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The $^{150}$Nd($^3$He,$t$) reaction at 140 MeV/u and $^{150}$Sm($t$,$^3$He)reaction at 115 MeV/u were measured, populating excited states in $^{150}$Pm.The transitions studied populate intermediate states of importance for the(neutrinoless) $\beta\beta$ decay of $^{150}$Nd to $^{150}$Sm. Monopole anddipole contributions to the measured excitation-energy spectra were extractedby using multipole decomposition analyses. The experimental results werecompared with theoretical calculations obtained within the framework ofQuasiparticle Random-Phase Approximation (QRPA), which is one of the mainmethods employed for estimating the half-life of the neutrinoless $\beta\beta$decay ($0\nu\beta\beta$) of $^{150}$Nd. The present results thus provide usefulinformation on the neutrino responses for evaluating the $0\nu\beta\beta$ and$2\nu\beta\beta$ matrix elements. The $2\nu\beta\beta$ matrix elementcalculated from the Gamow-Teller transitions through the lowest $1^{+}$ statein the intermediate nucleus is maximally about half of that deduced from thehalf-life measured in $2\nu\beta\beta$ direct counting experiments and at leastseveral transitions through $1^{+}$ intermediate states in $^{150}$Pm arerequired to explain the $2\nu\beta\beta$ half-life.  Because Gamow-Teller transitions in the $^{150}$Sm($t$,$^3$He) experiment arestrongly Pauli-blocked, the extraction of Gamow-Teller strengths wascomplicated by the excitation of the $2\hbar\omega$, $\Delta L=0$, $\Delta S=1$isovector spin-flip giant monopole resonance (IVSGMR). However, the nearabsence of Gamow-Teller transition strength made it possible to cleanlyidentify this resonance, and the strength observed is consistent with the fullexhaustion of the non-energy-weighted sum rule for the IVSGMR.

The $^{150}$Nd($^3$He,$t$) and $^{150}$Sm($t$,$^3$He) reactions with applications to $\beta\beta$ decay of $^{150}$Nd