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1

On some hydrodynamical aspects of quantum mechanics

100%

Spera M.

Open Physics

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2010

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vol. 8

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issue 1

42-48

EN

In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial (i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this “Schrödinger fluid”, together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.

2

Electric dipole strength distribution below the E1 giant resonance in N = 82 nuclei

100%

Guliyev E., Kuliev A., Guner M.

Open Physics

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2010

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vol. 8

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issue 6

961-969

EN

In this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in 136Xe, 138Ba, 140Ce, 142Nd, 144Sm and 146Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6–8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B(E1) value of the 1− excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1+ States in heavy N = 82 isotones in the energy interval 6–8 MeV which shows not all dipole excitations were of electric character in this energy range.

3

Fine structure of the dipole excitations of the even-even 160Gd nucleus in the spectroscopic region

88%

Ertuğral F., Guliyev E., Kuliev A., Yildirim Z.

Open Physics

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2009

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vol. 7

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issue 4

731-737

EN

In this study, the result of calculations using rotational, translational and Galilean invariant quasiparticle random-phase approximation is presented for the low-lying dipole excitations in the even-even 160Gd nucleus. Calculations are carried out for both ΔK=1 and ΔK=0 branches. The analysis shows that the main part of spin-1 states, observed at energy 2.4–4 MeV in 160Gd, have M1 character and are interpreted as main fragments of the scissors mode. The calculations indicate the presence of a few prominent negativeparity dipole ΔK=1 states in the investigated energy region, in agreement with experiment.

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On some hydrodynamical aspects of quantum mechanics

Electric dipole strength distribution below the E1 giant resonance in N = 82 nuclei

Fine structure of the dipole excitations of the even-even 160Gd nucleus in the spectroscopic region