New measurement of $^{51}$V($γ$,1n) cross section through the refined monochromatic cross section extraction method

TL;DR

The paper tackles the long-standing puzzle of the Giant Dipole Resonance (GDR) structure in $^{51}$V, where photoneutron data had suggested either a single peak or a split-peak pattern around the GDR energy. It introduces a refined monochromatic cross section extraction method by integrating Polynomial Regression and Support Vector Regression into an unfolding framework, enabling stable extrapolation of $\sigma$ from the measured energy spectrum across $S_{ m n}$ to $E_{\max}$ at the SLEGS facility. The results show a single broad peak for $^{51}$V($\gamma$,1n) in the GDR region, aligning with spherical/near-spherical shapes, while deliberately overfitted SVR reconstructions reproduce multi-peak structures similar to older datasets, indicating the splitting in those data is likely an unfolding artifact. The study provides a robust, generalizable unfolding framework for monoenergetic cross-section extraction at LCSS facilities and offers a methodological basis for resolving deformation in nuclei and refining $\gamma$-strength-function inputs.

Abstract

The Giant Dipole Resonance (GDR) in $^{51}$V has been a long-term conflicting interpretation, with existing photoneutron cross section data suggesting either a single peak or a pronounced splitting, leading to opposite conclusions on nuclear deformation. A new measurement of the $^{51}$V($γ$,1n) cross section, performed at the Shanghai Laser Electron Gamma Source (SLEGS) facility, employs a refined monochromatic cross section extraction method. By integrating Polynomial Regression and Support Vector Regression (SVR) for robust interpolation and extrapolation, the new extracted monoenergetic cross sections exhibit a single, broad peak with no evidence of GDR splitting. This result provides new support for a spherical or near-spherical shape of $^{51}$V. Furthermore, we found that deliberately overfitting the data using an SVR model reproduces multi-peak structures similar to those reported in historical datasets, implying that the previously claimed splitting might originated from analysis artifacts rather than physical phenomena.

Figures (8)

• Figure 1: Schematic diagram of the experimental setup for photoneutron cross section measurements.
• Figure 2: The incident $\gamma$-ray spectra used in the measurement, normalized to one hour. The consistency between the measured and reconstructed spectra for a representative case is exemplified in the inset.
• Figure 3: The converged MSE between $\sigma_{\rm{exp}}$ and $\sigma_{\rm{f}}^{i+1}$ as a function of the polynomial degree.
• Figure 4: Unfolded cross section for $^{51}$V($\gamma$,n)$^{50}$V (a) and its ratios (b) obtained from Polynomial Regression and SVR models with two different regularization strengths $\it{C}$.
• Figure 5: The final converged MSE values of the unfolding iteration for different combinations of the SVR hyperparameters $\it{C}$ and $\it{\Gamma}$ (RBF kernel). A region of optimal performance (MSE $\approx$ 0.3) is found for $\it{\Gamma}$ = 0.15 and $\it{C}$ between 2000 and 10000.