(He3,t) reaction on the double β decay nucleusCa48and the importance of nuclear matrix elements

Abstract

High-resolution ($^{3}\mathrm{He}$,$t$) measurements on the double \ensuremath{\beta}-decay ($\ensuremath{\beta}\ensuremath{\beta}$) nucleus $^{48}\mathrm{Ca}$ have been performed at RCNP (Osaka, Japan) to determine Gamow-Teller (${\mathrm{GT}}^{\ensuremath{-}}$) transitions to the nucleus $^{48}\mathrm{Sc}$, which represents the intermediate nucleus in the second-order perturbative description of the $\ensuremath{\beta}\ensuremath{\beta}$ decay. At a bombarding energy of ${E}_{{}^{3}\mathrm{He}}=420$ MeV an excitation energy resolution of 40 keV was achieved. The measurements were performed at two angle positions of the Grand Raiden Spectrometer (GRS): ${0}^{\ifmmode^\circ\else\textdegree\fi{}}$ and $2.{5}^{\ifmmode^\circ\else\textdegree\fi{}}$. The results of both settings were combined to achieve angular distributions, by which the character of single transitions could be determined. To characterize the different multipoles, theoretical angular distributions for states with ${J}^{\ensuremath{\pi}}={1}^{+},{2}^{+},{2}^{\ensuremath{-}}$, and ${3}^{+}$ were calculated using the distorted-wave Born approximation (DWBA) Code DW81. The ${\mathrm{GT}}^{\ensuremath{-}}$ strength was extracted up to ${E}_{x}=7$ MeV and combined with corresponding ${\mathrm{GT}}^{+}$ strength deduced from the $^{48}\mathrm{Ti}$($d$,$^{2}\mathrm{He}$)$^{48}\mathrm{Sc}$ data to calculate the low-energy part of the $\ensuremath{\beta}\ensuremath{\beta}$-decay matrix element for the $^{48}\mathrm{Ca}$ $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay. We show that after applying trivial momentum corrections to the ($^{3}\mathrm{He}$,$t$) spectrum, the two reaction probes, ($p,n$) and ($^{3}\mathrm{He}$,$t$) reveal a spectral response to an impressively high degree of similarity in the region of low momentum transfer.