1. for the A1 collaboration
Measurements with polarized 3He at MAMI
D. Rohe
for the A1 collaboration
3He at low Q2 (< 0.4 GeV/c2)
Results for 3He(e,e¢p)d and 3He(e,e¢p)np
Setup for Gen measurement at Q2 = 0.25 (GeV/c)2
Corrections and result (preliminary)
Summary

2. 3He as polarized neutron target
n is bound in 3-body system
Extrapolation to free neutron target
3He n
theoretical correction needed due to
reaction mechanism
nuclear structure
dependent on the
- kinematics
- reaction channel
Modern 3-body calculation:
e.g. non-relativistic Faddeev calculation (Bochum-Krakow group)
applicable for Q2 < 0.4 (GeV/c)2 ~
treating full FSI and MEC

3. Experimental measure of FSI and MEC contributions:
Target asymmetry Ayo via 3He (e,e¢ n)
3He spin ^ scattering plane
PWIA: Ayo = 0 (invariance under time reversal)
+ FSI, MEC: Ayo  0
Result:
Bochum-Krakow group
FSI
FSI + MEC
Gep = Gmp = 0
(no charge exchange)
A_y_3.agr
J.Bermuth, P.Merle et al.,
Phys. Lett. B 564, 199
(2003)

4. Theoretical corrections to Gen from 3He (e,e¢ n)
increasing with decreasing Q2
example:
Q2 = 0.67 (GeV/c)2: (3.4 ± 1.7) % due to FSI
(C. Carasco, et al., Phys. Lett. B 559, 41 (2003))
Q2 = 0.35 (GeV/c)2: ~ 25% due FSI
Q2 = 0.25 (GeV/c)2: large corrections
measured
at MAMI/A1
Q2 = 0.15 (GeV/c)2: FSI + MEC
important to test reliability of theory
data help to understand nuclear structure
& reaction mechanisms

5. ST Setup in spectrometer hall at MAMI e¢ e rotation of the target spin
spectr. A
coils around m
- metal
28 msr e¢ B
= 4 G o e
53o
29o
735 MeV
68o
3He,
5 bar
lead
shielding
n,p p
1.80 m
n,p
rotation of the target spin | A+ A- ||
nucleon
detector q A+ || ST A- |
spectr. B
5.6 msr, 48.5o

6. Electron-target asymmetries in q.e. kinematics (Q2=0.31GeV/c2)
N( ) - N( )
N( ) + N( )
A = 1
Pe PT
Pe = (76.2 +/- 0.2 (stat) +/- 1.3 (syst)) %
PT = (49.8 +/- 0.3 (stat) +/- 2 (syst)) %
Separation of 2 and 3- body breakup (BB)
- reconstruction of the missing energy Em
Em = Ee - Ee¢ - Tp¢ - TA-1
3He(e,e’p)d
data
simulation
3He(e,e’p)pn
2BB
2BB+3BB

7. FSI: strong influence in 3BB but negligible in 2BB MEC: negligible
Results:
parallel perpendicular
FSI+MEC
PWIA
Achenbach et al.,
Eur. Phys. A 25, 177 (2005)
very good agreement between data and theory (Golak’s calculation)
FSI: strong influence in 3BB
but negligible in 2BB
MEC: negligible

8. Interpretation: 2BB: polarized proton target
P2BB = (-)1/3 (simple Clebsch-Gordon relation) p n e - d
3He
measured : A|| = 12.3 %
PWIA (Pp = 100%): A|| = 39.2 %
3BB:
in PWIA:
both protons are in a S-state
P(3BB) = 0
+ FSI: mainly rescattering p n e -
3He
rescattering direct FSI
rescattering
small in 2BB and
3BB
Singlet +Triplet np T-matrix

9. Setup in spectrometer hall for Gen at Q2 = 0.25 (GeV/c)2
spectr. A
coils around m
- metal
28 msr e¢ B
= 4 G o e
53o
51.5o
645 MeV
3He
p,n
lead
shielding
Kinematics:
E Q E’e qe qh
MeV (GeV/c) MeV deg deg
nucleon
detector

10. a Gen Gmn sin(qSq) cos(fSq) + b G2mn cos(qSq)
Gen measurement via 3He (e ,e´n )
spin orientation plane
Kinematics
quasielastic ST
fSq e´
qSq qe h q
3He n e
scattering plane
here: ST in scattering plane
target - electron asymmetry:
N( ) - N( )
N( ) + N( )
A =
ST fixed,
h flipping
a Gen Gmn sin(qSq) cos(fSq) + b G2mn cos(qSq)
c G2en + d G2mn
= Pe Pn
beam neutron
polarization

11. no absolute cross section measurement independent of Pe Pn
Ratio of asymmetries:
A(qSq =90o) A a
Gen ^ = =
A(qSq =0o) A b
Gmn
fSq=0o
Advantage:
no absolute cross section measurement
independent of Pe Pn
(we measured it: dPe < 2%, dPT < 4% (rel.))
only relative measurement needed
note: PT > Pn
possible dilution of the asymmetry drops out
- due to unpolarized background
- due to charge exchange: Pb(p,n)
Further:
alternate measurement of , ,- ,- A ^
reduction of systematic errors

12. Correction to A due to FSI & MEC^
calculation
from J. Golak
Cut to avoid large correction (particular MEC)
Correction to A : x 1.65
to A : x 1.06 ^ ||

13. data_gen_corr5_sh
preliminary

14. Summary: 3He as polarized neutron target
- at low Q2 large corrections from MEC,FSI
- confirmed by Ay measurement
test of 3-body theories
Separation of 2BB and 3BB on top of the q.e. peak
Measurement of A and A in 3He(e,e’p)
- 2BB: “polarized proton target”,
close to PWIA
- 3BB: large FSI effect ^ ||
very good agreement with theory
Measurement of Gen at Q2 = 0.25 (GeV/c)2
preliminary result:
statistical error: ~12 %
correction factor: 1.6

16. Understanding of reaction mechanisms & nuclear ground state
Modern 3-body calculations:
e.g. non-relativistic Faddeev calculation (Bochum-Krakow group)
applicable for Q2 < 0.4 (GeV/c)2 ~
Reaction mechanisms
- interaction during scattering process: MEC (Meson Exchange Current)
p,r
p,r
- interaction after scattering process: FSI (Final State Interaction)
rescattering
direct

17. - correcting the experimental asymmetries Aexp
for
radiation tail of 2BB in 3BB region
A3BB = A2+3BB - A2BB a23
a23 : amount of 2BB in 3BB region (43%)
1 - a23
electron polarization Pe = (76.2 +/- 0.2 (stat) +/- 1.3 (syst)) %
target polarization PT = (49.8 +/- 0.3 (stat) +/- 2 (syst)) %
Aexp
Pe PT
A =

18. N( ) - N( ) ST Principle of the measurement electron-target asymmetry
target spin ST fixed in scattering plane,
electron helicity h flips
parallel asymmetry A||: ST || q
perpendicular asymmetry A : ST ^ q ^
rotation of the target spin every hour | A+ A- || e- q A+ || ST A- |
magnetic field box