References - Bogoliubov Laboratory of Theoretical Physics - JINR

Figure 2: The differential cross section and the
analyzing power of the �p+ 6,8 He elastic scatteirng
at 71 MeV/A.
Figure 3: Phenomenological optical potnetials
between a proton and 6,8 He as functions of the
radius.
The potentials obtained are shown in Fig. 3 as a function of radius. The upper panel
displays real and imaginary parts of the central term, while the lower one presents a
spin-orbit term with error bands resulted from fitting uncertainty. Due to the target
polarization uncertainty, there is an additional scale error of 28% for 6 He and 23% for 8 He
in the depth of the spin-orbit potentials.
3.2 Feature of the spin-orbit potentials
The shape of the spin-orbit potentials in neutron-rich helium isotopes is discussed here.
In order to extract the gross feature of the potentials, we focus on the radius and the
amplitude of the peak of spin-orbit potential as shown by the dotted lines in Fig. 3. We
call the former “LS radius” and the latter “LS amplitude”. Since the spin-orbit potential
is usually approximated by the radial derivative of density distribution, LS radius and
LS amplitude should be closely related to the radius and the gradient of the density
distribution, respectively.
TheLSradiiandLSamplitudesof 6 He and
8 He are presented in Fig. 4 by closed squares.
Those of neighboring even-even stable nuclei
[5, 6] and a global optical potential [7] are also
plotted by closed and open circles. It is clearly
demonstrated that the LS amplitudes of 6 He and
8 He are remarkably smaller than those of stable
nuclei. The LS amplitudes of stable nuclei
are almost constant and distributed between
4−5.5 MeV, whereas those of 6 He and 8 He are as
small as 1.3 and 2.0 MeV. It can be concluded
that the spin-orbit potentials in neutron-rich helium
isotopes are characterized by the significantly
shallow shape. This can be intuitively
explained from the largely diffused density distribution
of 6 He and 8 He, whose gradient is more
Figure 4: Two-dimensional distribution of
LS radius and LS amplitude.
than twice as small as that of 4 He. Results of more detailed analysis with microscopic
optical model calculation will be reported elsewhere.
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