Role of vacuum in relativistic nuclear model
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Transcript of Role of vacuum in relativistic nuclear model
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
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.
① the vacuum polarization gives the large effective mass automatically, and② if we allow the large effective mass, the vacuum contribution becomes natural.
There are the facts that,
① → Parameters in RMF might include the vacuum polarization inadequately.② → The vacuum polarization can be treated explicitly.
Motivation
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.
Effective Lagrangian of the Walecka modelwith the vacuum contribution
VF and ZF describe the vacuum effect of nucleons,
Leading-order derivative expansion
G. Mao, Phys. Rev. C67, (2003)
Leading-order derivative expansion
Derivative expansion gives fairly good
approximation to obtain the vacuum correction.
(a) Vacuum correction to baryon density
(b) Vacuum correction to scalar density
A. Haga et al., Phys. Rev. C70 (2004)
vacBB ,0
vacSS ,
Parameter sets used in the present study
sN gmm * ; Relativistic effective mass
Strength of the meson fields is suppressed by the vacuum.
Vacuum
Total
Scalar potential as a function of coupling constant gσ
in nuclear matter.
Nucleons
Fully-consistent RPA calculation
RPA equation
H: Uncorrelated response function obtained by RHA mean-field potential
FDH
Density partFeynman (vacuum polarization) part
Vacuum-polarization (Feynman) part
BAABF
2 Effective actionA B
ABF
Vacuum polarization is given by the functional derivatives of the effective action.
Decoupling of spurious state
Isoscalar giant quadrupole resonances (ISGQR)
The model with the vacuum polarization reproduces the data on the ISGQR !
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.
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.
Isoscalar giant dipole resonances (ISGDR)
The inclusion of the vacuum polarization shifts the ISGDR peaks to the lower energy.
Energy-weighted sum rules (EWSR)
EWSR of B(EL) is approximately proportional to the relativistic effective mass:
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.
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.
Profiles of proton and neutron densities
Proton Ca40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7 8
RHAT1NL3
Neutron Ca40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1 2 3 4 5 6 7 8
RHAT1NL3
40Ca
Proton density
Neutron density
Profiles of proton and neutron densities
90Zr
Proton density
Neutron density
Neutron Zr90
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
RHAT1NL3
Proton Zr90
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
RHAT1NL3
Profiles of proton and neutron densities
208Pb
Proton density
Neutron densityNeutron Pb208
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
RHAT1NL3
Proton Pb208
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12
RHAT1NL3
Scalar meson field Vector meson field
Scalar and vector mean-field potentials
gσ= 6.05
gω= 8.26
RHA (RHAT1)
gσ= 10.22
gω= 12.87
RMF (NL3)
Why were small coupling constants required in RHA calculation?