Recent experiments on three nucleon systems and problems to be solved

After 2π3NF was found in 1998, many experiments were made on Nd elastic scattering, Nd breakup andpd capture, and many discrepancies between experiments and calculations were revealed. Systematic experimental data are still being accumulated. From the systematic data, 3 NF other than 2 π3NF such asπρ3NF and ρρ3NF, and origins of low-energy anomalies are expected to be found in the future.


Introduction
One of the purposes to study three-nucleon (3N) systems is to find effects of three-nucleon forces (3NF) and to determine their strengths. As is well known, Fujita-Miyazawa predicted existence of 2π-exchange three nucleon force (2π3NF) in 1957 [1]. Faddeev equations for 3N systems have been numerically solved since late 1960's. In 1980's, it became widely known that 3 H binding energy cannot be reproduced by 2NF alone and can be reproduced using 2π3NF with an adjustable parameter. To justify the value of the parameter, further evidences were necessary.
From systematic measurement of pd elastic scattering cross section in energy range of E p = 2 -18 MeV at Kyushu University tandem laboratory (KUTL), systematic discrepancy between experiment and calculation in the cross section minima around 110 • was found in 1994 [2]. The discrepancy was, however, paid no attention because Coulomb force was not correctly treated in pd calculations at that time. In 1996, pd scattering cross section was measured at E d = 270 MeV (E p = 135 MeV) to construct a d-beam polarimeter at RIKEN. Koike found by chance the same discrepancy at the cross section minimum also at 135 MeV, and he introduced the discrepancy as Sagara discrepancy in FB15 in 1997 [3]. In 1998, Witała et al., excellently solved the binding energy problem and Sagara discrepancy by introducing the same 2π3NF [4].
After 2π3NF was discovered, many theoretical studies and experiments on 3NF have been made. The experimental studies have been widely made at higher energy region on Nd elastic scattering, and also made on pd breakup and pd capture.
In pd elastic scattering, many kinds of spin observables, such as analyzing powers of A y , iT 11 , A yy , A xx and A xz , and polarization transfer coefficients have been measured. Also cross section of pd elastic scattering was measured at various energies. In pd breakup, cross section and A y have been measured. Our experiment on pd breakup at E p = 247 MeV is presented in this conference [5]. In pd a e-mail: sagara@phys.kyushu-u.ac.jp capture, tensor analyzing powers A yy , A zz and also A xx have been measured in the last decade at E d = 100 -200 MeV.
All the experimental observables at higher energy disagree more or less with calculations even after 2π3NF being included. The disagreements seem, at least in part, to be caused by 3NF other than 2π3NF. We report the disagreements in some detail later.
At low energy region, there are long-standing problems of A y puzzle and Space Star anomaly (SS anomaly), which seem to be irrelevant to 3NF. Now, we have sufficient data for A y puzzle. Experimentalists are just waiting for theoretical investigations. As for SS anomaly, which is a discrepancy between experiment and calculation in Nd breakup cross section around 10 MeV, there were a few experiments in 20 th century, because there were no reliable calculations on pd breakup and SS anomaly was studied only in nd breakup. Experiments on pd breakup are far more precise and far easier than nd breakup experiments. Experimentalists desired for a long time for pd breakup calculations. During the time, for example, combination of nd breakup Faddeev calcualtion and Watson-Migdal pp FSI formula was tried to approximate pd breakup calculation, and experimental data were fairly well reproduced.
A breakthrough was made by A. Deltuva et al. in 2005[6]. They succeeded in calculations of all kinds of pd reactions including pd breakup using fast-damping screened Coulomb force. After the success of pd breakup calculation, we started to measure pd breakup cross section systematically, to search for origin(s) of the star anomaly. Figure 1 illustrates discrepancies in 3N systems. We have already solved discrepancies in 3N binding energy and in pd scattering cross section minimum by 2π3NF. There are still many disagreements remaining at higher energy as well as at lower energy. Some of the disagreements may indicate effects of 3NF other than 2π3NF. EPJ Web of Conferences pd CS discrepancy 1 9 9 4 -1 9 9 6 -1 9 9 7 ( S a g a r a d is c r e p a n c y ) 3N BE problem

Experiments on pd elastic scattering at higher energy
After 2π3NF was discovered, many experiments were made on pd elastic scattering and 2π3NF effects were examined. As so many groups measured pd and nd elastic scattering, we Kyushu group did not measure it, instead, measured pd breakup and pd capture. Below E p = 200 MeV, the cross section minimum of elastic scattering was well reproduced by introducing 2π3NF. Above 140 MeV, it was found that the scattering cross section at backward angle becomes larger than calculation, and the disagreement increases monotonically with energy. Experimental values are about twice of calculated values at 250 MeV [7]. This systematic disagreement seems to indicate effects of short-range 3NF other than 2π3NF and/or relativistic effects.
Many kinds of polarization observables of pd scattering have been measured. They were found to disagree with calculations. Disagreements in polarization observables are complicated and are not so large as that of the cross section (for example see [8]). Besides systematic feature like cross section enhancement has not been found in disagreements of polarization observables.
It may be better to investigate first the systematic disagreement in the cross section of elastic scattering, and to study other disagreements after the problems in the cross section are completely solved. Cross section is a basic scalar quantity, and modification of cross section influences more or less polarization observables.

Experiments on pd breakup at higher energy
After 2π3NF was discovered, we started pd breakup experiment at E p = 247 MeV at RCNP. To see global feature, we first made D(p,p 1 )p 2 n experiment by detecting only one proton p1 out of three outgoing nucleons. To significantly reduce backgrounds from the target, we used an almost pure liquid D 2 target instead of an ordinary CD 2 target. We had developed the liquid hydrogen target for our pd capture experiment described below.
Experimental results for D(p,p 1 )p 2 n cross section at 247 MeV are shown in Figure 2 with calculations by Witała. Measured cross section is larger than calculation. The disagreement increases at forward angle. Effects of 2π3NF are not enough to explain the experiment. We measured also A y in the same experiment, but we first investigate cross section disagreement.
The disagreement is of similar magnitude with the disagreement in pd scattering cross section at background at the same energy described above. It may be natural to think that the same origin enhances both cross sections of pd elastic scattering and of pd breakup reaction.
In order to see microscopically the enhancement of cross section in pd breakup, we recently measured D(p,p 1 p 2 )n cross section at E p = 247 MeV by detecting two protons in coincidence. We focused to investigate microscopically enhancement of D(p,p 1 )p 2 n cross section at θ 1 = 15 • and E 1 being around 150 MeV. Another proton p 2 was detected at θ 2 = 35 • , 50 • , 65 • and 80 • on the opposite side of the beam axis, as reported in this conference by Kuroita [5]. In the same experiment, D(p,p 1 )p 2 n cross section was also measured again, and our previous data were completely confirmed.
In figure 3, θ 2 dependence of D(p,p 1 p 2 )n cross section at E 1 = 150 MeV is illustrated with calculations by Kamada [10]. Cross section enhancement is large at θ 2 = 35 • 05002-p.2 where cross section is large. On the contrary, cross section enhancement is small at backward θ 2 where cross section is small. When θ 1 and E 1 are fixed, the remaining pair of p 2 and n has fixed total momentum, p 2 + p n , and absolute value of relative momentum |p 2 − p n | is also fixed. At θ 1 = 15 • and θ 2 = 35 • , the three outgoing nucleons approximately form a line, i.e., satisfy the collinear condition.
Above information may be useful to guess the origin of the cross section enhancement. Experimental data at more forward angle may be also useful. To measure at forward angles we need new counters, because the present two big counters cannot come to each other closer than 48 • ( = 15 • +33 • ).

Experiments on pd capture at higher energy
By p + d → 3 He+γ reaction, pd scattering state comes to 3 He ground state. Momentum transfer is large. It is interesting to search for effects of short-range 3NF in this highmomentum transfer reaction. Cross section of pd capture is, however, very small as below 1µbarn. Hence we used a liquid hydrogen target and detected 3 He recoils simultaneously in a wide angular range from 20 • to 160 • in c.m. system.
A polarized d-beam of energy of 196 MeV from RCNP cyclotron was used in our first experiment. The beam polarization axis was in the vertical direction, and recoiled 3 He detection was made in the horizontal plane to measure A y and A yy , and in the vertical plane to measure A xx . Measured A xx and A yy took roughly the same negative values, A xx ≈ A yy , and A yy roughly agreed with calculation, but A xx remarkably disagreed with calculation.
Next we measured A xx and A yy of pd capture at E d = 137 MeV. Preliminary data indicated again the relation of A xx ≈ A yy and remarkable disagreement in A xx . Since pd capture cross section is small and identification of true events was disturbed by overwhelming background events, data analysis took time. Meanwhile, A yy and A zz of pd capture at E d = 180 MeV and 133 MeV were measured at KVI. Their data agreed with calculations. They used a vertically polarized d-beam and a liquid hydrogen target, and detected 3 He and γ ray in coincidence. A yy was measured by detecting γ-rays in the horizontal plane. A zz was measured by detecting γ-rays in two planes inclined by ±45 • from the horizontal plane, and assuming the relation A xx + A yy + A zz = 0. KVI A yy data roughly agree with our data, but A zz data are about 1.5 times smaller in magnitude than ours.
Finally, a confirming measurement was made at RCNP on A xx , A yy and A zz of pd capture at E d = 196 MeV. The d-beam was polarized in the vertical direction, 3 He recoils were detected in the vertical plane for A xx , in the horizontal plane for A yy , and in two planes inclined by ±45 • from the horizontal plane for A zz in a way similar to KVI's. Dataanalysis method was improved so as to increase 3 He detection efficiency, and both new data and previous data were analyzed by the new method.
Our previous data and new data essentially agree to each other, and indicate the relation A xx ≈ A yy and large discrepancy in A xx (also in A zz ). Figure 4 shows various "A zz " data; -A xx -A yy in our previous experiment at 196 MeV, -A xx -A yy in our new experiment at 196 MeV, and A zz (±45 • ) in our new experiment at 196 MeV, together with A zz (±45 • ) in KVI experiment at 180 MeV. Curves are calculations at 200 MeV with and without 2π3NF by Golak. Although our "A zz " data are scattered to some extent, there is a large discrepancy between our "A zz " data and calculations.
In our data A xx ≈ A yy relation holds, but calculated A xx and A yy are significantly different to each other, therefore a large discrepancy in A xx (also in A zz ) results. The relation A xx ≈ A yy means the symmetry of pd capture with respect to the z-axis (the beam axis). When a d-beam is polarized in y-direction (vertically), d-induced reactions in the verti-05002-p.3 cal (yz) plane and in the horizontal (xz) plane are expected to proceed differently in general. Therefore it is natural to expect A xx A yy also in the present case.
In many other d-induced reactions, a relation A xx ≈ −A yy holds approximately. A deuteron has a prolate shape. If a d-beam is vertically polarized and d-induced reactions take place in peripheral region of target nuclei, the reactions may be enhanced in vertical plane and suppressed in horizontal plane, or oppositely suppressed and enhanced.
The relation A xx ≈ A yy in pd capture is curious. It is interesting to investigate the origin(s) of this relation, including to estimate effects from short-range 3NF.

Experiments on pd star anomaly at low energy
Discrepancies at higher energy have candidates for their origin(s), e.g., short-range 3NF, relativity, high-angular momentum reactions. On the contrary, discrepancies at lower energy have not apparent candidates for their origin(s).
A y puzzle is well known for a long time. We have already enough data sets for A y puzzle and no systematic measurements on A y puzzle have been made recently. Many theoretical attempts such as modifications of 2NF and introduction of LS dependent 3NF have been examined, but A y puzzle has not been solved yet.
Another big problem at low energy is Space-Star anomaly. SS anomaly was found first in nd breakup at E n = 13 MeV and 10.5 MeV [11], and was confirmed at 13 MeV by another experiment [12]. Experiments of pd breakup at SS configuration were also made, and SS anomaly in pd breakup was first found when a reliable pd calculation was made [6].
At 13 MeV, nd breakup cross section at SS configuration is about 25% higher than calculation, and pd breakup cross section at SS is about 15% lower than calculation. So far no theoretical suggestions have been made for SS anomaly and its large charge asymmetry.
Because a reliable calculation on pd breakup has become available since 2005 [6], we have been making a systematic measurement of pd star cross section at E p = 13 MeV and 9.5 MeV. At Koeln University, measurement of pd star cross section at E d = 19 MeV (E p = 9.5 MeV) was made [13].
When three outgoing nucleons from Nd breakup have the same energy and form an equilateral triangle, we call the configuration as Star. When the Star triangle is perpendicular to the beam axis, we call the configuration as Space Star. An angle between Star plane and the beam axis in c.m. frame is called as α, as defined in Fig. 5. We usually detect two protons from pd breakup at symmetrical angles with respect to the beam axis, and we define α = 0 • when a p-beam is used and two detected protons are at forward angles in the horizontal plane. See Figure 5.
To see characteristics of Star anomaly, α-dependence of pd Star anomaly has been measured recently by Koeln group [13] and Kyushu group. Star configuration at α=0 •  is close to QFS configuration, and possible anomaly at QFS is also being investigated at Kyushu. Y. Maeda and Y. Eguchi report on these subjects in this conference.
As seen in Figure 6, star anomaly at 13 MeV is confined at around 90 • . The plane perpendicular to the beam axis is special. Only in the perpendicular plane, pd breakup reaction is suppressed. It seems to be enough to think of curious suppression in the perpendicular plane. At 9.5 MeV, however, remarkable Star anomaly appears also at backward angles, as indicated by Koeln experiment at E d = 19 MeV. Complex consideration may be necessary to explain the wide-range Star anomaly.
Before thinking of origins of pd Star anomaly, it is better to make a confirming experiment at E d = 19 MeV. A polarized d-beam was used in Koeln experiment, but an unpolarized d-beam will be used in the confirming experiment to measure cross section alone.
Our strategy is (a) confirmation of pd Star anomaly by additional experiments, (b) investigation of origin(s) of pd Star anomaly, then (c) elucidation of nd Star anomaly. So far large charge asymmetry between nd SS anomaly and pd SS anomaly has been reported. The large charge asymmetry is hard to explain. We will first elucidate pd Star anomaly, based on systematic and reliable measurements. Elucidation of pd Star anomaly may include suggestion on the charge asymmetry. Experimental data for nd Star are insufficient at present, and reliable nd experiments are hard 05002-p.4 19 th International IUPAP Conference on Few-Body Problems in Physics to make. So we will not investigate nd Star anomaly till pd Star anomaly is completely elucidated.

Experiments on pd QFS at low energy
Cross section enhancement of 16-18% was reported in nd QFS at E n = 25 MeV and 26 MeV. Also cross section suppression in pd QFS was reported at E p = 10.5 MeV and 19 MeV.
We are making systematic measurement of pd QFS cross section at KUTL, and no apparent pd QFS anomaly has been found at both 9.5 MeV and 13 MeV. We will measure pd QFS cross section at 10.5 MeV and 19 MeV to see if pd QFS anomaly exists or not.

Summary
Studies of 3N systems are summarized and illustrated in Figure 1. We are on the way to search for short-range 3NF at higher energy in pd scattering, pd breakup and pd capture, and to investigate origins of Star anomaly as well as of A y puzzle at low energy. Experimental studies have made steady progress. At low energy, success of reliable pd calculation enabled systematic studies of pd Star anomaly.
Challenging 3N calculations aiming to solve remaining problems in 3N reactions are expected.