Model Independent Spin Parity Determination
by the d 2 He Reaction
and Possible Evidence for a 0 State in 12 B
H. Okamura , T. Uesaka†, K. Suda , H. Kumasaka , R. Suzuki ,
A. Tamii , N. Sakamoto‡ and H. Sakai ‡
Department of Physics, Saitama University, 255 Shimo-Ohkubo, Saitama 338-8570, Japan
Center for Nuclear Study, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
‡
The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan
†
Abstract. A method of model-independent spin-parity determination is proposed for the d 2 He
reaction by using the tensor analyzing power A zz at θ 0Æ , which shows extreme values for 0 and
natural-parity states solely by parity-conservation. It is applied to the 12 Cd 2 He12 B reaction at
Ed 270 MeV and a possible indication of 0 state is found at Ex 93 MeV in 12 B. The bump at
Ex 75 MeV appears to have more 2 strength than 1 strength, consistent with our earlier work.
INTRODUCTION
In spite of extensive studies particularly by using charge-exchange reactions, the understanding of spin-flip dipole states is still rather limited. The d 2 He reaction can be a
powerful tool for pursuing this subject further. Here the two-proton system in the 1 S0
state is denoted by 2 He, though it is unbound. Besides its unique feature as an n ptype reaction with exclusive excitation of spin-flip states, the tensor analyzing powers of
the d 2 He reaction, Axx and Ayy , show characteristic behavior depending on the spinparity of the final states. Their usefulness for identifying the spin-parity, particularly 2 ,
1 , and 0 in spin-dipoles, was first demonstrated at E d 270 MeV on the 12 C target
in our previous work [1]. There, the bump at E x 75 MeV in residual 12 B, which had
been believed to be dominated by 1 states, was unexpectedly found to have larger contributions from 2 states. This finding is supported by the heavy-ion charge-exchange
reaction [2] and also theoretically by calculations including the tensor correlation [3] and
the deformation effect [4], where the quenching of 1 states at low excitation energies
due to fragmentation is reported. It must be said, however, that the above conclusion is
not widely accepted. The aim of this work is to present a method for model-independent
spin-parity determination of states excited by the d 2He reaction and to report the
results of its application to the 12 C target.
For reactions having a spin-parity structure of 1 0 0 I π , such as d α and
d 2 He reactions on even-even targets, the tensor analyzing power Azz shows extreme
values at θ 0Æ and 180Æ for some I π residual states solely by the requirement of parity-
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
671
conservation:
Æ
Azz 0 180
Æ
2
1
if I π
0 if π
I (1)
These relations allow one to determine spin-parity states unambiguously. While the
d α cross section rapidly decreases with increasing incident energy, due to momentum
mismatch, the importance of the d 2 He reaction increases at several hundred MeV because of the relative enhancement of the spin-dependent part of the two-body interaction
and of the simple reaction mechanism. Furthermore the spin-dipole states, 2 , 1 , and
0 , are fairly strongly excited even at 0Æ , and two out of three are identified by Eq. (1)
without ambiguity. It is a matter of interest to know the distribution of 0 states, which
is expected to reflect pion correlations in nuclei.
EXPERIMENT
The experiment was performed at RIKEN Accelerator Research Facility. The deuteron
beam produced by the polarized ion source [5] was accelerated up to 270 MeV by the
AVF and ring cyclotrons, to bombard the target. Two states of tensor polarization having
theoretical maxima of pZZ 2 and 1 were used, as well as the unpolarized state
(pZZ 0), changed every 5 s to minimize systematic uncertainties. Here the rotation
symmetry axis at the ion source defines the polarization axis Z, as distinct from the beam
axis z. The beam polarization was monitored continuously throughout the experiment
at the beam transport line using d p elastic scattering [6, 7]. The averaged value of
each state was pZZ 116 and 079 . The best way to measure Azz is to align the
polarization axis parallel to the beam. The cross section is then related to A zz simply
by d σ dΩ d σ dΩ01 12 pZZ Azz where d σ dΩ0 is the cross section for the
unpolarized beam. However, this technique, which is common at Tandem accelerators,
is rarely used at higher energies, because of difficulties in rotating the spin direction due
to the small anomalous gyromagnetic ratio of the deuteron. In this respect RIKEN is a
unique facility, that allows one to freely control the direction of the polarization axis [8].
The polarization axis is readily rotated by using the Wien filter downstream of the ion
source at energies as low as 14 keV. Although the spin precesses during acceleration
by the cyclotrons, the magnitude of polarization is not reduced, owing to the single-turn
extraction available at RIKEN. The direction of the polarization axis after acceleration
is determined by the beam-line polarimeter. The field strength and the rotation angle of
the Wien filter were tuned so that Z z.
2 He was measured by the coincidence detection of two protons in close geometries.
Protons emitted from the target were momentum-analyzed by the magnetic spectrometer SMART [9] and detected at the first focal-plane by using a pair of multi-wire drift
chambers and a plastic scintillator hodoscope. Data acquisition was triggered by requiring the multiplicity of the hodoscope to be greater than or equal to two. Details of the
detector system and the analysis procedure can be found in [10]. The whole system was
the same as the one used in the previous publication [1] except for the data acquisition
system, which has been upgraded to increase speed by a factor of 10 [11]. After correction for the detection efficiency of two protons based on the Monte-Carlo simulation,
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FIGURE 1. Double differential cross sections at θ c.m. 067Æ (averaged over 0 Æ –1Æ ) plotted as a
function of 12 B excitation energy (a), a result of peak-fitting for the spectrum with p ZZ 116 (b), and
the corresponding A zz spectra (c). Azz for each peak obtained by the fitting is shown by the closed circle,
while Azz for the continuum binned in 1 MeV shown by open circles.
the d 2 He cross section is obtained by integrating the d pp triple-differential cross
section over two-proton relative energies. The integration limit was set to be less than 1
MeV to minimize contributions from p-p partial waves higher than 1 S0 [1, 10].
RESULTS AND DISCUSSION
The cross sections at θc.m. 067Æ with pZZ 116 and 079 are presented in Fig.
1(a). Concerning the 1 ground state and the bump at Ex 75 MeV, as well as the
continuum at Ex 12 MeV, only a small difference is observed between the spectra. The
large difference at Ex 93 MeV is striking; a clear peak appears in the pZZ 116
spectrum but vanishes for pZZ 079, indicating quite a large negative value for A zz .
The contribution from continuum background, however, makes A zz less prominent
if it is directly derived from the raw spectra [open circles in Fig. 1(c)]. The dominant
contribution of the continuum can be ascribed to quasifree scattering. Following the
commonly employed procedure, as in ref. [12] for example, the spectra are fitted by
using the least-squares method. Figure 1(b) shows the result of such fitting for the
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FIGURE 2. Angular distributions of A zz for the ground (closed square), E x 75 MeV (open circle), and
Ex 93 MeV (closed circle) states. Results of calculation [13] for Gamow-Teller (1 1 ) and spin-dipole
(0
2 , 11 , and 2 2 ) states are also shown by solid curves.
pZZ 116 spectrum. Azz for each state thus deduced from the peak-fitting is presented
by the closed circle in Fig. 1(c). Obviously A zz at Ex 4 MeV is subject to ambiguities
in estimation of the continuum. For various sets of fitting parameters, however, A zz at
Ex 93 MeV takes large negative values stably less than or equal to 1, suggesting
large contributions from 0 states.
One must remember that Eq. (1) holds only at exact θ 0 Æ . Indeed very steep angular
distributions of Azz are predicted generally by calculations, without strong dependence
on the parameters employed, but depending only on spin-parity. Figure 2 shows the
angular distributions for the bumps at E x 93 and 75 MeV and for the 1 ground state
together with the results of calculations for Gamow-Teller and spin-dipole states using
the adiabatic coupled-channels Born approximation [13]. At this very forward angle,
transitions with higher orbital angular-momentum transfers are unlikely to be observed.
Since there is no other state predicted to have a negative Azz , and also from the steep
angular dependence of the experimental data, it is natural to conclude that the bump
at 93 MeV is dominated by 0 states. The target form factors have been obtained by
using the effective interactions by Millener and Kurath [14] (other parameters employed
in the calculation can be found in ref. [13]) but Azz does not reflect details of the
wave functions. Calculations using the interactions by Warburton and Brown [15], for
example, give similar results. It is worth noting that both shell-model calculations predict
the existence of a 0 state at Ex 9 MeV and support the above conclusion.
Concerning the 1
1 ground state, the monotonous distribution with a small magnitude
of Azz is reasonably well described by the calculation. The prediction for 2 2 state is
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very similar to that for the 1
1 state. Likewise the bump at 75 MeV shows a distribution
similar to that for the ground state, substantially deviating from the expected behavior for
1 states. Although the prediction for 2 is model-dependent, it appears that the bump
at 75 MeV is dominated not by 1 , but most likely by 2 . Ambiguities in estimation of
the continuum background do not seriously influence the discussion because A zz of the
continuum has a similar value to that of the bump at 75 MeV.
SUMMARY AND CONCLUSIONS
The 12 Cd 2He12 B reaction has been measured at 270 MeV as an application of the
method proposed for model-independent spin-parity determination, which uses the tensor analyzing power Azz at θ 0Æ and the relations required by parity-conservation,
Eq. (1). Owing to an enhanced sensitivity to A zz achieved by aligning the polarization
axis parallel to the beam, a possible indication of a 0 state has been found at Ex 93
MeV in 12 B for the first time. The bump at Ex 75 MeV appears to have more 2
strength than 1 strength at θ 0Æ , supporting our results in a previous study [1]. These
findings, and further studies applying this novel method to other nuclei, will provide
valuable information in studies of nuclear structure, e.g., tensor correlations in nuclear
spin-excitation modes.
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