Possible evidence of tensor interactions in 16O observed via (p,d) reaction

We have measured 16O(p,d) reaction using 198-, 295- and 392-MeV proton beams to search for a direct evidence on the effect of the tensor interactions in light nucleus. Differential cross sections of the one-neutron transfer reactions populating the ground states and several low-lying excited states in 15O were measured. Comparing the ratios of the cross sections for each excited state to the one for the ground state over a wide range of momentum transfer, we found a marked enhancement for the positive-parity state(s). The observation indicates large components of high-momentum neutrons in the initial ground-state configurations, due possibly to the tensor interactions.

Tensor interactions are some of the most important nuclear interactions acting between two nucleons. The tensor interactions, originate mainly from the pion-exchange interactions, provide the most significant attraction in nuclear interactions. The necessity to include tensor interactions in theoretical calculations to reproduce the quadrupole moment [1] as well as the binding energy [2] of the deuteron, which is the simplest and only stable two-nucleon composite system, affords decisive evidences on the importance of the tensor interactions.
The tensor interactions provide 70 ∼ 80% of the attractive interactions [3,4] in deuteron and induce nucleons with high momenta [4] through the D-wave component.
Besides the deuteron, earlier theoretical studies [5] had also pointed out the importance of the tensor interactions to the binding of three-and four-nucleon systems, accounting for almost 50% of the nuclear attraction. Several experiments using polarized deuteron beams had since been performed to measure the tensor analyzing powers for stripping reactions [6] and deuteron capture reaction [7], providing evidences on the existence of the D-state components in the 3 H and 3,4 He.
For heavier nuclei, recent ab-initio calculations [8] on light nuclei also show essential importance of the tensor interactions for binding nuclei up to mass number A = 12. The pion exchange interactions, in which the tensor interactions are the dominant components, constitute 70-80% of the whole two-body potentials. In addition, detailed studies on experimental data [9] and the subsequent theoretical studies [10] have indicated a possible important role of the tensor interactions in changing the magic numbers and the orders of single-particle orbitals in neutron-rich nuclei, although the strength of the tensor interactions in the shellmodel space is not large, and is treated only as a perturbation. More recently, theoretical calculations on 9−11 Li that include explicitly the tensor interactions have pointed out [11] the importance of the tensor interactions in understanding the structure of those nuclei, and predicted high momentum components in the ground states. The results offered a possible intriguing explanation to the development of the neutron-halo structure through the Pauli blocking effect in 11 Li.
Experiments using the electron [12,13] or proton-induced [14] knockout reaction had been performed to probe the tensor correlations in nuclei from 12 C to 208 Pb. However, since it is difficult to isolate the tensor effects unambiguously in these experiments due to the presence of other correlations such as the short-range repulsion, alternative methods that could provide more direct experimental evidences are called for.
In this paper, we report a possible direct observation of the tensor-force effect in the "doubly-closed-shell" 16 O using the one-neutron transfer (p,d) reaction. The tensor interactions mix large orbital angular momentum states, giving rise to high momentum components through D-wave component in the relative coordinate of two nucleons in finite nuclei. In fact, recent theoretical calculations [16][17][18] have predicted enhanced momentum distributions at around 2 fm −1 due to the tensor interactions. In this work, we measured the cross sections of the one-neutron pickup reaction at momentum transfer around 2 fm −1 by observing the ground state as well as excited states in 15  The (p,d) reaction has been applied extensively to study the single particle nature of nuclei. In this reaction, a neutron is picked up from the target nuclei to form a deuteron.
The advantage of this reaction lies in the selectivity of the momentum of the picked-up neutron. Under the single-step pickup reaction using a deuteron target, the momentum of the picked-up neutron in the target deuteron is equivalent to the momentum transfer, namely the difference between the momenta of the outgoing deuteron and the incident proton P d -P p . Neutron pickup reactions with a nuclear target, when a deuteron is observed at small scattering angles, are expected to occur under the same reaction mechanism and thus can be used to extract spectroscopic information on the neutron residing in the target nucleus.
The experiment was performed at the WS beamline of the RCNP cyclotron facility.
Proton beams at E p = 198, 295 and 392 MeV were provided by the RCNP ring cyclotron and transported in the achromatic mode to a target placed in a scattering chamber. The typical beam spot size at the target was 1 mm in diameter. We used a windowless and self-supporting thin ice sheet [20] as the target. The thin ice sheet, which was made of pure water, was cooled by liquid nitrogen and kept below 140 K throughout the experiment. A new ice target was prepared before each measurement with different proton beam energy to reduce 12 C contaminants from vacuum pump oil. The thicknesses of the targets were determined to be 32 ± 2, 30 ± 3 and 62 ± 5 mg/cm 2 for the measurements with E p = 198, 295 and 392 MeV respectively, through measurement of the elastic scattering off the hydrogen.
The deuterons produced in the one-neutron pickup reactions were momentum analyzed by the Grand Raiden spectrometer [21] and detected by two multi-wire drift chambers and Nonetheless, this should not alter our conclusion. For comparison, the energy spectrum for E p = 45.34 MeV at 20.1 • replicated from the figure in ref. [22] is also shown (Fig. 1(c)).
Since the ground 1 2 − and the 6.176-MeV excited 3 2 − states in 15 O can be assumed to be neutron p 1/2 and p 3/2 hole states, one expects such states to be relatively strongly populated through direct pickup of a neutron. It is, however, surprising that the positive-parity states    Fig.1(c), the cross section to the positive-parity state is smaller than those to the negative-parity states.
In general, the cross sections of all states diminish with increased proton beam energy, i.e. increased momentum transfer, due to momentum mismatching. This trend is particularly pronounced for the ground state, which is an evidence of diminishing high-momentum Note that the contributions from the 12 C contaminant have been estimated and subtracted.
The acceptance and detection efficiency of the deuterons corresponding to the ground and excited states were almost constant. Other data were taken from the previous measurements at proton energies of 45.34 MeV [22], 65 MeV [23], 100 MeV [24], 200 MeV [25] and 800 MeV [26]. As evidence from the figure, the ratios for the positive-parity states increase drastically by a factor of 30 from q transfer 0.3 fm −1 to 2.6 fm −1 , whereas the ones for the negative-parity states only triple over the same momentum-transfer range.
The energy dependence of the differential cross sections at the first l=1 maxima, which lie between 10 • and 20 • in the center-of-mass frame close to 10 • at the laboratory frame, has been reported for proton energies from 18.5 MeV to 100 MeV [22]. The present data, together with the data at E p =800 MeV, indicate that R − remains almost constant (∼ 3.7/1.68, see below) above q=1 fm −1 .
To investigate the relative strengths, we performed theoretical calculations to obtain the ratios for the Coupled-Channel method with Born Approximation to the transition operatorV tr for the transfer, i.e. CDCC-BA [28] calculation. We made zero-range approximation with finiterange correction toV tr , and used nucleon-nucleus distorting potentials based on the Dirac phenomenology [29]. In obtaining the calculated ratios, we have adopted the shell-model spectroscopic factors of 1.68 and 3.7 [30] for the p 1/2 and p 3/2 states, respectively. The calculations are qualitatively consistent with the experimental data above E p =100 MeV (or q > ∼ 0.8 fm −1 ), indicating that the ratios of the 1p 3/2 and 1p 1/2 states can be understood within the present shell-model framework. Although not shown in Fig. 2, calculations using the Adiabatic Distorted-Wave Born Approximation [27] with relativistic correction for the reaction with 200-MeV incident protons also give a ratio consistent with the experimental data.
For the positive-parity states, calculations using the shell model which include twoparticle two-hole (2p2h) configuration were reported to reproduce the experimental data at proton energy below 45.34 MeV. The sum spectroscopic factors were found to be as small as 0.15 and 0.02 for the 1d 5/2 and the 2s 1/2 states respectively [22]. Assuming only the 1d 5/2 orbital and the spectroscopic factor of 0.15, we performed calculations for the positiveparity state. The ratios, which are represented by the dotted curve in Fig. 2 We shall note that the scattering angle of deuteron was set to ≥ 10 • to obtain momentum transfer ∼2 fm −1 , due to the limitation of the proton-beam energy at RCNP. It would be more desirable to use higher energy proton beam and measure the cross section near 0 • to minimize possible complications due to reaction mechanisms.
In summary, we have performed an experiment at RCNP, Osaka University using the