Experimental renormalization factors $\frac{g_{\alpha }^{\mathrm{eff}}}{g_{\alpha }}$ for first forbidden $\beta$ transitions and experimental energies $E_{\alpha }^{\mathrm{GR}}$ for isovector mode giant resonances with $\Delta l=1\mathrm{}$ are discussed in terms of the effective spin isospin interactions. Simple analytical forms for the $\frac{g_{\alpha }^{\mathrm{eff}}}{g_{\alpha }}$ and the $E_{\alpha }^{\mathrm{GR}}$ are given. The observed values $\frac{g_{\tau }^{\mathrm{eff}}}{g_{\tau }}\simeq 0.3$ for the vector transitions are consistent with the expectation based on such isospin interaction ${\chi }_{\tau }$ as to reproduce the observed $E_{\alpha }^{\mathrm{GR}}$ for $E1\mathrm{}$ $\gamma$ giant resonances. The values $E_{\alpha }^{\mathrm{GR}}$ for the $\Delta l=1\mathrm{}$ giant resonances observed in ($p, n$) reactions are consistent with the value for the axial mode based on the spin isospin interaction ${\chi }_{\tau \sigma }$ similar to that of the Gamow-Teller resonance energy. Precise comparison of the observed $\frac{g_{\tau \sigma }^{\mathrm{eff}}}{g_{\tau \sigma }}$ and the $E_{\tau \sigma }^{\mathrm{GR}}$ ($p, n\Delta l=1\mathrm{}$), however, revealed some finite inconsistency, indicating some $\Delta \mathrm{}\left(1232\right)\mathrm{}$ isobar effect and the tensor interaction effect.

NUCLEAR STRUCTURE Comparison of experimental data for first forbidden $\beta$ decay matrix elements and associated ($p, n$) giant resonance energies. Schematic model and RPA analysis for spin isospin collective modes.

• Received 4 May 1982

DOI:https://doi.org/10.1103/PhysRevC.26.2628