Double charge exchange reactions as a probe for neutrinoless double beta decay nuclear matrix elements

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 3.0 h ps://c ea i ecommons.o g/licenses/by/3.0/ Double cha ge exchange eac ions as a p obe o neu inoless double be a decay nuclea ma ix elemen s © Au ho s, 2020 Published e sion San opin o, E.; Fe e i, J.; Ga cía-Tecocoa zi, H.; Magana Vse olodo na, R. San opin o, E., Fe e i, J., Ga cía-Tecocoa zi, H., & Magana Vse olodo na, R. (2020). Double cha ge exchange eac ions as a p obe o neu inoless double be a decay nuclea ma ix elemen s. In L. Acos a, P. Amado -Valenzuela, & D. J. Ma ín-Lámba i (Eds.), SNP '20 : XLIII Symposium on Nuclea Physics. Ins i u e o Physics. Jou nal o Physics : Con e ence Se ies, 1610. h ps://doi.o g/10.1088/1742-6596/1610/1/012013 2020 Jou nal o Physics: Con e ence Se ies PAPER • OPEN ACCESS Double cha ge exchange eac ions as a p obe o neu inoless double be a decay nuclea ma ix elemen s To ci e his a icle: E. San opin o e al 2020 J. Phys.: Con . Se . 1610 012013 View he a icle online o upda es and enhancemen s. This con en was downloaded om IP add ess 130.234.21.0 on 26/11/2020 a 13:15 Con en om his wo k may be used unde he e ms o heC ea i e Commons A ibu ion 3.0 licence. Any u he dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and he i le o he wo k, jou nal ci a ion and DOI. Published unde licence by IOP Publishing L d XLIII Symposium on Nuclea Physics 2020 Jou nal o Physics: Con e ence Se ies 1610 (2020) 012013 IOP Publishing doi:10.1088/1742-6596/1610/1/012013 1 Double cha ge exchange eac ions as a p obe o neu inoless double be a decay nuclea ma ix elemen s E. San opin o1, J. Fe e i2, H. Ga c´ıa-Tecocoa zi3, R. Magana Vse olodo na1and wi hin he NUMEN p ojec . E-mail: [email p o ec ed] 1INFN, Sezione di Geno a, ia Dodecaneso 33, Geno a 16146, I aly 2Depa men o Physics, Uni e si y o Jy ¨askyl¨a, P.O. Box 35 (YFL), 40014 Jy ¨askyl¨a, Finland 3Depa men o Physics, Uni e si y o La Pla a (UNLP), 49 y 115 cc. 67, 1900 La Pla a, A gen ina Abs ac . The o malism o desc ibe hea y-ion double cha ge exchange (DCE) p ocesses in he eikonal and small-momen um ans e app oxima ions in oduced in Phys. Re . C 98, 061601(R) (2018) is b ie ly discussed. I is also shown ha , unde he p e ious app oxima ions, he hea y-ion DCE c oss-sec ion can be ac o ized in e ms o a eac ion and a nuclea pa . A double cha ge exchange e ec i e po en ial is explici ly de i ed in he closu e app oxima ion and also o he i s ime he explici o m o he DCE nuclea ma ix elemen s, ha a e o he o m o double Gamow-Telle and double Fe mi. The ecen hypo hesis o a linea co ela ion be ween double Gamow-Telle neu inoless double be a decay and DCE nuclea ma ix elemen s is con i med hanks o he i s explici de i a ion o DCE nuclea ma ix elemen s, and by means o mic oscopic IBM2 calcula ions. 1. In oduc ion Neu inoless double be a (0νββ) decays ank as one o he mos in e es ing Beyond he S anda d Model p ocesses. Thei expe imen al obse a ion would imply ha he conse a ion o he lep on numbe is iola ed and ha he neu inos a e Majo ana- ype pa icles. Mo eo e , i may also p o ide a mean o measu e he neu ino mass. The e a e se e al ongoing expe imen al sea ches, including EXO [1], Cuo e [2], KamLAND-Zen [3] and Ge da [4]. None o hem has p o ided indica ions o 0νββ decays ye . The e ha e been s ong heo e ical e o s o p o ide guidelines o he expe imen alis s. Howe e , he e a e s ong disc epancies among he esul s in he di e en app oaches [5, 6, 7, 8, 9, 10]. In pa icula , he Nuclea Ma ix Elemen s (NMEs) compu ed wi hin he di e en nuclea models disag ee by mo e han a ac o o wo. Fu he mo e, hese esul s may equi e addi ional eno maliza ion o quenching [11]. A possible mean o o e come hese di icul ies is o use hea y-ion double-cha ge exchange (DCE) p ocesses o pu cons ain s on neu inoless 0νββ nuclea ma ix elemen s. Se e al hea y-ion DCE expe imen s a e ongoing a RNCP Osaka [12, 13], RIBF RIKEN [14], and LNS INFN [15, 16, 17]. The i s wo o hem make use o high-ene gy hea y-ion double- XLIII Symposium on Nuclea Physics 2020 Jou nal o Physics: Con e ence Se ies 1610 (2020) 012013 IOP Publishing doi:10.1088/1742-6596/1610/1/012013 2 cha ge exchange p ocesses in o de o s udy mul i-spin-isospin lip exci a ion modes, such as a high-ene gy double Gamow-Telle gian esonance (DGT-GR) [12], ha has been p edic ed h ee decades ago [18, 19]. The expe imen a LNS-INFN is aiming o ex ac in o ma ion o pu cons ain s on some o he nuclea ma ix elemen s ele an o 0νββ decays [15, 16, 17]. All hese expe imen s ha e igge ed a s ong heo e ical in e es [20, 21, 22, 23], including he e o in he imp o emen o he eac ion pa [24, 25, 26]. In he p esen con ibu ion, we b ie ly discuss some aspec s o he hea y-ion DCE o malism o Re . [21]. The e, o he i s ime he o malism o desc ibe hea y-ion DCE was explici ly de eloped by making use o he eikonal app oxima ion. 2. DCE po en ial In DCE eac ions, wo pai s o nucleons – one om he a ge and one om he p ojec ile – in e ac . In pa icula , wo p o ons (neu ons) a e con e ed in o wo neu ons (p o ons) in he a ge , and wo neu ons (p o ons) a e con e ed in o wo p o ons (neu ons) in he p ojec ile, wi h he mass numbe o he a ge , A, and he p ojec ile, a, bo h emaining unchanged. A de i a ion o a DCE e ec i e po en ial, desc ibing bo h long- and sho - ange in e ac ions, was ca ied ou in Re . [21] by conside ing he one-pion-exchange and sho - ange-in e ac ion diag ams depic ed in Fig. 1. Figu e 1. Leading diag ams in a double-cha ge-exchange p ocess. F om le o igh , hey ep esen a double-pion-exchange in e ac ion, a double con ac e m and a mixed one-pion- exchange plus con ac e m. Figu e aken om Re . [21]; APS CopyRigh . By making use o he closu e app oxima ion, which consis s in a e aging o e he in e media e nuclea s a es [27, 28], one ob ains [21] VDCE(~q1, ~q2) = 4 3 π mπ4(~σP1·~q1)(~σT1·~q1) ω1(ω1+¯ EP)~τP1 ·~τT1 (~σP2·~q2)(~σT2·~q2) ω2(ω2+¯ EP)(ω2+¯ ET)~τP2 ·~τT2 + 2 c2 T ¯ EF P+¯ EF T +c2 GT(~σP1·~σT1)(~σP2·~σT2) ¯ EGT P+¯ EGT T +cTcGT(~σP2·~σT2) ¯ EGT P+¯ EF T +cTcGT(~σP1·~σT1) ¯ EF P+¯ EGT T ×(~τP1 ·~τT1)(~τP2 ·~τT2) +  π mπ2(~σP1·~q1)(~σT1·~q1) ω1(ω1+¯ EP)(ω1+¯ ET)~τP1 ·~τT1 ×cT(~τP2 ·~τT2) + cGT(~σP2 ·~σ2)(~τP2 ·~τT2)+ 1 ↔2i, (1) whe e  π mπ2≃400 MeV· m3[29], he alues o he pa ame e s cGT = 217 MeV m3and cT= 151 MeV m3a e aken om he li e a u e [29], and ωi=q~q2 i+m2 π. The labels P1, P2, T1 and T2 s and o he nucleons wi hin he p ojec ile (P1 and P2) and he a ge (T1 and T2) in ol ed in he DCE p ocess. The p ojec ile and a ge closu e ene gies a e gi en by ¯ Eα p=hEa n−Ea iiαand ¯ Eα =hEA n−EA iiα, espec i ely, and he supe sc ip α=GT o F, indica es he ype o ene gy exci a ion. The i s line o Eq. (1) co esponds o he double-pion-exchange con ibu ion ( i s diag am o Fig. 1), he second o he double-con ac e m (second diag am o Fig. 1), inally he hi d line o he mixed pion-exchange con ac - e m ( hi d diag am o Fig. 1). XLIII Symposium on Nuclea Physics 2020 Jou nal o Physics: Con e ence Se ies 1610 (2020) 012013 IOP Publishing doi:10.1088/1742-6596/1610/1/012013 3 3. DCE c oss-sec ion and mic oscopic IBM2 nuclea ma ix elemen s The p e ious o malism can be used o compu e he DCE nuclea ma ix elemen s wi hin he mic oscopic In e ac ing Boson Model (IBM2) [30] and he DCE c oss-sec ions in he low- momen um ans e limi by making use o he dis o ed-wa e Bo n app oxima ion (DWBA). I one conside s ansi ions be ween 0+and 0+g ound s a es, he di e en ial c oss sec ion is gi en by [21] dσ dΩ=k k0µ 4π2¯h22 |Ti |2,(2) whe e µis he educed mass o he a ge -p ojec ile sys em, kand k0a e he incoming and ou going momen a, and Ti is he T-ma ix o he eac ion. Ti can be calcula ed by means o he Dis o ed Wa e Bo n App oxima ion (DWBA), Ti =DΨ− ~ k0Φ VΨ+ ~ kΦiE=1 (2π)3/2Zd~ Rei(χ(b)−~ Q·~ R)Mi (~m),(3) whe e one also uses he eikonal app oxima ion o he c.m. sca e ing. In he p e ious equa ion, Ψ+ ~ k,~ k0a e he wa e unc ions which desc ibe he c.m. mo ion o he a ge and p ojec ile ions, Φi, he in insic wa e unc ions o he nuclei be o e and a e he in e ac ion, which can be w i en as he p oduc o p ojec ile and a ge nucleon wa e unc ions. In he pa icula case o 0+ i→0+ ansi ions o he a ge , one ge s [21] Mi (m)→2" MDGT T→T0MDGT P→P0 ¯ EGT P+¯ EGT T!+ MDF T→T0MDF P→P0 ¯ EF P+¯ EF T!# ,(4) whe e MDGT and MDF a e Double-Gamow-Telle (DGT) and Double-Fe mi (DF) nuclea ma ix elemen s, espec i ely, o he p ojec ile/ a ge (A = P, T). The p e ious ma ix elemen s a e de ined as [21] MDGT A→A0=cGT DΦ(A0) J0X n,n0 [~σn×~σn0](0)~τn~τn0Φ(A) JE(5) and MDF A→A0=c DΦ(A0) J0X n,n0 ~τn~τn0Φ(A) JE,(6) whe e he sum uns o e he nucleons (n, n0) in ol ed in he p ocess. They a e calcula ed in he mic oscopic In e ac ing Boson Model (IBM2) [21, 30]. Finally, he c oss sec ion o Eq. (2) can be w i en in he eikonal app oxima ion and low-momen um ans e limi as dσ dΩ→k k0µ 4π2¯h22 2F(θ) MDGT T→T0MDGT P→P0 ¯ EGT P+¯ EGT T +MDF T→T0MDF P→P0 ¯ EF P+¯ EF T! 2 ,(7) whe e F(θ) is an angula dis ibu ion [21, Eq. (14)]. 4. Linea co ela ion be ween DCE and 0νββ nuclea ma ix elemen s In Re . [20], he au ho s discussed he possible eme gence o a linea co ela ion be ween DGT DCE and 0νββ nuclea ma ix elemen s by means o a la ge-scale shell-model calcula ion. In Re . [21], he p e ious hypo hesis was con i med by making use o a di e en nuclea model, he mic oscopic IBM2. Mo eo e , as also discussed in he p e ious sec ions, he exis ence o a p ocedu e o ac o ize he DCE c oss sec ions in e ms o eac ion and nuclea pa s was explici ly XLIII Symposium on Nuclea Physics 2020 Jou nal o Physics: Con e ence Se ies 1610 (2020) 012013 IOP Publishing doi:10.1088/1742-6596/1610/1/012013 4 demons a ed in he eikonal app oxima ion. Mos impo an , a mic oscopic desc ip ion o DCE p ocesses was de eloped wi h he de i a ion o a DCE po en ial in he closu e app oxima ion [21]. Thanks o his, one may hink o use he p esen and o hcoming expe imen al da a o hea y-ion DCE c oss-sec ions o place an uppe limi on 0νββ NMEs in e ms o he DCE expe imen al da a a e y o wa d angles, whe eas in he case o la ge sca e ing angles, he nuclea pa is expec ed o be a con olu ion o beam and a ge NMEs. The eme gence o he linea co ela ion be ween DCE and 0νββ nuclea ma ix elemen s can be shown by calcula ing he p e ious DCE and 0νββ NMEs wi hin he same nuclea model and o a su icien ly la ge se o nuclei. Then, a simple linea eg ession analysis can be conduc ed and a eg ession line can be d awn. I one plo s he mic oscopic IBM2 esul s [21, 31] o he 116Cd →116Sn, 128Te →128Xe, 82Se →82K , and 76Ge →76Se DGT DCE and 0νββ NMEs, one ob ains he clea eg ession line shown in Fig. 2. Figu e 2. Co ela ion be ween calcula ed DCE-DGT NMEs [21] and 0νββ-DGT NMEs [31]. The o ange squa e, g een iangle, ed s a , and blue ci cle s and o 116Cd →116Sn, 128Te → 128Xe, 82Se→82K and 76Ge →76Se da a, espec i ely. Figu e om Re . [21]; APS CopyRigh . Finally, i is wo h o no e ha he slopes o ou cu es in Fig. 2 and [21, Figs. 3] and o hose epo ed in [20, Figs. 4] a e qui e di e en . The main eason o his misma ch esides in he p ocedu es used in Re . [20] and [21] o ex ac he o m o he DCE po en ial, which is needed o calcula e he DCE NMEs. In he i s case, he au ho s did no de i e he DCE ma ix elemen s explici ly, bu hey made a guess on he o m only o he DGT DCE nuclea ma ix elemen s ; see [20, Eq. (6)]. In he second case, he au ho s de i ed he DCE po en ial o Eq. (1) and [21, Eq. (3)] explici ly om he diag ams o Figs. 1. Because o his, in he esul s o [20, Figs. 4] one can app ecia e he eme gence o a linea co ela ion be ween DGT DCE and 0νββ nuclea ma ix elemen s, bu he slopes o he cu es a e “ andom”. On he con a y, he slopes o he cu es in Fig. 2 and [21, Figs. 3] a e he “physical” ones. 5. Conclusion The o malism o calcula e he c oss-sec ions and Nuclea Ma ix Elemen s (NMEs) o hea y-ion Double Cha ge Exchange (DCE) p ocesses o Re . [21] was b ie ly desc ibed. 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