Determination of the Gamow-Teller Quenching
Factor via the90Zrn p Reaction at 293 MeV
K. Yako , H. Sakai , M.B. Greenfield†, K. Hatanaka, M. Hatano ,
J. Kamiya , Y. Kitamura , Y. Maeda , C.L. Morris‡ , H. Okamura§ ,
J. Rapaport¶ , T. Saito , Y. Sakemi , K. Sekiguchi , Y. Shimizu ,
K. Suda††, A. Tamii , N. Uchigashima and T. Wakasa
Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
†
International Christian University, Mitaka, Tokyo 181-8585, Japan
Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
‡
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
§
Department of Physics, Saitama University, Saitama, Saitama 338-8570, Japan
¶
Department of Physics, Ohio University, Athens, Ohio 45701, USA
The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan
††
Department of Physics, Saitama University, Urawa, Saitama 338-8570, Japan
Abstract. The double differential cross sections at 0 Æ –12Æ were measured for the 90 Zrn p reaction at 293 MeV in a wide excitation energy region of 0–70 MeV. The experiment was performed
by using the n p facility at the Research Center for Nuclear Physics. The multipole decomposition (MD) technique was applied to the measured cross sections to extract the GT component in
the continuum. After subtracting the contribution of the isovector spin-monopole excitation we obtained the GT strength of S β 30 03 08 05 up to 31.4 MeV excitation. The quenching
factor Q was deduced by using the present result and the S β value obtained from the MD analysis of the 90 Zr p n spectra. The result is Q 083 006 in regards to Ikeda’s sum rule value of
3N Z 30.
INTRODUCTION
Gamow-Teller (GT) resonances have been extensively studied since its discovery in
1975 [1]. The GT transition involves the operator σ τ and is characterized as spin-flip
(∆S 1), isospin-flip (∆T 1) and no transfer of orbital angular momentum (∆L 0).
There exists a model-independent sum rule, S β Sβ 3N Z , where Sβ and Sβ are the GT strength of β and β types, respectively [2]. Surprisingly, however, only a
half of the GT sum rule value was identified from the p n measurement on targets
throughout the periodic table [3]. This problem, so-called the quenching of the GT
strengths, has been one of the most interesting phenomena in nuclear physics because it
is related to non-nucleonic (∆-isobar) degrees of freedom in nuclei; the quenching factor
sets a strong constraint on the Landau-Migdal parameters, g NN and gN∆ , in the π +ρ +g
model [4].
Recently, Wakasa et al. have measured the angular distribution of the double differential cross sections for the 90 Zr p n reaction at 295 MeV [5]. By performing multipole
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
700
Focal Plane
Detectors
0
1
2 m
Charged
Particle Veto
7Li
MWDC
p
Large
Acceptance
Spectrograph
n
p
(n,p) Clearing
to Beam Target Magnet
Dump
FIGURE 1. A schematic drawing of the RCNP n p facility.
decomposition (MD) analysis, the GT strengths of S β 280 16 has been obtained
in the continuum up to 50 MeV excitation in 90 Nb [5]. Determination of the ∆-isobar
contribution to the GT sum rule, however, requires precise n p cross section data at the
same energy. For this purpose we have constructed an n p facility at Research Center
for Nuclear Physics (RCNP) and measured the double differential cross sections for the
90 Zrn p90 Y reaction at 293 MeV.
EXPERIMENT
Figure 1 shows a schematic layout of the RCNP n p facility in the WS beam course.
A nearly mono-energetic neutron beam was produced by the 7 Li p n reaction at 295
MeV. The primary proton beam, after going through the 7 Li target, was bent away by 23Æ
by the clearing magnet [6] to a beam dump in the floor. The typical intensity of the beam
was 450 nA and the thickness of the 7 Li target was 320 mg/cm2. About 2 106 sec
neutrons bombarded the target area of 30W 20H mm2 downstream by 95 cm from the
7 Li target. Three 90 Zr targets with thicknesses of 200–400 mgcm 2 and a polyethylene
(CH2 ) target with a thickness of 46 mgcm 2 were mounted in a multiwire drift chamber
(target MWDC). Wire planes placed between the targets detected outgoing protons and
enabled one to determine the target in which a reaction occurred. Charged particles
coming from the beam line were rejected by the veto scintillator with a thickness
of 1 mm. The 1 Hn p events from the CH2 target were used for normalization of
the neutron beam flux. The position of outgoing protons were detected by six wire
planes installed just behind the targets in the target MWDC. Another MWDC, front end
MWDC, was installed at the entrance of the Large Acceptance Spectrometer (LAS). The
scattering angle of the n p reaction was determined by the information from the two
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90Zr(n,p )90Y
at 293 MeV
FIGURE 2. The result of MD analysis on the double differential cross sections for the 90 Zrn p90 Y
reaction at 293 MeV. The upper and lower panels show the results at angular region close to the maximum
of GT and dipole angular distributions.
MWDCs. The outgoing protons were momentum analyzed by LAS and were detected by
the focal plane detectors. Blank target data were also taken for background subtraction.
The 1 Hn p cross sections given by the program SAID [7] was used to normalize the
90 Zrn p cross sections.
We have obtained the differential cross sections up to 70 MeV excitation energy over
an angular range of 0Æ –12Æ with a statistical accuracy of 1.7%/2 MeV1Æ at 1Æ –2Æ . The
overall energy resolution expected from the target thicknesses and the energy spread of
the beam is 1.5 MeV. The angular resolution is 10 mr which is dominated by the the
effect of multi scattering in the 90 Zr targets.
ANALYSIS
The MD analysis has been performed on the excitation energy spectra to extract the GT
strengths.
First of all, the cross section data was binned in 2-MeV energy intervals to reduce
the statistical fluctuation. For each excitation energy bin from 0 MeV to 70 MeV, the
experimentally obtained angular distribution σ exp θcm Ex has been fitted by means
of the least-squares method with the linear combination of calculated distributions
σ calc θlab Ex defined by
σ calc θcm Ex calc
π θcm Ex ∑ a∆Jπ σ ph;∆J
∆J π
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(1)
where the variables a∆J π are the fitting coefficients with positive values.
The angular distributions for various J π states have been obtained by DWIA calculations by using the computer code DW81 [8]. To calculate the distortions in the incident and the outgoing channels, the energy-dependent global optical model potentials
(OMPs) were used. The OMP for incident neutrons towards 90 Zr is taken from Ref. [9].
The OMP for outgoing protons is taken from Ref. [10] and varied as a function of the
kinetic energy of the outgoing protons. The effective NN interaction is taken from the tmatrix parameterization of the free NN interaction by Franey and Love at 325 MeV [11].
Two kinds of the radial wave functions have been tried. One is the harmonic oscillator
(HO) shape with a range parameter of b 212 fm [12], and the other is the radial wave
functions generated from a Woods-Saxon (WS) potential.
The one-body transition densities (OBTDs) are calculated from pure 1p1h configurations. The angular distributions for the following final J π states have been calculated: 1 ∆L 0, 0 1 2 ∆L 1, 3 ∆L 2, and 4 ∆L 3. According to the
independent-particle model, where the protons fill up to the 2p orbital and the neutrons
to 1g92 orbital, the ∆L 0 transitions with 0h̄ω are completely blocked. Thus, in order
1
to take into account the GT strength due to ground state correlation, the ν 1g 72 π 1g
92
1 configurations are activated for the ∆L 0 states. For the transition
and ν 1g92 π 1g
92
with ∆L 1, the active neutron particles are restricted to the 1g 72 , 2d52 , 2d32 , 1h112 ,
or 3s12 shells, which covers from N 51 to N 82 while the active proton holes are
restricted to the 1g92 , 2p12 , 2p32 , 1 f52 , or 1 f72 shells, which covers from Z 21 to
Z 40 assuming 40 Ca to be a core. All the 0 h̄ω and 1 h̄ω excitations are included in this
choice of configuration.
The minimizing procedure was performed for all the possible 58080 combinations.
The combination of the ph configurations at each energy window was chosen so that the
χ 2 value was minimized.
Figure 2 shows the result of the MD analysis. The ∆L 0 component has a broad
( 10 MeV in FWHM) bump at Ex 20 MeV mainly due to the isovector spin monopole
(IVSM) resonance [13], which is excited through the r 2 σ τ operator. The ∆L 0 component of the cross section, σ∆L0 q ω , is related to the GT strengths through the proportionality relation, i.e. σ∆L0 q ω σ̂GT F q ω BGT, where σ̂GT is the GT unit
cross section [5] and F q ω is the kinematical correction factor [14]. The upper limit
energy of integration, Exmax , is determined so that it corresponds to E xmax 50 MeV in
the p n work [5]. Considering the difference in the Coulomb energy between the 90 Y
and the 90 Nb nuclei and the difference in the reaction Q value, we use the Exmax value
of 31.4 MeV and have obtained a total GT strength of S β 54 03 09, where the
errors are uncertainties of the MD analysis and the GT unit cross section.
The contribution of IVSM is estimated by the DWIA calculations in which all the
IVSM strengths are assumed to lie below 31 MeV excitation [5] . After subtracting
the IVSM contribution of 24 08 GT units, we have obtained a total GT strength of
Sβ 30 03MD 08IVSM 05σ̂GT up to 31.4 MeV excitation.
By using the Sβ value by Wakasa et al.[5] the quenching factor Q, which is defined
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by Q Sβ Sβ , has been deduced to be Q 083 006 in regard to Ikeda’s sum
3N Z rule value of 3N Z 30. Therefore the quenching of the GT strength due to the
∆N1 admixture into the 1p1h GT state is significantly smaller than the quenching of
50%, observed in the previous studies [3] where the GT strengths in the continuum
are not taken into account. Then the Landau-Migdal parameters, g N∆ and gNN , have
been determined from the quenching factor. The deduction by Suzuki and Sakai [4] in
Chew-Low model leads to gNN 06 and 016 gN∆ 035 for g∆∆ 06. Therefore
the universality ansatz of the Landau-Migdal parameters, i.e. g NN gN∆ g∆∆ 06 08, does not hold.
ACKNOWLEDGMENTS
The authors acknowledge H.P. Yoshida for the support on the trigger system. This project
is supported by the Ministry of Education, Science, Sports and Culture of Japan with
the Grant-in-Aid for Scientific Research No. 10304018 and the Japan Society for the
Promotion of Science.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Doering, R., Galonsky, A., Patterson, D., and Bertsch, G., Phys. Rev. Lett., 35, 1691 (1975).
Ikeda, K., Fujii, S., and Fujita, J. I., Phys. Rev. Lett., 3, 271 (1963).
Gaarde, C. et al., Nucl. Phys., A369, 258 (1981).
Suzuki, T., and Sakai, H., Phys. Lett., B455, 25 (1999).
Wakasa, T. et al., Phys. Rev. C, 55, 2909 (1997).
Kamiya, J. et al., RCNP annual report 1998, p. 113.
Arndt, R.A. and Roper, L.D., Scattering Analysis Interactive Dial-in (SAID) program, phase shift
solution SP02, Virginia Polytechnic Institute and State University, unpublished.
Schaeffer, M. A., and Raynal, J., Program DW81, unpublished.
Quing-biao, S., Da-chun, F., and Yi-zhong, Z., Phys. Rev. C, 43, 2773 (1991).
Cooper, E. D., Hama, S., Clark, B. C., and Mercer, R. L., Phys. Rev. C, 47, 297 (1993).
Franey, M. A., and Love, W. G., Phys. Rev. C, 31, 488 (1985).
Love, W. G., and Franey, M. A., Phys. Rev. C, 24, 1073 (1981).
Raywood, K. J. et al., Phys. Rev. C, 41, 2836 (1990).
Taddeucci, T. N. et al., Nucl. Phys., A469, 125 (1987).
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