Transcript Highligh in Physics 2005

Congresso del Dipartimento di Fisica
Highlights in Physics 2005
11–14 October 2005, Dipartimento di Fisica, Università di Milano
Microscopic theory of
charge-exchange nuclear excitations
S.
*
Fracasso and
G.
*
Colò
* Dipartimento
di Fisica, Università di Milano and
INFN – Sezione di Milano
What are charge-exchange excitations?
The Isobaric Analog and the Gamow-Teller Resonances
Nuclear charge-exchange transitions from the (N,Z) ground state
excite states in the neighbour (N 1,Z ±1) systems.
They can spontaneously occur in nature as β-decay or be the
nuclear response to an external field
in a (p,n) or (n,p) type reaction.
±
n
p n
These resonances occur at zero angular momentum transfer (ΔL=0) as, respectively, pure isospin
and spin-isospin fluctuation.
n
p n
(a)
n
p
p
jl
t
1
2
 t
jl
N
Z
F   t ( i )
IVSGMR
i
ΔL=0
1
2
N
Z
A

Y    ( i )t (i )
A
i
1
IVGDR
IVSGDR
IVSGDR
IVGQR
K. Pham et al. Phys. Rev. C 51, 526 (1995)
The IAR is strictly related to the isospin symmetry, since it belongs to the parent ground state
isobaric multiplet:
H
ΔL=1
Collective isovector vibrational states,
in which protons and neutrons move in
opposition of phase (T=1), are excited.
Besides energy and angular momentum,
also a spin transfer can occur (S=1),
leading to spin-flip modes.
0°-2°
118Sn(3He,t)118Sb
The operators which rule these transitions
are the same of the allowed β-decay:
(b)
IVGMR
0°- 2°

2
,
T
0
nucl
EIAR  0.
For this reason, the calculation of IAR is a very serious benchmark for testing models.
When the Coulomb force and the other charge-breaking forces are switched on in the nuclear
Hamiltonian, a strong energy displacement is produced (Fig. 1), without however inducing a
large isospin mixing (see below).
ΔL=2
IAR
Theoretical framework: the Self-Consistent QRPA
1
1
2
These results2 are only sensitive to
the charge-breaking terms in the
Hamiltonian.
The linear response theory known as Random Phase Approximation (RPA) is a standard approach to
calculate collective nuclear excitations when they occur as small amplitude oscillations of the ground
state in magic nuclei.
The extension to open shell systems is the Quasiparticle-RPA, which includes the treatment of pairing
correlations, responsible for nuclear superfluidity.
Solving the QRPA equations, the excited states are written as a linear superposition of two quasiparticle
states, the simplest excitations around the Hartree-Fock-Bardeen-Cooper-Schrieffer (HF-BCS) ground state.
(n)
(n)
A
B




X 

 X
J

 ( n )   En  ( n ) 
  B  A  Y 
Y 
 
(n)  
n J    X pn
 p n  Ypn( n )  p n


pn
J
FIGURE 1. Results obtained [2] for the IAR energy
along the Sn isotopic chain by using our model
(full dots), compared with the experimental results
(open squares) taken from [1].
J
2
The general framework is based on the Density-Functional Theory, using a Skyrme force as effective
interaction in the particle-hole (p-h) channel and a density dependent pairing in the particle-particle (p-p)
channel :
1. the energy density functional E is built;
2. subsequent derivatives of E  provide both the mean-field and the residual interaction, responsible
for collective motion.
E 
 0 U

Hˆ  T  V
E   gs Hˆ gs   H r dr 3
 2 E 
v
2

Z
S. Fracasso and G. Colò, Phys. Rev. C (in press)
Unlike the case of IAR, the GTR is sensitive to the choice of the Skyrme parametrization (Fig. 2.b).
It should be due to the different treatment of spin and spin-isospin dependent terms of the forces.
This could help to improve the understanding of the isospin dependence of the effective interaction,
which is still an open question.
Besides nuclear structure, it also rules many astrophysical processes.
N
HF-BCS
GTR
Ground state
In the p-p channel, the results for
124Sn show that isoscalar pairing
plays a role, but that here GTR is
not sensitive to its strength variation
(Fig. 2.a).
QRPA
Excited states
In this sense, the method is fully Self-Consistent.
Terms neglected in the previous literature have now been included.
FIGURE 2. Dependence of the Gamow-Teller
transition strength in 124Sn on the strength (in
MeV fm3 ) of the residual isoscalar pairing (left)
and on different Skyrme parametrizations (right).
The arrow indicates the experimental value of
the GT main peak [1] .
1
Restoration of spontaneously
broken symmetry
No spurious contributions
Increase in predictive power
Extrapolation to unstable systems
Self-consistency
Interactions
The isospin mixing
The calculation of Fermi transitions allows a microscopic estimation (Fig. 3) of the isospin mixing
amount in the parent ground state, defined as the probability to find a |T+1,T> component admixed
in the |T,T> ground state.
A. Bohr and B. Mottelson Nuclear Structure vol. 1 (New York: Benjamin 1969 )
particle-hole channel
3
4
 k  U k ak  Vk ak

 k  U k ak  Vk ak
p
p
Skyrme effective interaction
n-1
with all the residual terms

n-1
charge-independence and
charge-symmetry breaking forces (CIB-CSB),
electromagnetic spin-orbit
particle-particle channel
ISOSPIN SYMMETRY
p
p
n
n
proton-neutron pairing
T. Babacan et al. J. Phys. G 30, 759 (2004)
v1, 1  v1,0  v1,1
pp
pn
nn
   r  r  / 2    
1
2
  r1  r2 
V  V0 1  
 
c
 

Isospin mixing
influence on superallowed
Fermi
transitions
breaking of transition
selection rules
(appearance of
new E1 in N=Z nuclei)
unitarity of
Cabibbo-Kobayashi-Maskawa
(CKM) matrix
weak vector coupling
constant GV
FIGURE 3. Results obtained for the isospin mixing in the Sn isotopic chain
employing different Skyrme parametrizations (full marks), compared with
the hydrodinamical estimate [3] (open diamonds) and a phenomenological
QRPA [4] (open circles).
We have a valuable tool: the calculation of other states is envisaged, in order to extract
information about the isovector effective NN interaction and the associated physical observables.