Few-Body Syst (2013) 54:1353–1356 DOI 10.1007/s00601-013-0611-7

K. Miki · A. Tamii · N. Aoi · T. Fukui · T. Hashimoto · K. Hatanaka · T. Ito · T. Kawabata · H. Matsubara · K. Ogata · H. J. Ong · H. Sakaguchi · S. Sakaguchi · T. Suzuki · J. Tanaka · I. Tanihata · T. Uesaka · T. Yamamoto

Study of Tensor Correlations in 4 He via the 4 He(p, dp)d and 4 He(p, dp) pn Reactions Received: 4 October 2012 / Accepted: 6 January 2013 / Published online: 26 January 2013 © Springer-Verlag Wien 2013

Abstract Tensor correlations in 4 He were studied via the (p, dp) reaction at the incident energy of 392 MeV cor ). The with a focus on spin configurations of correlated pn pairs in 4 He at high relative momenta (Prel cor = 310 MeV/c predominantly has the channel spin preliminary results show that the correlated pn pair at Prel S = 1, which is consistent with the characteristics of tensor correlations. 1 Introduction: Tensor Correlations and the (p, dp) Reaction The tensor force is a crucial component of the nucleon–nucleon (N − N ) interaction. For example, a deuteron cannot be bound without the tensor force, and a half of the large binding energy of 4 He is also attributed to the tensor force. Recent theoretical works suggested that the tensor force effects play an important role in the structure of unstable nuclei such as in the appearance of new quantum numbers [1]. In spite of this, experimental methods for probing the tensor correlations in nuclei have not been established yet. For the experimental study of the tensor correlation in nuclei, it is important to focus on two things. One is the relative momentum distribution of two nucleons in nuclei. It has been predicted that the tensor force enhances the high momentum component of such a distribution around 2 fm−1 (400 MeV/c) [2,3]. The other is the deuteron-like coupling. Theoretical studies [4] suggested that the tensor correlated nucleons should favor the spin and isospin channel of (S, T ) = (1, 0), which is the same as that of deuteron. The enhancement of high momentum component and the dominance of T = 0 pairing have been experimentally studied by using the electron scattering [5], but the dominance of S = 1 has not been well investigated. In this work, we used the (p, dp) reaction to study the spin configuration of the correlated pn pair in 4 He. A schematic picture of this reaction is shown in Fig. 1. A high momentum neutron is picked up by the incident proton forming a deuteron and a correlated proton is emitted in the opposite direction of the neutron momentum. It has been pointed out [6,7] that the (p, d) reaction at a forward scattering angle can selectively pick up Presented at the 20th International IUPAP Conference on Few-Body Problems in Physics, 20–25 August, 2012, Fukuoka, Japan. K. Miki (B) · A. Tamii · N. Aoi · T. Fukui · T. Hashimoto · K. Hatanaka · T. Ito · K. Ogata · H. J. Ong · H. Sakaguchi · T. Suzuki · J. Tanaka · I. Tanihata · T. Yamamoto Research Center for Nuclear Physics, Osaka University, Osaka, Ibaraki 567-0047, Japan E-mail: [email protected] T. Kawabata Department of Physics, Kyoto University, Kyoto 606-8502, Japan H. Matsubara · T. Uesaka RIKEN Nishina Center, Wako, Saitama 351-0198, Japan S. Sakaguchi Department of Physics, Kyushu University, Fukuoka 812-8581, Japan

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(i)

(f)

(f)

Fig. 1 Schematic picture of the (p, dp) reaction. χ p , χd and χ p are the wave functions for the incoming proton, outgoing cor and ψ res are the wave functions with a channel spin S for correlated and residual pn deuteron and proton, respectively. ψ pn;S pn;S FSI pairs in the initial state and ψ pn;S is that for residual pn pair in the final state

high momentum neutrons, and thus it can be a clean probe of tensor correlations in nuclei. Detection of the emitted protons in coincidence with deuterons makes it possible to determine the relative energy of the residual pn pair via the missing mass method. By selecting kinematical configurations, we can keep the residual pn pair at rest in the reaction process and regard it as a spectator. Since the initial 4 He has the spin J π = 0+ , the correlated and residual pn pair must have the same spin due to the angular momentum conservation. As will be discussed in Sect. 3, we can identify the spin state of the residual pn pair from its relative energy, and eventually that of the correlated pn pair. We expect that the fraction of spin S = 1 states would significantly enhance around 400 MeV/c, and that provides a new evidence of the tensor correlations.

2 Experiment In order to study the feasibility of the (p, dp) measurement, a test experiment was carried out at the WS course at Research Center for Nuclear Physics (RCNP) in Osaka university. A proton beam was accelerated by the AVF and Ring cyclotrons up to 392 MeV and bombarded onto a cryogenic 4 He target [8]. The intensity of the beam was typically 10 nA. A target cell was filled with 4 He gas with a purity of better than 99.9 % and a pressure of 2 atm, and was cooled down to 10 K by a cryogenic refrigerator. Thin aramid foils with a thickness of 12.5 µm were used as window foils. The thickness of the 4 He gas was approximately 10 mm along the beam axis, including the effects of the deformation of the foil. Deuterons and protons scattered from the target cell were momentum-analyzed by the Grand Raiden (GR) spectrometer and the large acceptance spectrometer (LAS), respectively, and were detected by vertical drift chambers (VDCs) and plastic scintillation counters installed at the focal-plane of each spectrometer. By changing the setting angles and magnetic fields of the spectrometers, cor in Fig. 1) between 300 and 400 MeV/c. we could cover the relative momentum of the correlated pn pair (Prel Note that the lower relative momentum regions are also accessible by decreasing the incident beam energy. The test experiment was performed at one kinematical setting: the scattering angle and momentum of outgoing deuterons were θGR = 13.5◦ and PGR = 1,140 MeV/c, and those of outgoing protons were θLAS = 121.5◦ cor = 310 MeV/c with the and PLAS = 310 MeV/c. This configuration probes the correlated pn pair with Prel center-of-mass motion of the residual pn pair at rest. The measured missing mass spectra are shown in Fig. 2. The black histogram in the left panel represents the differential cross section spectra measured with the target cell filled by the 4 He gas, while the gray histogram represents the background measured with an empty cell and an aramid-foil target. The spectrum after res = −2.2 MeV background subtraction is presented in the right panel in Fig. 2. It consists of a large peak at E rel res due to the deuteron and a small amount of the continuum component at E rel > 0 MeV. All data in Fig. 2, including the background spectra, were obtained only in 5 h, which demonstrates the high feasibility of this (p, dp) experiment. 3 Deducing the Fraction of S = 1 States The fraction of the S = 1 and S = 0 pn pairs was determined by fitting a sum of theoretically calculated spectra of the two states to the experimental data. The cross section of the 4 He(p, dp) reaction for given initial and final states is described by

Study of Tensor Correlations

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Fig. 2 [Left] Differential cross section spectra for the 4 He target cell (black) and the background component (gray). [Right] Differential cross section spectra for the 4 He(p, dp) reaction after the background subtraction

Fig. 3 [Left] Calculated overlap functions for the residual pn pairs in the S = 1 (solid) and S = 0 (dot-dashed) states. [Right] Results of the fitting. The experimental data were reproduced only with the S = 1 component

(f) (f)

res FSI σ S (E rel ) ∝ |ψ pn;S χ p χd |Vint | χ p(i) Ψ4 He |2 (f) (f)

cor FSI res ∼ |χ p χd |Vint | χ p(i) ψ pn;S |2 · |ψ pn;S | ψ pn;S |2 cor cor 2 res ∼ K |ψ˜ pn;S (Prel )| · I S (E rel ),

where Vint is the interaction between the projectile and the target nucleon, Ψ4 He is the wave function of 4 He, cor (P cor )|2 is the number of pn pairs with the channel spin S at a relaK is a proportionality factor, |ψ˜ pn;S rel cor , and I (E res ) is the overlap between the initial and final states of the residual pn pair. tive momentum Prel S rel Other notations can be found in Fig. 1. The second line was obtained by regarding the residual pn pair as a spectator and neglecting three-body and higher-order correlations in 4 He. We used a zero-range approximation cor (P cor )|2 is neglected in the acceptance of the to obtain the third line. The momentum dependence of |ψ˜ pn;S rel res ) can be decomposed into spectrometers. Under these assumptions, the total cross section σtot (E rel res cor cor 2 res cor cor 2 res ) = K [|ψ˜ pn;S=1 (Prel )| I S=1 (E rel ) + |ψ˜ pn;S=0 (Prel )| I S=0 (E rel )]. σtot (E rel

In the following discussion, we focus on the low relative energy region of the residual pn pair, and take into account only the s-wave components. res ) was calculated with the following parameters. |ψ res  was approximated by a product of two I S (E rel pn;S FSI  was obtained as a solution of the gaussian form factors with the center-of-mass motion excluded. |ψ pn Schrödinger equation with the AV18 N − N interaction by Wiringa et al. [9], assuming strong final state interaction between the residual pn pair. The bound and continuum states were treated on an equal footing by using continuum-discretization technique. The calculated overlap functions are shown in Fig. 3. The solid and dot-dashed lines represents the S = 1 and S = 0 calculations, respectively. The S = 1 component concentrates at the deuteron ground state while the S = 0 component dominates in the continuum region. res ≤ 4 MeV via the χ 2 minimiThe simulated profiles were then fitted to the experimental data in −4 ≤ E rel zation. The number of fitting parameters was two: the S = 1 fraction and the overall normalization. The result +0 of the fitting is shown in the right panel of Fig. 3. The S = 1 ratio was determined as 100−2 %, where the error

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includes only the statistical uncertainty in the experimental data. This result suggests the dominance of the deuteron-like state, in consistent with the characteristics of the tensor correlations. The systematic uncertainty in the simulation is now under discussion. 4 Summary The spin configuration of the correlated pn pair in 4 He was studied via the (p, dp) reaction at 392 MeV. A sufficient amount of the data was accumulated in only 5 h, which represents the high feasibility of the (p, dp) cor = 310 MeV/c was reproduced well by the simulation only with experiment. The measured spectrum at Prel the S = 1 component. This is consistent with the dominance of deuteron-like configurations in the tensor correlations. The S = 1 fraction will be further investigated as a function of the relative and also total momenta of the correlated pn pair. Acknowledgements The authors acknowledge K. Sagara for his suggestions in the preparation and maintenance of the cryogenic target system. They also thank all of the accelerator staffs in RCNP for providing a clean and stable proton beam.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

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