Prediction of ground state charge radius using support vector regression

Abstract

Abstract We systematically investigate the prediction of nuclear charge radii using a support vector regression (SVR) model in machine learning(ML), specifically employing a radial basis function (RBF) kernel. Our model is designed to capture the global structure of the radius surface through the utilization of feature spaces encompassing both ( N , Z ) and ( N , Z , A ). We achieved a root mean square deviation of 0.019 fm with respect to 885 measured charge radii ( Z <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext>⩾</mml:mtext> </mml:mrow> </mml:math> 8). By incorporating the atomic mass number as an additional feature, the model successfully reproduces the charge radii of ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>40</mml:mn> <mml:mo>−</mml:mo> <mml:mn>50</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> Ca), ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>74</mml:mn> <mml:mo>−</mml:mo> <mml:mn>96</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> Kr), ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>120</mml:mn> <mml:mo>−</mml:mo> <mml:mn>148</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> Ba), and ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>183</mml:mn> <mml:mo>−</mml:mo> <mml:mn>199</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> Au) isotopes. Furthermore, our ML method demonstrated an extrapolation capability with a deviation of 0.016 fm relative to 10 022 calculated charge radii based on the Weizsacker–Skyrme model. The SVR model’s performance is further tested across different regions of the charge radii table, demonstrating significant agreement with experimental data and underscoring the efficacy of the RBF kernel in nuclear charge radii prediction.