The nd→p(nn) quasi elastic reaction at energy T n = 0.55 – 2.0 GeV Our research program 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) for the longitudinal (L) or transverse (T) beam and target polarizations and spin- correlation parameters A 00kk (np) and A 00nn (np) as well as unpolarized measurements of values Δσ 0,tot (np), dσ/dt(np→pn) and R dp ratio of yields of quasi elastic and elastic charge exchange reactions using the D 2 and H 2 targets R dp = dσ/dt (nd→p(nn)) / dσ/dt (np→pn). Main task of these studies is to determine the Real and Imaginary parts of np amplitudes over the energy region 1.2 – 3.7GeV. The knowledge of R dp could provide an additional constraint and will allow one of some sign uncertainties to be eliminated for the direct reconstruction of the Re parts of the scattering amplitudes. It has appeared that the nd→p(nn) reaction are related with a think effect of Fermi momentum distribution in deuteron. About this subject and also about method of determination such effect will be talking in my presentation Roman Shindin Experiment Delta-Sigma

Magnetic spectrometer for detection of protons from np elastic or nd quasi elastic charge exchange reactions under 0°Lab SP-94 - analyzing magnetic dipole Gx, Gy, 1x, 2x, 3x,y, 4x,y – multiwire propotional chambers MPT-polarized proton target or liquid D 2 /H 2 target, surrounded by DTS system for detecting of ∆ recoils which decay to π, p and γ Trigger counters – A, S 1, ST 1,2,3 and time-of-flight system – S 1, TOF 1,2

Resolution

Rejection the np→dπ° and nd→d+π+X background Using the 2-dimensional plot in coordinates of momentum and time-of-flight and with the help of hyperbola cut the background np→dπ° or nd→d+π+X yields rejected from the proton momenta spectra.

Rejection the np→dπ° and nd→d+π+X background The capture reaction np→dπ° and nd→d+π+X begin appear after the threshold of meson production 290 MeV. Their yields achieve a maximum about energy MeV. After that this background decreases.

After the threshold T n > 580 MeV the ∆- resonance excitation appears and become more considerable for large energy. Inelastic events from ∆ production begin to close the elastic peak on the left side, and the calculation of number of elastic ones receive an additional problem. Rejection the np→dπ° and nd→d+π+X background

Breit-Wigner + Gauss fit The separation of inelastic and elastic peaks can be performed by the Breit-Wigner and Gauss functions. In this way the mass scale is translated to the momentum.

Breit-Wigner + Gauss fit An additional this method was tested by the Monte-Carlo simulation and we obtain a good χ2 ~ 1. But we fined also its error about 15% of elastic events calculation that is related with two cases of ∆-resonance excitation with the target or beam nucleons. For the case of target ∆ the momentum spectrum (see blue histogram) well approximated using the Breit-Wigner function. In the second case the ∆ have any spatial angle θ ∆ and the proton from ∆ have itself θ p angle too. As a result we obtain more complex distribution (see green) which did not describe by this fit.

Suppression inelastic events by the DTS system This equipment is intended for the registration of recoil particle from ∆-resonances such as a protons, mesons or gamma quanta. According to our calculation the DTS efficiency for charged and neutral modes of ∆-decay should be equal 92% и 67% respectively. It means that the inelastic yields will be suppressed with a factor of 5.

Suppression inelastic events by the DTS system The blue shaded histograms present the protons spectra without the DTS signal. The transparent histograms with errors bars show the same as ones but the DTS works in anticoincidence with the spectrometer trigger. The problem of inelastic background is solved for the np→pn reaction at hydrogen target. For the nd → p(nn) charge exchange process obtained at deuterium target the number of inelastic events under left side of elastic peak remains significant.

Inelastic events under the right side of elastic peak Energy GeV Hydrogen Deuterium Energy GeV Hydrogen Deuterium Table 1. Inelastic background in units %. Calculated without DTS system. Table 2. Inelastic background in units %. Calculated using DTS system. The inelastic yields from the Δ resonances does not go further the centroid of elastic or quasi elastic peaks. At the right side of both peaks this background is negligible. For calculation the numbers of events which are belonged to these peaks we should use only their right parts. It is more simple, but in this way the centroid position must be defined very clearly.

Relative shift between the np → pn and nd → p(nn) peaks At low energy the inelastic backgrounds are almost excluded from protons spectra. It is convenient for observation of elastic and quasi elastic peaks. They have a similar shapes and parameters σ H2 and σ D2 are almost identical. But the quasi elastic peaks is shifted to the smaller values relative the elastic one. This shift δ P equals 6 ± 2 MeV/c.

Relation between two Gausses Supposed that the both Gauss functions have equivalent shapes but their centroid are differed among themselves by the shift δ P. Then we can define the R function If the value δ P is more less then the σ parameter the derivative function d R /d P can be written as very simple formula Thus the relation between G 1 and G 2 function can be approximated by the direct line and the tangent of line inclination will be proportional to the value of shift δ P.

δPδP tg α Modeling of relation between two Gausses Let’s call this method as the “Line-Shift”

Determination of δP shifting Using the δP value the D 2 momentum spectrum is shifted and divided by the H 2 spectrum. The histogram of D 2 /H 2 yield is fitted by a constant at the region of “well plateau”, and it provides the value of R dp ratio over the angular range 0 ≤ θ ≤ 20 mrad.

Determination of δP shifting The “well plateau” is limited by MeV/c after the centroid position of elastic peak at H 2 target. The R dp ratio begin to rise before the left side of “well plateau”, that is related with the inelastic background form the ∆- resonances excitation. It shows also, that the inelastic events in the right half of elastic or quasi-elastic peaks are negligible.

The “Line-Shift” method supposed above doesn’t take into account the possible difference among the shapes of elastic and quasi elastic peaks. However we can redefine the R function without this simplification It gives five parameters from which the C and δ P should be absolutely free but the parameters M H2, σ H2 and σ D2 are limited in the frames of errors of their values which are defined preliminary. We shall accept also a sound condition relative to the shapes of elastic and quasi elastic peaks Directly fit by R function

This method have some advantages. For the first we need not to make the many iterations and can define the δP value at once (p3 parameter). For the second the R dp ratio is defined simultaneously R dp = C · σ D2 / σ H2 ≈ C (it is p1 · p5/p4).

Experimental data of relative shift These points have agreement among themselves. All values are near 7 MeV/c. It show that the relative shift is really effect of quasi elastic reaction. But haw can we get this value from theory?

Simple explanation Neutron-spectator Is lost during the nd reaction and recoil neutron takes transfer momentum q Using low of energy conservation it gives For the relative shift we define

Simple explanation It gives only qualitative agreement and big differences with the values of δP. The transfer momentum q can be shared to the both neutrons but our calculation will give again this discrepancy. We need more fundamental approach.

Correct approach In the frame of impulse approximation the differential cross section of nd→p(nn) reaction expresses by the Dean formula which used the spin-flip and spin-non-flip contribution of np→pn charge exchange process If scattering angle of proton equals zero the t closes to zero too and F(t) ≈ 1. First term on the right side of Dean formula is vanished. Therefore the charge exchange reaction nd→p(nn) under 0º is performed by the spin-flip only. At once after the impact the wave function of relative motion of two neutrons will have the next form Spin (nn) = 1 Spin (nn) = 0 Spin d = 1 There the Ψ d (r) is the Hulthen expression for normalized S-wave deuteron wave function having the correct asymptotic behavior. The ρ = 4.31 Fm is the deuteron radius, d = 1.7 Fm is the effective radius of the low energy neutron- proton interaction and α = 6.25.

Correct approach

Two neutrons interact among themselves and (nn) -system as a whole receives the transfer momentum q Correct approach

Experimental data of R dp and r nfl/fl ratios Energy dependences of the ratios R dp (0) and r nfl/fl (0). The PSA solutions VZ40, FA91 and SP07 were taken from the SAID data base as amplitudes for the np backward reaction and transformed to the representation of charge exchange forward process by the unitary transition.