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• Rdp 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 Rdp at 0°,

respective values of the ratio rnf/fl andgood agreement with the Phase Shift Analysis

np interaction in the c.m.s.

Elastic backwardElastic backwardCharge Exchange forwardCharge Exchange forward

These both cases These both cases havehave

identical cinematicidentical cinematicand therefore and therefore

can`t be separated can`t be separated using experimentusing experiment

__

__

k

k`n

pn

p

__

__

k

k`

n

pn

p

– t = P2CM · (1– 4sin2

– t = P2CM · 4sin2

Born approach

2

f ii i

de Ue

k r k r

2

1 2 i if fi id de U e U

k k r k k r

1 2 12U U U P

Enrico Fermi, in book Yadernaya Fizika 1951

CM degreenp

r

U2

U1

NN formalism

1 M M M nn nnpp pp

1 01 2

M M M M p p p pn n n n

1 01 2

M M M M n n n np p p p

1 2 1 20 1

1 3, , ,

4 4M k k M k k M k k

General view of the NN scattering matrix

If both nucleons are identical then

For the np elastic scattering we have

For the Charge Exchange

1 21 34

T

n

m

l

k

k̀k-k`

k+k`

k k̀ *

1 2

1 2 1 2

1 2 1 2

1 2

1

21

2

,

T

T

T T

T

T

C n n

G m m l lM k k B S T

H m m l l

N n n

n np p

, , k k k k k kn m lk k k k k k

1 21 14

S

1,2 1,2 , ,P P k k k k

According to the antisymmetry of two fermions wave functionrelative to the total permutation, including permutation of scattering

vector (k`→ –k` ), permutation of spin and isotopic-spin (n↔p), we define

1,2 1 21

2

1P 1,2 1 21

2

1P

1,2 , ,P M k k M k k n n n np p p p

1,2 , ,pnP k k k k

Charge-Exchange np→pn(θ)

, M k k SS ST pn pn

1 2

1 2 1 2

1 2 1 2

1 2

1

21

2

,

T

T

T T

T

T

C n n

G m m l lM k k B S T

H m m l l

N n n

p pn n

d ddt dt

pn np p pn n

, M k k SS ST pn pn

Rdp 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 ΔσL (np) and ΔσT(np), spin-correlation parameters A00kk(np) and A00nn(np) as well as unpolarized measurements of values σtot(np), dσ/dt(nppn). For the Direct Reconstruction of the Re parts of the Scattering Amplitudes we measure also the ratio Rdp = 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.

H2 targets D2 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 5 1661; Phys. Rev D 5 2832

( ) 023

lim 1 Flip

nd p nn np pntd dF tdt dt

-

( )1 1 1 3

Non Flip Flip

nd p nn np pn np pnd d dF t F tdt dt dt

dp nfl/f

( ) 2 1 3 1

d nd p nndtd np pndt

lr

R

Measurement of neutron-proton spin obsevables at 0°Measurement of neutron-proton spin obsevables at 0°using highest energy polarized d, n probesusing highest energy polarized d, n probes

------------------------------------------------------------------------------------------------------------------------------L.N. StrunovL.N. Strunov et al.: Czechoslovak Journal of Physics, Vol. 55 et al.: Czechoslovak Journal of Physics, Vol. 55

(2005)(2005)

PreliminarPreliminaryy 20052005

V.L. Luboshitz remark

The Dean formula have been obtainedfor small momentum transfer

when the scattering angle θ closes to 0. And for the calculation the Rdp ration

we can use the amplitudesof the Charge Exchange only!

--------------------------------------------------------------------------------------------------------------------------------------------------------V.V.Glagolev, V.L.Luboshitz, V.V.Luboshitz, N.M.PiskunovV.V.Glagolev, V.L.Luboshitz, V.V.Luboshitz, N.M.Piskunov

CHARGE-EXCHANGE BREAKUP OF THE DEUTRONCHARGE-EXCHANGE BREAKUP OF THE DEUTRONWITH THE PRODUCTION OF TWO PROTONSWITH THE PRODUCTION OF TWO PROTONSAND SPIN STRUCTURE OF THE AMPLITUDEAND SPIN STRUCTURE OF THE AMPLITUDE

OF THE NUCLEON CHARGE TRANSFER REACTIONOF THE NUCLEON CHARGE TRANSFER REACTION

The citation from Dean ‘‘Then one obtains Which is simply a generalization of the result found originally for K d K pp 0 by Lee. For the non-charge-exchange reaction, however, no such simple result follows’’.

---------------------------------------------------- N.W. Dean, Phys. Rev. D 5 (1972) 2832-2835

1 1 1 3

nf flad bppd dd S S

d d d

wrong approachwrong approachwhich used amplitudeswhich used amplitudes

of of nnpp--nnpp(180)(180)

Spin Singlet interaction S = 0

n

pn

p

n

pn

pInitial and final neutronsInitial and final neutronshave parallel spin projectionhave parallel spin projection Initial and final neutronsInitial and final neutronshave antiparallel spin projectionhave antiparallel spin projection

REPRESENTATIONREPRESENTATION

Elastic backward Charge ExchangeElastic backward Charge Exchange Non-Flip Spin-Flip

REPRESENTATIONREPRESENTATION

Elastic backward Charge ExchangeElastic backward Charge Exchange Spin-Flip Non-Flip

Goldberger-Watson amplitudes representation

-2

Non Flipd adt

(1) (2) (1) (2) (1) (2) (1) (2), n n n n m m l lM k k a b c e f

1

41

4

1

41

4

3

2

2

a B G N

b N B G

c C

e G H B N

f G H B N

1

41

4

1

41

4

3

2

2

CEX

CEX

CEX

CEX

CEX

a B G N

b G B N

c C

e N H B G

f N H B G

2 22 2 2Flipd b c e f

dt

Directly unitary transition

1

21

2

1

21

2

CEX CEX CEX CEX

CEX CEX CEX CEX

CEX

CEX CEX CEX CEX

CEX CEX CEX CEX

a a b e f

b a b e f

c c

e a b e f

f a b e f

1

21

2

1

21

2

CEX

CEX

CEX

CEX

CEX

a a b e f

b a b e f

c c

e a b e f

f a b e f

If scattering angle θ equal 0°, then:

0 CEX CEX CEXc c b f b e

If to use now the next labels:

1

2

3

T

T T

T

c a

c b e

c f

CEX

CEX CEX

CEX

1

2

3

T

T T

T

c ac b fc e

1 1 2 3

2 1 3

3 1 2 3

12

21

21

22

c c c c

c c c

c c c c

1 1 2 3

2 1 3

3 1 2 3

12

21

21

22

c c c c

c c c

c c c c

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) E3-2007-23, p.64-74.

SS

ST

Non-Flip

Flip

0

Ba

CEXa

If the amplitudes a and aCEX are identicalthen the Non-Flip equals to the SS amplitude

RdpFor calculation theFor calculation the RRdpdp energy dependenceenergy dependencethe the PSAPSA solutions solutions VZ40VZ40, , FA91FA91, , SP07SP07 from from

SAID DATA BASE was usedSAID DATA BASE was usedsaid@gwdac.phys.gwu.edusaid@lux2.phys.va.gwu.edu

(R.A. Arnd, I.I. Strakovsky et al.)(R.A. Arnd, I.I. Strakovsky et al.)

The values of the The values of the Charge ExchangeCharge Exchange amplitudes amplitudesat the at the θθ = 0° have been obtain from the = 0° have been obtain from the

npnp --Elastic backwardElastic backward amplitudes amplitudesusing presented formulasusing presented formulas

The experimental The experimental Delta SigmaDelta Sigma points of points of RRdpdp are the directly relation of yieldsare the directly relation of yieldsof of nd→p(nn) and and np→pn processprocess

r nfl/fl

2 1 13

nfl / fl

dpr

R

The ratio r nfl/fl is defined as follows

Non Flip Flip

np pn np pn

d ddt dt

nfl / flrTeoretical values from PSA

Experimental points

r nfl/fl

CONCLUSIONCONCLUSION

• Using Dean formula and the values of Rdp ratio we define the ratio rnfl/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 Rdp and rnfl/fl is a good observables and it will be used as an additional constraint for DRSA method