Alpha-like correlations in "Equation missing" Ne, comparison of quartetting wave function and THSR approaches
G. Röpke, Chang Xu, Bo Zhou, Zhizhou Ren, Y. Funaki, H. Horiuchi, Mengjiao Lyu, A. Tohsaki, T. Yamada
Abstract
Abstract $$^{20}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>20</mml:mn> </mml:msup> </mml:math> Ne can be considered as a double-magic $$^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>16</mml:mn> </mml:msup> </mml:math> O core nucleus surrounded by four nucleons, the constituents of an $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -like quartet. Similar to other nuclei ( $$^{212}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>212</mml:mn> </mml:msup> </mml:math> Po, $$^{104}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>104</mml:mn> </mml:msup> </mml:math> Ti, etc.) with a quartet on top of a double-magic core nucleus, significant $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -like correlations are expected. Correlations in the ground state of $$^{20}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>20</mml:mn> </mml:msup> </mml:math> Ne are investigated using different approaches. The quartetting wave function approach (QWFA) predicts a large $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -like cluster contribution near the surface of the nuclei. The Tohsaki-Horiuchi-Schuck-Röpke (THSR) approach describes $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -like clustering in nuclear systems. The results of the QWFA in the Thomas-Fermi and shell-model approximation are compared with THSR calculations for the container model. Results for the $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> formation probability and the rms radii are shown.