Nuclear density dependence of polarization transfer in quasi-elastic \({\rm A}(\vec{e},e' \vec{p})\) reactions

• Published in: arXiv.org 2024-04
• Main Authors: Kolar, T, Cosyn, W, Giusti, C, Achenbach, P, Ashkenazi, A, Böhm, R, Bosnar, D, Brecelj, T, Christmann, M, Cohen, E O, Distler, M O, Doria, L, Eckert, P, Esser, A, Gilman, R, Geimer, J, Gülker, P, Hoek, M, Izraeli, D, Kegel, S, Klag, P, Kohl, Y, Korover, I, Lichtenstadt, J, Littich, M, Manoussos, T, Mardor, I, Markus, D, Merkel, H, Mihovilovič, M, Müller, J, Müller, U, Olivenboim, M, Pätschke, J, Paul, S J, Piasetzky, E, Plura, S, Pochodzalla, J, Požun, M, Ron, G, Schlimme, B S, Schoth, M, Schulz, F, Sfienti, C, Stengel, S, Spreckels, R, Štajner, S, Stephan, E, Strauch, S, Szyszka, C, Širca, S, Thiel, M, Weber, A, Wilczek, A, Yaron, I, the A1 Collaboration
• Format: Article
• Language: English
• Subjects: Density; Form factors; Mathematical analysis; Polarization; Protons; Ratios
• ISSN: 2331-8422

The ratio of the transverse and longitudinal component of polarization transfer to protons in quasi-elastic \((\vec{e}, e^{\prime} \vec{p}\,)\) reaction, \(P^{\prime}_x/P^{\prime}_z\), is sensitive to the proton's electromagnetic form factor ratio, \(G_E/G_M\). To explore density-dependent in-medium modifications, a comparison of polarization transfer ratios involving protons from distinct nuclear shells, each with different local nuclear densities, has been proposed. In this study, we present such comparisons between four shells, \(1s_{1/2}\), \(1p_{3/2}\) in \(^{12}\mathrm{C}\) and \(1d_{3/2}\), \(2s_{1/2}\) in \(^{40}\mathrm{Ca}\). In an effort to account for other many-body effects that may differ between shells, we use state-of-the-art relativistic distorted-wave impulse-approximation (RDWIA) calculation and present the double ratios, \((P^{\prime}_x/P^{\prime}_z)_{\rm Data}/(P^{\prime}_x/P^{\prime}_z)_{\rm RDWIA}\) as well as the super ratios, \(\left[(P^{\prime}_x/P^{\prime}_z)_{\rm A}/(P^{\prime}_x/P^{\prime}_z)_{\rm B}\right]_{\rm Data}/\left[(P^{\prime}_x/P^{\prime}_z)_{\rm A}/(P^{\prime}_x/P^{\prime}_z)_{\rm B}\right]_{\rm RDWIA}\), for chosen shells A and B, as a function of effective local nuclear densities. We find that double ratios for individual shells show a dependence on the probed effective nuclear densities. Studying the ratios, we observed a systematic variation between pairs of higher- and lower-density shells.