395 research outputs found

    A new way to perform partial wave decompositions of few-nucleon forces

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    We formulate a general and exact method of partial wave decomposition (PWD) of any nucleon-nucleon (NN) potential and any three-nucleon (3N) force. The approach allows one to efficiently use symbolic algebra software to generate the interaction dependent part of the program code calculating the interaction. We demonstrate the feasibility of this approach for the one-boson exchange BonnB potential, a recent nucleon-nucleon chiral force and the chiral two-pion-exchange three-nucleon force. In all cases very good agreement between the new and the traditional PWD is found. The automated PWD offered by the new approach is of the utmost importance in view of future applications of numerous chiral N3LO contributions to the 3N force in three nucleon calculations.Comment: 10 pages, 6 figures (24 eps files

    The Tucson-Melbourne Three-Nucleon Force in the automatized Partial Wave Decomposition

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    A recently developed procedure for a partial-wave decomposition of a three-nucleon force is applied to the pi-pi, pi-rho and rho-rho components of the Tucson-Melbourne three-nucleon potential. The resulting matrix elements for the pi-pi and pi-rho components are compared with the values obtained using the standard approach to the partial-wave decomposition, in which the pi-rho expressions for the matrix elements are also derived and presented. Several numerical tests and results for the triton binding energy and the correlation function prove the reliability and efficiency of the new method

    A Three-Dimensional Treatment of the Three-Nucleon Bound State

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    Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces.Comment: 25 pages, 7 figures (34 eps files

    Nogga,A.: A Three-Dimensional Treatment of the Three-Nucleon Bound State

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    Abstract Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces

    Different Methods for the Two-Nucleon T-Matrix in the Operator Form

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    We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006, (2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon-nucleon scattering observables using a chiral next-to-next-to-leading-order neutron-proton potential. We also apply our three-dimensional framework to the demanding problem of proton-proton scattering, using a corresponding version of the nucleon-nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton-proton scattering.Comment: 18 pages, 10 figures (54 eps files

    Deuteron disintegration in three dimensions

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    We compare results from the traditional partial wave treatment of deuteron electro-disintegration with a new approach that uses three dimensional formalism. The new framework for the two-nucleon (2N) system using a complete set of isospin - spin states made it possible to construct simple implementations that employ a very general operator form of the current operator and 2N states.Comment: 24 pages, 15 eps figure

    The European Union in the World ‚ÄĒ A Community of Values

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    These are momentous times in Europe. The Euro has been successfully introduced, the enlargement negotiations are approaching their climax, and the European Convention (‚ÄúConvention‚ÄĚ) is moving towards the drafting of a constitution for a new, continent-wide political entity. At the same time, unrest is manifest, particularly in two areas. On the one hand, many of our citizens, and not just the political elites, are dissatisfied with Europe\u27s performance on the world stage and are concerned about the maintenance of peace and security within the Union. In these areas they would like to see a strengthened, more effective entity-- ‚Äúmore Europe.‚ÄĚ On the other hand, their disenchantment with the long reach of European Union (‚ÄúEU‚ÄĚ or ‚ÄúUnion‚ÄĚ) regulation in the first pillar area of economic policy is growing. The feeling of loss of local control over their destiny and a vague feeling of potential loss of identity within an ever more centralized polity is palpable. Here, they want ‚Äúless Europe.‚ÄĚ In the outside world, change is also the order of the day. The ice-sheet of bipolarity, which overlaid and hid the complexity of international relations during the Cold War, is breaking up at an ever-increasing speed and revealing a world in which two paradigms are competing to become the underlying ordering principles for the new century. The traditional paradigm of interacting Nation States, each pursuing its own separate interests, with alliances allowing the small to compete with the large, is alive and well, and its proponents like Machiavelli or Churchill continue to be in vogue in the literature of international relations and the rhetoric of world leaders. At the same time, there is a school of thought which points to the growing economic and ecological interdependence of our societies and the necessity for new forms of global governance to complement national action. It is also becoming abundantly clear that the concept of a ‚ÄúNation State‚ÄĚ is often a fiction, positing as it does an identity between the citizens of a State and the members of a culturally homogenous society. For both reasons, the concept of the Nation State as the principal actor on the world stage, is called into question. The experience of the Union with the sharing of State sovereignty is clearly related to the second paradigm and also to the EU\u27s firm support for the development of the United Nations (‚ÄúU.N.‚ÄĚ) as well as other elements of multilateral governance. It would hardly be wise to suggest that any foreign policy, and certainly not that of the EU, should be based only on this paradigm. Given the recurrent threats to security, which seem to be part of the human condition expressed by some as the ‚Äúinevitability of war‚ÄĚ--the defense of territorial integrity; action against threats of aggression; and resistance to crimes against humanity such as genocide--the ability to conduct a security policy based much more on the old paradigm of interacting interests will continue to be required. That the EU needs to develop such a capability will be taken here as a given. Such a crisis-management capability will be essential to the Union, but will be distinguished here from the more long-term elements of foreign policy, which can be thought of as being designed to reduce the need for crisis management in the context of a security policy to a minimum. The crisis-management area of policy will not be treated further here. The thesis of this Essay is that the same set of political concepts can serve as a guide to the future internal development of the EU and as the basis of such a long-term foreign policy. Furthermore, it suggests that neither should be seen in terms of the balancing of interests but rather, as the expression of a small list of fundamental values. The list is as follows: (1) the rule of law as the basis for relations between members of society; (2) the interaction between the democratic process and entrenched human rights in political decision-making; (3) the operation of competition within a market economy as the source of increasing prosperity; (4) the anchoring of the principle of solidarity among all members of society alongside that of the liberty of the individual; (5) the adoption of the principle of sustainability of all economic development; and (6) the preservation of separate identities and the maintenance of cultural diversity within society. These values can be seen as the answer to the question posed both, by citizens of the Union and by our fellow citizens of the world: ‚ÄúWhat does the EU stand for?‚ÄĚ In exploring these values we should, however, remember that in the real world there will be occasions on which Realpolitik will intrude and the interest-based paradigm will prevail

    Measurement of the total cross section and ŌĀ -parameter from elastic scattering in pp collisions at ‚ąös=13 TeV with the ATLAS detector

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