Role%20of%20vacuum%20in%20relativistic%20nuclear%20model

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,
? the vacuum polarization gives the large
effective mass automatically, and ? if we
allow the large effective mass, the vacuum
contribution becomes natural.
? ? Parameters in RMF might include the vacuum
polarization inadequately. ? ? 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 gs 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/m0.8 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
RHA (RHAT1)
RMF (NL3)
gs 6.05
gs 10.22
g? 8.26
g? 12.87
Why were small coupling constants required in RHA
calculation?