# Nuclear Response to Second-Order Isospin Probes in Connection to Double Beta Decay

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{0ν}and (iii) a function $f({m}_{i},{U}_{ei},{\zeta}_{i})$ of the neutrino masses m

_{i}, the mixing coefficients U

_{ei}and the Majorana phases ζ

_{i}. Thus, if the NMEs are established with sufficient precision, the $f({m}_{i},{U}_{ei},{\zeta}_{i})$ factor, containing physics beyond the standard model, can be accessed from 0νββ decay rate measurements [2].

## 2. First-Order Isospin Probes: Single Charge Exchange Reactions

#### 2.1. Connection of Single Charge Exchange Reactions with β Decay

_{v}and g

_{A}control the isospin and spin-isospin operators. As a consequence, SCE reaction studies are complementary to β-decay ones as far as the nuclear response to isovector probes are concerned.

^{π}= 1

^{+}, ∆L = 0; ∆σ = 1; ∆τ = 1) by β decay is only possible within a reduced accessible energy window, but this is not the case for SCE reactions. Since the στ operator is not a symmetry for nuclear systems, the associated GT strength is broadly fragmented over many states corresponding to different excitation energies in the region of the Gamow–Teller Resonance (GTR) [54,55]. The GT distribution is a fingerprint of the nucleus, reflecting in detail its peculiar many-body nature. Therefore, the nuclear physics community has continuously put efforts into the exploration of GT strength.

^{π}= 1

^{+}, ∆L = 2; ∆σ = 1; ∆τ = 1) give a small contribution to the observed ∆J

^{π}= 1

^{+}strength. Such condition is typically matched at incident energy above 100 MeV/u and very forward scattering angles. Under these experimental conditions, the measured cross-sections for (n,p) and (p,n) SCE reactions were found to be proportional to known β

^{+}and β

^{-}strengths, respectively. However, the experimental resolution did not always allow to separate all the states populated by GT transitions in the energy spectra, somewhat limiting the accuracy of these analyses. In the years, GT studies have also been performed via SCE reactions induced by heavier projectiles, such as the (d,

^{2}He), (t,

^{3}He), (

^{7}Li,

^{7}Be) (

^{12}C,

^{12}N) (

^{18}O,

^{18}F) for the β

^{+}-like target transitions or the (

^{3}He,t), (

^{12}C,

^{12}B) for the β

^{−}-like class.

^{3}He,t) reactions mainly conducted at the Grand Raiden magnetic spectrometer of Research Center for Nuclear Physics of Osaka University (RCNP) laboratories [56,57,58] at 140 MeV/u incident energy has led to state-of-art results mainly thanks to the zero-degree mode for the spectrometer and the high energy resolution achieved (typical full-width-half-maximum ~25 keV) from the application of the powerful dispersion matching technique. A remarkable proportionality (better than 5%) between measured cross-sections and known β

^{-}strengths are reported as a general finding, at least for the less suppressed transitions, for several nuclei widely distributed in the nuclear chart. Consequently, the RCNP facility has represented an ideal tool for high-resolution GT studies, fostering tremendous progress in the field. For the transitions of β

^{+}type, remarkable results have been obtained by the (d,

^{2}He) studies at KVI-Center for Advanced Radiation Technology, University of Groningen and RIKEN facilities [59,60,61,62,63,64]. The detection of the two protons decaying from

^{2}He with high efficiency has guaranteed an overall energy resolution of about 100 keV in the missing mass spectra. The results of these experiments show that at center-of-mass detection angle for the

^{2}He system around zero degrees and at 100 MeV/u bombarding energy, a close roportionality is found between NMEs extracted from SCE cross-sections and NMEs extracted from β

^{+}and EC studies.

^{3}He,t) and (d,

^{2}He) studies is to map the GT response of specific nuclei, which represent the intermediate systems in 2νββ decay. The GT response of the even-even parent and daughter nucleus populating the odd-odd intermediate system is separately explored. The 1

^{+}states of the intermediate system, which are significantly populated in both SCE reactions, are inferred to give the main contribution to the 2νββ. A drawback is that the experiments access only the transition probabilities to individual 1

^{+}states, while the 2νββ calculations require the amplitudes with the proper phase since their coherent sum is needed to determine the decay rate. The easiest case is when a single 1

^{+}state is dominant in the intermediate state, as this prevents any coherent sum of amplitudes in this case. Approximate schemes have also been successfully adopted for 1

^{+}transitions close to the Fermi level [65]. Recently, the (

^{3}He,t) reaction has been used to map also the 2

^{−}state distribution, opening a new promising way to provide accurate information for 0νββ NME [66].

#### 2.2. Heavy-Ion Single Charge Exchange Reactions

^{12}C,

^{12}B) [75], (

^{12}C,

^{12}N), (

^{13}C,

^{13}N) [76] and in (

^{7}Li,

^{7}Be) [77,78,79,80,81,82] reactions on several targets at incident energies from 5 to 70 MeV/u. In references [79,81] GT matrix elements were extracted from (

^{7}Li,

^{7}Be

_{gs}(3/2

^{−})) and (

^{7}Li,

^{7}Be

_{0.43}MeV(1/2

^{−})) measured cross-sections for isolated transitions on light neutron-rich nuclei such as

^{11}Be,

^{12}B,

^{15}C and

^{19}O at about 8 MeV/u incident energy. A good accuracy (better than 10%) is achieved when a fully consistent microscopic approach for the ISI, FSI and reaction form factors is adopted in the calculations.

## 3. Second-Order Isospin Probes: Double Charge Exchange Reactions

^{+},π

^{−}) or (π

^{−},π

^{+}) reactions. Furthermore, double beta (ββ) decay processes induce the same transition in the parent nucleus, although allowed only for positive Q-value. As for SCE, DCE reactions probe nuclear response to the isospin degree of freedom, despite in DCE selects second-order effects.

^{−1}, and consequently excite virtual states up to high multipolarities [85]. Therefore, despite 2νββ and 0νββ decays are both weak processes, connecting the same states in the parent and daughter nuclei, they map different regions of the involved nuclear wave functions in the momentum space. The connection between the two phenomena is thus not strong enough for a safe extrapolation of 0νββ NMEs from 2νββ NMEs.

^{+},π

^{−}) or (π

^{−},π

^{+}) pion-induced DCE reactions, in which the isospin components of the strong interaction act twice in the sequential interaction of two independent nucleons with the π fields. In the first step, n (π

^{+},π

^{0}) p, the charged incident pion is converted to a neutral one; in the second step, n (π

^{0},π

^{−}) p, the neutral pion is converted to a charged one. Contextually two neutrons of the initial target nucleus are converted into two protons of the final residual system, similarly for DCE induced by negative pions, where a p (π

^{−},π

^{0}) n step is followed by a p (π

^{0},π

^{+})n one, with the transformation of two protons in two neutrons in the nucleus. Extensive exploration of (π

^{+},π

^{−}) reactions was performed in the 80′s leading to the discovery of second-order collective excitations as the double isobaric analog state (DIAS) and the isobaric analog state built on the top of the giant dipole resonance (GDR-IAS). The Double Gamow–Teller (DGT) was instead missed in the energy spectra. This fact was attributed to the spin-less nature of pions, making spin-isospin nuclear responses not directly accessible and thus difficult to be observed in pion-induced reactions. Johnson et al. have outlined the role of the Δ

_{33}(1232) resonance in pion-induced DCE reactions [86]. The (π

^{+},π

^{−}) process is described as a two-nucleon mechanism through the excitation and decay of intermediate Δ

_{33}(1232) resonances. Auerbach et al. have deeply investigated the relevant nuclear structure features in (π

^{+},π

^{−}) reactions [87,88,89], emphasizing the central role of nucleon–nucleon correlations. Recently, Lenske et al. [53] have pointed out that correlation-driven processes are not specific for pion-induced DCE and can also manifest in other hadronic reactions. In addition, since nucleon-nucleon correlations influence 0νββ dynamics, the study of such correlations in DCE reactions may provide key information.

^{3}He. However, in this case, the reactions of interest, the (t,3p) or (

^{3}He,3n), are very challenging from the experimental point of view since one should detect with high efficiency the three emitted protons or neutrons in coincidence in order to reconstruct the DCE ejectile momentum. When heavier projectiles are considered, the experiments are still rather demanding. If one requires that the final ejectile is in a bound state, in order to easily identify the DCE channel in the experiments, no light nucleus can be practically used as a projectile and

^{12}C,

^{18}O,

^{20}Ne or heavier projectiles are needed. Pioneering explorations of the heavy-ion-induced DCE were performed at Berkeley, Institut de Physique Nucléaire d’Orsay, Australian National University-Pelletron, National Superconducting Cyclotron Laboratory—Michigan State University, Los Alamos laboratories [90,91,92,93,94]. These studies focused on the (

^{14}C,

^{14}O), (

^{18}O,

^{18}Ne) and (

^{18}O,

^{18}C) reactions at energies above the Coulomb barrier, often with the main purpose of measuring the mass of neutron-rich isotopes by reaction Q-value measurements. However, these experiments were not conclusive for spectroscopic purposes, mainly because of the poor statistical significance of the few DCE collected events; thus, no further DCE measurement was performed for a long time. Furthermore, the development of theories to investigate the DCE reaction mechanism [95,96] soon slowed down, and the field was almost abandoned for many years.

#### DCE Reactions and 0νββ Decays

^{8}He,

^{8}Be) reaction was adopted to search for the tetra-neutron (4n) resonances by the

^{4}He(

^{8}He,

^{8}Be)4n at 186 MeV/u [97]. The (

^{11}B,

^{11}Li) [98] and the (

^{12}C,

^{12}Be) [99] were investigated to search for the Double Gamow–Teller Giant Resonance (DGTGR) and provide quantitative information about the DGT sum-rule, of interest for modern nuclear structure theories [100]. Another DCE reaction, the (

^{20}Ne,

^{20}O), has been introduced for the first time by the NUMEN (NUclear Matrix Elements for Neutrinoless double beta decay) and NURE (NUclear REactions for neutrinoless double beta decay) projects [41,48] with the aim to probe nuclear response to a β

^{−}β

^{−}-like transition. In addition, renewed use of the (

^{18}O,

^{18}Ne) reaction in upgraded experimental conditions has allowed achieving important results. The

^{40}Ca(

^{18}O,

^{18}Ne)

^{40}Ar DCE reaction, studied in ref. [40] at 15 MeV/u at the MAGNEX facility at Istituto Nazionale di Fisica Nucleare-Laboratori Nazionali del Sud (INFN-LNS) [44,45,47,101,102] has shown that high mass, angular and energy resolution energy spectra and accurate absolute cross-sections are at reach, even at very forward angles including zero-degree. Moreover, in the same paper, a schematic analysis of the measured cross-sections has demonstrated that DCE matrix elements can be extracted from the data and compared with nuclear structure calculations.

^{th}order in the nucleon-nucleus potential since four nucleons are involved; two protons (neutrons) are stripped from the projectile, and two neutrons (protons) are picked-up from the target. In ref. [40] it was shown that the contribution of multi-nucleon transfer is negligible (less than 1%) for the

^{40}Ca(

^{18}O,

^{18}Ne)

^{40}Ar reaction under the experimental conditions set for the measurement at INFN-LNS. Similar results are found in the preliminary analysis of the other explored cases [74]. The leading DCE reaction mechanism is thus mainly driven by the nucleon-nucleon isovector interaction, with negligible contribution from the exchange of nucleons between projectile and target. A useful way to model the DCE direct process is by means of the exchange of two charged π or ρ mesons between two nucleons in the projectile and two nucleons in the target. A pertinent open question is whether the two mesons are exchanged independently of each other in analogy to 2νββ-decays [104] or in a correlated way, as in the 0νββ-decays [53,105]. Answering this question is relevant for the connection of the nuclear response probed by DCE reaction and 0νββ decay. In addition, this aspect could have an impact on nuclear reaction theory since it could indicate a new way to access selective features of nucleon-nucleon short-range correlations [53].

- The initial and final states (parent and daughter) of the 0νββ decay are the same as the initial and final states (target and residual nuclei) in the DCE reaction;
- Both operators present short-range Fermi, Gamow–Teller and rank-2 tensor components, even if with different relative weights, depending in principle on the incident energy in the reaction case. The DCE experiments at different beam energies could give information on the individual contribution of each component;
- In both processes, a large linear momentum (~100 MeV/c) is available in the virtual intermediate channel [106]. It is worth to underline that other processes such as single β decay, 2νββ decay, SCE reactions induced by light ions are characterized by small momentum transfer, so they cannot probe this feature [107]. The recently proposed μ-capture experiments [108,109] could represent interesting developments in this context;
- In both cases, the processes require non-local operators acting on the same pairs of nucleons;
- Both transitions take place in the same nuclear medium. Since effects due to the presence of the medium are expected in both cases, DCE experimental data could give a helpful constraint on the theoretical determination of quenching phenomena in 0νββ;
- Off-shell propagation through virtual intermediate nuclear states features both cases. Since the virtual states do not represent asymptotic channels, their energies are not well defined as those (measurable) at stationary conditions [110].

^{+}to 0

^{+}transition from the ground state of an even–even parent to the ground state of the even-even daughter nucleus. This factorization is found to be possible for the differential cross-section at θ = 0, where the transition matrix elements can be written as the sum of double Gamow–Teller and double Fermi-type parts and that they can both be further factorized in terms of target and projectile NMEs.

^{+}to 0

^{+}transitions was proven to hold in a more advanced nuclear reaction model based on a fully quantum mechanical distorted wave two-step approach at vanishing momentum transfer. These conditions are verified at a very forward scattering angle for heavy-ion-induced DCE reactions. In the same work, a similarity between two-step sequential component of DCE cross-section and 2νββ decay is emphasized, despite DCE reactions cover a larger spectrum of momentum transfer. A comparison of the calculation with DCE differential cross-section data gives promising results in terms of the description of an absolute cross-section. However, room is left for additional contributions from correlated one-step DCE mechanism in order to explain the shape of the angular distribution at very forward angles. This aspect is further deepened in ref. [53], where the correlated one-step DCE mechanism, called “Majorana DCE mechanism”, is calculated in a fully microscopic approach and found to be essential in order to reproduce the experimental data. The Majorana DCE mechanism is indeed very interesting, as it is driven by short-range nucleon–nucleon correlations, similarly to 0νββ decay.

^{48}Ca and the 0νββ NME feeding the ground state of the daughter nucleus, both quantities calculated within a large scale shell model framework. DGTGR cannot be accessed in a double beta decay as it sits mainly in the particle continuum portion of the energy spectrum; instead, it is in principle accessible by DCE reactions. If measured, DCE cross-section energy distribution would allow getting the associated DGT strength distribution, using, for example, recently developed techniques as that proposed by V. dos S. Ferreira et al. [43]. In addition, the DGT matrix element for the transitions to the ground state of the final nucleus and the 0νββ decay NMEs are also found to be inherently connected for several nuclei, including ββ emitters. Such connection holds for different calculation schemes, with the important deviation found for QRPA.

## 4. The Renormalization of the Spin-Isospin Coupling Constant

^{3}He,t) reaction could mitigate this discrepancy.

^{113}Cd β-decay spectral shape with different nuclear structure models indicates the need for about 20% reduction of the fourfold forbidden nonunique decay matrix element in all cases [126], thus showing persistence of quenching at high momentum transfer in β-decay. A standard way to incorporate this feature in the data analyses is to adopt a quenched coupling constant for the axial vector weak interaction and for the spin-isospin strong interactions.

^{14}O,

^{48}Ca and

^{90}Zr, showing a sizeable and mass-dependent reduction of the strength from about 20% (

^{14}O) to about 40% (

^{90}Zr) when two-body currents are introduced. It would be very interesting to extend this exploration to SCE, including the projectile-target interaction in the same approach. However, to our knowledge, ab-initio methods are still not sufficiently developed for SCE reactions, so to date, the role of two-body currents in SCE can be explored with less detail.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Dolinski, M.J.; Poon, A.W.P.; Rodejohann, W. Neutrinoless Double-Beta Decay: Status and Prospects. Ann. Rev. Nucl. Part. Sci.
**2019**, 69, 219–251. [Google Scholar] [CrossRef] [Green Version] - Ejiri, H.; Suhonen, J.; Zuber, K. Neutrino–nuclear responses for astro-neutrinos, single beta decays and double beta decays. Phys. Rep.
**2019**, 1, 797. [Google Scholar] [CrossRef] - Caurier, E.; Menendez, J.; Nowacki, F.; Poves, A. Influence of pairing on the nuclear matrix elements of the neutrinoless betabeta decays. Phys. Rev. Lett.
**2008**, 100, 052503. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Iwata, Y.; Shimizu, N.; Otsuka, T.; Utsuno, Y.; Menéndez, J.; Honma, M.; Abe, T. Large-Scale Shell-Model Analysis of the Neutrinoless ββ Decay of 48Ca. Phys. Rev. Lett.
**2016**, 116, 112502. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Coraggio, L.; Gargano, A.; Itaco, N.; Mancino, R.; Nowalki, F. Calculation of the neutrinoless double-β decay matrix element within the realistic shell model. Phys. Rev. C
**2020**, 101, 044315. [Google Scholar] [CrossRef] - Suhonen, J.; Kortelainen, M. Nuclear matrix elements for double beta decay. Int. J. Mod. Phys. E
**2008**, 1, 17. [Google Scholar] [CrossRef] - Simkovic, F.; Rodin, V.; Faessler, A.; Vogel, P. 0νββ and 2νββ nuclear matrix elements, quasiparticle random-phase approximation, and isospin symmetry restoration. Phys. Rev. C
**2013**, 87, 045501. [Google Scholar] - Vaquero, N.L.; Rodriguez, T.R.; Egido, J.L. Shape and Pairing Fluctuation Effects on Neutrinoless Double Beta Decay Nuclear Matrix Elements. Phys. Rev. Lett.
**2013**, 111, 142501. [Google Scholar] [CrossRef] [Green Version] - Rodriguez, T.R.; Martinez-Pinedo, G. Energy Density Functional Study of Nuclear Matrix Elements for Neutrinoless ββ Decay. Phys. Rev. Lett.
**2010**, 105, 252503. [Google Scholar] [CrossRef] [Green Version] - Yao, J.M.; Song, L.S.; Hagino, K.; Ring, P.; Meng, J. Systematic study of nuclear matrix elements in neutrinoless double-β decay with a beyond-mean-field covariant density functional theory. Phys. Rev. C
**2015**, 91, 024316. [Google Scholar] [CrossRef] [Green Version] - Barea, J.; Kotila, J.; Iachello, F. Nuclear matrix elements for double-β decay. Phys. Rev. C
**2013**, 87, 014315. [Google Scholar] [CrossRef] [Green Version] - Barea, J.; Kotila, J.; Iachello, F. 0νββ and 2νββ nuclear matrix elements in the interacting boson model with isospin restoration. Phys. Rev. C
**2015**, 91, 034304. [Google Scholar] [CrossRef] [Green Version] - Kwiatkowski, A.A.; Brunner, T.; Holt, J.D.; Chaudhuri, A.; Chowdhury, U.; Eibach, M.; Engel, J.; Gallant, A.T.; Grossheim, A.; Horoi, M.; et al. New determination of double-β-decay properties in
^{48}Ca: High-precision Q_{ββ}-value measurement and improved nuclear matrix element calculations. Phys. Rev. C**2014**, 89, 045502. [Google Scholar] [CrossRef] [Green Version] - Engel, J.; Menendez, J. Status and future of nuclear matrix elements for neutrinoless double-beta decay: A review. Rep. Progr. Phys.
**2017**, 80, 046301. [Google Scholar] [CrossRef] [PubMed] - Wang, X.B.; Hayes, A.C.; Carlson, J.; Dong, G.X.; Mereghetti, E.; Pastore, S.; Wiringa, R.B. Comparison between variational Monte Carlo and shell model calculations of neutrinoless double beta decay matrix elements in light nuclei. Phys. Lett. B
**2019**, 798, 134974. [Google Scholar] [CrossRef] - Belley, A.; Payne, C.G.; Stroberg, S.R.; Miyagi, T.; Holt, J.D. Ab initio neutrinoless double-beta decay matrix elements for
^{48}Ca,^{76}Ge, and^{82}Se. arXiv**2020**, arXiv:2008.06588. [Google Scholar] - Report to the Nuclear Science Advisory Committee, Neutrinoless Double Beta Decay. 2014. Available online: https://science.osti.gov/ (accessed on 23 November 2015).
- Suhonen, J.T. Value of the axial-vector coupling strength in β and ββ decays: A review. Front. Phys.
**2017**, 5, 55. [Google Scholar] [CrossRef] - Fujita, J.; Ikeda, K. Existence of isobaric states and beta decay of heavier nuclei. Nucl. Phys.
**1965**, 67, 145. [Google Scholar] [CrossRef] - Wilkinson, D.H. Renormalization of the axial-vector coupling constant in nuclear β-decay (III). Nucl. Phys. A
**1974**, 225, 365. [Google Scholar] [CrossRef] - Iachello, F.; Barea, J.; Kotila, J. Quenching of g
_{A}and its impact in double beta decay. In Proceedings of the NEUTEL 2015: XVI International Workshop on Neutrino Telescopes, Venice, Italy, 2–6 March 2015. [Google Scholar] - Suhonen, J.; Civitarese, O. Probing the quenching of gA by single and double beta decays. Phys. Lett. B
**2013**, 725, 153. [Google Scholar] [CrossRef] [Green Version] - Faessler, A.; Fogli, G.L.; Lisi, E.; Rodin, V.; Rotunno, A.M.; Šimkovic, F. Overconstrained estimates of neutrinoless double beta decay within the QRPA. J. Phys. G Nucl. Part. Phys.
**2008**, 35, 075104. [Google Scholar] [CrossRef] - Robertson, R.G.H. Empirical survey of neutrinoless double beta decay matrix elements. Mod. Phys. Lett. A
**2013**, 28, 1350021. [Google Scholar] - Dell’Oro, S.; Marcocci, S.; Vissani, F. New expectations and uncertainties on neutrinoless double beta decay. Phys. Rev. D
**2014**, 90, 033005. [Google Scholar] [CrossRef] [Green Version] - Menendez, J.; Gazit, D.; Schwenk, A. Chiral Two-Body Currents in Nuclei: Gamow-Teller Transitions and Neutrinoless Double-Beta Decay. Phys. Rev. Lett.
**2011**, 107, 062501. [Google Scholar] [CrossRef] [PubMed] - Measday, D.F. The nuclear physics of muon capture. Phys. Rep.
**2001**, 354, 243. [Google Scholar] [CrossRef] - Ejiri, H.J. Double Beta Decays and Neutrino Masses. Phys. Soc. Jpn.
**2005**, 74, 2101. [Google Scholar] [CrossRef] [Green Version] - Brown, B.A.; Horoi, M.; Sen’kov, R.A. Nuclear Structure Aspects of Neutrinoless Double-β Decay. Phys. Rev. Lett.
**2014**, 113, 262501. [Google Scholar] [CrossRef] [Green Version] - Schiffer, J.P. Nuclear Structure Relevant to Neutrinoless Double β Decay:
^{76}Ge and^{76}Se. Phys. Rev. Lett.**2008**, 100, 112501. [Google Scholar] [CrossRef] [Green Version] - Roberts, A.; Howard, A.M.; Kolata, J.J.; Villano, A.N.; Becchetti, F.D.; DeYoung, P.A.; Febbraro, M.; Freeman, S.J.; Kay, B.P.; McAllister, S.A.; et al. Proton pair correlations and the neutrinoless double-β decay of
^{76}Ge. Phys. Rev. C**2013**, 87, 051305. [Google Scholar] [CrossRef] [Green Version] - Toh, Y.; Chiara, C.J.; McCutchan, E.A.; Walters, W.B.; Janssens, R.V.F.; Carpenter, M.P.; Zhu, S.; Broda, R.; Fornal, B.; Kay, B.P.; et al. Evidence for rigid triaxial deformation at low energy in
^{76}Ge. Phys. Rev. C**2013**, 87, 041304. [Google Scholar] [CrossRef] - Mukhopadhyay, S.; Crider, B.P.; Brown, B.A.; Ashley, S.F.; Chakraborty, A.; Kumar, A.; McEllistrem, M.T.; Peters, E.E.; Prados-Estévez, F.M.; Yates, S.W. Nuclear structure of
^{76}Ge from inelastic neutron scattering measurements and shell model calculations. Phys. Rev. C**2017**, 95, 014327. [Google Scholar] [CrossRef] [Green Version] - Peters, E.E.; Van Isacker, P.; Chakraborty, A.; Crider, B.P.; Kumar, A.; Liu, S.H.; McEllistrem, M.T.; Mehl, C.V.; Prados-Estévez, F.M.; Ross, J.L.; et al. Seniority structure of
^{136}Xe_{82}. Phys. Rev. C**2018**, 98, 034302. [Google Scholar] [CrossRef] [Green Version] - Henderson, J.; Wu, C.Y.; Ash, J.; Brown, B.A.; Bender, P.C.; Elder, R.; Elman, B.; Gade, A.; Grinder, M.; Iwasaki, H.; et al. Triaxiality in selenium-76. Phys. Rev. C
**2019**, 99, 054313. [Google Scholar] [CrossRef] - Mukhopadhyay, S.; Crider, B.P.; Brown, B.A.; Chakraborty, A.; Kumar, A.; McEllistrem, M.T.; Peters, E.E.; Prados-Estévez, F.M.; Yates, S.W. Inelastic neutron scattering studies of
^{76}Se. Phys. Rev. C**2019**, 99, 014313. [Google Scholar] [CrossRef] [Green Version] - Pietralla, N.; Scheit, H. Experiments on the Competitive Double-Gamma (γγ/γ) Decay. J. Phys. Conf. Ser.
**2018**, 1056, 012045. [Google Scholar] [CrossRef] - Frekers, D. Nuclear reactions and the double beta decay. Prog. Part. Nucl. Phys.
**2010**, 64, 281. [Google Scholar] [CrossRef] - Guess, C.J.; Adachi, T.; Akimune, H.; Algora, A.; Austin, S.M.; Bazin, D.; Brown, B.A.; Caesar, C.; Deaven, J.M.; Ejiri, H.; et al. The
^{150}Nd(^{3}He,t) and^{150}Sm(t,^{3}He) reactions with applications to ββ decay of^{150}Nd. Phys. Rev. C**2011**, 83, 064318. [Google Scholar] [CrossRef] [Green Version] - Cappuzzello, F.; Cavallaro, M.; Agodi, C.; Bondì, M.; Carbone, D.; Cunsolo, A.; Foti, A. Heavy-ion double charge exchange reactions: A tool toward 0νββ nuclear matrix elements. Eur. Phys. J. A
**2015**, 51, 145. [Google Scholar] [CrossRef] [Green Version] - Cappuzzello, F.; Agodi, C.; Cavallaro, M.; Carbone, D.; Tudisco, S.; Lo Presti, D.; Oliveira, J.R.B.; Finocchiaro, P.; Colonna, M.; Rifuggiato, D.; et al. The NUMEN project: NUclear Matrix Elements for Neutrinoless double beta decay. Eur. Phys. J. A
**2018**, 54, 72. [Google Scholar] [CrossRef] [Green Version] - Shimizu, N.; Menéndez, J.; Yako, K. Double Gamow-Teller Transitions and its Relation to Neutrinoless ββ Decay. Phys. Rev. Lett.
**2018**, 120, 142502. [Google Scholar] [CrossRef] [Green Version] - Ferreira, V.d.S.; Samana, A.R.; Krmpotić, F.; Chiapparini, M. Nuclear structure model for double-charge-exchange processes. Phys. Rev. C
**2020**, 101, 044314. [Google Scholar] [CrossRef] - Cavallaro, M.; Agodia, C.; Brischettoab, G.A.; Calabreseab, S.; Cappuzzelloab, F.; Carbonea, D.; Ciraldoab, I.; Pakouc, A.; Sgourosa, O.; Soukerasa, V.; et al. The MAGNEX magnetic spectrometer for double charge exchange reactions. Nucl. Instr. Meth. B
**2020**, 463, 334. [Google Scholar] [CrossRef] - Cavallaro, M.; Santagatia, G.; Cappuzzelloab, F.; Carbonea, D.; Linaresc, R.; Torresia, D.; Acostad, L.; Agodia, C.; Bonannoe, D.; Bongiovannia, D.; et al. Charge-state distributions of
^{20}Ne ions emerging from thin foils. Results Phys.**2019**, 13, 102191. [Google Scholar] [CrossRef] - Calabrese, S.; Cappuzzello, F.; Carbone, D.; Cavallaro, M.; Agodi, C.; Acosta, L.; Bonanno, D.; Bongiovanni, D.; Borello-Lewin, T.; Boztosun, I.; et al. First measurement of the 116cd(20ne,20o)116sn Reaction at 15 AMeV. Acta Phys. Pol.
**2018**, 49, 275. [Google Scholar] [CrossRef] - Calabrese, S.; Cappuzzello, F.; Carbone, D.; Cavallaro, M.; Agodi, C.; Torresi, D.; Acosta, L.; Bonanno, D.; Bongiovanni, D.; Borello-Lewin, T.; et al. [the NUMEN collaboration] Analysis of the background on cross section measurements with the MAGNEX spectrometer: The (20Ne,20O) Double Charge Exchange case. Nucl. Instrum. Methods Phys. Res. A
**2020**, 980, 164500. [Google Scholar] [CrossRef] - Cavallaro, M.; Aciksoz, E.; Acosta, L.; Agodi, C.; Auerbach, N.; Bellone, J.; Bijker, R.; Bianco, S.; Bonanno, D.; Bongiovanni, D.; et al. NURE: An ERC project to study nuclear reactions for neutrinoless double beta decay. In Proceedings of the 55th International Winter Meeting on Nuclear Physics, Bormio, Italy, 23–27 January 2017. [Google Scholar]
- Matsubara, H.; Takaki, M.; Uesaka, T.; Shimoura, S.; Aoi, N.; Dozono, M.; Fujii, T.; Hatanaka, K.; Hashimoto, T.; Kawabata, T.; et al. Spectroscopic Measurement in 9He and 12Be. Few-Body Syst.
**2013**, 54, 1433. [Google Scholar] [CrossRef] - Alford, W.P.; Spicer, B.M. Nucleon charge-exchange reactions at intermediate energy. Adv. Nucl. Phys.
**1998**, 1, 24. [Google Scholar] - Osterfeld, F. Nuclear spin and isospin excitations. Rev. Mod. Phys.
**1992**, 64, 491. [Google Scholar] [CrossRef] - Taddeucci, T.N.; Goulding, C.A.; Carey, T.A. The (p, n) reaction as a probe of beta decay strength. Nucl. Phys. A
**1987**, 469, 125. [Google Scholar] [CrossRef] - Lenske, H.; Cappuzzello, F.; Cavallaro, M.; Colonna, M. Heavy ion charge exchange reactions as probes for nuclear β-decay. Prog. Part. Nucl. Phys.
**2019**, 109, 103716. [Google Scholar] [CrossRef] - Ikeda, K.; Fujii, S.; Fujita, J.I. The (p,n) reactions and beta decays. Phys. Lett.
**1963**, 3, 271. [Google Scholar] [CrossRef] - Bainum, D.E.; Rapaport, J.; Goodman, C.D.; Horen, D.J.; Foster, C.C.; Greenfield, M.B.; Goulding, M.B. Observation of Giant Particle-Hole Resonances in 90Zr(p, n)90Nb. Phys. Rev. Lett.
**1980**, 44, 1751. [Google Scholar] [CrossRef] - Fujita, Y.; Hatanaka, K.; Berg, G.P.A.; Hosono, K.; Matsuoka, N.; Morinobu, S.; Noro, T.; Sato, M.; Tamura, K.; Uenoa, H. Matching of a beam line and a spectrometer New beam line project at RCNP. Nucl. Instrum. Methods Phys. Res. B
**1997**, 126, 274. [Google Scholar] [CrossRef] - Diel, F.; Fujita, Y.; Fujita, H.; Cappuzzello, F.; Ganioğlu, E.; Grewe, E.-W.; Hashimoto, T.; Hatanaka, K.; Honma, M.; Itoh, T.; et al. High-resolution study of the Gamow-Teller (GT−) strength in the 64Zn(3He,t)64Ga reaction. Phys. Rev. C
**2019**, 99, 054322. [Google Scholar] [CrossRef] - Fujita, Y.; Rubio, B.; Gelletly, W. Spin-isospin excitations probed by strong, weak and electro-magnetic interactions. Prog. Part. Nucl. Phys.
**2011**, 66, 549. [Google Scholar] [CrossRef] - Okamura, H.; Fujitaa, S.; Harab, Y.; Hatanakad, K.; Ichiharac, T.; Ishidaa, S.; Katohb, K.; Niizekib, T.; Ohnumab, H.; Otsua, H.; et al. Tensor analyzing power of the (d, 2He) reaction at 270 MeV. Phys. Lett. B
**1995**, 345, 1. [Google Scholar] [CrossRef] - Rakers, S.; Ellinghaus, F.; Bassini, R.; Bäumer, C.; M van den Berg, A.; Frekers, D.; De Frenne, D.; Hagemann, M.; M Hannen, V.; N Harakeh, M.; et al. Measuring the (d,2He) reaction with the focal-plane detection system of the BBS magnetic spectrometer at AGOR. Nucl. Instrum. Methods A
**2002**, 481, 253. [Google Scholar] [CrossRef] - Ohnuma, H.; Hatanaka, K.; Hayakawa, S.I.; Hosaka, M.; Ichihara, T.; Ishida, S.; Kato, S.; Niizeki, T.; Ohura, M.; Okamura, H.; et al. (d,2He) reactions at Ed=260 MeV as a possible probe to nuclear spin-isospin excitation. Phys. Rev. C
**1992**, 47, 648. [Google Scholar] [CrossRef] - Dohmann, H.; Bäumer, C.; Frekers, D.; Grewe, E.-W.; Harakeh, M.N.; Hollstein, S.; Johansson, H.; Popescu, L.; Rakers, S.; Savran, D.; et al. The (d,2He) reaction on 96Mo and the double-β decay matrix elements for 96Zr. Phys. Rev. C
**2008**, 78, 041602(R). [Google Scholar] [CrossRef] - Grewe, E.-W.; Bäumer, C.; Dohmann, H. The (d,2He) reaction on 76Se and the double-β-decay matrix elements for A=76. Phys. Rev. C
**2008**, 78, 044301. [Google Scholar] [CrossRef] - Frekers, D. Facets of charge-exchange reactions: From astrophysics to double beta decay. Prog. Part. Nucl. Phys.
**2006**, 57, 217. [Google Scholar] [CrossRef] - Ejiri, H.J. Nuclear Matrix Element for Two Neutrino Double Beta Decay from 136Xe. Phys. Soc. Jpn.
**2012**, 81, 033201. [Google Scholar] [CrossRef] [Green Version] - Jokiniemi, L.; Ejiri, H.; Frekers, D.; Suhonen, J. Neutrinoless ββ nuclear matrix elements using isovector spin-dipole J
^{π}=2^{−}data. Phy. Rev. C**2018**, 98, 024608. [Google Scholar] [CrossRef] [Green Version] - Lenske, H.; Bellone, J.I.; Colonna, M.; Lay, J.-A. Theory of single-charge exchange heavy-ion reactions. Phys. Rev. C
**2018**, 98, 044620. [Google Scholar] [CrossRef] [Green Version] - Cavallaro, M.; Cappuzzello, F.; Bondì, M.; Carbone, D.; Garcia, V.N.; Gargano, A.; Lenzi, S.M.; Lubian, J.; Agodi, C.; Azaiez, F.; et al. Quantitative analysis of two-neutron correlations in the 12C(18O,16O)14C reaction. Phys. Rev. C
**2013**, 88, 054601. [Google Scholar] [CrossRef] - Cavallaro, M.; De Napoli, M.; Cappuzzello, F.; Orrigo, S.E.A.; Agodi, C.; Bondí, M.; Carbone, D.; Cunsolo, A.; Davids, B.; Davinson, T.; et al. Investigation of the 10Li shell inversion by neutron continuum transfer reaction. Phys. Rev. Lett.
**2017**, 118, 012701. [Google Scholar] [CrossRef] - Carbone, D.; Ferreira, J.L.; Cappuzzello, F.; Lubian, J.; Agodi, C.; Cavallaro, M.; Foti, A.; Gargano, A.; Lenzi, S.M.; Linares, R.; et al. Microscopic cluster model for the description of new experimental results on the 13C(18O,16O)15C two-neutron transfer at 84 MeV incident energy. Phys. Rev. C
**2017**, 95, 034603. [Google Scholar] [CrossRef] [Green Version] - Ermamatov, M.J.; Cappuzzello, F.; Lubian, J.; Cubero, M.; Agodi, C.; Carbone, D.; Cavallaro, M.; Ferreira, J.L.; Foti, A.; Garcia, V.N.; et al. Two-neutron transfer analysis of the 16O(18O,16O)18O reaction. Phys. Rev. C
**2016**, 94, 024610. [Google Scholar] [CrossRef] - Ermamatov, M.J.; Linares, R.; Lubian, J.; Ferreira, J.L.; Cappuzzello, F.; Carbone, D.; Cavallaro, M.; Cubero, M.; De Faria, P.N.; Foti, A.; et al. Comprehensive analysis of high-lying states in 18O populated with (t, p) and (18O,16O) reactions. Phys. Rev. C
**2017**, 96, 044603. [Google Scholar] [CrossRef] - Spatafora, A.; Cappuzzello, F.; Carbone, D.; Cavallaro, M.; Lay, J.A.; Acosta, L.; Agodi, C.; Bonanno, D.; Bongiovanni, D.; Boztosun, I.; et al. [the NUMEN Collaboration]: 20Ne + 76Ge elastic and inelastic scattering at 306 MeV. Phys. Rev. C
**2019**, 100, 034620. [Google Scholar] [CrossRef] [Green Version] - Carbone, D.; Ferreira, J.L.; Calabrese, S.; Cappuzzello, F.; Cavallaro, M.; Hacisalihoglu, A.; Lenske, H.; Lubian, J.; Vsevolodovna, R.M.; Santopinto, E.; et al. [the NUMEN Collaboration]: Analysis of two-nucleon transfer reactions in the 20Ne+116Cd system at 306 MeV. Phys. Rev. C
**2020**, 102, 044606. [Google Scholar] [CrossRef] - Bohlen, H.G.; Gebauer, B.; Kolbert, D.; Kubono, S.; von Oertzen, W.; Pellegrin, P.O.; Stiliaris, E.; Wllpert, M.; Wilpert, T. The mechanism of the (12C,12N) charge exchange reaction on 12C between 30 and 100 MEV/U. Nucl. Phys. A
**1988**, 488, 89–94. [Google Scholar] [CrossRef] - von Oertzen, W. Excitation of isovector modes in heavy ion induced charge exchange reactions. Nucl. Phys. A
**1988**, 482, 357–372. [Google Scholar] [CrossRef] - Nakayama, S.; Akimune, H.; Daito, I.; Fujimura, H.; Fujita, Y.; Fujiwara, M.; Fushimi, K.; Inomata, T.; Ishibashi, K.; Kohri, H.; et al. Gamow-Teller transitions in the (7Li, 7Be) reaction at 65AMeV. Phys. Rev. C
**1999**, 60, 047303. [Google Scholar] [CrossRef] - Nakayama, S.; Yamagata, T.; Yuasa, K.; Tanaka, M.; Inoue, M.; Itahashi, T.; Ogata, H. Dominance of the direct reaction process in the 12C(7Li, 7Be)12B reaction at θ
_{L}= 0° and E_{L}≥ 21MeVA. Phys. Lett. B**1990**, 246, 342. [Google Scholar] [CrossRef] - Cappuzzello, F.; Lenske, H.; Cunsolo, A.; Beaumel, D.; Fortier, S.; Foti, A.; Lazzaro, A.; Nociforo, C.; Orrigo, S.E.A.; Winfield, J.S. Analysis of the 11B(7Li, 7Be)11Be reaction at 57 MeV in a microscopic approach. Nucl. Phys. A
**2004**, 739, 30. [Google Scholar] [CrossRef] - Cappuzzello, F.; Orrigo, S.E.A.; Cunsolo, A.; Lenske, H.; Allia, M.C.; Beaumel, D.; Fortier, S.; Foti, A.; Lazzaro, A.; Nociforo, C.; et al. Excited states of 15C. Europhys. Lett.
**2004**, 65, 766. [Google Scholar] [CrossRef] - Cavallaro, M. Preliminary study of the 19F(7Li, 7Be)19O reaction at 52MeV with MAGNEX. Nuovo Cimento C
**2011**, 34. [Google Scholar] - Etchegoyen, A.; Etchegoyen, M.C.; Izquierdo, E.D.; Abriola, D.; Di Gregorio, D.E.; Fernandez Niello, J.O.; Ferrero, A.M.J.; Gil, S.; Pacheco, A.J. B-10 (Li-7, Be-7) Be-10 charge-exchange reaction. Phys. Rev. C
**1988**, 38, 2124. [Google Scholar] [CrossRef] - Ejiri, H.; Soukouti, N.; Suhonen, J. Spin-dipole nuclear matrix elements for double beta decays and astro-neutrinos. Phys. Lett. B
**2014**, 729, 27. [Google Scholar] [CrossRef] [Green Version] - Jokiniemi, L.; Suhonen, J.; Ejiri, H. Magnetic Hexadecapole γ\gammaγ Transitions and Neutrino-Nuclear Responses in Medium-Heavy Nuclei. Adv. High Energy Phys.
**2016**, 2016, 8417598. [Google Scholar] [CrossRef] [Green Version] - Suhonen, J.; Civitarese, O. Weak-interaction and nuclear-structure aspects of nuclear double beta decay. Phys. Rep.
**1998**, 300, 123. [Google Scholar] [CrossRef] - Johnson, M.B.; Siciliano, E.R.; Toki, H.; Wirzba, A. Delta(33) Dynamics In Pion Double Charge Exchange. Phys. Rev. Lett.
**1984**, 52, 593–596. [Google Scholar] [CrossRef] - Auerbach, N.; Zamick, L.; Zheng, D.C. Double Gamow-Teller strenght in nuclei. Ann. Phys.
**1989**, 192, 77. [Google Scholar] [CrossRef] - Auerbach, N.; Gibbs, W.R.; Ginocchio, J.N.; Kaufmann, W.B. Pion-nucleus double charge exchange and the nuclear shell model. Phys. Rev. C
**1988**, 38, 1277–1296. [Google Scholar] [CrossRef] - Auerback, N.; Gibbs, W.R.; Piasetzky, E. Pion double charge exchange and the nuclear shell model. Phys. Rev. Lett.
**1987**, 59, 1076. [Google Scholar] [CrossRef] - Cerny, J. Studies of exotic light nuclei. In Proceedings of the 3rd International Conference on Nuclei Far from Stability, Cargese, France, 26 May 1976. [Google Scholar]
- Blomgren, J.; Lindh, K.; Anantaraman, N.; Austin, S.M.; Berg, G.P.A.; Brown, B.A.; Casandjian, J.-M.; Chartier, M.; Cortina-Gil, M.D.; Fortier, S.; et al. Search for double Gamow-Teller strength by heavy-ion double charge exchange. Phys. Lett. B
**1995**, 362, 34. [Google Scholar] [CrossRef] - Fifield, L.K.; Durell, J.L.; Hotchkis, M.A.C.; Leigh, J.R.; Ophel, T.R.; Weisser, D.C. The mass of 18C from a heavy ion double-charge-exchange reaction. Nucl. Phys. A
**1982**, 385, 505. [Google Scholar] [CrossRef] - Naulin, F.; Détraz, C.; Roy-Stéphan, M.; Bernas, M.; de Boer, J.; Guillemaud, D.; Langevin, M.; Pougheon, F.; Roussel, P. Mass of 18C from the double-charge-exchange reaction 48Ca(18O, 18C) 48Ti. Phys. Rev. C
**1982**, 25, 1074. [Google Scholar] [CrossRef] - Drake, D.M.; Moses, J.D.; Peng, J.C.; Stein, N.; Sunier, J.W. Exotic Heavy-Ion Reactions on 40Ca(14C,14O) Double Charge Exchange and (14C,15O) Rearrangement Transfer. Phys. Rev. Lett.
**1980**, 45, 1765. [Google Scholar] [CrossRef] - Bes, D.R.; Dragun, O.; Maqueda, E.E. The (14C, 14O) reaction considered as simultaneous pair-exchange or double-charge-exchange processes. Nucl. Phys. A
**1983**, 405, 313. [Google Scholar] [CrossRef] - Dasso, C.H.; Vitturi, A. Mechanism for double-charge exchange in heavy ion reactions. Phys. Rev. C
**1986**, 34, 743. [Google Scholar] [CrossRef] [PubMed] - Kisamori, K.; Shimoura, S. Candidate Resonant Tetraneutron State Populated by the 4He(8He,8Be) Reaction. Phys. Rev. Lett.
**2016**, 116, 052501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Takahisa, K.; Takahisa, K.; Ejiri, H.; Akimune, H.; Fujita, H.; Matumiya, R.; Ohta, T.; Shima, T.; Tanaka, M.; Yosoi, M. Double charge exchange (11B,11Li) reaction for double beta decay response. arXiv
**2017**, arXiv:1703.08264. [Google Scholar] - Takaki, M.; Uesaka, T.; Shimoura, S.; Aoi, N.; Dozono, M.; Gotanda, S.; Hashimoto, T.; Kanaya, Y.; Kawabata, T.; Kisamori, K.; et al. New type of spectroscopy via heavy-ion double charge exchange (12C, 12Be(0+2)) reaction. RIKEN Accel. Prog. Rep.
**2014**, 47. Available online: https://indico.cns.s.u-tokyo.ac.jp/event/189/contributions/750/attachments/407/496/33_takaki.pdf (accessed on 26 October 2020). - Sagawa, H.; Uesaka, T. Sum rule study for double Gamow-Teller states. Phys. Rev. C
**2016**, 94, 064325. [Google Scholar] [CrossRef] [Green Version] - Cappuzzello, F.; Agodi, A.; Carbone, D.; Cavallaro, M. The MAGNEX spectrometer: Results and perspectives. Eur. Phys. J. A
**2016**, 52, 167. [Google Scholar] [CrossRef] - Torresi, D. An upgraded focal plane detector for the MAGNEX spectrometer. Nucl. Instrum. Methods A
**2020**. submitted. [Google Scholar] - Finocchiaro, P.; Acosta, L.; Agodi, C.; Altana, C.; Amador-Valenzuela, P.; Boztosun, I.; Brasolin, S.; Brischetto, G.A.; Brunasso, O.; Calabrese, S.; et al. The NUMEN Heavy Ion Multidetector for a Complementary Approach to the Neutrinoless Double Beta Decay. Universe
**2020**, 6, 129. [Google Scholar] [CrossRef] - Bellone, J.I.; Burrello, S.; Colonna, M.; Lay, J.-A.; Lenske, H. Two-step description of heavy ion double charge exchange reactions. Phys. Lett. B
**2020**, 807, 135528. [Google Scholar] [CrossRef] - Santopinto, E.; García-Tecocoatzi, H.; Magaña Vsevolodovna, R.I.; Ferretti, J. Heavy-ion double-charge-exchange and its relation to neutrinoless double-β decay. Phys. Rev. C
**2018**, 98, 061601. [Google Scholar] [CrossRef] [Green Version] - Barea, J.; Kotila, J.; Iachello, F. Limits on Neutrino Masses from Neutrinoless Double-β Decay. Phys. Rev. Lett.
**2012**, 109, 042501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Puppe, P.; Frekers, D.; Adachi, T.; Akimune, H.; Aoi, N.; Bilgier, B.; Ejiri, H.; Fujita, H.; Fujita, Y.; Fujita, M.; et al. High-resolution (He,t) reaction on the double-β decaying nucleus 136Xe. Phys. Rev. C
**2011**, 84, 051305. [Google Scholar] [CrossRef] - Jokiniemi, L.; Suhonen, J.; Ejiri, H.; Hashim I., H. Pinning down the strength function for ordinary muon capture on 100Mo. Phys. Lett. B
**2019**, 794, 143. [Google Scholar] [CrossRef] - Ejiri, H.; Hashim, I.H.; Hino, Y.; Kuno, Y.; Matsumoto, Y.; Ninomiya, K.; Sakamoto, H.; Sato, A.; Shima, T.; Shinohara, A.; et al. Nuclear γ Rays from Stopped Muon Capture Reactions for Nuclear Isotope Detection. J. Phys. Soc. Jpn.
**2013**, 82, 044202. [Google Scholar] [CrossRef] - Mandelstam, L.; Tamm, I. The uncertainty relation between energy and time in nonrelativistic quantum mechanics. J. Phys. USSR
**1945**, 9, 249. [Google Scholar] - Menéndez, J.; Shimizu, N.; Yako, K. Is it possible to study neutrinoless decay by measuring double Gamow-Teller transitions? IOP Conf. Ser. J. Phys. Conf. Ser.
**2018**, 1056, 012037. [Google Scholar] [CrossRef] [Green Version] - Markish, B.; Mest, H.; Saul, H.; Wang, X.; Abele, H.; Dubbers, D.; Klopf, M.; Petoukhov, A.; Roick, C.; Soldner, T.; et al. Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam. Phys. Rev. Lett.
**2019**, 122, 242501. [Google Scholar] [CrossRef] [Green Version] - Towner, I.S. Quenching of spin matrix elements in nuclei. Phys. Rep.
**1997**, 155, 263. [Google Scholar] [CrossRef] - Bertsch, G.F.; Hamamoto, I. Gamow-Teller strength at high excitations. Phys. Rev. C
**1982**, 26, 1323. [Google Scholar] [CrossRef] - Arima, A.; Shimizu, K.; Bentz, W.; Hyuga, H. Nuclear Magnetic Properties and Gamow-teller Transitions. Adv. Nucl. Phys.
**1987**, 18, 1. [Google Scholar] [CrossRef] - Park, T.-S.; Jung, H.; Min, D.-P. In-medium effective axial-vector coupling constant. Phys. Lett. B
**1997**, 409, 26. [Google Scholar] [CrossRef] [Green Version] - Vetterli, M.C.; Hausser, O.; Abegg, R. Gamow-Teller strength deduced from charge exchange reactions on 54Fe at 300 MeV. Phys. Rev. C
**1989**, 40, 559. [Google Scholar] [CrossRef] [PubMed] - Bloom, S.D.; Goodman, C.D.; Grimes, S.M.; Hausman, R.F., Jr. Gamow-Teller strength function for 26Mg -> 26Al. Phys. Lett. B
**1981**, 107, 336. [Google Scholar] [CrossRef] - Yako, K.; Sakai, H.; Greenfield, M.B.; Hatanaka, K.; Hatano, M.; Kamiya, J.; Kato, H.; Kitamura, Y.; Maeda, Y.; Morris, C.L.; et al. Determination of the Gamow–Teller quenching factor from charge exchange reactions on 90Zr. Phys. Lett. B
**2005**, 615, 193. [Google Scholar] [CrossRef] [Green Version] - Douma, C.A.; Agodi, C.; Akimune, H.; Alanssari, M.; Cappuzzello, F.; Carbone, D.; Cavallaro, M.; Colò, G.; Diel, F.; Ejiri, H.; et al. Gamow–Teller strength distributions of 116Sb and 122Sb usingthe (3He, t) charge-exchange reaction. Eur. Phys. J. A
**2020**, 56, 51. [Google Scholar] [CrossRef] [Green Version] - Caurier, E.; Zuker, A.P.; Poves, A.; Martinez-Pinedo, G. Full pf shell model study of A=48 nuclei. Phys. Rev. C
**1994**, 50, 225. [Google Scholar] [CrossRef] [Green Version] - Iwata, Y.; Shimizu, N.; Utsuno, Y.; Honma, M.; Abe, T.; Otsuka, T. Ingredients of Nuclear Matrix Element for Two-Neutrino Double-Beta Decay of 48Ca. JPS Conf. Proc.
**2015**, 6, 030057. [Google Scholar] - Horoi, M.; Stoica, S.; Brown, B.A. Shell-model calculations of two-neutrino double-β decay rates of 48Ca with the GXPF1A interaction. Phys. Rev. C
**2007**, 75, 034303. [Google Scholar] [CrossRef] [Green Version] - Wildenthal, B.H.; Curtin, M.S.; Brown, B.A. Predicted features of the beta decay of neutron-rich sd-shell nuclei. Phys. Rev. C
**1983**, 28, 1343. [Google Scholar] [CrossRef] - Martinez-Pinedo, G.; Poves, A.; Caurier, E.; Zuker, A.P. Effective gA in the pf shell. Phys. Rev. C
**1996**, 53, R2602. [Google Scholar] [CrossRef] [PubMed] [Green Version] - 126. Bodenstein-Dresler, L.; Chu, Y.; Gehre, D.; Gößling, C.; Heimbold, A.; Herrmann, C.; Hodak, R.; Kostensalo, J.; Kröninger, K.; Küttler, J.; et al. [COBRA collaboration]: Quenching of gA deduced from the β-spectrum shape of 113Cd measured with the COBRA experiment. Phys. Lett. B
**2020**, 800, 135092. [Google Scholar] [CrossRef] - Gysbers, P.; Hagen, G.; Holt, J.D.; Jansen, G.R.; Morris, T.D.; Navrátil, P.; Papenbrock, V.; Quaglioni, S.; Schwenk, A.; Stroberg, S.R.; et al. Discrepancy between experimental and theoretical β-decay rates resolved from first principles. Nat. Phys.
**2019**, 15, 428. [Google Scholar] [CrossRef] - Mustonen, M.T.; Engel, J. Large-scale calculations of the double-β decay of 76Ge,130Te,136Xe, and 150Nd in the deformed self-consistent Skyrme quasiparticle random-phase approximation. Phys. Rev. C
**2013**, 87, 064302. [Google Scholar] [CrossRef] [Green Version] - Wang, L.-J.; Engel, J.; Yao, J.M. Quenching of nuclear matrix elements for 0νββ decay by chiral two-body currents. Phys. Rev. C
**2018**, 98, 031301. [Google Scholar] [CrossRef] [Green Version] - Pastore, S.; Wiringa, R.B.; Pieper, S.C.; Schiavilla, R. Quantum Monte Carlo calculations of electromagnetic transitions in 8Be with meson-exchange currents derived from chiral effective field theory. Phys. Rev. C
**2014**, 90, 024321. [Google Scholar] [CrossRef] - King, G.B.; Andreoli, L.; Pastore, S.; Piarulli, M.; Schiavilla, R.; Wiringa, R.B.; Carlson, J.; Gandolfi, S. Chiral effective field theory calculations of weak transitions in light nuclei. Phys. Rev. C
**2020**, 102, 025501. [Google Scholar] [CrossRef]

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Cappuzzello, F.; Cavallaro, M.
Nuclear Response to Second-Order Isospin Probes in Connection to Double Beta Decay. *Universe* **2020**, *6*, 217.
https://doi.org/10.3390/universe6110217

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Cappuzzello F, Cavallaro M.
Nuclear Response to Second-Order Isospin Probes in Connection to Double Beta Decay. *Universe*. 2020; 6(11):217.
https://doi.org/10.3390/universe6110217

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Cappuzzello, Francesco, and Manuela Cavallaro.
2020. "Nuclear Response to Second-Order Isospin Probes in Connection to Double Beta Decay" *Universe* 6, no. 11: 217.
https://doi.org/10.3390/universe6110217