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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 [email protected]@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