We have examined the importance of momentum dependent induced nucleon currents such as weak-magnetism and pseudoscalar couplings to the amplitude of neutrinoless double beta decay (0νββ-decay) in the mechanisms of light and heavy Majorana neutrino as well as in that of Majoron emission.Such effects are expected to occur in all nuclear models in the direction of reducing the light neutrino matrix elements by about 30%. To test this we have performed a calculation of the nuclear matrix elements of the experimentally interesting nuclei A = 76, 82, 96, 100, 116, 128, 130, 136 and 150 within the proton-neutron renormalized Quasiparticle Random Phase Approximation (pn-RQRPA). We have found that indeed such corrections vary * Permanent address:

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Using the renormalized quasiparticle random phase approximation (RQRPA), we calculate the light neutrino mass mediated mode of neutrinoless double beta decay (0νββ-decay) of 76 Ge, 100 M o, 128 T e and 130 T e. Our results indicate that the simple quasiboson approximation is not good enough to study the 0νββ-decay, because its solutions collapse for physical values of g pp . We find that extension of the Hilbert space and inclusion of the Pauli Principle in the QRPA with proton-neutron pairing, allows us to extend our calculations beyond the point of collapse, for physical values of the nuclear force strength.

Large-mode-number magnetohydrodynamic instability driven by sheared flows in a tokamak plasma with reversed central shear Analytic solutions of the magnetohydrodynamic equilibrium equations for a symmetric magnetically confined plasma with sheared incompressible flows associated with electric fields similar to those observed in the transition from the low-to the high-confinement mode in tokamaks are constructed in cylindrical and toroidal geometries. In particular, an exact toroidal solution is obtained which for vanishing flows reduces to the Solovév equilibrium which has been extensively employed in tokamak confinement studies. Owing to the flow, several toroidal configurations having either one or two stagnation points are possible in addition to the usual ones with a single magnetic axis. For flows pertaining to tokamak operational regime the extremum of the electric field becomes larger as flow and its shear increase, the location of the extremum being, however, nearly independent of these variations. In addition, the flow affects the safety factor profile and the shape of the magnetic surfaces and results in an increase of the magnetic shear and a decrease of the toroidal beta. The impact of plasma elongation on the above-mentioned confinement figures of merit is also evaluated.

The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function ψ, in which four profile functionals of ψ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfvén velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equlibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having i) a flat current density and ii) a peaked current density *

The validity of the commonly assumed closure approximation has been tested by explicit calculations of the Ov PP-decay matrix elements of Ge Se performed in the context of quasiparticle random-phase approximation with a realistic model space. The closure approximation seems to work well for those matrix elements not very suppressed. Our results indicate that unlike the 2v decay, the Ov PP-decay matrix elements are not greatly suppressed but are comparable to those of shell model calculations. They are dominated by multipoles other than 0+ and 1+.Although at present there exist no data which contradict the standard model of the electroweak [SU (2) xU(1)] and the strong SU3(3), interactions there is a general belief that the standard model with its 23 unspecified parameters cannot be the ultimate fundamental theory of nature. Therefore during the last years various extensions of the standard model have been considered. Among them the most popular have been various unification schemes of the electroweak and strong forces, including the grand unified theories (GUT's) with their supersymmetric extensions and, more recently, superstring and superstring-inspired models.An interesting feature of such extensions of the standard model is that the neutrino turns out quite naturally to be a massive majorana particle, i.e. , loosely speaking identical with its own antiparticle. In such a situation the neutrinoless double P decay' (Ov PP decay) becomes possible. Thus if such a process is eventually detected it would indicate physics beyond the standard model. ' ' But, even if one is not able to observe the neutrinoless double P decay, an upper limit on its transition probability or a lower bound on its lifetime can provide rather stringent restrictions on the parameters of these models.For the extraction of these constraints from the data a reliable calculation of the nuclear matrix elements involved is quite crucial. Since the natural final states of Ov PP decay, i.e. , the double isobaric analog (DIA) and the double Gamow-Teller (DGT) states, cannot be reached due to the limited available energy, the populated states (ground state or low-lying excited states ) are very weak. Thus the transition probability depends on fine details of nuclear structure. Thus one may have to worry about problems which are normally assumed not be be critical." In this class of problems one may include the validity of closure approximation, the short-range correlations between the nucleons, and the role of the weak magnetism term of the weak hadronic current.The closure approximation in the usual two neutrino double P decay has to be circumvented. It has, however, been assumed to be good in Ov PP decay since in this case the propagator is expected to be dominated by the virtual neutrino momentum.Nevertheless, some groups ' have not used closure in the sense that they explicitly used the intermediate nuclear states. They did not, however, use the exact energy-dependent transition operator.In this Rapid Communication we are going to employ a method...

1W, 128 and 130 systems is examined in the context of the QRPA formalism without invoking the closure approximation. All possible nuclear matrix elements are calculated including the nucleon recoil contributions as well as those resulting from the exchange of heavy intermediate Majorana neutrinos. Using the hest presently available experimental limit TEP(Ov) > 1.1 x 1@' y the following limits on the lepton violating parameters are extracted: I(my)l<2.0eV. (1/M,)p126.7X 10'GeV. As3.3XlO-" and n s 4 . 2 ~ 10-8.

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