Fine Structure of the Gamow-Teller Resonance in ${}^{90}\mathrm{Nb}$ and Level Density of $1^{+}$ States

The fine structure of the Gamow-Teller resonance in a medium-heavy nucleus is observed for the first time in a high-resolution ${}^{90}\mathrm{Zr}({}^3\mathrm{He},t){}^{90}\mathrm{Nb}$ experiment at the Research Center for Nuclear Physics, Osaka. Using a novel wavelet analysis technique, it is possible to extract characteristic energy scales and to quantify their relative importance for the generation of the fine structure. This method combined with the selectivity of the reaction permits an extraction of the level density of $1^{+}$ states in ${}^{90}\mathrm{Nb}$.

Figure 1

(a) Spectrum of the ${}^{90}\mathrm{Zr}({}^3\mathrm{He},t){}^{90}\mathrm{Nb}$ reaction at $E_0=140\mathrm{MeV}/u$ and $\Theta <0.9°$. (b) Zoom on the GTR region. The prominent peak at $E_x\approx 12\mathrm{MeV}$ stems from the ${}^{12}\mathrm{B}$ ground state excited in the ${}^{12}\mathrm{C}({}^3\mathrm{He},t)$ background reaction.

Figure 2

(a) Continuous wavelet transform analysis of the spectrum of the ${}^{90}\mathrm{Zr}({}^3\mathrm{He},t){}^{90}\mathrm{Nb}$ reaction (upper panel) and absolute values of the wavelet coefficients, Eq. (1), as a function of excitation energy and scale, and their projection on the scale axis (lower panel). (b) Same as (a) but for the GT strength distribution in ${}^{90}\mathrm{Nb}$ calculated with the QPM.

Figure 3

Discrete wavelet transform decomposition of the ${}^{90}\mathrm{Zr}({}^3\mathrm{He},t){}^{90}\mathrm{Nb}$ spectrum of Fig. 1 into approximations $A_i$ and details $D_i$. The dashed line in the total spectrum represents the deduced background (see text).

Figure 4

Top: Reconstruction (dotted line) of the spectrum plotted in Fig. 1 (solid line) including either the scale ranges predicted to be important (left-hand side) or unimportant (right-hand side) in the DWT analysis. Bottom: Differences to the original spectrum.

Figure 5

Level density for $1^{+}$ states in ${}^{90}\mathrm{Nb}$ obtained from the ${}^{90}\mathrm{Zr}({}^3\mathrm{He},t){}^{90}\mathrm{Nb}$ measurement. Dashed line: Backshifted Fermi gas model [12]. Solid line: Hartree-Fock-BCS calculations [13].