RAPID COMMUNICATIONS
PHYSICAL REVIEW C 78, 021601(R) (2008)
Dipole polarizability of
7
Li from precision measurement of the elastic scattering on
208
Pb below the Coulomb barrier
V. V. Parkar,
*
V. Jha,
†
B. J. Roy, S. Santra, K. Ramachandran, A. Shrivastava, A. Chatterjee, S. R. Jain, A. K. Jain, and S. Kailas
Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
(Received 31 March 2008; published 27 August 2008)
The effect of dipole polarizability (α
0
) of
7
Li due to its cluster structure has been determined from a high
precision elastic scattering measurement of
7
Li on
208
Pb, over a range of energies from E
lab
= 18–28 MeV(V
Coul
≈
30 MeV). Continuum discretized coupled channel (CDCC) calculations have been performed to describe the
measured elastic scattering data.
DOI: 10.1103/PhysRevC.78.021601 PACS number(s): 25.70.Bc, 24.10.Eq, 21.60.Gx, 25.70.De
Nucleus-nucleus elastic scattering at energies well below
the Coulomb barrier is influenced by the polarizability
of the light projectile, induced by the strong Coulomb field
of the heavy target nucleus [1]. The interaction of the induced
dipole moment of the projectile with the electric field E(R)
generated by the target, leads to a polarization potential which,
in the adiabatic limit, is given as [2]
V
pol
(R) =−
1
2
α
0
E(R)
2
=−
1
2
α
0
Z
2
T
e
2
r
4
, (1)
where α
0
is the dipole polarizability, Z
T
e is the charge of the
target nucleus, and r is the separation between the center of
masses of the projectile and target. As a result, the effective
Coulomb potential (V
eff
= Z
P
Z
T
e
2
/r + V
pol
) gets reduced
and the effect shows up as a small but measurable deviation
(reduction) from pure Rutherford scattering in the elastic
scattering of the projectile from the target.
Careful measurements have been carried out to determine
the α
0
values for d [3] and
3
He [4] from highly accurate elastic
scattering data of these projectiles from
208
Pb target. In the
case of weakly bound stable projectiles like
6,7
Li,
9
Be and
light radioactive nuclei, due to the low break-up threshold,
the Coulomb field is expected to alter the elastic scattering in
the following ways: (i) the strong Coulomb field will lead to
breakup of the weakly bound projectiles, resulting in a loss
of flux and the consequent reduction in the elastic scattering
process; (ii) the projectile will be polarized due to the Coulomb
field and this will lead to a decrease in the elastic scattering
cross section. For stable projectiles, the dipole strength is
usually located at fairly high excitation energies and hence
coupling of the ground state (g.s.) to the dipole states is not
significant. However, due to low break-up threshold for the
weakly bound projectiles, substantial dipole strength could
be energetically possible at the lower excitation energies for
these nuclei [5]. This, in turn, will favour a strong dipole
coupling between the ground state and states in the continuum
lying above the break-up threshold. The polarizability of the
*
vvparkar@barc.gov.in
†
vjha@barc.gov.in
projectile is related to the dipole distribution B (E1) as [6]
α
0
=
8π
9
n=0
B (E1; gs → n)
n
(2)
where
n
is the energy of the nth dipole state.
It is possible to treat all these aspects in case of weakly
bound projectiles in terms of a complex polarization potential,
where the real term of the polarization potential will take
care of the polarizability effect and the associated imaginary
part will account for loss of flux due to absorption. The
above features are also amenable to CDCC calculations so
that one could attempt a consistent description of not only
the elastic but also the inelastic and fusion channels. It may
be remarked that the coupling to low lying continuum for
a weakly bound projectile may lead to both attractive and
repulsive contributions depending on the bombarding energies.
This feature will have a bearing on the final behavior of the
elastic scattering cross section. The CDCC formalism has
been applied successfully to describe the elastic scattering
data involving
6
He [7] and
7
Li [8]. In particular, the absence
of a characteristic Coulomb rainbow and a strong reduction in
elastic cross section for
6
He +
208
Pb system has been attributed
to the couplings due to dipole excitations [7]. Attempts have
been made to deduce the value of α
0
for
7
Li from analyses of
elastic and inelastic scattering of
7
Li from
208
Pb [8,9]. We have
carried out high precision cross section measurements for this
system, reducing the systematic and statistical uncertainties.
We have analyzed the present data set combining it with
related inelastic (excitation of
7
Li) and fusion data within
the framework of the CDCC formalism assuming α-t cluster
model for
7
Li nucleus. The contribution to the value of α
0
due
to the coupling of the low-lying break-up states and its effect
on elastic scattering cross section has been calculated.
We have made a theoretical estimate of the polarizability
α
0
of
7
Li within the α-t cluster model. The dipole moment is
induced by a perturbative potential V
pert
, which is given as
V
pert
=−
2
7
Z
T
e
2
R
3
( r ·
R), (3)
where r is the relative displacement between clusters,
R is the
center of mass coordinate, and θ is the angle between them.
The polarizability is expressed in terms of second-order Stark
effect due to this potential in the presence of the electric field
0556-2813/2008/78(2)/021601(5) 021601-1 ©2008 The American Physical Society