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Register a new userVilen Mitrofanovich Strutinskys impact on nuclear and many particle physics
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Matthias Brack
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This paper is dedicated to the memory of Vilen Mitrofanovich Strutinsky who would have been 80 this year. His achievements in theoretical nuclear physics are briefly summarized. I discuss in more detail the most successful and far-reaching of them, namely (1) the shell-correction method and (2) the extension of Gutzwillers semiclassical theory of shell structure and its application to finite fermionic systems, and mention some applications in other domains of physics.
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$mu-e$ conversion is the experimentally most interesting lepton flavor violating process. From a theoretical point of view it is an interesting interplay of particle and nuclear physics. The effective transition operator, depending on the gauge model, is in general described in terms of a combination of four terms of transition operators (isoscalar and isovector, Fermi-like as well as axial vector-like). The experimentally most interesting ground state to ground state transition is adequately described in terms of the usual proton and neutron form factors. These were computed in both the shell model and RPA. Since it is of interest to know the portion of the strength exhausted by the coherent (ground state to ground state) transition, the total transition rate to all final states must also be computed. This was done i) in RPA by explicitly summing over all final states ii) in the context of the closure approximation (using shell model and RPA for constructing the initial state) and iii) in the context of nuclear matter mapped into nuclei via a local density approximation. We found that, apart from small local oscillations, the conversion rate keeps increasing from light to heavy nuclear elements. We also find that the coherent mode is dominant (it exhausts more than 90% of the sum rule). Various gauge models are discussed. In general the predicted branching ratio is much smaller compared to the present experimental limit.
We propose the use of pure spin-3/2 propagator in the $(3/2,0) oplus (0,3/2)$ representation in particle and nuclear physics. To formulate the propagator in a covariant form we use the antisymmetric tensor spinor representation and we consider the $Delta$ resonance contribution to the elastic $pi N$ scattering as an example. We find that the use of conventional gauge invariant interaction Lagrangian leads to a problem; the obtained scattering amplitude does not exhibit the resonance behavior. To overcome this problem we modify the interaction by adding a momentum dependence. As in the case of Rarita-Schwinger we find that a perfect resonance description could be obtained in the pure spin-3/2 formulation only if hadronic form factors were considered in the interactions.
Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $ell/a_B ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=hbar^2/m a_B^2$ and $ell$ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the on-set of system-specific non-universal effects. In this work we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which $a_Brightarrowinfty$, and show that nuclear systems belong to this class of universality.
Mass calculations carried out by Strutinskys shell correction method are based on the notion of smooth single particle level density. The smoothing procedure is always performed using curvature correction. In the presence of curvature correction a smooth function remains unchanged if smoothing is applied. Two new curvature correction methods are introduced. The performance of the standard and new methods are investigated using harmonic oscillator and realistic potentials.
This article presents several challenges to nuclear many-body theory and our understanding of the stability of nuclear matte r. In order to achieve this, we present five different cases, starting with an idealized toy model. These cases expose problems that need to be understood in order to match recent advances in nuclear theory with current experimental programs in low-energy nuclear physics. In particular, we focus on our current understanding, or lack thereof, of many-body forces, and how they evolve as functions of the number of particles . We provide examples of discrepancies between theory and experiment and outline some selected perspectives for future research directions.
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