1. Determination the Flip and Non-Flip parts of np - elastic scattering at 0 degree over the energy region 0.55 – 2.0 GeV and two interpretations of this process as Determination the Flip and Non-Flip parts of np - elastic scattering at 0 degree over the energy region 0.55 – 2.0 GeV and two interpretations of this process as np→np(π – θ) and np→pn(θ) R.A. Shindin History of this matter and Luboshitz remark History of this matter and Luboshitz remark Mutual transformations between the scattering matrixes М np–np(π – θ) and М np–pn(θ) using Wolfenstein amplitudes Mutual transformations between the scattering matrixes М np–np(π – θ) and М np–pn(θ) using Wolfenstein amplitudes Transition to the Goldberger-Watson amplitudes and determination the Flip and Non-Flip parts of np - elastic scattering in these both cases Transition to the Goldberger-Watson amplitudes and determination the Flip and Non-Flip parts of np - elastic scattering in these both cases New “Delta-Sigma” experiment data for the rations R dp, r nf/fl and good agreement with the Phase-Shift-Analysis for the Charge-Exchange process New “Delta-Sigma” experiment data for the rations R dp, r nf/fl and good agreement with the Phase-Shift-Analysis for the Charge-Exchange process

2. Rdp At the impulse approximation the differential cross section of nd → p(nn) can be expressed as a Dean formula using spin flip and spin non-flip contribution of charge exchange np → pn process: For R dp - ration we have: 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) N.W. Dean: Phys. Rev D 5 1661 N.W. Dean: Phys. Rev D 5 2832 R dp ration of yields nd → p(nn) and np → pn 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)

3. np interaction in the c.m.s. Elastic backward Charge Exchange process These both cases have identical cinematic and therefore can`t be separated using experiment Spin-Singlet scattering – S = 0 Variant 1. Initial and outgoing neutrons have parallel spin projection Variant 2. Initial and outgoing neutrons have antiparallel spin projection INTERPRETATION INTERPRETATION Elastic backward Charge Exchange Non-Flip Spin-Flip Non-Flip Spin-Flip INTERPRETATION INTERPRETATION Elastic backward Charge Exchange Spin-Flip Non-Flip Spin-Flip Non-Flip This anti-symmetry (between the definition of the spin-flip and spin non-flip parts at the S=0 station) shows the possible reason for the difference between these interpretations of the np-interaction. Though the differential cross section should be same, these both cases will can unequaled for the flip and non-flip.

4. NN formalism (Lapidus, Bilenky, Ryndin) General view of the NN scattering matrix If both nucleons are identical then For the np Elastic scattering we have For the Charge Exchange Wolfenstein amplitudes B, C, G, H, N are the complex functions of the interacted particles Energy and the scattering angle θ.

5. Charge-Exchange Charge-Exchange np→pn(θ) As a analogy for this process we can write the general view of the scattering matrix as follows However here we have the other amplitudes B CEX, C CEX, G CEX, H CEX, N CEX which belong to the Charge Exchange The vectors (n,m,l) form the new coordinates system also For comparison the np–np(π – θ) and np–pn(θ) interpretations among themselves we should obtain the matrix M np–pn (–k`,k) from the matrix M np–np (k`,k) directly Such representation of the Charge Exchange matrix is absolutely useless for our purposes Accordingly 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 Operators P 1,2 ( σ ) and P 1,2 (τ) are the unitary and Hermitian therefore the differential cross sections for the np-elastic and for the Charge-Exchange are equal

6. Goldberger-Watson amplitudes representation

7. If scattering angle θ equal 0°, then:

8. T=0 It does not give anything new and will be simple retelling If suddenly occurred that amplitudes and CEX are equal If suddenly occurred that amplitudes a and a CEX are equal then the coordinates systems would coincide and the Non-Flip would be precisely equal the SS amplitude  CEX T=0

9. Rdp For calculation the R dp energy dependence the PSA solutions VZ40, FA91, SP07 from SAID DATA BASE was used said@gwdac.phys.gwu.edu said@lux2.phys.va.gwu.edu 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 nd→p(nn) and np→pn process

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

11. CONCLUSION Using Dean formula and experimental R dp points we separated Flip & Non-Flip parts for np - Elastic scattering over the energy region 0.55 – 2.0 GeV Using Dean formula and experimental R dp points we separated Flip & Non-Flip parts for np - Elastic scattering over the energy region 0.55 – 2.0 GeV Good agreement with PSA have been obtain due to the transition to Charge Exchange Good agreement with PSA have been obtain due to the transition to Charge Exchange