1 / 21

Role of vacuum in relativistic nuclear model

Role of vacuum in relativistic nuclear model. A. Haga 1 , H. Toki 2 , S. Tamenaga 2 and Y. Horikawa 3 1. Nagoya Institute of Technology , Japan 2. RCNP Osaka University, Japan 3. Juntendo University, Japan. Motivation.

alban
Download Presentation

Role of vacuum in relativistic nuclear model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Role of vacuum in relativistic nuclear model A. Haga1, H. Toki2, S. Tamenaga2 and Y. Horikawa3 1. Nagoya Institute of Technology , Japan 2. RCNP Osaka University, Japan 3. Juntendo University, Japan

  2. Motivation Recently, it has been pointed out that, ・　the vacuum contribution is unnatural, and ・　the finite parameters fitted to experimental data encode the vacuum contribution. R. J. Furnstahl et al, Phys. Rev. C52 (1995); Nucl. Phys. A618(1997) etc. On the other hand， ・　typical relativistic models give the small effective mass, but ・　the large effective mass is required from the beta-decay analysis and isoscalar giant quadrupole resonances (ISGQR). T. Niksic, et al., Phys. Rev. C71 (2005); Phys. Rev. C72 (2005) etc.

  3. Motivation There are the facts that, ① the vacuum polarization gives the large effective mass automatically, and ②if we allow the large effective mass, the vacuum contribution becomes natural. ①　→　Parameters in RMF might include the vacuum polarization inadequately. ②　→　The vacuum polarization can be treated explicitly. In this symposium, we show the vacuum-polarization effect both in the nuclear ground states and the nuclear excitations by fully-consistent RHA and RPA calculations.

  4. Effective Lagrangian of the Walecka modelwith the vacuum contribution G. Mao, Phys. Rev. C67, (2003) Leading-order derivative expansion VF and ZF describe the vacuum effect of nucleons,

  5. Leading-order derivative expansion (a) Vacuum correction to baryon density (b) Vacuum correction to scalar density Derivative expansion gives fairly good approximation to obtain the vacuum correction. A. Haga et al., Phys. Rev. C70 (2004)

  6. Parameter sets used in the present study ; Relativistic effective mass

  7. Strength of the meson fields is suppressed by the vacuum. Vacuum Total Nucleons Scalar potential as a function of coupling constant gσ in nuclear matter.

  8. Fully-consistent RPA calculation RPA equation : Uncorrelated response function obtained by RHA mean-field potential Density part Feynman (vacuum polarization) part

  9. Vacuum-polarization (Feynman) part Effective action A B Vacuum polarization is given by the functional derivatives of the effective action.

  10. Decoupling of spurious state

  11. Isoscalar giant quadrupole resonances (ISGQR) The model with the vacuum polarization reproduces the data on the ISGQR !

  12. Excitation energies of ISGQR as a function of the relativistic effective mass. The relativistic effective mass m*/m~0.8 is required to reproduce experimental ISGQR energies.

  13. Isoscalar giant monopole resonances (ISGMR) The centroids of the ISGMR does not shift as far as the compression modulus is kept the same, even if the vacuum polarization is included.

  14. Isoscalar giant dipole resonances (ISGDR) The inclusion of the vacuum polarization shifts the ISGDR peaks to the lower energy.

  15. Energy-weighted sum rules (EWSR) EWSR of B(EL) is approximately proportional to the relativistic effective mass:

  16. Summary • We have developed the fully-consistent RHA and RPA calculation using the derivative-expansion method. • The RHA calculation produces the enhanced effective mass naturally, because the inclusion of vacuum effect makes meson fields weak. • We have found that the relativistic effective mass is about 0.8, to reproduce the ISGQR excitation energies. • While the inclusion of the vacuum polarization affects the dipole compression mode, it does not affect the monopole ones if the compression modulus is kept the same. • The EWSR is suppressed by including the vacuum polarization. The beta-decay and nuclear polarization analyses would also give us the evidence of the large effective mass, a role of the vacuum polarization.

  17. Properties of the nuclear ground states In spite of the large differences of the scalar and vector potentials, the nuclear ground-state properties come out to be similar for each other.

  18. Profiles of proton and neutron densities 40Ca Proton density Neutron density

  19. Profiles of proton and neutron densities 90Zr Proton density Neutron density

  20. Profiles of proton and neutron densities 208Pb Proton density Neutron density

  21. Scalar and vector mean-field potentials Scalar meson field Vector meson field RMF (NL3) RHA (RHAT1) gσ= 10.22 gσ= 6.05 gω= 12.87 gω= 8.26 Why were small coupling constants required in RHA calculation?

More Related