Abstract:
The organizers of this meeting have asked me to present perspectives of nuclear physics. This means to identify the areas where nuclear physics will be expanding in the next future. In six chapters a short overview of these areas will be given, where I expect that nuclear physics willdevelop quite fast: A. Quantum Chromodynamics and effective field theories in the confinement region; B. Nuclear structure at the limits; C. High energy heavy ion collisions; D. Nuclear astrophysics; E. Neutrino physics; F. Test of physics beyond the standard model by rare processes. After a survey over these six points I will pick out a few topics where I will go more in details. There is no time to give for all six points detailed examples. I shall discuss the following examples of the six topics mentionned above: 1. The perturbative chiral quark model and the nucleon $\Sigma$-term, 2. VAMPIR (Variation After Mean field Projection In Realistic model spaces and with realistic forces) as an example of the nuclear structure renaissance, 3. Measurement of important astrophysical nuclear reactions in the Gamow peak, 4. The solar neutrino problem. As examples for testing new physics beyond the standard model by rare processes I had prepared to speak about the measurement of the electric neutron dipole moment and of the neutrinoless double beta decay. But the time is limited and so I have to skip these points, although they are extremely interesting.

Abstract:
The Neutrinoless double beta Decay allows to determine the effectice Majorana electron neutrino mass. For this the following conditions have to be satisfied: (i) The neutrino must be a Majorana particle, i. e. identical to the antiparticle. (ii) The half life has to be measured. (iii)The transition matrix element must be reliably calculated. (iv) The leading mechanism must be the light Majorana neutrino exchange. The present contribution studies the accuracy with which one can calculate by different methods: (1) Quasi-Particle Random Phase Approach (QRPA), (2) the Shell Model (SM), (3) the (before the variation) angular momentum projected Hartree-Fock-Bogoliubov method (PHFB)and the (4) Interacting Boson Approach (IBA). In the second part we investigate how to determine experimentally the leading mechanism for the Neutrinoless Double Beta Decay. Is it (a) the light Majorana neutrino exchange as one assumes to determine the effective Majorana neutrino mass, ist it the heavy left (b) or right handed (c) Majorana neutrino exchange allowed by left-right symmetric Grand Unified Theories (GUT's). Is it a mechanism due to Supersymmetry e.g. with gluino exchange and R-parity and lepton number violating terms. At the end we assume, that Klapdor et al. have indeed measured the Neutrinoless Double Beta Decay(, although contested,)and that the light Majorana neutrino exchange is the leading mechanism. With our matrix elements we obtain then an effective Majorana neutrino mass of: = 0.24 [eV], exp (pm) 0.02; theor. (pm) 0.01 [eV]

Abstract:
Neutrinoless Double Beta Decay ($0\nu\beta\beta$) is presently the only known experiment to distinguisch between Dirac neutrinos, different from their antiparticles, and Majorana neutrinos, identical with their antiparticles. In addition $0\nu\beta\beta$ allows to determine the absolute scale of the neutrino masses. This is not possible with neutrino oscillations. To determine the neutrino masses one must assume, that the light Majorana neutrino exchange is the leading mechanism for $0\nu\beta\beta$ and that the matrix element of this transition can ba calculated reliably. The experimental $0\nu\beta\beta$ transition amplitude in this mechanism is a product of the light left handed effective Majorana neutrino mass and of this transition matrix element. The different methods, Quasi-particle Random Phase Approximation (QRPA), Shell Model (SM), Projected Hartree-Fock-Bogoliubov (PHFB) and Interacting Boson Model (IBM2) used in the literature and the reliability of the matrix elements in these approaches are reviewed. In the second part it is investigated how one can determine the leading mechanism or mechanisms from the data of the $0\nu\beta\beta$ decay in different nuclei. Explicite expressions are given for the transition matrix elements. is shown, that possible interference terms allow to test CP (Charge and Parity conjugation) violation.

Abstract:
We review the recent developments in the field of nuclear double beta decay, which is presently an important topic in both nuclear and particle physics. The mechanism of lepton number violation within the neutrinoless double beta decay is discussed in context of the problem of neutrino mixing and the R-parity violating supersymmetric extensions of the Standard model. The problem of reliable determination of the nuclear matrix elements governing both two-neutrino and neutrinoless modes of the double beta decay is addressed. The validity of different approximation schemes in the considered nuclear structure studies is analyzed and the role of the Pauli exclusion principle for a correct treatment of nuclear matrix elements is emphasized. The constraints on different lepton number violating parameters like effective electron neutrino mass, effective right-handed weak interaction parameters, effective Majoron coupling constant and R-parity violating SUSY parameters are derived from the best presently available experimental limits on the half life of neutrinoless mode of this process.

Abstract:
A method to calculate the nuclear double beta decay ($2\nu\beta\beta$- and $0\nu\beta\beta$-) amplitudes within the continuum random phase approximation (cQRPA) is formulated. Calculations of the $\beta\beta$ transition amplitudes within the cQRPA are performed for ^{76}Ge, ^{100}Mo and ^{130}Te. A rather simple nuclear Hamiltonian consisting of phenomenological mean field and zero-range residual particle-hole and particle-particle interaction is used. The calculated M^{2\nu} are almost not affected when the single-particle continuum is taken into account. At the same time, a regular suppression of the $0\nu\beta\beta$-amplitude is found that can be associated with additional ground state correlations due to collective states in the continuum. It is expected that future inclusion of the nucleon pairing in the single-particle continuum will somewhat compensate the suppression.

Abstract:
By making use of the isospin conservation by strong interaction, the Fermi $0\nu\beta\beta$ nuclear matrix element $M_{F}^{0\nu}$ is transformed to acquire the form of an energy-weighted double Fermi transition matrix element. This useful representation allows reconstruction of the total $M_{F}^{0\nu}$ provided a small isospin-breaking Fermi matrix element between the isobaric analog state in the intermediate nucleus and the ground state of the daughter nucleus could be measured, e.g. by charge-exchange reactions. Such a measurement could set a scale for the $0\nu\beta\beta$ nuclear matrix elements and help much to discriminate between different nuclear structure models in which calculated $M_{F}^{0\nu}$ may differ by as much as the factor of 5.

Abstract:
In the present work the sensitivity of the QRPA calculation results to a realistic residual interaction is analyzed in the framework of the approach of Refs. \cite{Rum98,Rodin05}. Both Gamow-Teller (GT) and Fermi (F) \bb-decay amplitudes $M^{2\nu}$, along with the corresponding energy-weighted sum rules $S$, are calculated. General expressions relating $S$ to a realistic residual particle-particle interaction are derived, which show a pronounced sensitivity of $S$ to the singlet-channel interaction in the case of F transitions, and to the triplet-channel interaction in the case of GT transitions. Decompositions of $M^{2\nu}$, as well as the monopole transition contributions to $M^{0\nu}$, are obtained by the method of Refs. \cite{Rum98,Rodin05}. It is shown that in most of the cases almost the whole dependence of $M^{2\nu}$ and $M^{0\nu}$ on the particle-particle renormalization parameter $g_{pp}$ is accounted for by the $g_{pp}$-dependence of the corresponding sum rules $S$. Thus, the $g_{pp}$-sensitivity of calculated $M^{2\nu}$ and $M^{0\nu}$ is unavoidable since it is dictated by the generic structure of the $\beta\beta$ amplitudes. Finally, a better isospin-consistent way of a renormalization of the realistic residual particle-particle interaction to use in QRPA calculations is suggested.

Abstract:
A continuum-QRPA approach to calculation of the $2\nu\beta\beta$- and $0\nu\beta\beta$-amplitudes has been formulated. For $^{130}$Te a regular suppression (about 20%) of the high-multipole contributions to the $0\nu\beta\beta$-amplitude has been found which can be associated with additional ground state correlations appearing from the transitions to collective states in the continuum. At the same time the total calculated $0\nu\beta\beta$-amplitude for $^{130}$Te gets suppressed by about 20% as compared to the result of the usual, discretized, QRPA.

Abstract:
The modern theories of Grand Unification (GUT) and supersymmetric (SUSY) extensions of standard model (SM) suppose that the conservation laws of the SM may be violated to some small degree. The nuclei are well-suited as a laboratory to test fundamental symmetries and fundamental interactions like lepton flavor (LF) and lepton number (LN) conservation. A prominent role between experiments looking for LF and total LN violation play yet not observed processes of neutrinoless double beta decay. The GUT's and SUSY models offer a variety of mechanisms which allow this process to occur. They are based on mixing of Majorana neutrinos and/or R-parity violation hypothesis. Although the neutrinoless double beta decay has not been seen it is possible to extract from the lower limits of the lifetime upper limits for the effective electron Majorana neutrino mass, effective right handed weak interaction parameters, the effective Majoron coupling constant, R-parity violating SUSY parameters etc. In this work the limits on the LN violating parameters extracted from current neutrinoless double beta decay experiments are listed. Studies in respect to future neutrinoless double beta decay experimental projects are also presented.

Abstract:
We present a unified description of the vector meson and dilepton production in elementary and in heavy ion reactions. The production of vector mesons ($\rho,\omega,\phi$) is described via the excitation of nucleon resonances ($R$). The theoretical framework is an extended vector meson dominance model (eVMD) for resonance decays $R\longmapsto NV$ with arbitrary spin which is covariant and kinematically complete. The eVMD includes thereby excited vector meson states in the transition form factors. The model has successfully been applied to $\omega$ and $\phi$ production in $p+p$ reactions. The same model is used to describe the dilepton production in elementary reactions where corresponding data are well reproduced. However, when the model is applied to heavy ion reactions in the BEVALAC/SIS energy range the experimental dilepton spectra measured by the DLS Collaboration are significantly underestimated at small invariant masses. In view of this fact we discuss further medium effects: One is a substantial collisional broadening of the $\rho$ and in particular of the $\omega$ meson in the vicinity of the $\rho/\omega$-peak. The second medium effect is the destruction of quantum interference in a dense medium. A decoherent dilepton emission through vector mesons decays enhances the corresponding low mass dilepton yield in heavy ion reactions and improves the agreement with existing data.