Remarcs on the shape transition from spherical to deformed gamma unstable nuclei

Energies and transition probabilities for low lying states in $^{134}$Ba and ^{104Ru were calculated within a hybrid model.The ground and the first $2^+$ states are described alternatively as a harmonic and anharmonic vibrator states while the remaining states as states with E(5) symmetry. One concludes that a gradual setting of the 'critical' potential yields a better agreement with the experimental data. Very good agreement with the data is obtained for $^{104}$Ru. Comparing the present results with those of E(5) symmetry, it is conspicuous that the present formalism add corrections to the E(5) formalism by bringing the predictions closer to the experimental data. Analytical relationship between the states with U(5) symmetry and those given by the E(5) description is established.Comment: 21 pages, 3 figures, submitted for publicatio

Ordering ambiguity revisited via position dependent mass pseudo-momentum operators

Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. An affine locally scaled first order differential introduced, in Eq.(9), as a PDM-pseudo-momentum operator. Upon intertwining our Hamiltonian, which is the sum of the square of this operator and the potential function, with the von Roos d-dimensional PDM-Hamiltonian, we observed that the so-called von Roos ambiguity parameters are strictly determined, but not necessarily unique. Our new ambiguity parameters' setting is subjected to Dutra's and Almeida's [11] reliability test and classified as good ordering.Comment: 10 pages, no figures, revised/expanded, mathematical presentations in section 2 (Especially, the typological Errors in Eqs.(9)-(12))are now corrected. To appear in the Int. J. Theor. Phy

PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation

PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.Comment: 13 page

FCC-ee: The Lepton Collider: Future Circular Collider Conceptual Design Report Volume 2

In response to the 2013 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) study was launched, as an international collaboration hosted by CERN. This study covers a highest-luminosity high-energy lepton collider (FCC-ee) and an energy-frontier hadron collider (FCC-hh), which could, successively, be installed in the same 100 km tunnel. The scientific capabilities of the integrated FCC programme would serve the worldwide community throughout the 21st century. The FCC study also investigates an LHC energy upgrade, using FCC-hh technology. This document constitutes the second volume of the FCC Conceptual Design Report, devoted to the electron-positron collider FCC-ee. After summarizing the physics discovery opportunities, it presents the accelerator design, performance reach, a staged operation scenario, the underlying technologies, civil engineering, technical infrastructure, and an implementation plan. FCC-ee can be built with today’s technology. Most of the FCC-ee infrastructure could be reused for FCC-hh. Combining concepts from past and present lepton colliders and adding a few novel elements, the FCC-ee design promises outstandingly high luminosity. This will make the FCC-ee a unique precision instrument to study the heaviest known particles (Z, W and H bosons and the top quark), offering great direct and indirect sensitivity to new physics

FCC Physics Opportunities: Future Circular Collider Conceptual Design Report Volume 1

We review the physics opportunities of the Future Circular Collider, covering its e+e-, pp, ep and heavy ion programmes. We describe the measurement capabilities of each FCC component, addressing the study of electroweak, Higgs and strong interactions, the top quark and flavour, as well as phenomena beyond the Standard Model. We highlight the synergy and complementarity of the different colliders, which will contribute to a uniquely coherent and ambitious research programme, providing an unmatchable combination of precision and sensitivity to new physics

HE-LHC: The High-Energy Large Hadron Collider: Future Circular Collider Conceptual Design Report Volume 4

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre-of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries

FCC-hh: The Hadron Collider: Future Circular Collider Conceptual Design Report Volume 3

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries

FCC-hh: The Hadron Collider: Future Circular Collider Conceptual Design Report Volume 3

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries

HE-LHC: The High-Energy Large Hadron Collider

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre-of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries

FCC-hh: The Hadron Collider: Future Circular Collider Conceptual Design Report Volume 3

Particle physics has arrived at an important moment of its history. The discovery of the Higgs boson, with a mass of 125 GeV, completes the matrix of particles and interactions that has constituted the “Standard Model” for several decades. This model is a consistent and predictive theory, which has so far proven successful at describing all phenomena accessible to collider experiments. However, several experimental facts do require the extension of the Standard Model and explanations are needed for observations such as the abundance of matter over antimatter, the striking evidence for dark matter and the non-zero neutrino masses. Theoretical issues such as the hierarchy problem, and, more in general, the dynamical origin of the Higgs mechanism, do likewise point to the existence of physics beyond the Standard Model. This report contains the description of a novel research infrastructure based on a highest-energy hadron collider with a centre-of-mass collision energy of 100 TeV and an integrated luminosity of at least a factor of 5 larger than the HL-LHC. It will extend the current energy frontier by almost an order of magnitude. The mass reach for direct discovery will reach several tens of TeV, and allow, for example, to produce new particles whose existence could be indirectly exposed by precision measurements during the earlier preceding e+e– collider phase. This collider will also precisely measure the Higgs self-coupling and thoroughly explore the dynamics of electroweak symmetry breaking at the TeV scale, to elucidate the nature of the electroweak phase transition. WIMPs as thermal dark matter candidates will be discovered, or ruled out. As a single project, this particle collider infrastructure will serve the world-wide physics community for about 25 years and, in combination with a lepton collider (see FCC conceptual design report volume 2), will provide a research tool until the end of the 21st century. Collision energies beyond 100 TeV can be considered when using high-temperature superconductors. The European Strategy for Particle Physics (ESPP) update 2013 stated “To stay at the forefront of particle physics, Europe needs to be in a position to propose an ambitious post-LHC accelerator project at CERN by the time of the next Strategy update”. The FCC study has implemented the ESPP recommendation by developing a long-term vision for an “accelerator project in a global context”. This document describes the detailed design and preparation of a construction project for a post-LHC circular energy frontier collider “in collaboration with national institutes, laboratories and universities worldwide”, and enhanced by a strong participation of industrial partners. Now, a coordinated preparation effort can be based on a core of an ever-growing consortium of already more than 135 institutes worldwide. The technology for constructing a high-energy circular hadron collider can be brought to the technology readiness level required for constructing within the coming ten years through a focused R&D programme. The FCC-hh concept comprises in the baseline scenario a power-saving, low-temperature superconducting magnet system based on an evolution of the Nb3Sn technology pioneered at the HL-LHC, an energy-efficient cryogenic refrigeration infrastructure based on a neon-helium (Nelium) light gas mixture, a high-reliability and low loss cryogen distribution infrastructure based on Invar, high-power distributed beam transfer using superconducting elements and local magnet energy recovery and re-use technologies that are already gradually introduced at other CERN accelerators. On a longer timescale, high-temperature superconductors can be developed together with industrial partners to achieve an even more energy efficient particle collider or to reach even higher collision energies.The re-use of the LHC and its injector chain, which also serve for a concurrently running physics programme, is an essential lever to come to an overall sustainable research infrastructure at the energy frontier. Strategic R&D for FCC-hh aims at minimising construction cost and energy consumption, while maximising the socio-economic impact. It will mitigate technology-related risks and ensure that industry can benefit from an acceptable utility. Concerning the implementation, a preparatory phase of about eight years is both necessary and adequate to establish the project governance and organisation structures, to build the international machine and experiment consortia, to develop a territorial implantation plan in agreement with the host-states’ requirements, to optimise the disposal of land and underground volumes, and to prepare the civil engineering project. Such a large-scale, international fundamental research infrastructure, tightly involving industrial partners and providing training at all education levels, will be a strong motor of economic and societal development in all participating nations. The FCC study has implemented a set of actions towards a coherent vision for the world-wide high-energy and particle physics community, providing a collaborative framework for topically complementary and geographically well-balanced contributions. This conceptual design report lays the foundation for a subsequent infrastructure preparatory and technical design phase.In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centreof-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries