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Register a new userSolution of the eta-4He problem with quasi-particle formalism
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The Alt-Grassberger-Sandhas equations for the five-body eta-4N problem are solved for the case of the driving eta N and NN potentials limited to s-waves. The quasi-particle (Schmidt) method is employed to convert the equations into the effective two-body form. Numerical results are presented for the eta-4He scattering length.
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A formalism for spin observables of the reaction $pdto ~^3Heeta$ is derived in a model independent way. The general case with a full set of six independent spin amplitudes is studied. Furthermore, approximations by five and four spin amplitudes are investigated in the near threshold region. This region is of great interest to search for a quasi-bound $^3He-eta$ state, in particular, by measurement of energy dependence of relative phases of s- and p-wave amplitudes. Complete polarization experiments, allowing determination of spin amplitudes, are analyzed. It is shown that measurement of only analyzing powers and spin correlation coefficients hardly allows one to separate the s- and p-wave amplitudes, but additional measurement of polarization transfer coefficients simplifies this problem. Specific observables, given by products of one s- and one p-wave amplitudes, are found. Measurement of these observables will provide new independent information on the $^3He-eta$ pole position.
An exclusive measurement of the excitation function for the dd->3Heppi- reaction was performed at the Cooler Synchrotron COSY-Juelich with the WASA-at-COSY detection system. The data were taken during a slow acceleration of the beam from 2.185 GeV/c to 2.400 GeV/c crossing the kinematic threshold for the eta meson production in the dd->4He-eta reaction at 2.336 GeV/c. The corresponding excess energy with respect to the 4He-eta system varied from -51.4MeV to 22MeV. The integrated luminosity in the experiment was determined using the dd->3Hen reaction. The shape of the excitation function for the dd->3Heppi- was examined. No signal of the 4He-eta bound state was observed. An upper limit for the cross-section for the bound state formation and decay in the process dd->(4He-eta)bound->3Heppi- was determined on the 90% confidence level and it varies from 20nb to 27nb for the bound state width ranging from 5MeV to 35MeV, respectively.
We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.
We apply tensor version of antisymmetrized quasi cluster model (AQCM-T) to 4He and 8Be while focusing on the NN correlations in alpha clusters. We adopt the NN interactions including realistic ones containing a repulsive core for the central part in addition to the tensor part. In 4He, the pn pair in the 3D channel has been known to play a decisive role in the tensor correlation and the framework is capable of treating not only this channel but also the NN correlations in the 1S and 3S channels. In 8Be, when two alpha clusters approach, the 3D pair is suppressed because of the Pauli blocking effect, which induces the decrease of the 3S component through the 3S-3D coupling. This effect results in the reduction of the attractive effect of the central-even interaction in the middle-range region.
We propose a three-potential formalism for the three-body Coulomb scattering problem. The corresponding integral equations are mathematically well-behaved and can succesfully be solved by the Coulomb-Sturmian separable expansion method. The results show perfect agreements with existing low-energy $n-d$ and $p-d$ scattering calculations.
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