Complete Set of Polarization Transfer Observables for the $^{12}{\rm
  C}(p,n)$ Reaction at 296 MeV and 0$^{\circ}$
arXiv:0704.0670v1  [nucl-ex]  5 Apr 2007
Typeset with jpsj2.cls <ver.1.2> Letter
Complete Set of Polarization Transfer Observables
for the 12C(p, n) Reaction at 296 MeV and 0◦
Masanori Dozono∗, Tomotsugu Wakasa, Ema Ihara, Shun Asaji, Kunihiro Fujita1, Kichiji Hatanaka1,
Takashi Ishida2, Takaaki Kaneda1, Hiroaki Matsubara1, Yuji Nagasue, Tetsuo Noro, Yasuhiro Sakemi3,
Yohei Shimizu1, Hidemitsu Takeda, Yuji Tameshige1, Atsushi Tamii1 and Yukiko Yamada
Department of Physics, Kyushu University, Fukuoka 812-8581
Research Center for Nuclear Physics, Osaka University, Osaka 567-0047
Laboratory of Nuclear Science, Tohoku University, Sendai 982-0826
Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578
A complete set of polarization transfer observables has been measured for the 12C(p, n)
reaction at Tp = 296 MeV and θlab = 0
◦. The total spin transfer Σ(0◦) and the observable
f1 deduced from the measured polarization transfer observables indicate that the spin–dipole
resonance at Ex ≃ 7 MeV has greater 2
− strength than 1− strength, which is consistent
with recent experimental and theoretical studies. The results also indicate a predominance of
the spin-flip and unnatural-parity transition strength in the continuum. The exchange tensor
interaction at a large momentum transfer of Q ≃ 3.6 fm−1 is discussed.
KEYWORDS: complete set of polarization transfer observables, spin–dipole resonance, exchange tensor
interaction
The charge exchange reaction at intermediate ener-
gies (T & 100 MeV/A) is one of the best probes to
study spin–isospin excitations in nuclei, such as spin–
dipole (SD) excitations characterized by ∆L = 1, ∆S =
1, and ∆Jπ = 0−, 1−, and 2−. In previous (p, n)
and (n, p) experiments on 12C,1, 2 spin–dipole resonances
(SDRs) were found at Ex ≃ 4 and 7 MeV. Analysis of the
angular distributions of the SDRs at Ex ≃ 4 and 7 MeV
indicate that they consist of mainly 2− and 1− compo-
nents, respectively. However, a recent 12C(~d, 2He)12B ex-
periment3 suggested that the SDR at Ex ≃ 7 MeV in
has more 2− components than 1− components. This sug-
gestion is supported by a 12C(12C, 12N)12B experiment4
and by theoretical calculations including tensor correla-
tions.5 Thus the spin-parity assignment of the SDR at
Ex ≃ 7 MeV for the A = 12 system is still controversial.
A complete set of polarization transfer (PT) observ-
ables at 0◦ is a powerful tool for investigating the spin-
parity Jπ of an excited state. The total spin transfer
Σ(0◦) deduced from such a set gives information on the
transferred spin ∆S, which is independent of theoreti-
cal models.6 Furthermore, information can be obtained
on the parity from the observable f1.
7 On the other
hand, each PT observable is sensitive to the effective
nucleon–nucleon (NN) interaction. The PT observables
for ∆Jπ = 1+ transitions have been used to study the
exchange tensor interaction at large momentum trans-
fers.8, 9
In this Letter, we present measurements of a com-
plete set of PT observables for the 12C(p, n) reaction
at Tp = 296 MeV and θlab = 0
◦. We have deduced
the total spin transfer Σ and the observable f1 using
the measured PT observables in order to investigate the
spin-parity structure in both the SDR and continuum
regions. We also compare the PT observables for the
∗E-mail address: dozono@kutl.kyushu-u.ac.jp
12C(p, n)12N(g.s.; 1+) reaction with distorted-wave im-
pulse approximation (DWIA) calculations employing the
effective NN interaction in order to assess the effective
tensor interaction at a large exchange momentum trans-
fer of Q ≃ 3.6 fm−1.
Measurements were carried out at the neutron time-
of-flight facility10 at the Research Center for Nuclear
Physics (RCNP), Osaka University. The proton beam
energy was 296 MeV and the typical current and polar-
ization were 500 nA and 0.70, respectively. The neutron
energy and polarization were measured by the neutron
detector/polarimeter NPOL3.11 We used a natural car-
bon (98.9% 12C) target with a thickness of 89 mg/cm2.
The measured cross sections were normalized to the
0◦ 7Li(p, n)7Be(g.s. + 0.43 MeV) reaction, which has
a center of mass (c.m.) cross section of σc.m.(0
27.0±0.8 mb/sr at this incident energy.12 The systematic
uncertainties of the data were estimated to be 4–6%.
Asymmetries of the 1H(~n, p)n and 12C(~n, p)X reac-
tions in NPOL3 were used to deduce the neutron polar-
ization. The effective analyzing power Ay;eff of NPOL3
was calibrated by using polarized neutrons from the
12C(~p, ~n)12N(g.s.;1+) reaction at 296 MeV and 0◦. A
detailed description of the calibration can be found in
Ref. 11. The resulting Ay;eff was 0.151 ± 0.007 ± 0.004,
where the first and second uncertainties are statistical
and systematic, respectively.
Figure 1 shows the double differential cross section and
a complete set of PT observables Dii (i = S, N, and L)
at 0◦ as a function of excitation energy Ex. The labo-
ratory coordinates at 0◦ are defined so that the normal
(N̂ ) direction is the same as N̂ at finite angles (nor-
mal to the reaction plane), the longitudinal (L̂) direc-
tion is along the momentum transfer, and the sideways
(Ŝ) direction is given by Ŝ = N̂ × L̂. The data of the
cross section in Fig. 1 have been sorted into 0.25-MeV
http://arxiv.org/abs/0704.0670v1
2 J. Phys. Soc. Jpn. Letter Author Name
Fig. 1. Double differential cross section (top panel) and a com-
plete set of polarization transfer observables (bottom three pan-
els) for the 12C(p, n) reaction at Tp = 296 MeV and θlab = 0
The error bars represent statistical uncertainties only.
bins, while the data of Dii(0
◦) have been sorted into
1-MeV bins to reduce statistical fluctuations. A high en-
ergy resolution of 500 keV full width at half maximum
(FWHM) was realized by NPOL3, which enabled us to
observe clearly two SDR peaks at Ex ≃ 4 and 7 MeV.
It should be noted that the DNN(0
◦) value should be
equal to the corresponding DSS(0
◦) value because the
N̂ direction is identical to the Ŝ direction at 0◦. The ex-
perimental DNN (0
◦) and DSS(0
◦) values are consistent
with each other within statistical uncertainties over the
entire range of Ex, demonstrating the reliability of our
measurements.
Figure 2 shows the total spin transfer Σ(0◦) and the
observable f1 defined as
Σ(0◦) =
3− [2DNN(0
◦) +DLL(0
1− 2DNN(0
◦) +DLL(0
2[1 +DLL(0◦)]
as a function of excitation energy Ex. The Σ(0
◦) value is
either 0 or 1 depending on whether ∆S = 0 or ∆S = 1,
which is independent of theoretical models.6 The f1
value is either 0 or 1 depending on the natural-parity
or unnatural-parity transition if a single ∆Jπ transition
is dominant.7 The Σ(0◦) and f1 values of the spin-flip
unnatural-parity 1+ and 2− states at Ex = 0 and 4 MeV,
respectively, are almost unity, which is consistent with
theoretical predictions. The continuum Σ(0◦) values are
almost independent of Ex and take values larger than
0.88 up to Ex = 50 MeV, indicating the predominance
of the spin-flip strength. The solid line in the top panel
of Fig. 2 represents the free NN values of Σ(0◦) for the
Fig. 2. Total spin transfer Σ (top panel) and observable f1 (bot-
tom panel) for the 12C(p, n) reaction at Tp = 296 MeV and
θlab = 0
◦. The error bars represent statistical uncertainties only.
The solid line shows the values of Σ for free NN scattering.
corresponding kinematical condition.13 Enhancement of
Σ(0◦) relative to the free NN values means enhancement
of the ∆S = 1 response relative to the ∆S = 0 response
in nuclei at small momentum transfers, which is consis-
tent with previous studies of (p, p′) scattering.14, 15 The
large values of f1 ≥ 0.72 up to Ex = 50 MeV indicate a
predominance of the unnatural-parity transition strength
in the continuum, consistent with the 90Zr(p, n) result at
295 MeV.7
The top panel of Fig. 3 shows the spin-flip (σΣ) and
non-spin-flip (σ(1−Σ)) cross sections as filled and open
circles, respectively, as functions of Ex. The bottom panel
shows the unnatural-parity dominant (σf1) and natural-
parity dominant (σ(1 − f1)) components of the cross
section as filled and open circles, respectively. The solid
lines are the results of peak fitting of the spectra with
Gaussian peaks and a continuum. The continuum was as-
sumed to be the quasi-free scattering contribution, and
its shape was given by the formula given in Ref. 16.
It should be noted that the spin-flip unnatural-parity
1+ and 2− states at Ex = 0 and 4 MeV, respectively,
form peaks only in the σΣ and σf1 spectra. It is found
that the prominent peak at Ex ≃ 7 MeV is the spin-flip
unnatural-parity component with a Jπ value estimated
to be 2− because the Dii(0
◦) values are consistent with
the theoretical prediction for Jπ = 2−.17 In the σ(1−f1)
spectrum, possible evidence for SD 1− peaks is seen at
Ex ≃ 7, 10, and 14 MeV. The top and bottom panels of
Fig. 4 show theoretical calculations for the unnatural-
parity and natural-parity SD strengths, respectively.5
Experimentally extracted peaks in the σf1 and σ(1−f1)
spectra are also shown. Concentration of the SD 2−
strength at three peaks at Ex ≃ 4, 8, and 13 MeV has
been predicted. Our data agree with this prediction qual-
itatively, but give slightly different excitation energies of
Ex ≃ 4, 7, and 11 MeV. On the other hand, the SD
1− strength has been predicted to be quenched and frag-
mented due to tensor correlations.5 The experimental re-
J. Phys. Soc. Jpn. Letter Author Name 3
Fig. 3. Cross sections separated by Σ (top panel) and f1 (bottom
panel) for the 12C(p, n) reaction at Tp = 296 MeV and θlab = 0
The solid lines show peak fitting of the spectra with Gaussian
peaks and a continuum.
sults are spread over a wide region of Ex ≃ 5–16 MeV
and exhibit similar cross sections, which supports frag-
mentation of the SD 1− strength.
Effective tensor interactions at q ≃ 1–3 fm−1 have
mainly been studied using high spin stretched states.18, 19
The present Dii(0
◦) data can give information on the ex-
change tensor interaction at an extremely large exchange
momentum transfer of Q ≃ 3.6 fm−1. In the Kerman–
McNanus–Thaler (KMT) representation,20 the NN scat-
tering amplitude is represented as
M(q) =A+ 1
(B + E + F )σ1 · σ2 + C(σ1 + σ2) · n̂
(E −B)S12(q̂) +
(F −B)S12(Q̂),
where S12 is the tensor operator, q̂ and Q̂ are direct
and exchange momentum transfers, respectively, and
n̂ = Q̂ × q̂. In a plane-wave impulse approximation
(PWIA), the PT observables for the Gamow–Teller (GT)
transition at 0◦ are simply expressed using parameters
A–F as17
DNN(0
◦) = DSS(0
2B2 + F 2
DLL(0
−2B2 + F 2
2B2 + F 2
If there is no exchange tensor S12(Q̂) interaction (i.e.,
F = B), then Dii(0
◦) = −1/3.
The measured PT observables Dii(0
◦) for the GT
12C(~p, ~n)12N(g.s.;1+) transition are listed in Table I,
where the listed uncertainties are statistical only. The
presentDNN (0
◦) and DSS(0
◦) values are consistent with
each other, as expected, and the present DNN (0
◦) value
agrees with the previously measured DNN (0
◦) value at
the same energy.9 The experimental values deviated from
−1/3, which indicates that there are contributions from
both the exchange tensor interaction at Q ≃ 3.6 fm−1
and nuclear distortion effects.
Fig. 4. SD strengths for unnatural-parity (top panel) and
natural-parity (bottom panel) taken from Ref. 5. The solid lines
represent peaks obtained by fitting σf1 (top panel) and σ(1−f1)
(bottom panel) spectra.
In order to assess these effects quantitatively, we per-
formed microscopic DWIA calculations using the com-
puter code dw81.21 The transition amplitudes were cal-
culated from the Cohen–Kurath wave functions22 assum-
ing Woods–Saxon radial dependence.23 Distorted waves
were generated using the optical model potential (OMP)
for proton elastic scattering data on 12C at 318 MeV.24
We used the effective NN interaction parameterized by
Franey and Love (FL) at 270 or 325 MeV.25
First, we examined the sensitivity of the DWIA results
to the OMPs by using two different parameters.24, 26 The
OMP dependence of Dii(0
◦) was found to be less than
0.01. This insensitivity allows us to useDii(0
◦) as a probe
to study the effective NN interaction. Table I shows the
DWIA results for Dii(0
◦) with the NN interaction at
270 and 325 MeV. It is found that the Dii(0
◦) values,
and DLL(0
◦) in particular, are sensitive to the choice of
the NN interaction. These differences are mainly due to
the exchange tensor interaction S12(Q) at Q ≃ 3.6 fm
The real part of S12(Q) for the FL 325 MeV interaction
is about twice as large as that for the FL 270 MeV in-
teraction at Q ≃ 3.6 fm−1 (see Fig. 3 of Ref. 9). The
experimental Dii(0
◦) values support the DWIA results
with the FL 270 MeV interaction, which indicates that
the exchange tensor part of the FL 270 MeV interaction
has an appropriate strength at Q ≃ 3.6 fm−1. This con-
clusion has already been reported for DNN(0
◦) data,9
however, the present data make the conclusion more rig-
orous because of the high sensitivity of DLL(0
◦) to the
exchange tensor interaction.
In summary, a complete set of PT observables for the
12C(p, n) reaction at Tp = 296 MeV and θlab = 0
◦ has
been measured. The total spin transfer Σ(0◦) and the
observable f1 are deduced in order to study the spin-
parity structure in both the SDR and continuum re-
gions. The Σ(0◦) and f1 values show that the SDR at
4 J. Phys. Soc. Jpn. Letter Author Name
DNN (0
◦) DSS(0
◦) DLL(0
This work −0.216 ± 0.019 −0.210± 0.039 −0.554± 0.023
ref. 9 −0.215 ± 0.019 – –
FL 270 MeV −0.225 −0.225 −0.550
FL 325 MeV −0.191 −0.191 −0.619
Table I. PT observables Dii(0
◦) for the GT 12C(~p, ~n)12N(g.s.;1+) transition at 296 MeV and 0◦ compared with theoretical calculations.
Ex ≃ 7 MeV has greater 2
− strength than 1− strength,
which agrees with the recent theoretical prediction. In
the continuum up to Ex ≃ 50 MeV, a predominance
of the spin-flip and unnatural-parity transition strength
is also found. We have compared the PT observables of
the 12C(p, n)12N(g.s.;1+) reaction with DWIA calcula-
tions employing the FL interaction. The exchange tensor
interaction of the FL 270 MeV interaction is found to
be more appropriate at Q ≃ 3.6 fm−1 than that of the
FL 325 MeV interaction. Thus a complete set of PT ob-
servables provides rigorous information not only on the
spin-parity structure in nuclei but also on the effective
NN interaction.
Acknowledgment
We are grateful to the RCNP cyclotron crew for pro-
viding a good quality beam for our experiments. We also
thank H. Tanabe for his help during the experiments.
This work was supported in part by the Grants-in-Aid
for Scientific Research Nos. 14702005 and 16654064 of
the Ministry of Education, Culture, Sports, Science, and
Technology of Japan.
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