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--- science:giant_resonances [2024/11/28 10:45] – created jon-dokuwiki
+++ science:giant_resonances [2024/11/28 10:51] (current) – Add scissors mode jon-dokuwiki
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 ====== Giant Resonances ======
+This article contains my notes about the giant resonances in nuclear physics. The information is mainly from [[https://academic.oup.com/book/54689/chapter-abstract/422644891?redirectedFrom=fulltext&login=true| Giant Resonances: Fundamental High-Frequency Modes of Nuclear Excitation by M. N. Harakeh]]. Please see that book for more details!
 ==== The pygmy resonance ====
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 In heavier nuclei (\(A \geq 40\)), the coupling of \(1p\)-\(1h\) states to \(2p\)-\(2h\) states significantly dampens fine structure, leading to a more uniform strength distribution. However, in light sd-shell nuclei, such damping is less pronounced, and coupling to the continuum contributes to broadening and intrinsic widths in the range of a few MeV. The presence of isospin splitting further contributes to the fragmentation of IVGDR strength in non-self-conjugate nuclei (\(N \neq Z\)).
-Please see [[https://academic.oup.com/book/54689/chapter-abstract/422644891?redirectedFrom=fulltext&login=true|M. N. Harakeh]] for more details!
+==== The scissors mode ====
+The scissors mode is an orbital magnetic dipole (M1) excitation observed in deformed nuclei, first discovered in the strongly deformed nucleus \( ^{156} \mathrm{Gd} \) through inelastic electron scattering. This mode is characterized by an angular oscillation of the axially deformed distributions of protons and neutrons around an axis perpendicular to their symmetry axes. It exhibits a predominantly orbital nature, as evidenced by its weak excitation in inelastic proton scattering. The mean excitation energy of the mode is approximately \( E_x \approx 66 \delta A^{-1/3} \mathrm{MeV} \), where \( \delta \) is the nuclear deformation parameter, and its total M1 strength, typically around \( 3 \mu_N^2 \) for mid-shell rare earth nuclei, is proportional to \( \delta^2 \).
+A sum rule derived by Lo Iudice and Richter describes the total M1 strength \( B(\mathrm{M}1) \), incorporating factors like the deformation parameter \( \delta \), nucleon numbers \( Z \) and \( N \), and their respective orbital gyromagnetic factors \( g_p \) and \( g_n \):
+$$
+B(\mathrm{M} 1) \uparrow \approx 0.0042 \frac{4 N Z}{A^2} \omega_{s c} A^{5 / 3}\left(g_p-g_n\right)^2 \delta^2 \mu_N^2.
+$$
+This formula aligns well with experimental data, especially for well-deformed nuclei. The scissors mode has also been observed in actinide nuclei, showing a similar \( \delta^2 \)-dependent behaviour as in rare earth nuclei.