INVESTIGATION OF VIRTUAL STATE OF 8Be+n SYSTEM USING THE COMPLEX SCALING METHOD

Аннотация

Nuclear states observed around threshold energies provide us with interesting problems associated
with the nuclear cluster structure. Most of them are also interesting astrophysically from the viewpoint of
nucleosynthesis.
The first excited 1/2+ state in 9Be has been observed as a sharp peak above the 8Be+n threshold energy in the
photo-disintegration cross section of γ+9Be->α+α+n. Since the size of the peak has a strong influence on the reaction
rate of the 9Be synthesis, new experimental data have been investigated. Recently, we performed calculations using
an α+α+n three-cluster model together with the complex scaling method (CSM), which well reproduces the recentlyobserved
photo-disintegration cross section. The results indicate that the virtual-state character of the 1/2+ state plays
an important role in formation of the peak structure appearing in the cross section observed above the 8Be+n
threshold. From these results, we discuss that the first excited 1/2+ state in 9Be is a 8Be+n virtual state but not
resonant one. However, the virtual state cannot be directly obtained as an isolated pole solution in the CSM, because
the scaling angle in the CSM cannot be increased over the position of the virtual state pole on the negative imaginary
axis of the complex momentum plane.
In our previous work, the cross section form of the photodisintegration and the phase shift behavior of a virtual
state assuming a simple two-body model are discussed. In the CSM, the virtual state cannot be obtained as an
isolated solution, but the continuum solutions are considered to include the effect of the virtual state. There is no
previous study that the CSM can be applied successfully to virtual state. Applying the CSM to the simple schematic
potential model, we have shown that the sharp peak of the photodisintegration cross section calculated just above the
threshold which does not correspond to a usual Breit-Wigner type pole. A new approach for the CSM to describe the
virtual state was proposed, and we discussed the pole position of the virtual state using the continuum level density
(CLD), the scattering phase shift, and scattering length calculated in the CSM. The next problem is how to
distinguish a virtual state from a resonant state and how to see the difference in the observed photo-disintegration
cross sections.
The purpose of this work is to investigate the reliability of the virtual state solutions in the CSM as comparing
with the solutions of the Jost function method. To investigate the structure of the virtual state, we calculate the
energy eigenvalues, phase shifts and photodisintegration cross section of the two-body model with a two-range
Gaussian potential by changing the strength of the attractive potential.