Photodisintegration cross sections for resonant states and virtual states

The $s$-wave photodisintegration cross sections observed just above the neutron breakup threshold energy are calculated for resonant and virtual states by using a complex-scaled two-body model, which simulates the ${}^9\mathrm{Be}$ nucleus with a ${}^8\mathrm{Be}+ns$-wave channel. We investigate the differences between behaviors of the resonance and virtual states in the photodisintegration cross sections near threshold energy in detail. It is shown that, in the present two-body model, resonant states very near the threshold energy produce a peak structure in the photodisintegration cross section that is similar that of the virtual state.

Figure 1

The calculated photodisintegration cross section of the ${}^9\mathrm{Be}(1/2^{+})$, taken from Ref. [18], in comparison with experimental data [5, 6]. The black solid line represents the cross section calculated by using the complex scaled $\alpha +\alpha +n$ model with an attractive three-body potential $v_3=-1.02$ MeV. The arrow indicates the threshold energy of the ${}^8\mathrm{Be}\left(0^{+}\right)+n$ channel.

Figure 2

The photodisintegration cross section due to the $E1$ transition calculated with the two-body potential model with the strength $V_1=-1.42$ MeV. The arrow indicates the threshold energy. This result is taken from Ref. [23].

Figure 3

Left: Matrix elements $M_{\nu }^2\left(\text{Re}\left(E_{\nu }\right)\right)$, calculated by Eq. (11). The black and open circles represent the imaginary and real parts, respectively. Middle: Real (cross) and imaginary (black circle) parts of the level density $\rho \left(E\right)$ calculated by Eq. (12). Right: The $E1$ strength distribution given in Eq. (10). Dotted, broken, and solid lines are $\text{Re}\left(M_{\nu }^2\right)\times \text{Im}\left(\rho \left(E\right)\right)$, $\text{Im}\left(M_{\nu }^2\right)\times \text{Re}\left(\rho \left(E\right)\right)$, and their sum, respectively.

Figure 4

The $E1$ strength functions for the photodisintegration cross section calculated by using the wave functions of $s$ waves for different $V_2$ values ($V_2=0\text{–}0.01$ MeV) in the CSM.

Figure 5

Pole trajectory of the resonance state in a complex energy plane by changing $V_2$ potential strength.

Figure 6

The $E1$ transition strength for different values of $V_2$ parameter.