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ELSEYIER Nuclear Physics A734 (2004) 461464
Tri-nucleon cluster-states in 6Li
S. Nakayamaa *t, T. Yamagatab, H. Akimuneb, M. F’ujiwaracgd, K. Fushimi”, M.B. Greenfielde, K. Harac, K.Y. Harab, H. Hashimotoc, K. Ichiharaa, K. Kawasec, Y. Matsma, K. Nakanishi”, M. Sakamaf, M. Tanakas and M. Yosoih
&Department of Physics, University of Tokushima, Tokushima 770-8502, Japan
bDepartment of Physics, Konan University, Kobe 658-8501, Japan
‘Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan
dAdvanced Science Research Center, JAERI, Ibaragi 319-1195, Japan
eDepartment of Physics, International Christian University, Tokyo 113-0033, Japan
fSchool of Health Sciences, University of Tokushima, Tokushima 770-8509, Japan
sKobe Tokiwa College, Kobe 654-0838, Japan
hDepartment of Physics, Kyoto University, Kyoto 606-8502, Japan
Abstract Tri-nucleon cluster-structures in 6Li were investigated by using the 7Li(3He,a) reaction at 450 MeV and at &JL = 0”. A binary decay into tf3He from a broad peak at E, = 21 MeV was observed. The resonance at E,=21 MeV in 6Li was decomposed into two tri- nucleon cluster-states (t+3He); the ‘P-state at Ez=18.0f0.5 MeV with a width (FWHM) of 5.0f0.5 MeV and the 3P-state at E,=22fl MeV with a width of 8fl MeV.
Clustering is interesting phenomena in nuclear excitation as well as nuclear structure [l]. In the A=6 isobar system, existence of a tri-nucleon cluster-structure was suggested ex- perimentally [2-5] as well as theoretically [6,7]. The tri-nucleon system behaves as t or 3He particles. Therefore, such a structure is described as a two-fermion system and is analo- gous to the system consisted of two nucleons which are described as a tri-quark system. The t+3He cluster model in ‘jLi predicted P- and F-unbound states as well as S- and D- bound states with respect to the t+3He system . So far, nature of deuteron-like t+3He cluster configuration for the ground state of 6Li was reported by the 6Li(y,t) reaction .
*Electronic address: nakayamaOias.tokushima-u,ac.jp ‘This experiment was performed at the Research Center for Nuclear Physics (RCNP) under Program Nos. El84 and E172. The authors are grateful to the RCNP Ring cyclotron staff for their support. This work was supported in part by the Grant-in-Aid (No. 13640304) by the Japan Ministry of Education, Culture, Sports, Science, and Technology, and by the Japan Society for Promotion of Science (JSPS).
0375-94741s - see front matter 0 2004 Published by Elsevier B.V! doi:10.l016/j.nuclphysa.2004.01.086
462 S. Nahzyama et al./Nuclear Physics A734 (2004) 461-464
On the other side, there are also some data for unbound states. It is difficult to discuss their details because unbound states are expected to exist in a high excitation energy region above the threshold energies for various particle-decays. Data for unbound ‘P, 3P, ‘F and 3F states were obtained by the 3He+t elastic scattering  and the 3He(t,y) reac- tion . Here, the symbol denotes zs+lL. Theoretical predictions [6,7] were performed by using the resonating group method (RGM) calculations for negative-parity states in 6Li. However, there is still a serious contradiction among both theoretical and experimental results . So, unbound tri-nucleon structures in 6Li seem to be not yet confirmed.
Recently, Akimune et al. identified the di-triton molecular resonance at E,=18.0 MeV in 6He by measuring decay-tritons from states excited via the 6Li(7Li,7Be) reaction at 65A MeV . A comparison of the data with the RGM calculations for ‘jHe  suggests that the observed resonance is the 3P (t+t) cluster-state whose analog cluster-state (t+3He), based upon the isospin symmetry, should exist around E, = 21.6 MeV in 6Li. In the present work, the tri-nucleon cluster-states in 6Li were investigated via the 7Li(3He,a) reaction at 450 MeV by measuring triton and 3He decay-particles in coincidence with o-particles. The relevant cluster-structures in 6Li may be populated via the neutron pick-up reaction on a-cluster in 7Li [l]. The 7Li(3He,a) reaction is accessible to both isoscalar (T=O; ‘P and ‘F) and isovector (T=l; 3P and 3F) states in 6Li. Furthermore the injectile and ejectile have low spins of l/2 and 0, respectively, and spin populations of excited states are expected to be aligned by the reaction. Measurements of the angular correlations of decay-particles hopefully provide determination of angular momenta of populated states.
A 450-MeV 3He2+ beam was provided from the Ring Cyclotron of the Research Center for Nuclear Physics, Osaka University. The target used was a self-supporting foil of a separated 7Li isotope (99.9 %) with a thickness of 0.5 mg/cm2. The target was tilted by 45” with respect to the beam direction in order to reduce the energy loss of the decay- particle in the target. The o-particles were measured at 0~ = 0” by using the magnetic spectrometer “Grand RAIDEN” [lo]. After passing through the target, the 3He beam was stopped by a Faraday cup inside the Dl magnet of the spectrometer. Charged decay- particles were detected by using an array of 8 Si-detectors whose thicknesses were 500 pm. The Si-detectors were located from 0~ = 90” to 0~ = 160” at 10” intervals and apart by about 30 cm from the target. The threshold energy due to the noise discrimination level of the Si-detectors was about 0.1 MeV. A time of flight (TOF) method was utilized for an identification of decay-particles. Decay-particles, p, d, t/3He and q were well separated in a two-dimensional scatter plot for the TOF and an energy-output of decay-particle in the Si-detector. The triton and 3He were selected by gating on the t/3He particle-locus.
The thin solid curve in figure 1 shows the singles spectrum for the 7Li(3He,a)6Li reaction at 450 MeV and at 0~ = 0”. The well-known states of 6Li are prominently excited in a low excitation energy region. The low-lying states in ‘Li are known as cluster-states of d+a . In a high excitation energy region, on the other side, a broad bump was observed at E,=21 MeV. The existence of tri-nucleon cluster-states in this excitation region has been discussed [3-71. Around the peak at E,=21 MeV, a clear locus was observed along the threshold line for the binary decay into triton and 3He in a two-dimensional scatter- plot for an excitation energy in 6Li and an energy of t/3He decay-particles. The locus was recognizable in all the Si-detectors. The angular correlations obtained were fitted by using the Legendre polynomial functions. A reasonable fitting was obtained with
S. Nakayama et al./Nuclear Physics A734 (2004) 461-464 463
EXCITATION ENERGY WI
Figure 1. Singles (thin curve) and coincidence (closed circles) spectra for the 7Li(3He,a)6Li reaction at 450 MeV and at 0~ = 0”. Error bars reflect only statistical errors. A solid curve denotes the peak shapes calculated with the Breit-Wigner formula for two resonances at E,=18.0&0.5 MeV (dashed curve) and 22fl MeV (dot-dashed curve), respectively.
N(1.0 + 2.0[P&,J]2}, h w ere N is a normalization factor. This fact indicates that the (t+3He) cluster-state at E,=21 MeV is mainly a P state. A constant term may be caused by an incomplete spin alignment or by small admixtures of some L-values other than 1.
The coincidence spectrum in the ‘Li(3He,a)6Li reaction was obtained by gating on the binary t+3He decay-events. A random coincidence yield was subtracted. The coincidence yield was corrected by taking into account the solid angles of the Si-detectors and the multiplicity 2 for triton and 3He emissions. Here, the intensity of decay-particles was assumed to depend only on the polar angle 6,, in the spherical polar coordinates and to have the same angular correlations of decay-particles as those observed for the broad peak at E,=21 MeV. The coincidence spectrum thus obtained is shown by the closed circles in figure 1. A broad peak was observed at E,=21 MeV. The structure corresponds well to that observed in the singles spectrum. The width (FWHM) of this broad peak was estimated to be 12 f 2 MeV.
Akimune et al. observed a di-triton molecular resonance at E,=18.010.5 MeV with a width (FWHM) of 7.7fl.O MeV in 6He . They suggested that the observed resonance is the 3P-state by comparing their data with the RGM calculation for 6He . Based on the isospin symmetry, the analogue of the 3P-resonance is expected to be excited around E,=21.6 MeV in “Li. The width, 12 MeV, of the 21-MeV state presently observed is somewhat broader than the width of the resonance observed in 6He. Further, in the tri- nucleon LS-coupling cluster model [6,7], the ‘P-state was additionally expected only for 6Li. Therefore, the broad peak observed at E,=21 MeV seems to consist of two resonances with lP and 3P.
In order to deduce the resonance parameters, the coincidence spectral shape of the broad peak at E,=21 MeV was fitted by using the BreitWigner formula [ll] with L=l in
464 S. Nukuyamu et al. /Nuclear Physics A734 (2004) 461-464
the same way as Ref. . We investigated the structure of the 21-MeV peak by assuming that the peak was composed of two resonances. The main decay of the 21-MeV resonance is expected to proceed via neutron, proton, deuteron, t/3He, and cr emissions. The total width was defined as F = F3 + l?, where F3 and I” are a partial width for t/3He emissions and the sum of partial widths for all the other particle-emissions, respectively. Since the threshold energies for neutron, proton, deuteron, and a emissions are very low relative to the threshold energy (E,h=15.8 MeV) for t+3He decay in 6Li and is much lower than the peak position of E,= 21 MeV, the width I” was assumed for simplicity to be constant in the fitting procedure and a dimensionless reduced width 8’ to be 1.0 for the resonances, as discussed in Ref. .
The result of the peak fitting is shown by the solid curve in figure 1. Through the fitting procedure, we deduced the partial width I” to be 3 MeV. Here, the I” deduced for the di- triton resonance in 6He was equal to 3 MeV . It is remarkable that the branching ratio for tf3He binary decay, Fs/I’, averaged over the excitation energy region up to 40 MeV amounts to 70%. The branching ratio for the binary decay into t+3He is consistent with that obtained from the coincidence yield shown in figure 1. Two resonances were deduced at E,=18.010.5 MeV with a width of 5.0f0.5 MeV and at 22fl MeV with a width of 8fl MeV as shown by the dashed and dot-dashed curves in figure 1, respectively. The spectral shape is well reproduced in the E,=15-25 MeV range. In the higher excitation region of E,=25-35 MeV, the fit to the data is relatively poor. This might mean excitation of other resonances wit.h L > 1. But it is difficult to conclude definitely because of the large statistical errors.
The location and width of the 22-MeV resonance correspond well to those of the ana- logue of the 18-MeV resonance in 6He . Therefore, it is reasonable to assign the res- onances deduced at E,=18 and 22 MeV as the 'P- and 3P-state, respectively. Two resonances presently deduced are separated by about 4 MeV. It is noted that in the tri- nucleon cluster model [6,7] for 6Li, two states with L=l were predicted as a doublet of 'P- and 3P-states which are at most separated by about 1 MeV.
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