Two-Pion Exchange Cuens in Phoodisinegaion of he Deueon Dagaa Rozędzik and Jacek Goak Jagieonian Univesiy Kaków MENU00 3 May 00 Wiiasbug
Conen Chia Effecive Fied Theoy ChEFT Eecoagneic cuen oeaos wihin ChEFT Cacuaions of oaizaion obsevabes in hoodisinegaion of he deueon Concusions and ouook
Foces and cuens Many odes A o of exeience gained Pobe of consisence: we need a good heoy! Chia Effecive Fied Theoy Foces Cuens Exeiena daa
Foces and Cuens The L nuceon-nuceon oenia is given by one ion exchange PE and conac es. V L V con + V π V NL V con + V π + V π The NL coecions ae due o one and wo-ion exchanges TPE as we as new conac ineacions. The NL and N3L incude coecions wih any-ion exchanges and conac ineacions in highe odes. The cuen oeao us be consisen wih he nuceon-nuceon ineacion. The effecive oeao fo wo-nuceon N syse is a su of he singe nuceon oeaos and wo-nuceon oeao: µ N µ + µ + µ.
Two-nuceon eecoagneic cuens µ µ ec + µ con µ ec µ π + µ π + Two-ion exchange TPE cuens in NL aise fo any coicaed ocesses S.Pasoe e a.-tpe cuens based on he ie-ode eubaion heoy 08 Resus by S. Köing E. Eebau e a. 09 Redeived: singe-nuceon cuen oeaos one-ion exchange cuen oeaos using he ehod of uniay ansfoaion Deived: ong-anged wo-ion exchange cuen oeaos conaining no fee aaees + Wok in ogess: conac es Phys. Rev. C 80 04550 009
How do we ay he ong-anged wo-ion exchange cuen oeaos? We ge conibuions o: 0 h coonen of he cuen oeao chage densiy 0 veco coonens of he cuen oeao The os genea exession fo he cuen and he chage densiy in oenu sace is given by: 5 8 0 βs S fα α α β β T ; 5 4 α β f β α β T α - + ½ k - + ½ k k + Genea MEC diaga
So fo he hoodisinegaion of he deueon we wok wih he foowing oeaos: 8 7 6 5 4 3 + + + T Woking wih Maheaica is uie ioan! Fo exae: f 8 fo cobinaion T 8 τ τ T 3 0 9 8 + Resus fo S. Köing e a. Phys. Rev. C 80 04550 009 T 3 8 τ τ f 8 funcions Idvvv3 coesond o he hee-oin funcions whee z 3 T τ τ 3 3 T τ τ
Two nuceon eacions The foais euies knowedge of he consisen oenias and eecoagneic cuens. V N µ Ψ bound Ψ n sca + G n 0 V V G N + N 0 N µ n µ Ψ sca Ψbound G 0 he fee oagao of wo nuceon saisfies he Liann Schwinge euaion A cacuaions wee ade wih he chia oenias and cuens. The AV8 oenia and he coesonding cuens wee used as he efeence cacuaion. Fo a given chia NL NN oenia we oduce: he deueon wave funcion and aix eeens of he -oeao
γ + H + n n Phoodisinegaion of he deueon Cacuaions of oaizaion obsevabes fo wo hoon enegies. Fo oaized deueon age we have γ d d d Ω d dω 0 k k T k θ d d Ω d dω 0 [ + Rei i T + T + Re T + Re T ] 0 0 We cacuaed he foowing obsevabes: Deueon anayzing owes: T 0 T T γ θ d Phoon anayzing owe Σ Diffeenia coss-secion n
Resus fo he deueon enso anayzing owes fo he hoon enegy bin 5-45 MeV singe+pe+tpe singe+pe AV8 Exeiena daa fo A. Rachek e a. Phys. Rev. Le. 988303 007
Resus fo he deueon enso anayzing owes fo he hoon enegy bin 45-65 MeV Exeiena daa fo A. Rachek e a. Phys. Rev. Le. 988303 007
Resus fo he deueon enso anayzing owes fo he hoon enegy bin 65-00 MeV Exeiena daa fo A. Rachek e a. Phys. Rev. Le. 988303 007
E γ 30MeV E γ 60MeV E γ 00MeV Resus fo he hoon anayzing owe a hee enegies 30 60 and 00 MeV Exeiena daa fo S. Ying e a. Phys. Rev C38 4 988
E γ 30MeV E γ 60MeV E γ 00MeV Resus fo he diffeenia coss secion fo hee hoon enegies 30 60 and 00 MeV Exeiena daa fo S. Ying e a. Phys. Rev. C384 988
Concusions and ouook ChEFT has becoe a sandad oo in nucea hysics i offes a consisen icue of nucea foces and nucea cuen oeaos. Chia N and 3N oenias ae aeady used fo sudying he sucue of nucei and nucea eacions. We used esus of ChEFT o coue eecoagneic eacions wih few nuceon syses. In aicua we consideed ow enegy hoodisinegaion eacion. We coaed edicions based on his aoach o he esus obained wihin a oe adiiona faewok whee he high ecision nuceon-nuceon oenia AV8 and he cuen oeao incuding eson exchange cuens consisen wih his foce is eoyed. We have shown esus fo he unoaized coss secions and vaious oaizaion obsevabes. The ain ai of ou wok is o ceae a coee faewok fo he desciion of wo- and hee-nuceon ocesses incuding any-body eecoagneic cuens and foces in he ChEFT aoach.
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How we oceed Fo deueon one needs: > + + + < d N k i G i N φ ε ε µ µ 0 0 0 0 ; ˆ ; > < s z k s αβ How do we do PWD? ˆ ˆ ˆ ; ˆ ; ˆ ˆ * > >< < s s T f Y s C Y s C d d β α αβ αβ β
A inegas in aicua sin and isosin aix eeens: > >< < s s T f Y s C Y s C ˆ ˆ ˆ ; ˆ ; * β α αβ ae eaed using Maheaica Fo a given se of uanu nubes: } { s s we idenify a non-zeo cases and oduce a Foan code again using Maheaica o ge he inegas cacuaed on a aae achine.