ in the components $p_1, p_2$ of the linear momentum. We focus on doubly exotic potentials, i.e. potentials $V(x, y) = V_1(x) + V_2(y)$ where neither $V_1(x)$ nor $V_2(y)$ satisfy any linear ordinary differential equation. We present two new infinite families of superintegrable systems in $E_2$ with integrals of order $N$ for which $V_1(x)$ and $V_2(y)$ are given by the solution of a nonlinear ODE that passes the Painlev\'e test. This was verified for $3\leq N \leq 10$. We conjecture that this will hold for any doubly exotic potential and for all $N$, and that moreover the potentials will always actually have the Painlev\'e property., Comment: 36 pages, 1 figure

New experimental measurements of charge state distributions produced by a 20Ne10+ beam at 15 MeV/u colliding on various thin solid targets are presented. The use of the MAGNEX magnetic spectrometer enabled measurements of the 8+ charge state down to fractions of a few 10-5. The use of different post-stripper foils located downstream of the main target is explored, showing that low Z materials are particularly effective to shift the charge state distributions towards fully stripped conditions. The dependence on the foil thickness is also studied and discussed.

Neutrinoless double beta decay (0v\b{eta}\b{eta}) is considered the best potential resource to access the absolute neutrino mass scale. Moreover, if observed, it will signal that neutrinos are their own anti-particles (Majorana particles). Presently, this physics case is one of the most important research "beyond Standard Model" and might guide the way towards a Grand Unified Theory of fundamental interactions. Since the 0v\b{eta}\b{eta} decay process involves nuclei, its analysis necessarily implies nuclear structure issues. In the NURE project, supported by a Starting Grant of the European Research Council (ERC), nuclear reactions of double charge-exchange (DCE) are used as a tool to extract information on the 0v\b{eta}\b{eta} Nuclear Matrix Elements. In DCE reactions and \b{eta}\b{eta} decay indeed the initial and final nuclear states are the same and the transition operators have similar structure. Thus the measurement of the DCE absolute cross-sections can give crucial information on \b{eta}\b{eta} matrix elements. In a wider view, the NUMEN international collaboration plans a major upgrade of the INFN-LNS facilities in the next years in order to increase the experimental production of nuclei of at least two orders of magnitude, thus making feasible a systematic study of all the cases of interest as candidates for 0v\b{eta}\b{eta}.

Excitation energy spectra and absolute cross section angular distributions were measured for the 13C(18O,16O)15C two-neutron transfer reaction at 84 MeV incident energy. This reaction selectively populates two-neutron configurations in the states of the residual nucleus. Exact finite-range coupled reaction channel calculations are used to analyse the data. Two approaches are discussed: the extreme cluster and the newly introduced microscopic cluster. The latter makes use of spectroscopic amplitudes in the centre of mass reference frame, derived from shell-model calculations using the Moshinsky transformation brackets. The results describe well the experimental cross section and highlight cluster configurations in the involved wave functions.

Neutrinoless double beta decay (0{\nu}\b{eta}\b{eta}) is considered the best potential resource to determine the absolute neutrino mass scale. Moreover, if observed, it will signal that the total lepton number is not conserved and neutrinos are their own anti-particles. Presently, this physics case is one of the most important research beyond Standard Model and might guide the way towards a Grand Unified Theory of fundamental interactions. Since the \b{eta}\b{eta} decay process involves nuclei, its analysis necessarily implies nuclear structure issues. The 0{\nu}\b{eta}\b{eta} decay rate can be expressed as a product of independent factors: the phase-space factors, the nuclear matrix elements (NME) and a function of the masses of the neutrino species. Thus the knowledge of the NME can give information on the neutrino mass scale, if the 0{\nu}\b{eta}\b{eta} decay rate is measured. In the NURE project, supported by a Starting Grant of the European Research Council, nuclear reactions of double charge-exchange (DCE) will be used as a tool to extract information on the \b{eta}\b{eta} NME. In DCE reactions and \b{eta}\b{eta} decay, the initial and final nuclear states are the same and the transition operators have similar structure. Thus the measurement of the DCE absolute crosssections can give crucial information on \b{eta}\b{eta} matrix elements., Comment: arXiv admin note: substantial text overlap with arXiv:2001.09657; text overlap with arXiv:2001.09648

Background: Neutron transfer measurements for the $^{18}$O + $^{28}$Si system have shown that the experimental one-neutron and two-neutron transfer cross sections are well reproduced with spectroscopic amplitudes from two different shell model interactions for the Si isotopes: \textit{psdmod} for the two-neutron transfer, and \textit{psdmwkpn} for the one-neutron transfer. Purpose: The origin of this ambiguity can be related to a more complex mechanism in the one-neutron transfer that requires the unpairing of neutrons prior to its transfer in the ($^{18}$O,$^{17}$O) reaction. Studying a nucleus where this characteristic is absent ($^{13}$C) should help to elucidate this question. Method: One-neutron transfer cross sections were measured for the $^{13}$C + $^{28}$Si at E$_{lab}$ = 30, and 34 MeV, and compared with coupled reaction channel calculations using spectroscopic amplitudes derived from the \textit{psdmod} and \textit{psdmwkpn} shell model interactions. Results: The spectroscopic amplitudes from the \textit{psdmod} interaction for the relevant states in $^{29}$Si provide a good description of the experimental data and the corresponding values agree with previous estimates obtained from the (d,p) reaction. Conclusions: The experimental data for the one-neutron transfer to $^{28}$Si induced by ($^{13}$C,$^{12}$C) reaction is well reproduced using spectroscopic amplitudes from the \textit{psdmod}., Comment: 15 pages, 7 figures

Background: Recently, a systematic exploration of two-neutron transfer induced by the ($^{18}$O, $^{16}$O) reaction on different targets has been performed. The high resolution data have been collected at the MAGNEX magnetic spectrometer of the INFN-LNS laboratory in Catania and analyzed with the coupled reaction channel (CRC) approach. The simultaneous and sequential transfers of the two neutrons have been considered under the same theoretical framework without the need of adjustable factors in the calculations. Purpose: A detailed analysis of the one-neutron transfer cross sections is important to study the sequential two-neutron transfer. Here, we examine the ($^{18}$O, $^{17}$O) reaction on $^{16}$O, $^{28}$Si and $^{64}$Ni targets. These even-even nuclei allow for investigation of one-neutron transfer in distinct nuclear shell spaces. Method: The MAGNEX spectrometer was used to measure mass spectra of ejectiles and extract differential cross sections of one-neutron transfer to low-lying states. We adopted the same CRC formalism used in the sequential two-neutron transfer, including relevant channels and using spectroscopic amplitudes obtained from shell model calculations. We also compare with one-step distorted wave Born approximation (DWBA). Results: For the $^{18}$O + $^{16}$O and the $^{18}$O + $^{28}$O systems we used two interactions in the shell model. The experimental angular distributions are reasonably well reproduced by the CRC calculations. In the $^{18}$O + $^{64}$Ni system, we considered only one interaction and the theoretical curve describes the shape and order of magnitude observed in the experimental data. Conclusions: Comparisons between experimental, DWBA and CRC angle-integrated cross sections suggest that excitations before or after the transfer of neutron is relevant in the $^{18}$O + $^{16}$O and $^{18}$O + $^{64}$Ni systems., Comment: 10 pages, 6 figures

The nuclear scattering at energies well above the Coulomb barrier allows for a fairly sensitive examination of the parameters of the optical potential when the relevant couplings are included into the calculations. In this work we present experimental angular distribution data for the elastic and inelastic scatterings of $^{16}$O impinging on $^{27}$Al and $^{28}$Si target nuclei at \textit{E}$_{lab}=240$ MeV. The experimental data were measured at $7\degree < \theta_{c.m.} < 16\degree$ with good angular resolution. Experimental data are compared with coupled channel calculations with the inclusion of couplings to excited states in the target and projectile. We show that the shape of angular distributions are sensitive to the mass diffuseness parameter and the best agreement is achieved for $a = 0.62$ fm., Comment: 19 pages, 9 figures

Background: Double charge exchange (DCE) nuclear reactions have recently attracted much interest as tools to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-beta decay. In this framework, a good description of the reaction mechanism and a complete knowledge of the initial and final-state interactions are mandatory. Presently, not enough is known about the details of the optical potentials and nuclear response to isospin operators for many of the projectile-target systems proposed for future DCE studies. Among these, the 20Ne + 76Ge DCE reaction is particularly relevant due to its connection with 76Ge double-beta decay. Purpose: We intend to characterize the initial-state interaction for the 20Ne + 76Ge reactions at 306 MeV bombarding energy and determine the optical potential and the role of the couplings between elastic channel and inelastic transitions to the first low-lying excited states. Methods: We determine the experimental elastic and inelastic scattering cross-section angular distributions, compare the theoretical predictions by adopting different models of optical potentials with the experimental data, and evaluate the coupling effect through the comparison of the distorted-wave Born approximation calculations with the coupled channels ones. Results: Optical models fail to describe the elastic angular distribution above the grazing angle (9.4{\deg}). A correction in the geometry to effectively account for deformation of the involved nuclear systems improves the agreement up to about 14{\deg}. Coupled channels effects are crucial to obtain good agreement at large angles in the elastic scattering cross section.

In this work we study the simultaneous and sequential two-neutron transfer mechanisms to the $^{28}$Si nucleus induced by (t,p) and ($^{18}$O, $^{16}$O) reactions. New experimental cross sections for the $^{28}$Si($^{18}$O,$^{16}$O)$^{30}$Si reaction at 84 MeV are also presented. Direct reaction calculations are carried out within the Exact Finite Range Coupled Reaction Channel, for the simultaneous transfer of the two-neutron cluster, and the second order Distorted Wave Born Approximation, for the sequential transfer. Two different models are considered to describe the two-neutron cluster. The spectroscopic information was obtained from shell model calculation with {\it psdmod} interaction for the target overlaps where the 1p$_{3/2}$, 1p$_{1/2}$, 1d$_{3/2}$, 1d$_{5/2}$ and 2s$_{1/2}$ orbitals are included as valence sub-space. We show that simultaneous and sequential two-neutron transfer are competing mechanisms for the population of the ground state in $^{30}$Si. A systematic analysis of the two-neutron transfer induced by the ($^{18}O,^{16}O$) indicates that static deformation of target nuclei impacts on the two-neutron transfer mechanism.

The article describes the main achievements of the NUMEN project together with an updated and detailed overview of the related R&D activities and theoretical developments. NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave-functions in the two types of processes and the formal similarity of the transition operators. First experimental results obtained at the INFN-LNS laboratory for the 40Ca(18O,18Ne)40Ar reaction at 270 MeV, give encouraging indication on the capability of the proposed technique to access relevant quantitative information. The two major aspects for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer. The former is used for the acceleration of the required high resolution and low emittance heavy ion beams and the latter is the large acceptance magnetic spectrometer for the detection of the ejectiles. The use of the high-order trajectory reconstruction technique, implemented in MAGNEX, allows to reach the experimental resolution and sensitivity required for the accurate measurement of the DCE cross sections at forward angles. However, the tiny values of such cross sections and the resolution requirements demand beam intensities much larger than manageable with the present facility. The on-going upgrade of the INFN-LNS facilities in this perspective is part of the NUMEN project and will be discussed in the article.

The elastic scattering angular distribution of the $^{16}$O$+^{60}$Ni system at $260$ MeV was measured in the range of the Rutherford cross section down to $7$ orders of magnitude below. The cross sections of the lowest $2^{+}$ and $3^{-}$ inelastic states of the target were also measured over a several orders of magnitude range. Coupled channel (CC) calculations were performed and are shown to be compatible with the whole set of data only when including the excitation of the projectile and when the deformations of the imaginary part of the nuclear optical potential are taken into account. Similar results were obtained when the procedure is applied to the existing data on $^{16}$O$+^{27}$Al elastic and inelastic scattering at $100$ and $280$ MeV. An analysis in terms of Dynamical Polarization Potentials (DPP) indicate the major role of coupled channel effects in the overlapping surface region of the colliding nuclei., Comment: 8 pages, 5 figures

We consider the influence of breakup channels on the complete fusion of weakly bound cluster-type systems in terms of dynamic polarization potentials. It is argued that the enhancement of the cross section at sub-barrier energies may be consistent with recent experimental observations that nucleon transfer, often leading to breakup, is dominant compared to direct breakup. The main trends of the experimental complete fusion cross sections are analyzed in the framework of the Dynamic Polarization Potential approach. The qualitative conclusions are supported by CDCC calculations including a sequential breakup channel, the one neutron stripping of $^7$Li followed by the breakup of $^6$Li., Comment: 4 pages, 3 figures. Contribution to Cluster2012, Debrecen 24-28 September 2012, to appear in Journal of Physics Conference Proceedings Series (JPCS)

We consider the influence of breakup channels on the complete fusion of weakly bound systems in terms of dynamic polarization potentials. It is argued that the enhancement of the cross section at sub-barrier energies may be consistent with recent experimental observations that nucleon transfer, often leading to breakup, is dominant compared to direct breakup. The main trends of the experimental complete fusion cross section for $^{6,7}$Li + $^{209}$Bi are analyzed in the framework of the DPP approach., Comment: 12 pages, 2 figures

Performing a Scherk-Schwarz dimensional reduction of D=11 supergravity on a three-dimensional group manifold we construct five D=8 gauged maximal supergravities whose gauge groups are the three-dimensional (non-)compact subgroups of SL(3,R). These cases include the Salam-Sezgin SO(3) gauged supergravity. We construct the most general half-supersymmetric domain wall solutions to these five gauged supergravities. The generic form is a triple domain wall solution whose truncations lead to double and single domain wall solutions. We find that one of the single domain wall solutions has zero potential but nonzero superpotential. Upon uplifting to 11 dimensions each domain wall becomes a purely gravitational 1/2 BPS solution. The corresponding metric has a 7+4 split with a Minkowski 7-metric and a 4-metric that corresponds to a gravitational instanton. These instantons generalize the SO(3) metric of Belinsky, Gibbons, Page and Pope (which includes the Eguchi-Hanson metric) to the other Bianchi types of class A., Comment: 23 pages, 1 figure, minor changes, references added

We construct five different two-parameter massive deformations of the unique nine-dimensional N=2 supergravity. All of these deformations have a higher-dimensional origin via Scherk-Schwarz reduction and correspond to gauged supergravities. The gauge groups we encounter are SO(2), SO(1,1)^+, R, R^+ and the two-dimensional non-Abelian Lie group A(1), which consists of scalings and translations in one dimension. We make a systematic search for half-supersymmetric domain walls and non-supersymmetric de Sitter space solutions. Furthermore, we discuss in which sense the supergravities we have constructed can be considered as low-energy limits of compactified superstring theory., Comment: 35 pages, 2 figures, minor changes, published version