Separation of Flip and Non-Flip parts of np→pn (0º) Charge Exchange reaction at energies 0.55 – 2.0 GeV R.A. Shindin NN formalism and Charge Exchange process R dp measurements and tools Dean formula and Luboshitz remark Goldberger-Watson amplitudes and the Flip and Non-Flip parts of np-elastic scattering Delta-Sigma experimental data of the ratio R dp at 0°, respective values of the ratio r nf/fl and good agreement with the Phase Shift Analysis

np interaction in the c.m.s. Elastic backward Charge Exchange forward These both cases have identical cinematic and therefore can`t be separated using experiment – t = P 2 CM · (1– 4sin 2 Q/2) – t = P 2 CM · 4sin 2 Q/2

Born approach Enrico Fermi, in book Yadernaya Fizika 1951

NN formalism General view of the NN scattering matrix If both nucleons are identical then For the np elastic scattering we have For the Charge Exchange

According to the antisymmetry of two fermions wave function relative to the total permutation, including permutation of scattering vector (k`→ –k` ), permutation of spin and isotopic-spin (n↔p), we define

Charge-Exchange np→pn(θ)

R dp measurements and tools The Delta-Sigma experiment intends to obtain a complete np data set at the zero angle: the measurements of total cross section differences Δσ L (np) and Δσ T (np), spin- correlation parameters A 00kk (np) and A 00nn (np) as well as unpolarized measurements of values σ tot (np), dσ/dt(np  pn). For the Direct Reconstruction of the Re parts of the Scattering Amplitudes we measure also the ratio R dp = dσ/dt(nd) / dσ/dt(np) for the charge exchange quasi-elastic and elastic processes at 0° using the D2 and H2 targets. It will allow one of some sign uncertainties to be eliminated.

H 2 targetsD 2 targets

Dean formula Using the impulse approximation the differential cross section of nd → p(nn) reaction can be expressed by the Flip and Non-Flip contributions of charge exchange np → pn process: N.W. Dean: Phys. Rev D ; Phys. Rev D

Measurement of neutron-proton spin obsevables at 0° using highest energy polarized d, n probes L.N. Strunov et al.: Czechoslovak Journal of Physics, Vol. 55 (2005) Preliminary V.L. Luboshitz remark The Dean formula have been obtained for small momentum transfer when the scattering angle θ closes to 0. And for the calculation the R dp ration we can use the amplitudes of the Charge Exchange only! V.V.Glagolev, V.L.Luboshitz, V.V.Luboshitz, N.M.Piskunov CHARGE-EXCHANGE BREAKUP OF THE DEUTRON WITH THE PRODUCTION OF TWO PROTONS AND SPIN STRUCTURE OF THE AMPLITUDE OF THE NUCLEON CHARGE TRANSFER REACTION wrong approach which used amplitudes of np-np(180)

Spin Singlet interaction S = 0 Initial and final neutrons have parallel spin projection Initial and final neutrons have antiparallel spin projection REPRESENTATION REPRESENTATION Elastic backward Charge Exchange Non-Flip Spin-Flip REPRESENTATION REPRESENTATION Elastic backward Charge Exchange Spin-Flip Non-Flip

Goldberger-Watson amplitudes representation

Directly unitary transition If scattering angle θ equal 0°, then:

If to use now the next labels: Then we obtain the formulas: V.L.Luboshitz, V.V.Luboshitz: in Proceedengs of the XIV International Seminar on Interaction of Neuterons with Nuclei, Dubna (2007) E , p

If the amplitudes a and a CEX are identical then the Non-Flip equals to the SS amplitude 

R dp For calculation the R dp energy dependence the PSA solutions VZ40, FA91, SP07 from SAID DATA BASE was used (R.A. Arnd, I.I. Strakovsky et al.) The values of the Charge Exchange amplitudes at the θ = 0° have been obtain from the np -Elastic backward amplitudes using presented formulas The experimental Delta Sigma points of R dp are the directly relation of yields of and process of nd→p(nn) and np→pn process

r nfl/fl The ratio r nfl/fl is defined as follows Teoretical values from PSA Experimental points

r nfl/fl

CONCLUSION Using Dean formula and the values of R dp ratio we define the ratio r nfl/fl and separate Flip & Non-Flip parts of np – pn Charge Exchange forward process Good agreement with PSA solution have been obtain due to the unitary transformation Consistency between the theory and experimental data show that the ratios R dp and r nfl/fl is a good observables and it will be used as an additional constraint for DRSA method