Probing Beta Decay Matrix Elements through Heavy Ion Charge Exchange Reactions (1)( 2) (3) (2) (4) Bellone J.I. , Lenske H. , Colonna M. , J.A. Lay , within the NUMEN collaboration Dipartimento di Fisica e Astronomia, Università degli studi di Catania INFN/LNS, via S. Sofia, 62, CT – 95123, Catania , Italia Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, D-35392 Giessen, Germania Departamento de FAMA, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spagna

J. Barea, J. Kotila, F. Iachello, Phys. Rev. Lett. 109 042501(2012) Experimental observable → half – life : ● Dirac vs Majorana neutrino masses: 0νββ elementary particle physics factor Beyond Standard Model Physics? PF factor 0νββ NME calculated through different nuclear structure models → values differ of about a factor of 3 J. Barea, J. Kotila, F. Iachello, Phys. Rev. Lett. 109 042501(2012) DCEX reactions same initial and final nuclei involved same Gamow-Teller, Fermi and rank-2 tensor operators, but combined through different coefficients F. Cappuzzello, M. Cavallaro, C. Agodi, M. Bondì, D. Carbone, A.Cunsolo, A. Foti, Eur. Phys. J. A (2015), 51

First steps toward DCEX Cross Section Factorization ● 0νββ strength from DCEX Cross Section measurements → DCEX Cross Section factorization ● DCEX reaction ≈ sequence of 2 Single Charge Exchange (SCEX) processes analogy with 2νββ → DCEX = sequence of 2 uncorrelated SCEX processes ν A B n p e - a b p n π A B DCEX analogy with 0νββ → DCEX = sequence of 2 correlated SCEX processes n A B p e ν = ν - a b p n π A B

Zero – range approximation CEX Cross Section (CEX) Direct reactions are supposed to be dominated by elastic scattering processes, while the inelastic ones can be treated as perturbations → DWBA R. H. Bassel, R. M. Drisko, G. R. Satchler, The Distorted Wave Theory of Direct Nuclear Reactions DWBA → Transition matrix element can be written in terms of distorted waves and internal coordinate – depending nuclear wave functions → calculations done in momentum space Zero – range approximation

→ Nuclear Transition Matrix Element given by Reaction Kernels Distortion Factor Transition Form Factor radial transition density ~ β / ββ decay strength

→ Direct Reactions separation ansatz : Reaction Kernel Gaussian shaped for small momentum transfer (q << 1/σ) monopole component of j (qρ) multipole expansion dominates αβ not exact factorization H. Lenske, J. I. Bellone, M. Colonna, J. A. Lay , Heavy Ion Single Charge Exchange and Beta decay Matrix Elements, submitted.

Black Disk Approximation ( BDA ) |V | << |W| → χ(r) ~ 0 dove |W| ≠ 0 e χ(r) = PW dove |W| = 0 → analytical determination of Distortion Factor Distortion Factor H. Lenske, J. I. Bellone, M. Colonna, J. A. Lay , Heavy Ion Single Charge Exchange and Beta decay Matrix Elements, submitted.

● Is BDA a good approximation? Let’s check the effects of Real and Imaginary part of the Optical Potential on SCEX Cross Section for Heavy Ions. ( HIDEX code, by H. Lenske) F. Cappuzzello et al., Nucl. Phys. A 739 (2004) 30-56 40 Ca ( O, F) K 18 18 40 (1 state for both K and F ) + 40 18 @ 270 MeV H. Lenske, J. I. Bellone, M. Colonna, J. A. Lay , Heavy Ion Single Charge Exchange and Beta decay Matrix Elements, submitted.

● Is BDA a good approximation? Let’s check the effects of Real and Imaginary part of the Optical Potential on SCEX Cross Section for Heavy Ions. ( HIDEX code, by H. Lenske) F. Cappuzzello et al., Nucl. Phys. A 739 (2004) 30-56 40 Ca ( O, F) K 18 18 40 + 40 18 @ 270 MeV (1 state for both K and F )

SCEX Transition Matrix Element vs momentum transfer H. Lenske, J. I. Bellone, M. Colonna, J. A. Lay, Heavy Ion Single Charge Exchange and Beta decay Matrix Elements, submitted.

Ca + O → K + F → Ar + Ne DCEX - 2νββ DCEX Reaction Kernel 40 18 DCEX - 2νββ @ 270 MeV DCEX Reaction Kernel DCEX Distortion Factor free propagator under particular conditions, can be expressed in terms of SCEX Reaction Kernels product

→ Direct Reactions separation ansatz : Reaction Kernel Gaussian shaped off – shell angular integration easily performed + Pole Approximaxion + Single state dominance (SSD) is assumed considered 1 state at 2.29 MeV for K , studied through experiments on Ca ( n , p ) and Ar ( p , n ) reactions and F g.s. ( 1 ), studied through experiments on O ( p , n ) nuclear reaction and Ne β - decay 40 + 18 http://www.nndc.bnl.gov/chart/

+ + separation ansatz SSD Ca + O → K + F → Ar + Ne Pole Approximaxion 40 18

SUMMARY and CONCLUSIONS ♣ Direct Reactions separation ansatz : Reaction Kernel Gaussian shaped enable both SCEX and DCEX Cross Section factorization, for Heavy Ions at low energy ♣ Factorization “exact” for q = 0 (both for SCEX and DCEX), but it works well up to q ≈ 25 MeV (for SCEX processes); ♣ Distortion Factor N analytical determination in BDA and behaves like ≈ 1/A (both for SCEX and DCEX processes); ♣ “Work in progress” : (DCEX ≈ sequence of 2 uncorrelated SCEX processes) code development for DCEX factorized Heavy Ion Cross Section for reactions under study within the NUMEN collaboration. ♣ Next (main goal): analogy DCEX → 0νββ (DCEX ≈ sequence of 2 correlated SCEX processes) D αβ

THANK YOU FOR YOUR ATTENTION

M.A. Franey, W. G. Love, Phys. Rev. C 31 (1985) 488 Optical potential → Double folding approach both for Real and Imaginary part in HIDEX code Heavy ion reactions are strongly absorptive processes → elastic scattering and peripheral inelastic reactions are mainly sensitive to the nuclear surface regions of the interacting nuclei → Impulse approximation Real and Imaginary NN optical potentials → M.A. Franey, W. G. Love, Phys. Rev. C 31 (1985) 488 Coulomb interaction included in the evaluation of distorted waves and calculated by doubly folding Coulomb potential for a point-like charge with target and projectile charge densities. \rho_1 e \rho_2 = one-body local nuclear densities  Fermi distribution

A. K. Kerman, H. McManus, R. M. Thaler, Ann. Phys. 8 (1959) 551-635 Nuclear potential → Central term → Tensorial term with → Spin – Orbit term V (r) = sum of 2 (T) or 3 (C) Yukawians, with strengths and ranges chosen to represent the long – range tail (1.414 fm) of the One Pion Exchange Potential (OPEP) and medium and short-range parts, which corresponds to σ (0.40 fm) and ω, ρ and δ (0.25 fm) meson exchange, respectively. where c,t,LS NN A. K. Kerman, H. McManus, R. M. Thaler, Ann. Phys. 8 (1959) 551-635

Transition Form Factor Radial Transition Density (for each excitation energy ω) ~ β decay strength - calculated through HIDEX code (H. Lenske), using QRPA approach, starting from 1QP nuclear energy levels, g.s. calculated in HFB Mean Field Theory approach and excited states using a Wood – Saxon nuclear potential, with parameters set in order to fit experimental single – particle energies. - normalized in order to reproduce the transition amplitude belonging to GT multiple operator

(residual nucleus) belonging to the same SU(4) S, T multiplet ● DCEX reaction rates are expected to be small → yeld increased using projectile (target) and ejectile (residual nucleus) belonging to the same SU(4) S, T multiplet 18 O projectile ( 0 , g.s.) → + 18 Ne ejectile (0 , g.s.) + lightest non-radiactive T = 1 isotope; easily produced with high intensities. nearly 100% GT sum rule strength 3(N-Z) is exhausted by the 1 F g.s. involved in the T = 1, intermediate transition; not possible the reversed reaction because it should require a radioactive beam and the ( Ne, O) is characterized by smaller beta decay strength. + 18 20 20 40 Ca target (0 , g.s.) → + 40 Ar residual nucleus (0 , g.s.) + NOT members of the same T multiplet → GT transition NOT super allowed BUT GT transition is mainly distributed in the 1 excited state of K involved in the intermediate channel (above all 2.73 MeV state, followed by the states at 2.33 and 4.4 MeV) + 40 NMEs invariant under time reversal → possibility of studying a given reaction by esploring it’s time – reversal counterpart , i.e. the opposite reaction, in order to obtain a better (signal/bg) ratio.

Why are we interested on DCEX Cross Section? B p e ν = ν - a b p n π B First attempts to determine NMEs from nuclear reactions were done using ( π , π ) DCEX reactions, → but processes described by different kind of operators → no information about 0νββ NMEs Analogies between Heavy Ion DCEX reactions and 0νββ : ❶ same initial and final nuclei involved; ❷ same Gamow-Teller, Fermi and rank-2 tensor operators, but combined through different coefficients; ❸ large linear momentum (~ 100 MeV/c) involved in the intermediate off-shell stastes; ❹ non – local processes, characterized by 2 vertices localized in the same pair of valence nucleons; ❺ same nuclear medium involved, so in medium effects are expected to influence system in both cases (possibility to extract information about g quenching); ❻ off-shell propagator . p p ± ± π π p n n A W. R. Gibbs, M. Elghossain, W. B. Kaufmann, Phys. Rev. C 48 (1993) 1546 (es. Nucl. Phys. A 355 (1981) 437-476, E. Oset, D. Strottman  regarding pion induced SCEX and nuclear structure). A F. Cappuzzello, M. Cavallaro, C. Agodi, M. Bondì, D. Carbone, A.Cunsolo, A. Foti, Eur. Phys. J. A (2015), 51

decay amplitude is proportional to the effective Majorana mass 0ν ββ Not allowed by SM allowed if and m ≠ 0 ν ● Neutrinos involved in EW porcesses are flavour eigenstates → they do not have definite masses, but their masses are combinations of mass eigenstates decay amplitude is proportional to the effective Majorana mass neglegible with respect to the average neutrino energy and momentum if CP is conseved is real

Doppio Decadimento Beta Neutrino: particella di Dirac o di Majorana? (processo del 2° ordine) Spettro di energia continuo, analogamente al decadimento beta singolo processo a 4 leptoni processo a 2 leptoni proibito nell’ambito del Modello Standard possibile solo se il neutrino ha massa di Majorana Un nucleo che può decadere può anche decadere , sebbene con vite medie diverse.

effective Majoron coupling constant ● light neutrino exchange ● sterile neutrino exchange sterile neutrino mass ● heavy neutrino exchange ● light/heavy neutrino exchange with Majororn emission effective Majoron coupling constant

● SCEX Cross Section factorization is possible only making some approximations: Eikonal approximation → ok for E : U (x + Δx) – U (x) ~ const. per Δx ~ λ Strong absorption (or Black Disk) limit → ok for describing heavy nuclei; moreover this approximation allows to simplify distortion factor. b i/f i/f for (p, n) light ion reactions T. N. Taddeucci et al., Nucl. Phys. A 469 (1987) 125 – 172 for (p, n) heavy ion reactions F. Osterfeld, Rev. Mod. Phys., vol. 64, 2 (1992) |V | << |W| and χ ~ 0 in the range where |W| ≠ 0 and equale to PW elsewhere