Elastic nucleon-deuteron scattering and breakup with chiral forces

Transcription

1 Elastic nucleon-euteron scattering an breakup with chiral orces H.Witała, J.Golak, R.Skibiński, K.Topolnicki JAGIELLONIAN UNIVERSITY LENPIC Collaboration Jagiellonian University, Kraków Ruhr-Universität, Bochum Forschungszentrum, Jülich Bonn Universität, Ohio State University Iowa State University Technische Universität, Darmstat Kyutech, Fukuoka IPN, Orsay TRIUMF, Vancouver

2 Plan: 1. Formalism an calculational scheme 2. Results or n reactions low energies an stanar NN potentials 3. Results or n reactions higher energies an stanar NN potentials 4. Relativistic eects 5. Chiral eective iel theory potentials 6. Summary

3 Present ay moels o nucleon-nucleon potentials (semi-phenomenological: AV18, CDBonn,NijmI an II) provie very goo escritpion o 2-nucleon boun state (euteron) an very goo escription o NN scattering ata Boun state o three nucleons ( 3 H, 3 He) calculate with NN interactions only is unerboun IMPORTANT IMFORMATION: three-nucleon Hamiltonian H must contain also a three-nucleon potential a term which cannot be reuce to interactions o pairs o nucleons : H V 4 H V (1) 4 V 12 V (2) 4 V 23 V V (3) 4 31 V 4 splitting o 3N potential to three parts with proper symmetry Can we escribe the ata in 3N continuum with such three-nucleon Hamiltonian?

4 First moel o three-nucleon orce (3NF) came rom Japan: J.Fujita an H.Miyazawa, Prog. Theor. Phys. 17, 36 (1957)). Other important 3N potential moels: - Moel Tucson-Melbourne base on pion-nucleon scattering amplitue (S.A.Coon, W.Glöckle, PRC23, 179 (1981)) - Urbana IX 3NF moel is base on 2p-exchange with D-resonance exctitation in intermeiate state; there is also spin- an isospin-inepenent shortrange term (B.S.Puliner et al., PRC56, 172 (1997))

5 What equations must be solve? Theoretical escription o 3N continuum (elastic nucleoneuteron scattering an the euteron breakup reaction) requires solution o the ollowing Faeev-type equation or T > state: T tp 1 tg V (1) 1 P 4 tpg T 1 tg V (1) 1 P G T, 4 Free 3N propagator 2N transition operator generate rom L-S equation V V q is compose o the euteron internal wave unction an the state o the relative nucleon-euteron motion. t G 2N t Part o V 4 symmetrical with respect to exchange o nucleons 2 an 3 These equations can be solve numerically precisely or any 2N potential an 3N-orce.

6 The transition amplitue or elastic scaterring is given by: o P G T V PT P V PG U 1 ' ' 1 ' ' ' (1) 4 (1) 4 1 Transition amplitue or the euteron breakup is given by: T P U 1 The singularities o operator G an pole o operator t in calculations or positive energies, makes treatment o the 3N continuum much more iicult than o the 3N boun state!

7 Low energies (below about 3 MeV) an stanar NN potentials (AV18, CDBonn, Nijm1 an 2) Quite goo escritption o low energy ata (below about 3 MeV): it seems that at these energies one oes not nee a 3NF!

8 Exception: A y puzzle Remark: quite ierent eects o TM99 an UIX 3NF s (in spite o the act that both are o 2p-exchange origin. That can imply that consistency in erivation o NN- an 3N-orces is important.

9 Higher energies: large iscrepancies between ata an theory base only on NN orces starts to appear Elastic scattering (p,p) NN only (AV18, CD Bonn, Nijm1, Nijm2) NN+3NF TM99 Total n cross section: (W.P.Abalterer et al. PRL 81(1998)57) up to ~ 5 MeV goo agreement with preictions base on 2N orces aing 3NF provies explanation o the isagreement up to ~ 15 MeV at even larger energies a clear isagreement which increases with energy ata 7: K.Sekiguchi et al., PR C65, 343 (22) ata 25: x n Y.Maea et al., PR C76, 144 (27) o p K.Hatanaka et al., PR C 66, 442 (22)

10 what is responsible or large ierences between theory an ata in 25 MeV cross section an in the total n cross section even ater inclusion o 2p-exchange 3NF? it is evient, that in the applie ynamics something is wrong or missing one possibility is that omitte short-range components o 3NF become more an more important with increasing energy however, increasing energy means also a transition to a region, where relativity coul be important relativistic Faeev calculations

11 Relativistic Faeev calculations The ormal structure o the equations remains the same but the ingreients change Form o the ree Hamiltonian H (an G ) changes: H 2 m k q m q Interacting 2N subsystem (2-3) has nonzero total momentum -q in the 3N c.m. system, what leas to the booste potential V: ( PR C71, 541 (25), PR C77, 344 (28), PR C83, 441 (211) ) V(q) 2 m k v q 2 m k q V(q=) reuces to the relativistic potential v eine in the 2N c.m. system. From V(q) the booste t-matrix is obtaine The Lorentz transormation rom 2N to 3N c.m. is perorme along the total momentum o the 2N subsystem, which in general is not parallel to momenta o these nucleons. This leas to Wigner rotation o spin states. When eining 3N partial wave states care must be taken about spin states

12 Faeev approach with both 3NF an relativity inclue elastic scattering: (p,p) ata K.Sekiguchi et al., Phys. Rev. Lett. 95, (25) only NN orces (CDBonn): nrel soli re rel ashe blue --- NN + 3NF (TM99): nrel otte blue rel ashe-otte brown -.- ata 25: x n Y.Maea et al., PR C76, 144 (27) eects o relativity seen only in N elastic scattering backwar cross section! relativistic eects are not responsible or large iscrepancies in elastic N scattering cross section interplay o relativity an 3NF s leas to a slight increase o the cross section at angles larger than q cm ~ 1 o o p K.Hatanaka et al., PR C 66, 442 (22)

13 It ollows that: relativistic eects are not responsible or large iscrepancies in elastic N scattering those iscrepancies must come rom neglection o short-range 3NF components which become active at higher energies Challenge: apply NN an 3NF s erive consistently in the ramework o chiral perturbation theory

14 LENPIC (Low Energy Nuclear Physics International Collaboration): to unerstan nuclear structure an reactions with chiral orces perturbation in (Q/L) n

15 Few remarks on chiral orces: In orer to reprouce properly 2N ata up to about 25 MeV N3LO orer o chiral expansion is require About 2 years ago: NN interaction up to N3LO, 3NF interaction up to N4LO (N3LO use in preliminary calculations at low energies) nonlocal momentum space regularization has been applie: 6 p V (p,l) V(p,p) (p,l) with 6 / L ( p, L) e V 4 (p,q,l) V ( p.75q ) / L (p,q,p,q) (p,q,l) with ( p, q, L) e what leas to inite cut-o arteacts (problems when applie to higher energy N scattering) New, improve chiral orce, presente by Bochum-Bonn group in 214: E. Epelbaum, H. Krebs, U.-G. Meißner, Eur. Phys. J. A51 (215) 3,26 up to N3LO E. Epelbaum, H. Krebs, U.-G. Meißner arxiv: [nucl-th] up to N4LO 2 r R Local regularization in the coorinate space V lr (r) V lr (r)(r) with r e 2 / ( ) 1 n R= m what correspons to L=33-5 MeV Such regularization preserves more long-range OPE an TPE physics All LECs in the long-range part are taken rom pion-nucleon scattering without ine tuning Very goo escription o the euteron properties, phase shits etc.

16 Various topologies contributing to the 3NF up to an incluing N 4 LO N 2 LO: (a) + () + () (E.Epelbaum et al., PR C66, 641 (22)) N 3 LO: (a) + (b) + (c) + () + (e) + () + rel V.Bernar et al., PR C77, 644 (28) - long range contributions (a), (b), (c) V.Bernar et al., PR C84, 541 (211) - short range terms (e) an leaing relativistic corrections N 3 LO contributions o not involve any unknown low energy constants! The ull N 3 LO 3NF epens on two parameters c D an c E coming with () an () terms, respectively. They are ajuste to two chosen 3N observables. N 4 LO (longest range contributions): (a) + (b) + (c) + () + (e) + () (H.Krebs et al., arxiv:123.67)

17 Estimation o theoretical uncertainties (E.Epelbaum et al., arxiv: [nucl-th], arxiv: [nucl.th]): (i) (i) X(p) - observable an X, i, 2,3, preiction at orer Q in the chiral expansion (i) Orer-Q correction : DX DX (2) ( i) X X (2) ( i) X X () ( i1) i 3 The chiral expansion or X takes the orm: X X + DX + + DX (i) () (2) (i) (i) (i) () Size o corrections is expecte to be DX =O(Q X ) (i) ( i) Quantitative estimates o the theoretical uncertainty X o the preiction X is mae using the expecte an actual sizes o higher-orer contributions: X () Q 2 X X (2) max Q 3 X, Q 1 DX (2) i 3: X ( i) max Q i1 X (), Q i1 DX (2), Q i2 X (3) X (2) QX (), X ( i3) QX ( i1) Q=max(p/ L,m / L ) with L 6,5 an 4 MeV b p b b or regulator R=.8-1. m, R=1.1 m an R=1.2 m, respectively.

18 NN evelope up to N4LO: E.Epelbaum et al. arxiv: [nucl-th] Novel way o quantiying the theoetical uncertainty ue to the truncation o the chiral expansion: E.Epelbaum et al. arxiv: [nucl-th] Theoretical uncertainty grows with energy an ecreases with increasing orer

19 Exclusive breakup reaction: quasi ree pp scattering

20 Exclusive breakup reaction: symmetric space-star coniguration Big challenge: application o ull N3LO chiral orce: NN + 3NF

21 Summary: N elastic scattering an euteron breakup reaction reveal large sensitivity to unerlying nuclear orces --> goo tools to test nuclear Hamiltonian it is clear, that base on the present ay NN orces aitional term in nuclear Hamiltonian is neee --> 3NF 3NF moels, erive inepenently rom NN potentials, can account in some cases or iscrepancies between theory an ata call or consistency between 2N an 3N orces: support an guiance --> chiral perturbation theory Big challenge: application o chiral N 3 LO orces (2- an 3-boy) to 3N continuum at higher energies