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Low-Frequency Neutron-Proton Vibrations

  • A. Faessler
  • R. Nojarov
  • Z. Bochnacki
Conference paper

Abstract

The low-frequency isovector neutron-proton vibrations, which have been identified recently in experiment [1] as the lowest “mixed-symmetry” 2+ states in Ba-Ce nuclei near closed shells, were predicted a long time ago [2] in the framework of an extended vibrational model. Isospin-dependent collective coordinates allow the description of both isoscalar and isovector vibrations, coupled by the strength of the restoring force for isovector vibrations. The strength G is calculated microscopically [3,4] from the second (neutron-proton) derivative of a density-dependent symmetry energy using the wave functions of a spherical [3] (1) or and axially symmetric [4] (2) Woods-Saxon potential together with the BCS approximation:
$$ {G_{{sph}}} = D\int {\left[ {\rho_r^n\rho_r^p{r^4}/\left( {{\rho^n} + {\rho^n}} \right){/^{{1/3}}}} \right]} dr,\,\rho_{{_r}}^i = d{\rho^i}/dr,\,i = n,p\,{E_{{iv}}}\left( {{2^{ + }}} \right) = {E_{{is}}}\left( {{2^{ + }}} \right)\sqrt {{1 + 8G/{C_{{is}}}}} $$
(1)
$$ {G_{{def}}} = \pi D\int {\int {\frac{{\left[ {\rho_r^p\rho_r^n{z^2} + \rho_z^p\rho_z^n{r^2} - \left( {\rho_z^p\rho_r^n + \rho_r^p\rho_z^n} \right)rz} \right]}}{{{{\left( {{\rho^n} + {\rho^p}} \right)}^{{1/3}}}}}r\,drdz\,\rho_r^i = \partial {\rho^i}/\partial r}, \,\rho_z^i = \partial {\rho^i}/\partial z,\,{E_{{iv}}}\left( {{1^{ + }}} \right) = 2\sqrt {{{G_{{def}}}/J}} }, \,B\left( {M1;{0^{ + }} \to {1^{ + }}} \right) = 3J{E_{{iv}}}\left( {{1^{ + }}} \right)/16\pi, \,k = D{\rho^{{2/3}}},\,D = 91.6\,MeV\,f{m^2} $$
(2)

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • A. Faessler
    • 1
  • R. Nojarov
    • 2
  • Z. Bochnacki
    • 3
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingen 1F. R. Germany
  2. 2.Fellow of the AvHumboldt Foundation. Institute of Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Institute of Nuclear PhysicsKrakowPoland

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