Polarization Transfer Measurement for d–p
Elastic Scattering
– a Probe for Three Nucleon Force Properties –
K. Sekiguchi∗ , H. Sakai†, H. Okamura∗∗, A. Tamii† , T. Uesaka ∗∗ , K.
Suda∗∗ , N. Sakamoto† , T. Wakasa ‡, Y. Satou∗ , T. Ohnishi∗ , K. Yakou† , S.
Sakoda† , H. Kato† , Y. Maeda † , M. Hatano† , J. Nishikawa ∗∗ , T. Saito† , N.
Uchigashima† , N. Kalantar-Nayestanaki§ and K. Ermisch§
∗
RIKEN, the Institute of Physical and Chemical Research, Saitama 351-0198, Japan
†
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
∗∗
Department of Physics, Saitama University, Saitama 338-8570, Japan
‡
Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan
§
Kernfysisch Versneller Instituut (KVI), NL-9747 AAGroningen, The Netherlands
Abstract. Precise measurements of the deuteron to proton polarization transfer coefficients for the
d–p elastic scattering has been made at 135 MeV/u at RIKEN Accelerator Research Facility. The
obtained results are compared with the Faddeev calculations based on modern nucleon–nucleon
forces together with Tucson-Melbourne, Tucson-Melbourne and Urbana–Argonne type of three
nucleon forces.
INTRODUCTION
Recent advance in computational resources has made it possible to obtain rigorous
numerical Faddeev–type calculations for the three–nucleon scattering processes by using
two–nucleon(2N) and three–nucleon forces (3NF). It has also allowed us to search for
3NF effects by direct comparison between such theoretical predictions and precisely
measured data.
In Refs. [1,2] we have reported the precise measurement of the cross section and the
deuteron analyzing powers for d–p elastic scattering at incoming deuteron energies of
70, 100, and 135 MeV/u. The data have been compared with the Faddeev calculations
with or w/o 3NFs. For the cross section, the large discrepancy between the data and the
calculations w/o 3NFs has been found in the cross section minimum and it is essentially
removed by taking into account 3NFs. The vector analyzing power A dy is also explained
by the predictions incorporating 3NFs. However the tensor analyzing power data are not
reproduced by any theoretical prediction and these results indicate that the present day
3NF models have deficiencies in the spin parts. In order to assess further the study of
3NF effects, we have measured the deuteron-to-proton polarization transfer coefficients
for d-p elastic scattering, which are expected theoretically to have strong sensitivities to
the spin dependent parts of 3NF.
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
711
EXPERIMENT
The experiment was performed at the RIKEN Accelerator Research Facility using tensor
and vector deuteron beams of 135 MeV/u [3]. A liquid hydrogen (19.8 mg/cm 2 ) or CH2
(93.4 mg/cm2) target was bombarded and scattered protons were momentum analyzed
by the magnetic spectrograph SMART [4]. The polarization of the scattered protons
were measured with the focal-plane polarimeter DPOL [5]. The measured observables
y − K y , and K y )
were the deuteron to proton polarization transfer coefficients (K yy , Kxx
yy
xz
◦
◦
in the angular range of θ c.m. = 90 − 180 . This measurement also yielded an induced
polarization (Py ) of the outgoing protons. The relation between the polarizations and
the observables is expressed as
2 y
d σo y 3 y dσ
P + Ky py + Kxz
pxz
=
py dΩ
dΩ
2
3
1 y
1 y
y
y
+ (Kxx
− Kzz
)pxx + (Kyy
− Kzz
)pyy ,
3
3
with
y
y
y
+ Kyy
+ Kzz
= 0,
Kxx
where x, y, and z are the coordinates
of the incident deuterons; x , y , and z are those of
d σo
the emitted protons; and dΩ denotes the cross section with unpolarized beams.
RESULTS AND DISCUSSIONS
y − K y with open squares. The
Figure 1 shows a part of the experimental data Kxx
yy
statistical errors are only shown. The statistical errors are smaller than 0.03 for all
the polarization transfer coefficients, and 0.01 for the induced polarization P y . The
systematic uncertainties for the polarization transfer coefficients are estimated to be 3%
at most.
In Fig. 1, four theoretical predictions in terms of Faddeev theory are shown together
with the experimental results. The dark (light) shaded band in the figure is the Faddeev
calculations with (w/o) Tucson-Melbourne (TM) 3NF [6] based on the modern nucleon–
nucleon(NN) potentials, namely CDBonn [7], AV18 [8], Nijimegen I, II and 93 [9]. The
solid line is the calculation with including Urbana IX 3NF [10] based on AV18 potential.
The dotted line is the predictions in which TM 3NF is taken into account and CDBonn
potential is considered as the NN potential. The TM 3NF is a modified version of the
TM 3NF closer to chiral symmetry.
y − K y the clear
Comparing the theoretical predictions with the observed values, for K xx
yy
discrepancies exist between the data and the 2N force predictions and these deviations
are explained well by inclusion of 3NFs. All 3NF potentials considered here (TM, TM ,
Urbana IX ) provide almost the same 3NF effects (magnitude and direction). However
y
for the other polarization transfer coefficients K yy and Kxz
which are not shown here,
712
FIGURE 1.
270 MeV.
y − K y for d-p elastic scattering at
Deuteron to proton polarization transfer coefficients K xx
yy
large differences between the data and the 2N force predictions are not reproduced by
including the 3NF models.
The results of the comparison for the polarization transfer coefficients reveal reveal
that the present 3NF models have deficiencies in its spin parts and that these observables
are useful to clarify the spin dependence of 3NF effects.
SUMMARY
In order to study of the properties of the three nucleon forces, we have measured the
deuteron to proton polarization transfer coefficients for d–p elastic scattering at 135
MeV/u which cover the angular range of θ c.m. = 90◦ − 180◦ . Highly accurate data
have been obtained. These results are compared with the Faddeev calculations with and
without the Tucson-Melbourne 3NF, or a modification thereof closer to chiral symmetry
TM , or the Urbana IX 3NF. The large difference are obtained between the data and the
2N force predictions. However not all spin observables are reproduced by incorporating
the present three nucleon force models and the results clearly show the deficiency of
these models in spin parts.
713
ACKNOWLEDGMENTS
We would like to thank H. Witała, W. Glöckle and H. Kamada for their strong theoretical
support. We would also like to thank S. Nemoto and P. U. Sauer for their useful
comments on theoretical issues. We would also like to express our appreciation to the
continuous help of the staff of RIKEN Accelerator Research Facility.
REFERENCES
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