Influence of the pion-nucleon interaction on the collective pion flow in heavy ion reactions

We investigate the influence of the real part of the in-medium pion optical potential on the pion dynamics in intermediate energy heavy ion reactions at 1 GeV/A. For different models, i.e. a phenomenological model and the $\Delta$--hole model, a pionic potential is extracted from the dispersion relation and used in Quantum Molecular Dynamics calculations. In addition with the inelastic scattering processes we thus take care of both, real and imaginary part of the pion optical potential. A strong influence of the real pionic potential on the pion in-plane flow is observed. In general such a potential has the tendency to reduce the anticorrelation of pion and nucleon flow in non-central collisions.Comment: 12 pages Latex, 4 PS-figure

Scalar and vector decomposition of the nucleon self-energy in the relativistic Brueckner approach

We investigate the momentum dependence of the nucleon self-energy in nuclear matter. We apply the relativistic Brueckner-Hartree-Fock approach and adopt the Bonn A potential. A strong momentum dependence of the scalar and vector self-energy components can be observed when a commonly used pseudo-vector choice for the covariant representation of the T-matrix is applied. This momentum dependence is dominated by the pion exchange. We discuss the problems of this choice and its relations to on-shell ambiguities of the T-matrix representation. Starting from a complete pseudo-vector representation of the T-matrix, which reproduces correctly the pseudo-vector pion-exchange contributions at the Hartree-Fock level, we observe a much weaker momentum dependence of the self-energy. This fixes the range of the inherent uncertainty in the determination of the scalar and vector self-energy components. Comparing to other work, we find that extracting the self-energy components by a fit to the single particle potential leads to even more ambiguous results.Comment: 35 pages RevTex, 7 PS figures, replaced by a revised and extended versio

Correlations and the relativistic structure of the nucleon self-energy

A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter is to decompose the self energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the dependence of the single-particle energy on the small component in the Dirac spinors used to calculate the matrix elements of the underlying NN interaction. The resulting Dirac components of the self-energy depend on the momentum of the nucleons. At densities around and below the nuclear matter saturation density this momentum dependence is dominated by the non-locality of the Brueckner G matrix. At higher densities these correlation effects are suppressed and the momentum dependence due to the Fock exchange terms is getting more important. Differences between symmetric nuclear matter and neutron matter are discussed. Various versions of the Bonn potential are considered.Comment: 18 pages LaTeX, including 6 figure

Influence of the in-medium pion dispersion relation in heavy ion collisions

We investigate the influence of medium corrections to the pion dispersion relation on the pion dynamics in intermediate energy heavy ion collisions. To do so a pion potential is extracted from the in-medium dispersion relation and used in QMD calculations and thus we take care of both, real and imaginary part of the pion optical potential. The potentials are determined from different sources, i.e. from the $\Delta$--hole model and from phenomenological approaches. Depending on the strength of the potential a reduction of the anti-correlation of pion and nucleon flow in non-central collisions is observed as well as an enhancement of the high energetic yield in transverse pion spectra. A comparison to experiments, in particular to $p_t$-spectra for the reaction Ca+Ca at 1 GeV/nucleon and the pion in-plane flow in Ne+Pb collisions at 800 MeV/nucleon, generally favours a weak potential.Comment: 25 pages, using REVTeX, 6 postscript figures; replaced by published versio

Origin of subthreshold K^+ production in heavy ion collisions

We investigate the origin of subthreshold $K^+$ production in heavy ion collisions at intermediate energies. In particular we study the influence of the pion induced $K^+$ creation processes. We find that this channel shows a strong dependence on the size of the system, i.e., the number of participating nucleons as well as on the incident energy of the reaction. In an energy region between 1--2 GeV/nucleon the pion induced processes essentially contribute to the total yield and can even become dominant in reactions with a large number of participating nucleons. Thus we are able to reproduce recent measurements of the KaoS Collaboration for 1 GeV/nucleon Au on Au reactions adopting a realistic momentum dependent nuclear mean field.Comment: 6 pages Latex using RevTex, revised version accepted for publication in Phys. Rev.

Probing the nuclear equation of state by K+K^+ production in heavy ion collisions

The dependence of $K^+$ production on the nuclear equation of state is investigated in heavy ion collisions. An increase of the excitation function of $K^+$ multiplicities obtained in heavy ($Au+Au$) over light ($C+C$) systems when going far below threshold which has been observed by the KaoS Collaboration strongly favours a soft equation of state. This observation holds despite of the influence of an in-medium kaon potential predicted by effective chiral models which is necessary to reproduce the experimental $K^+$ yields.Comment: 4 pages Revtex, 4 PS figures, to appear in Phys. Rev. Let

Density Dependent Hadron Field Theory

A fully covariant approach to a density dependent hadron field theory is presented. The relation between in--medium NN interactions and field--theoretical meson--nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson--nucleon vertices on the baryon field operators. As a consequence, the Euler--Lagrange equations lead to baryon rearrangement self--energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy--momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean--field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac--Brueckner calculations with the Bonn NN-potentials are used. Results from Hartree calculations for energy spectra, binding energies and charge density distributions of $^{16}O$, $^{40,48}Ca$ and $^{208}Pb$ are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultanuous improvement of charge radii, charge densities and binding energies. The results indicate the appearance of a new "Coester line" in the nuclear matter equation of state.Comment: 48 LateX pages, 12 Figures, figures and full paper are available as postscript files by anonymous ftp at ftp://theorie.physik.uni-giessen.de/dd

Semi-supervised learning towards automated segmentation of PET images with limited annotations: Application to lymphoma patients

The time-consuming task of manual segmentation challenges routine systematic quantification of disease burden. Convolutional neural networks (CNNs) hold significant promise to reliably identify locations and boundaries of tumors from PET scans. We aimed to leverage the need for annotated data via semi-supervised approaches, with application to PET images of diffuse large B-cell lymphoma (DLBCL) and primary mediastinal large B-cell lymphoma (PMBCL). We analyzed 18F-FDG PET images of 292 patients with PMBCL (n=104) and DLBCL (n=188) (n=232 for training and validation, and n=60 for external testing). We employed FCM and MS losses for training a 3D U-Net with different levels of supervision: i) fully supervised methods with labeled FCM (LFCM) as well as Unified focal and Dice loss functions, ii) unsupervised methods with Robust FCM (RFCM) and Mumford-Shah (MS) loss functions, and iii) Semi-supervised methods based on FCM (RFCM+LFCM), as well as MS loss in combination with supervised Dice loss (MS+Dice). Unified loss function yielded higher Dice score (mean +/- standard deviation (SD)) (0.73 +/- 0.03; 95% CI, 0.67-0.8) compared to Dice loss (p-value<0.01). Semi-supervised (RFCM+alpha*LFCM) with alpha=0.3 showed the best performance, with a Dice score of 0.69 +/- 0.03 (95% CI, 0.45-0.77) outperforming (MS+alpha*Dice) for any supervision level (any alpha) (p<0.01). The best performer among (MS+alpha*Dice) semi-supervised approaches with alpha=0.2 showed a Dice score of 0.60 +/- 0.08 (95% CI, 0.44-0.76) compared to another supervision level in this semi-supervised approach (p<0.01). Semi-supervised learning via FCM loss (RFCM+alpha*LFCM) showed improved performance compared to supervised approaches. Considering the time-consuming nature of expert manual delineations and intra-observer variabilities, semi-supervised approaches have significant potential for automated segmentation workflows