JAEA-Conf 2011-002 - 日本原子力研究開発機構

The measured double-differential cross sections for light-ion production in silicon were determined
using the following expression:
2
θ, E
Y θ, E
d σ
dEdΩ
N Φ Ω dσ f ( E)
Si
H CH
1
2 CH 2 H CH 2
, (3)
Y N Φ Ω dΩ f ( E)
ΔE
H
Si
Si
where YSi(E,θ) is the net counts in a certain energy bin ΔE at laboratory scattering angle θ for each particle,
YH is the net counts in the recoil proton peak. The number of the net counts due to np scattering is obtained
using measurement at 20° for both polyethylene and carbon targets. The np scattering spectrum is deduced
by subtracting the contribution of C(n,xp) reaction from polyethylene measurement. The effective
efficiency which includes the energy loss effect in the CsI(Tl) scintillator is f(E), Φ is the relative neutron
flux and N is the number of the target nuclei. The differential np scattering cross section (dσH/dΩ) is taken
from NN-online[12]. In Eq. (3), the solid angle ΔΩ was given under an assumption that the target is treated
as a point source. It was confirmed that this assumption is valid by a comparison of the PHITS simulation
between a point source and a plane source, in which the difference is only 1%.
Thickness of the reaction target causes non-negligible effects on both energy-loss and particle-loss
of generated light ions. As a consequence, the measured spectrum is distorted in the low-energy region. To
correct these effects, we used the TCORR code [13] developed previously in the data analysis of light-ion
production measurements with the Medley setup.
The measured double-differential cross sections are analyzed using the exciton models with focus
on pre-equilibrium particle emission. As mentioned in the preceding section, the experimental data contains
the events from tail-neutron down to 70 MeV. Therefore, the measured spectra should be compared with the
following folding spectrum:
fold
E
upper
cal
E E , θ σ E , E θ W E
σ , , dE , (4)
n
i
i
E
lower
n
JAEA-Conf 2011-002
i
i
where Ei and θi are the emission energy and angle for charged particle i, W(En) is the ratio of the number of
neutrons around En to the number of peak neutrons, Elower (=70MeV) is lower limits of the neutron energy
selected by TOF cut, Eupper (=175 MeV) is the peak neutron energy, and σ cal (En, Ei, θi) is the calculated
double-differential cross section.
The GNASH code is designed to calculate particle production cross sections from the statistical
decay and pre-equilibrium processes. To take account of pick-up contributions from pre-equilibrium
light-ion production, the Iwamoto-Harada-Sato (IHS) coalescence model [3] has recently been incorporated
into the GNASH code [15]. The GNASH code outputs the angle-integrated emission spectra in the center
of mass (c.m.) system. After that, double-differential cross sections were obtained using the Kalbach
systematics [16] in order to compare them with the present measurements. The c.m.-to-lab transformation
was made using the kinematics of one-particle emission.
Both transmission coefficients and inverse reaction cross sections needed for GNASH with the
IHS model were calculated using optical potential parameters (OMPs). The OMPs were chosen on
condition that OMPs are available up to the maximum energy of emitted particles. As a result, we used
Koning and Delaroche [17] for protons and neutrons, An and Cai [18] for deuterons, Pang et al. [19] for
tritons and 3 He particles, and Avrigeanu, Hodgson and Avrigeanu [20] for alpha particles. In the GNASH
calculation, the Kalbach normalization factor was 120 MeV 3 which was determined by analysis of (n,xp)
spectra for incident energies up to 96 MeV. The single-particle state density g= A/13 was used, where A is
the mass number.
Some adjustable parameters are included in the IHS coalescence model. In the present analysis, we
have investigated intensively the energy dependence of the ΔR parameter (i.e., the pick-up radius of surface
region), which was chosen to be 1.0 fm from the analyses of (p,x) data for energies below 70 MeV in the
original paper [3]. It is also known that the Fermi energy is somewhat sensitive to the slope of
pre-equilibrium energy spectrum. It was chosen to be 40 MeV from our preliminary analysis.
Si
n
n
Si