High Resolution Study of Pionic 0 − State in 16O
T. Wakasa ∗, G. P. A. Berg∗ , H. Fujimura∗ , K. Fujita∗ , K. Hatanaka∗ ,
M. Itoh∗ , J. Kamiya∗ , T. Kawabata †, Y. Kitamura∗ , E. Obayashi ∗,
H. Sakaguchi∗∗ , N. Sakamoto∗ , Y. Sakemi∗ , Y. Shimizu∗ , H. Takeda ∗∗,
M. Uchida∗∗, Y. Yasuda∗∗, H. P. Yoshida∗ and M. Yosoi∗∗
∗
Research Center for Nuclear Physics (RCNP), Ibaraki, Osaka 567-0047, Japan
†
Center for Nuclear Study (CNS), University of Tokyo, Tokyo 113-0033, Japan
∗∗
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
Abstract. The cross sections and analyzing powers of the 16 O(p, p)16 O(0− , T = 1) scattering
were measured at a bombarding energy of 295 MeV and an angular range of 14◦ ≤ θlab ≤ 30◦ .
The isovector 0− state at Ex = 12.80 MeV is clearly separated from the neighboring states with
an energy resolution of ∆E 30 keV. The data have been compared with distorted wave impulse
approximation (DWIA) calculations. The analyzing powers are sensitve to the effective nucleonnucleon (NN) interaction used in DWIA calculations, and our data support the medium modification
of the NN interaction in nuclei. The DWIA calculation employing a random phase approximation
(RPA) response function predicts an enhancement of the cross sections around a momentum transfer
of q 1.7 fm−1 , and it gives a reasonable agreement with the data.
INTRODUCTION
Isovector J π = 0− , 0± → 0∓ excitations are of particular interest since they carry
the simplest pion-like quantum number. At low momentum transfers, they have been
investigated in beta decay and muon capture experiments [1, 2, 3]. Axial-vector and
pseudoscalar currents are responsible for these first-forbidden transitions in nuclear
weak processes. Gagliardi et al. [1] reported an enhancement of the decay rate by more
than a factor of 3 for the first-forbidden beta decay of the 120 keV, 0 − state in 16 N. This
enhancement can be explained by considering meson-exchange effects [4].
The (p, n) and (p, p) reactions are suited to study these transitions for a wide range
of momentum transfer [5]. Orihara et al. [6] measured the angular distribution for the
16 O(p, n)16 N(0− , 0.12 MeV) reaction at T = 35 MeV. They reported discrepancies
p
between distorted wave Born approximation (DWBA) calculations and their data in
the large momentum transfer region of q = 1.4–2.0 fm −1 that might be due to an
enhancement of the pion probability in the nucleus [7, 8, 9, 10, 11]. However, in
the proton inelastic scattering to the 0 − , T = 1 state in 16 O at Tp = 65 MeV, such
an enhancement was not observed [12]. The differences between (p, n) and (p, p)
results might indicate contributions from complicated reaction mechanisms as these low
incident energies.
At intermediate energies of Tp > 100 MeV, where reaction mechanisms are expected
to be simple, there are data only for the 0 − , T =0 transition at Tp = 135 [13, 14], 180
[14], 200 MeV [15], 318 MeV [16], and 400 MeV [17]. Most of these measurements
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
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were not performed with sufficient energy resolution to separate the 0 − , T = 0 state at
Ex = 10.96 MeV from its strong neighboring doublet (3 + and 4+ ) which is only about
140 keV away. It should be noted that there are no published experimental data for the
0− , T = 1 state at Ex = 12.80 MeV in this energy region.
In this article, we present the measurement of cross sections and analyzing powers for
the excitation of the 0− , T =1 (12.80 MeV) unnatural-parity state in 16 O using 295 MeV
inelastic proton scattering. The results will be compared with distorted wave impulse
approximation (DWIA) calculations with shell-model wave functions. This provides
information on tensor and spin-spin components of effective nucleon-nucleon (NN)
interactions. Furthermore, the data will be compared with DWIA calculations employing
random phase approximation (RPA) response functions in order to assess the pionic
enhancement in a large momentum-transfer region.
EXPERIMENTAL METHODS
The measurement was carried out by using the West-South (WS) beam line and Grand
Raiden (GR) spectrometer at the Research Center for Nuclear Physics (RCNP), Osaka
University. The WS beam line and GR spectrometer are described in detail in Refs. [19,
20]. Here we only present a brief description of the experimental apparatus and discuss
details relevant to the present experiment.
The high resolution WS beam line [20] has been designed and constructed to accomplish complete matching including both lateral and angular dispersion and focus
matching with the high-resolution Grand Raiden spectrometer at RCNP. The WS beam
line consists of six dipole magnets with a total bending angle of 270 ◦. This beam line is
divided into five sections. The beam is focused horizontally and vertically at the end of
each section. Beam line polarimeter systems positioned at the ends of the first and second sections allow the measurement of all polarization components of the beam. They
are separated by a bending angle of 115 ◦ for the determination of horizontal components
of the beam polarization. In dispersive mode, lateral and angular dispersions of the WS
beam line are b16 = 37.1 m and b26 = −20.0 rad, necessary to satisfy dispersion matching conditions for Grand Raiden. The magnifications of the beam line are (Mx , My ) =
(−0.98, 0.89) and (−1.00, −0.99) for dispersive and achromatic modes, respectively.
A windowless and self-supporting ice target [21] was used as an oxygen target. The
thin ice target with a thickness of 14.1 mg/cm 2 was mounted on a thin aluminum frame
attached to a copper frame that was cooled down to 77K using liquid nitrogen.
Scattered particles were momentum-analyzed by the GR spectrometer. The spectrometer consists of two dipole (D1 and D2) magnets, two quadrupoles (Q1 and Q2), a sextupole (SX), and a multipole (MP). The spectrometer is characterized by a high resolving
power of R = 37,000.
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DATA REDUCTION
The elastic scattering data on 16 O are shown in Fig. 1. Differential cross sections were
normalized to the known p + p cross section at θ lab = 14◦ by utilizing the hydrogen
present in the ice target. The beam energy was determined to be 295 ± 1 MeV, based
on the kinematic energy shift between elastic scattering from 1 H and 16 O. The beam
polarization was continuously monitored with the hydrogen polarimeter in the WS beam
line. Its typical value was 0.70 ± 0.01. The hydrogen in the ice target limited the useful
scattering angles for inelastic scattering on 16 O to larger than 14 ◦ . At smaller angles, the
p + p events overlap the 16 O excited states of interest in this measurement.
The elastic scattering data were analyzed using optical model potentials generated
phenomenologically. The solid curves in Fig. 1 are the results with the global optical
potential optimized for 16 O [22]. The gray bands represent the results by using several
optical potentials parameterized for nuclei from 12 C to 208 Pb with a smooth mass
number dependence [22]. The global optical potential for 16 O shown by the solid curves
reproduces the experimental data fairly well not only for cross sections but also for
analyzing powers. Thus, in the following, we will use this optical potential in DWIA
calculations for inelastic scattering.
RESULTS AND DISCUSSION
Figure 2 shows the excitation energy spectrum of the 16 O(p, p) scattering at Tp = 295
MeV and θlab = 30◦. The isovector 0− state at Ex = 12.80 MeV is clearly separated from
the neighboring states with an energy resolution of ∆E = 29–34 keV depending on the
reaction angle.
We have performed DWIA calculations by using the computer code DWBA98 [23]
in which the knock-on exchange amplitude is treated exactly. The one-body density
matrix elements (OBDME) for the isovector 0 − transitions of the 16 O(p, p) scattering
were obtained from Ref. [24]. This shell-model calculation was performed in the 0s0p-1s0d-0 f 1p configurations by using phenomenological effective interactions. The
single particle radial wave functions were generated by using a Woods-Saxon potential,
the depth of which was adjusted to reproduce the binding energy. The effective NN
interaction was taken from the t-matrix parameterization of the free NN interaction by
Franey and Love [25] at 325 MeV.
Figure 3 compares the preliminary result of the angular distribution for the isovector
0− state with the DWIA calculation. The calculation reproduces the cross sections
around the 2nd maximum at 14 ◦ without a normalization factor, while it underestimates
and slightly misses the 3rd maximum. Furthermore the analyzing power data are not
reproduced by this calculation completely by giving the opposite sign. We have also
performed a DWIA calculation by using the density- and energy-dependent in-medium
t-matrix evaluated from the G-matrices [26]. The G-matrix calculations were performed
by using the Paris NN potential. The results are shown in Fig. 3 as the dashed curves. The
calculated cross sections give a similar angular distribution compared with those with
the Franey and Love free t-matrix, but they are larger by a factor of 2. On the contrary,
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Figure 1: Differential cross sections σ c.m. and
analyzing powers Ay of elastic scattering. Statistical errors are smaller than the data points.
Figure 2: A typical energy spectrum
of the 16 O(p, p) scattering at Tp =
295 MeV and θlab = 30◦ . Results of
Hyper-Gaussian peak-fitting are also
shown.
the results of DWIA calculations for the analyzing powers depend on the choice of the
t-matrix. The calculated analyzing powers with the in-medium t-matrix give the correct
sign, but they are smaller compared with the experimental data.
Finally we compared our experimental data with the DWIA+RPA calculation. The
RPA calculations are performed without the commonly used universality ansatz (g NN
= gN∆ = g∆∆), namely all of the g s are treated independently [27]. The nonlocality of
the mean field is treated by an effective mass m∗ . These parameters in the present RPA
calculation are (gNN , gN∆ , g∆∆) = (0.6, 0.4, 0.5) and m∗ (0)=0.7mN . The formalism of
DWIA calculations is described in Ref. [28].
The results of DWIA+RPA and DWIA+free response calculations are shown in Fig. 4
as solid and dashes curves, respectively. The DWIA+RPA calculation predicts an enhancement of the 3rd maximum of the cross sections compared with the 2nd maximum,
and it reproduces the 2nd and 3rd maxima simultaneously with a normalization factor
of 0.5. Thus the experimental data supports the enhancement of the pionic 0 − mode in
nuclei as is predicted in the RPA calculation.
ACKNOWLEDGMENTS
We are grateful to M. Ichimura and H. Sakai for their helpful correspondence. This
work is supported in part by the Grants-in-Aid for Scientific Research Nos. 12740151,
and 14702005 of the Ministry of Education, Science, Sports and Culture of Japan.
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Figure 3: Angular distribution for the isovector 0− state via 16 O(p, p ) scattering at Tp =
295 MeV. The solid and dashed curves are the
results of DWIA calculations. See text for details.
Figure 4: The results of DWIA+RPA
and DWIA+free calculations.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
G. A. Gagliardi et al., Phys. Rev. Lett. 48, 914 (1982).
P. Guichon et al., Phys. Rev. C 19, 987 (1979).
E. G. Adelberger et al,, Phys. Rev. Lett. 46, 695 (1981).
K. Kubodera et al., Phys. Rev. Lett. 40, 755 (1978).
W. G. Love et al., in Proceedings of International Conference on Spin Excitations, Telluride, Colorado, 1982, edited by F. Petrovich et al., (1982).
H. Orihara et al., Phys. Rev. Lett. 49, 1318 (1982).
C. H. Llewellyn Smith, Phys. Lett. 128B, 107 (1983).
M. Ericson and A. W. Thomas, Phys. Lett. 128B, 112 (1983).
B. L. Friman, V. R. Pandharipande, and R. B. Wiringa, Phys. Rev. Lett. 51, 763 (1983).
E. L. Berger, F. Coester, and R. B. Wiringa, Phys. Rev. D 29, 398 (1984).
D. Stump, G. F. Bertsch, and J. Pumlin, AIP Conf. Proc. 110, 339 (1984).
K. Hosono et al., Phys. Rev. C 30, 746 (1984).
J. J. Kelly et al., Phys. Rev. C 39, 1222 (1989).
J. J. Kelly et al., Phys. Rev. C 41, 2504 (1991).
R. Sawafta et al. IUCF Scientific and Technical Report, May 1988–April 1989, p.19.
J. J. Kelly et al., Phys. Rev. C 43, 1272 (1991).
J. D. King et al., Phys. Rev. C 44, 1077 (1991).
W. M. Alberico, M. Ericson, and A. Molinari, Nucl. Phys. A379, 429 (1982).
M. Fujiwara et al., Nucl. Instrum. Methods Phys. Res. A 422, 484 (1999).
T. Wakasa et al., Nucl. Instrum. Methods Phys. Res. A 482, 79 (2002).
T. Kawabata et al., Nucl. Instrum. Methods Phys. Res. A 459, 171 (2001).
S. Hama et al., Phys. Rev. C 41, 2737 (1990).
J. Raynal, Program DWBA 98, NEA 1209/05, 1999.
T. Kawabata et al., Phys. Rev. C 65, 064316 (2002), and references therein.
M. A. Franey and W. G. Love, Phys. Rev. C 31, 488 (1985).
H. V. von Geramb, AIP Conf. Proc. 97, 44 (1982).
K. Nishida and M. Ichimura, Phys. Rev. C 51, 269 (1995).
K. Kawahigashi, K. Nishida, A. Itabashi, and M. Ichimura, Phys. Rev. C 63, 044609 (2001).
680