High-precision Q-value measurement and evaluation of nuclear matrix elements for $$^{122}$$Sn and $$^{124}$$Sn neutrinoless double beta decays

Abstract We have determined the decay energy ( Q value) of the double beta decay of $$^{122}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>122</mml:mn> </mml:mmultiscripts> </mml:math> Sn with the JYFLTRAP double Penning trap mass spectrometer using the Phase-Imaging Ion Cyclotron Resonance technique. Our new Q value, 373.58(12) keV, agrees with the literature value but is 20 times more precise. We also measured the Q value for the double beta decay of $$^{124}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>124</mml:mn> </mml:mmultiscripts> </mml:math> Sn with unprecedented precision, 2293.542(83) keV. The Q values of $$^{122}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>122</mml:mn> </mml:mmultiscripts> </mml:math> Sn and $$^{124}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>124</mml:mn> </mml:mmultiscripts> </mml:math> Sn were used to calculate precisely the phase-space factors for the neutrinoless double beta ( $$0\nu \beta \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mi>ν</mml:mi> <mml:mi>β</mml:mi> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> ) decay mode of these nuclei. With the phase-space factor and our computed nuclear matrix elements (NMEs) we predict the $$0\nu \beta \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mi>ν</mml:mi> <mml:mi>β</mml:mi> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> -decay half-life of $$^{122}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>122</mml:mn> </mml:mmultiscripts> </mml:math> Sn based on the recently extracted upper limit of the effective neutrino mass by the KamLAND-Zen experiment. We used three nuclear-structure frameworks to compute the NMEs, namely the proton-neutron quasiparticle random-phase approximation (pnQRPA), the microscopic interacting boson model (IBM-2), and a hybrid model exploiting both the pnQRPA and the nuclear shell model (NSM). We find that including the short-range components enhances the total NME in the IBM-2 model, making it significantly larger than the NMEs calculated with the pnQRPA and hybrid models. Nevertheless, for all models, the obtained half-lives are very long for $$^{122}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>122</mml:mn> </mml:mmultiscripts> </mml:math> Sn ( $$\approx 10^{27}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>27</mml:mn> </mml:msup> </mml:mrow> </mml:math> – $$10^{29}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>29</mml:mn> </mml:msup> </mml:math> years), making the observation of $$0\nu \beta \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mi>ν</mml:mi> <mml:mi>β</mml:mi> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> decay of $$^{122}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>122</mml:mn> </mml:mmultiscripts> </mml:math> Sn experimentally challenging. On the other hand, the hybrid-model calculated value of the NME for $$^{124}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>124</mml:mn> </mml:mmultiscripts> </mml:math> Sn goes, interestingly enough, toward those previously computed by the NSM and the ab initio model.