Ex) Article Title, Author, Keywords
New Phys.: Sae Mulli 2023; 73: 934-940
Published online November 30, 2023 https://doi.org/10.3938/NPSM.73.934
Copyright © New Physics: Sae Mulli.
Yong Joo Kim*
Department of Physics, Jeju National University, Jeju 63243, Korea
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
A phase shift analysis of the elastic scattering angular distributions for α + 112,120,124Sn systems at 386 MeV is performed using the McIntyre parametrized phase shift model. The calculated results not only reproduced well the structure of measured angular distribution of three scattering systems, but also showed very good agreements with the experimental data. Average of input parameter values extracted from the best ﬁt to each α + 112,120,124Sn elastic data also provided a fairly well reproduction of experimental results. The oscillatory structure of angular distributions observed near the crossing angle is explained in terms of the strong interference between the near-side and the far-side scattering amplitudes. The behaviors of elastic cross section in the region of relatively large angles are mainly governed by the far-side contribution. As the target mass number increases, the magnitude of strong absorption radius, reaction cross section and nuclear rainbow angle tended to increase slightly.
Keywords: Phase shift analysis, McIntyre parametrized phase shift model, Elastic scattering, &alpha, + 112,120,124Sn
The parametrized phase shift model (PPSM)[1-3] is known to be convenient tool for the analysis of measured data of heavy-ion elastic scattering. The McIntyre PPSM has been used[4-12] for a long time to interpret the elastic scattering data. In this model, the nuclear scattering matrix element (SL) is analytically expressed in terms of angular momentum L, and its parameters are determined by the
The elastic scatterings between alpha particle and various target nuclei have been extensively studied[13-16]. Li et al. measured the angular distributions for
This work presents the numerical analysis of the experimental data of 386 MeV alpha particle elastic scattering on three tin isotopes using the McIntyre model. The best input parameter values are determined from the minimized
The elastic scattering amplitude
where first and second terms are the Rutherford and nuclear scattering amplitudes, respectively. In this equation, k the wave number,
and the real nuclear phase shift is
The grazing angular momentum Lg and its width Δ are related to the reduced radius r1/2 and the diffusivity d through the two following semiclassical formula :
The deflection function is defined as twice the angular momentum derivative of the Coulomb phase shift (
The McIntyre model is used to describe the differential cross section of 386 MeV alpha particle elastic scattering on three tin isotopes. Each of five input parameter values (
The decomposition of elastic scattering amplitude into near-side and far-side (
In this subsection, we use the average input parameter values (hereinafter named as ``AIPV") to examine whether AIPV can describe the
The calculated results using AIPV are shown in Fig. 3 as dotted curves, together with the best fits (solid curves). As expected, AIPV provides successful agreement (
In order to improve the quality of fit, we calculated the elastic angular distributions of each scattering systems by varying only the parameter μ related with the strength of
The transmission functions TL (
Figure 4(b) displays the behavior of the deflection functions
In this subsection, the effect of reduced radius r1/2 on differential and reaction cross sections of α + 120Sn system is investigated. As described in Eqs. (6) and (7), the r1/2 is an important factor in determining the grazing angular momentum Lg and its width Δ included in
In this study, an analysis of
Another approach using the average of best input parameter values has been made to examine whether this input values can describe the experimental data of α + 112,120,124Sn systems. The results reproduced fairly well the pattern of the angular distributions and provided acceptable fits to the elastic data, although the results displayed somewhat higher (lower) values for 112Sn (124Sn) target at scattering angles beyond about 150. In order to improve the quality of fit, we calculated the elastic cross sections by varying only the parameter μ related with the strength of real nuclear phase shift
The rapidly decreasing region of the transmission function is moved toward slightly larger L values as the AT increases. This movement produced slightly larger the critical angular momentum L1/2 and the strong absorption radius Rs. The geometrically obtained reaction cross section (
This research was supported by the 2023 scientific promotion program funded by Jeju National University.