On the Interpretation of Elastic Scattering of 10.3 MeV Deuterons on He4
Abstract Generated abstract
Elastic scattering of 10.3 MeV deuterons by helium-4 is analyzed using a rectangular complex optical potential, motivated by earlier applications to proton scattering. Differential cross sections are calculated by the Chase and Rohrlich method and compared with published experimental angular distributions. The model reproduces the qualitative form of the data but does not give uniformly precise agreement, with a representative best fit near V0 = -41 MeV and W0 = -5 MeV for r0 = 1.50 x 10^-13 cm, and a calculated reaction cross section of 0.34 barn consistent with the experimental estimate. The comparison suggests that deuteron breakup contributes substantially to absorption and that the deuteron may interact with the helium nucleus primarily through one nucleon.
Full Text
On the Interpretation of Elastic Scattering of Deuterons with an Energy of 10.3 MeV by \(He^4\)
L. S. Sokolov, A. P. Mamontov
Comparatively few works have been devoted to the elastic scattering of deuterons by \(He^4\). Almost all the data have been collected in [1]. These data give a general picture of the change in the angular distribution of elastically scattered deuterons by \(He^4\) with energy. However, attempts to interpret theoretically the available experimental data are not known.
The successful interpretation of proton scattering by \(He^4\) on the basis of a rectangular complex potential [2] permits one to hope that this potential can be applied to the interpretation of deuteron scattering by \(He^4\).
In the present work a potential of the form
\[ V = \begin{cases} V_0 + iW_0, & \text{for } r < R;\\[6pt] \dfrac{zz'e^2}{r}, & \text{for } r > R, \end{cases} \]
where \(R = r_0 A^{1/3}\) is the range radius of the nuclear forces, \(A\) is the mass number of the target nucleus, \(z\) is the atomic number of the target nucleus, \(z'\) is the atomic number of the incident nucleus, and \(V_0\) and \(W_0\) are the parameters of the interaction potential, is used to describe the elastic scattering of deuterons with an energy of 10.3 MeV by \(He^4\). The method for calculating the differential cross sections of elastic scattering \(\sigma(\theta)\) was borrowed from Chase and Rohrlich [3], and the experimental data on elastic scattering were taken from [4].
Figure 1 shows the experimental differential cross sections and those calculated for various values of the parameters \(V_0\) and \(W_0\) (with \(r_0 = 1.50 \times 10^{-13}\ \text{cm}\)) as functions of the scattering angle \(\varphi^\circ\) in the center-of-mass system. The curves calculated for different parameters of the interaction potential qualitatively reproduce the selected experimental curve; however, good agreement could not be achieved.
At small angles it was possible to fit the calculated curve to the experimental one for \(V_0 = -42\) MeV, \(W_0 = -3\) MeV. The first minimum was fitted for \(V_0 = -41\) MeV, \(W_0 = -6\) MeV. At larger angles the calculated curves oscillate considerably more strongly than the experimental one. The best agreement between the calculated and experimental curves over the entire
interval of angles was obtained with \(V_0=-41\) MeV, \(W_0=-5\) MeV, but fitting is also possible with another set of parameters.
For example, for \(r_0=1.45\cdot 10^{-13}\) cm, one may take \(V_0=-42\) MeV in order to obtain the same agreement with experiment as for \(r_0=1.5\cdot 10^{-13}\) cm and \(V_0=-41\) MeV.
The optical model makes it possible to calculate not only the elastic-scattering cross section, but also the deuteron reaction cross section. Integration of the differential reaction cross section for 10.3 MeV deuterons on \(\mathrm{He}^4\), obtained from experiment, gives \(0.3\div 0.1\) barn [4]. The calculated deuteron reaction cross section for \(V_0=-41\) MeV, \(W_0=-5\) MeV is equal to 0.34 barn, which is an independent confirmation of the correctness of the adopted parameters of the interaction potential.
Fig. 1
Comparison of these parameters with the corresponding parameters for the scattering of protons and neutrons [2] (excluding the imaginary part) does not show any noticeable difference between them.
The imaginary part for deuterons is somewhat larger than for protons (\(W_0=-3\) MeV), or thermal neutrons (\(W_0=-1.26\) MeV), but smaller than for \((d,d)\)-scattering on heavy nuclei (\(W_0=-12\) MeV) [5]. Apparently, the breakup of the deuteron plays an essential role here [4, 5], and it entirely determines the reaction cross section. The total breakup cross section of 10.3 MeV deuterons on \(\mathrm{He}^4\) amounts to 30% of the total elastic-scattering cross section in the angular region \(20\div160^\circ\) [4]. The breakup cross section of deuterons-
of 14–20 MeV on \(He^4\) has approximately the same value as the elastic-scattering cross section [5].
The data show that the deuteron breakup cross section increases sharply with the deuteron energy and with the atomic number of the target nucleus.
The approximate equality of \(r_0\) and \(V_0\) for protons and neutrons to the corresponding quantities for deuterons suggests that the deuteron interacts with the nucleus through only one of its nucleons, while the second nucleon most probably passes outside the region of action of the nuclear forces.
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