Absolute partial decay branching-ratios in 16O

The a-transfer reaction 126C(63Li, d)168O* has been performed at a 6Li bombarding energy of 42 MeV to populate excited states in 13C and 16O. Absolute branching ratios have been unambiguously determined for states in the excitation energy range 13.85 to 15.87 MeV and reduced widths are extracted.


Introduction
Clustering is a well-established phenomenon in certain light nuclei [1], the most ubiquitous form of which is based on systems with at least one α-particle sub-unit. Precise measurements can be made to elucidate the underlying structure. One of the most useful properties in this regard is the reduced width for a particular state and decay branch. This enables the characterisation of the partial decay widths with the effect of barrier penetrabilities removed, allowing the degree of clustering to be quantified. In order to extract reduced widths a precise determination of the total width and the decay branching ratios is needed. This paper reports such measurements for excited states in 16 O.

Experimental Method
Beams of 42 MeV 6 Li 3 + ions were provided by the 14 MV tandem accelerator of the Maier Leibnitz Laboratory of the Technical and Ludwig-Maximillian Universities, Munich. A selfsupporting target of nat. C (100 µg/cm 2 ) was bombarded at the centre of the target chamber and the deuteron ejectiles analysed by the Q3D high-resolution spectrograph [3] yielding focalplane position (recoil excitation energy), energy-loss and energy [4,5]. The operation of the spectrograph is such that ejectiles of a particular energy are focused to the same point on the focal plane, independent of angle. The recoils or the recoil break-up products were detected in a 2×2 array of 50×50 mm 2 double-sided silicon-strip detectors covering a large angular range: 8.4 • to 84.5 • and −35.4 • to +36.4 • in the horizontal and vertical planes respectively. The master trigger condition required one good event at the Q3D focal plane after which a 5 µs time window was opened for reading all ADC events.
where E d is the deuteron (ejectile) kinetic energy. The data recorded in the current work were dominated by multiplicity 1 events in the silicon array, corresponding to detection of only one of the two break-up particles. The assumption is made that particle 1 is detected and its energy is corrected for losses in the target (E 1corr. ). Via conservation of momentum the total momentum of the undetected particle 2 is Substituting into Eqn. 1 gives Plotting the square of the 'missing' momentum p 2 (tot) 2 /2 on the abscissa and the 'missing' energy ) on the ordinate yields the mass, m 2 , of the undetected particle as the inverse gradient of the loci, and the intercept on the ordinate is minus the three-body Qvalue. All that is required is an assumption of the mass of particle 1 to calculate its initial momentum (p 1 (tot) = √ 2E 1corr. m 1 ). In the current analysis, for each pair of break-up particles, Catania plots were constructed assuming that the heavier particle was detected as particle 1. Figure 3a shows the Catania plot assuming the 16 O → p+ 15 N break-up channel. In the adjacent panel (Fig. 3b) Monte-Carlo simulations [7,8] have been performed including the proton, α+ 12 C(g.s.) and α+ 12 C(2 + 1 ) break-up channels. Five loci can be clearly seen, four corresponding to the detection of the α and carbon nuclei for each channel respectively, and one representing detection of 15 N nuclei. The final locus would correspond to detection of the proton, which has a large spatial distribution and, therefore, is only very weakly present in Fig. 3. The particle identification is confirmed with a line of gradient 1 (=1/m p ) and intercept 6.439 MeV (=−Q 3 ) on Fig. 3b.
The Monte-Carlo simulations have been used to extract the geometrical efficiency for each gate/break-up channel. For the proton channel, ϵ N (g.s.) =0.41±0.01 and for the α channels ϵ C(g.s.) =0.40±0.01 and ϵ C(2 + 1 ) =0.37±0.01. Finally, the efficiency-corrected ratio of [counts detected at the focal plane in coincidence with a particle event in the silicon array] to [all events at the focal plane] yields the decay branching ratios,  . ( The results obtained from this analysis are summarised in Table 1. Due to the conservation of angular momentum, I( 16 O * ) − l α = I( 12 C * ), only natural parity states can undergo α-decay to the 12 C ground state. The 14.6 MeV I π = 5 − level is the only state in this region to decay exclusively to the 12 C ground state. The only significant proton decay branch is observed for the 14.911 MeV level with a branching ratio obtained in the current work of Γ p0 /Γ tot. =0.22±0.12. This is in agreement with the published value of Γ p0 /Γ tot. =0.36±0.06 [9].

Discussion
In the preceding section precise measurements have been reported for all of the absolute partial decay branching ratios on a state-by-state basis. These can be used together with the total widths to extract the reduced widths, γ 2 i , with the effect of the Coulomb barrier (i.e. the barrier penetrabilities, P i ) removed; Expressing the penetrabilities in terms of the Coulomb wavefunctions, for the i th decay channel, with wavenumber, k i , and radius, r i = 1.4(A 1/3 2 ) fm, dependent on the masses, 1 and 2, of the break-up fragments leads to a The experimental resolution of 60(4) keV has been removed from the widths measured in the current work. b The quantity . c Calculated using excitation energies and Γ tot. measured in the current work; columns 1 and 2 respectively. See text for details.
Note that the orbital angular momentum carried by the decay particle is denoted by l. Taking the ratio of the reduced width to to the Wigner limit [10,11] yields [12], where µ i is the reduced mass of the break-up particles. These reduced widths, θ 2 i , are tabulated (see Table 1) for each state and decay channel observed in the current work.
Examining the final column of Table 1 the majority of states exhibit relatively low reduced widths. The two exceptions are the 14.6 and 14.8 MeV level for the α0 and α1 channels respectively. The 14.6 MeV state is a strong candidate for the I π = 5 − member of the cluster band build on the 9.585 MeV 1 − bandhead. The current result demonstrates a significant degree of α clustering (33%) which is backed up by its exclusive decay to the 12 C ground stateimplying a large radius compared to other states in this excitation energy range. The increased radius for the resonance makes it easier for the α particle to accommodate the orbital angular momentum. The large total width is also consistent with that of other members of the cluster band in 16 O [6].
For the 14.8 MeV level, the situation is less clear. With almost equal decay branches to both the ground state and first excited state of 12 C, it is only the latter that shows a large α-reduced width (42%), suggesting a configuration with smaller radius than the above mentioned 14.6