Probing Beta Decay Matrix Elements through Heavy Ion Charge Exchange Reactions

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, Universit degli studi di Catania 2) INFN/LNS, via S. Sofia, 62, CT 95123, Catania , Italia Institut f r Theoretische Physik, Justus-Liebig-Universit t Giessen, D-35392 Giessen, Germania Departamento de FAMA, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spagna 1) 3) 4)

Dirac vs Majorana neutrino masses: 0 -Experimental observable half life : elementary particle physics factor Beyond Standard Model Physics? PF factor 0 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. Bond , D. Carbone, A.Cunsolo, A. Foti, Eur. Phys. J. A (2015), 51

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

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 Zero range approximation calculations done in momentum space

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

Reaction Kernel Direct Reactionsseparation ansatz : Reaction Kernel Gaussian shaped for small momentum transfer (q << 1/ ) monopole component of j(q ) multipole expansion dominates 0 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| (r) ~ 0 dove |W| 0 e (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 18 18 40 (1 state for both K and F ) + 40 18 Ca ( O, F) K @ 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 18 18 40 40 Ca ( O, F) K (1 state for both K and F ) + 40 18 @ 270 MeV

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.

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

Direct Reactionsseparation ansatz : Reaction Kernel Gaussian shaped off shell angular integration easily performed + Pole Approximaxion + Single state dominance (SSD) is assumed + 40 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 - decay 40 40 http://www.nndc.bnl.gov/chart/ 18 + 18 18 +

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

SUMMARY and CONCLUSIONS Direct Reactionsseparation 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); D 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 0 (DCEX sequence of 2 correlated SCEX processes)

THANK YOU FOR YOUR ATTENTION

Optical potential 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 Double folding approach both for Real and Imaginary part in HIDEX code 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.

Nuclear potential Central term Tensorial term with Spin Orbit term where c,t,LS 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 (0.40 fm) and , and (0.25 fm) meson exchange, respectively. 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 ) ~ 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

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 18O projectile ( 0 , g.s.) + 18Ne 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 40Ca target (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) 40Ar residual nucleus (0 , g.s.) + + + 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? Why are we interested on DCEX Cross Section? - e e- B b B First attempts to determine NMEs from nuclear reactions were done using ( , ) DCEX reactions, but processes described by different kind of operators no information about 0 NMEs p p n p = - p n 0 p p n n n n a A A W. R. Gibbs, M. Elghossain, W. B. Kaufmann, Phys. Rev. C 48 (1993) 1546 Analogies between Heavy Ion DCEX reactions and 0 : same initial and final nuclei involved; same Gamow-Teller, Fermi and rank-2 tensor operators, but combined through different coefficients; large linear momentum (~ 100 MeV/c) involved in the intermediate off-shell stastes; non local processes, characterized by 2 vertices localized in the same pair of valence nucleons; same nuclear medium involved, so in medium effects are expected to influence system in both cases (possibility to extract information about g quenching); A off-shell propagator . F. Cappuzzello, M. Cavallaro, C. Agodi, M. Bond , D. Carbone, A.Cunsolo, A. Foti, Eur. Phys. J. A (2015), 51

0 Not allowed by SM allowed if and m 0 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 (processo del 2 ordine) Neutrino: particella di Dirac o di Majorana? 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 pu decadere pu anche decadere , sebbene con vite medie diverse.

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