Effect of nuclear deformation on the observation of a low-energy super-Gamow-Teller state

A well-known structure with concentrated Gamow-Teller (GT) transitions is the Gamow-Teller resonance, which has been observed at higher-energy regions (usually $>6$ MeV) of nuclear excitation. It has been found that the GT strength can also concentrate in the lowest $J^{\pi }=1^{+}$ GT state named the “low-energy super-GT (LeSGT) state” when the initial even-even nucleus has the structure of “LS-closed-shell core nucleus $+$ 2 neutrons (or 2 protons)” and the final nucleus “LS-closed-shell core nucleus $+$ 1 proton and 1 neutron.” Such concentrations are realized with the core nuclei ${}^4\mathrm{He}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, corresponding to the shell closures of $s$, $p$, and $sd$ shells, respectively. It is natural to speculate that the LeSGT state may also be observed in the $A=82$ systems if the $N=Z=40$ shell gap is significant and ${}^{80}\mathrm{Zr}$ represents a good core nucleus corresponding to the $pf$ shell closure. Possible conditions that allow the formation of the LeSGT state in the ${}^{82}\mathrm{Zr}\to {}^{82}\mathrm{Nb}$ charge-exchange reaction (or ${}^{82}\mathrm{Mo}\to {}^{82}\mathrm{Nb}\beta$ decay) are discussed by evaluating the results of projected shell model calculations, which are based on deformed model space. Our calculations show that with increasing deformation, the LeSGT feature found in the spherical limit (zero deformation) evolves gradually into a broad distribution in the higher-energy region. This lets us conclude that no LeSGT state is expected in ${}^{82}\mathrm{Nb}$ because the shape of the ${}^{80}\mathrm{Zr}$ core nucleus is ellipsoidal.

Figure 1

Schematic illustration for the configurations that are involved in the ${\beta }^{-}$-type ${}^{82}\mathrm{Zr}\to {}^{82}\mathrm{Nb}$ GT transitions: (1) Transition if the nuclei are spherical (indicated by green arrows), and (2) transition if the nuclei are well deformed (indicated by orange arrows). The shaded bar shows roughly the Fermi surfaces. Thick (thin) arrows represent stronger (weaker) GT strengths.

Figure 2

Upper panel: Experimental ${}^{42}\mathrm{Ca}{(}^3\mathrm{He},t){}^{42}\mathrm{Sc}$ spectrum taken at 0 degrees. Lower panel: The $B({\mathrm{GT}}^{-}$) distribution calculated for the ${}^{42}\mathrm{Ca}\to {}^{42}\mathrm{Sc}$ GT transition from the ground state of ${}^{42}\mathrm{Ca}$ to excited states up to 12 MeV in ${}^{42}\mathrm{Sc}$ by assuming deformation parameter ${\varepsilon }_2=0.01$.

Figure 3

Theoretical $B({\mathrm{GT}}^{-}$) distributions for the ${}^{82}\mathrm{Zr}\to {}^{82}\mathrm{Nb}$ transition from the ground state of ${}^{82}\mathrm{Zr}$ to excited states up to 12 MeV in ${}^{82}\mathrm{Nb}$ by assuming different deformations. Note the plot (a) has different vertical scales than (b)–(e).

Figure 4

Accumulated $B({\mathrm{GT}}^{-}$) values for the ${}^{82}\mathrm{Zr}\to {}^{82}\mathrm{Nb}$ transition from the ground state of ${}^{82}\mathrm{Zr}$ to excited states in ${}^{82}\mathrm{Nb}$ by calculations with different deformations.