High-resolution study of Gamow-Teller transitions with the ${}^{37}$Cl(${}^3\text{He},t$)${}^{37}$Ar reaction

Under the assumption of isospin symmetry, $T_z=\pm 3/2\to \pm 1/2$ Gamow-Teller (GT) transitions in an isobar quartet with a mass $A$ are analogous, where $T_z=(1/2)(N-Z)$ is the $z$ component of the isospin $T$. We studied the $T_z=+3/2\to +1/2$ GT transitions by the ${}^{37}$Cl(${}^3\mathrm{He},t$)${}^{37}$Ar reaction at an incoming beam energy of $E_{\mathrm{beam}}=140$ MeV/nucleon with an energy resolution of $\Delta E=30$ keV. The distribution of the GT strength was obtained up to an excitation energy ($E_x$) of 14.2 MeV. This distribution was compared with that of the $T_z=-2/3\to -1/2$ transitions studied in ${}^{37}$Ca $\beta$ decay up to $E_x=8.6$ MeV. Although the overall distributions were similar, details of the fine structure were not necessarily reproduced. The experimental results were compared with a shell-model (SM) calculation using the USD interaction and the effective GT operator that compensates for the effect of limited model space. Although the overall distribution was reproduced by the SM calculation, the fragmentation of states was not reproduced. Neutrino cross sections were derived for the ${}^8$B solar-neutrino source.

Figure 1

A schematic view of the isospin symmetry structure and the GT transitions by a charge-exchange reaction and the $\beta$ decay in the $A=37$ isobars. The Coulomb displacement energy is subtracted in this figure. Under the assumption of isospin symmetry the transition strength distributions between transitions from the ground state of the $T_z=+3/2$ nucleus to the excited states in the $T_z=+1/2$ nucleus and those from the ground state of the $T_z=-3/2$ nucleus to the excited states in the $T_z=-1/2$ nucleus are the same. ${}^{37}$Cl, ${}^{37}$Ar, ${}^{37}$K, and ${}^{37}$Ca correspond to $T_z=-3/2$, $-1/2$, $+1/2,$ and $+3/2$, respectively. The transition strengths between ${}^{37}$Cl $\to$ ${}^{37}$Ar and ${}^{37}$Ca $\to$ ${}^{37}$K should have the same distributions in the energy spectra.

Figure 2

Energy spectrum of the ${}^{37}$Cl(${}^3\mathrm{He},t$)${}^{37}$Ar experiment at $\Theta =0^{\circ }–0.5^{\circ }$. The energy resolution is 30 keV (FWHM).

Figure 3

Schematic description of quasifree scattering. The upper drawing shows the the trajectories and the lower drawing the energies. The drawings are not to scale.

Figure 4

A part of the energy spectrum. The counts indicated by the dotted line were calculated with Eq. (1). They were subtracted as quasifree scattering events in the analysis.

Figure 5

Ratios of counts for scattering angles $\Theta =1.0^{\circ }–1.5^{\circ }$ and $\Theta =0.0^{\circ }–0.5^{\circ }$. The dotted lines show the 20$\%$ differences from unity. Transitions with the error bars overlapping the region between two dotted lines were identified as $\Delta L=0$.

Figure 6

Correction function $F({\theta }_{\mathrm{lab}}=0.{35}^{\circ },\omega )$ obtained by using DWBA calculations. The filled circles show the DWBA calculations using the shell-model wave functions for individual states. The solid curve fits these filled circles with a quadratic function. The dotted and dashed curves show the DWBA calculations with pure ($d_{3/2},d_{3/2}^{-1}$) and ($d_{3/2},d_{5/2}^{-1}$) configurations, respectively, assumed. For $E_x<5$ MeV, the filled circles are distributed along the dotted line. Above $E_x=5$ MeV, the filled circles follow the dashed line.

Figure 7

Comparison of experimental $B\left(\mathrm{GT}\right)$ distributions of ${}^{37}$Cl $\to$ ${}^{37}$Ar and ${}^{37}$Ca $\to$ ${}^{37}$K GT transitions obtained from ${}^{37}$Cl(${}^3\mathrm{He},t$)${}^{37}$Ar and ${}^{37}$Ca $\beta$ decay [20] measurements, respectively. The ${}^{37}$Cl $\to$ ${}^{37}$Ar $B\left(\mathrm{GT}\right)$ values are normalized by using the ${}^{37}$Ca $\beta$-decay data [20] in the region $E_x=5.93$–8.15 MeV. The thin and thick bars indicate the $B$(GT) values and uncertainties, respectively. The regions of the clusters having similar strengths between the ${}^{37}$Cl $\to$ ${}^{37}$Ar and ${}^{37}$Ca $\to$ ${}^{37}$K GT transitions are indicated by the arrows. These regions in $5.7–6.7$, $6.7–8.0$, and $8.2–8.7$ MeV are indicated in (b).

Figure 8

Comparison of cumulative sums of $B\left(\mathrm{GT}\right)$ between ${}^{37}$Cl $\to$ ${}^{37}$Ar (gray, red online) and ${}^{37}$Ca $\to$ ${}^{37}$K (black) GT transitions by ${}^{37}$Cl(${}^3\mathrm{He},t$)${}^{37}$Ar and ${}^{37}$Ca $\beta$ decay [20], respectively. The band widths represent the accumulated errors.

Figure 9

The SM calculation of $B$(GT) values for the (a) ${}^{37}$Cl $\to$ ${}^{37}$Ar and (b) ${}^{37}$Ca $\to$ ${}^{37}$K GT transitions using the USD-INC interaction. The strengths were multiplied by a quenching factor of 0.53 to compensate for the effects of the limited model space used in the calculation.

Figure 10

Cumulative sums of the GT transition strengths calculated by the SM code oxbash using the USD-INC interaction. The solid and dotted lines represent the ${}^{37}$Cl $\to$ ${}^{37}$Ar and ${}^{37}$Ca $\to$ ${}^{37}$K transitions, respectively. The strengths were multiplied by the quenching factor of 0.53.

Figure 11

Comparison of the empirical and the SM $B\left(\mathrm{GT}\right)$ data: (a) the $B\left(\mathrm{GT}\right)$ values obtained by the present ${}^{37}$Cl(${}^3\mathrm{He},t$)${}^{37}$Ar study, (b) the $B\left(\mathrm{GT}\right)$ values obtained by the ${}^{37}\mathrm{Ca}{\to }^{37}\mathrm{K}$ measurement [20], (c) the SM calculations using the USD interaction without isospin-violating forces and using the effective ($p,n$) operator, and (d) the SM calculations on the USD interaction without isospin-violating forces and using the effective $\beta$ operator.

Figure 12

Comparison of cumulative sums of $B\left(\mathrm{GT}\right)$ values for ${}^{37}$Cl $\to$ ${}^{37}$Ar transitions of the experiment and the SM calculation. The gray (red online) and black bands show the data without and with the continuum, respectively. The solid line represents the SM calculation based on the USD interaction with the effective ($p,n$) operator. The cumulative sum of the SM calculation is reduced by multiplying by the quenching factor of 0.53.