Few-body aspects of hypernuclear physics

Few-body aspects of hypernuclear physics

Structure of light hypernuclei Emiko Hiyama (RIKEN) Recently, we had three epoch-making data from the view point of few-body problems. Then, in hypernuclear physics, we are so excited. n He n n 7 6 JLAB experiment-E011,

Phys. Rev. Lett. 110, n 12502 (2013). n 3 n H t n FINUDA collaboration & A. Gal, Phys. Rev. Lett. 108, 042051 (2012). C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013) OUTLINE He

7 n n 1. Introduction 3. 4. He 7 2. 6

n H 6 3 n 5. Summary n n 3 n H t

n Section 1 Introduction Major goals of hypernuclear physics 1) To understand baryon-baryon interactions 2) To study the structure of multi-strangeness systems In order to understand the baryon-baryon interaction, two-body scattering experiment is most useful. Total number of Nucleon (N) -Nucleon (N) data: 4,000 Total number of differential cross section Hyperon (Y) -Nucleon (N) data: 40 NO YY scattering data Study of NN intereaction has been developed. YN and YY potential models so far proposed (ex. Nijmegen, Julich, Kyoto-Niigata) have large ambiguity.

since it is difficult to perform YN scattering experiment even at J-PARC. No Pauli principle Between N and particle can reach deep inside, and attract the surrounding nucleons towards the interior of the nucleus. N Due to the attraction of N interaction, the resultant hypernucleus will become more stable against the neutron decay. Hypernucleus neutron decay threshold nucleus hypernucleus

Nuclear chart with strangeness Multi-strangeness system such as Neutron star Extending drip-line! Interesting phenomena concerning the neutron halo have been observed near the neutron drip line of light nuclei. How is structure change when a into neutron-rich nuclei ? particle is injected Question : How is structure change when a particle is injected into neutron-rich nuclei? n He n n 6

7 H t n Observed at JLAB, Phys. Rev. Lett. Observed by FINUDA group, 110, 12502 (2013). Phys. Rev. Lett. 108, 042051 (2012). n n 3 n

C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013) In order to solve few-body problem accurately, Gaussian Expansion Method (GEM) , since 1987, A variational method using Gaussian basis functions Take all the sets of Jacobi coordinates Developed by Kyushu Univ. Group, Kamimura and his collaborators. Review article : E. Hiyama, M. Kamimura and Y. Kino, Prog. Part. Nucl. Phys. 51 (2003), 223. High-precision calculations of various 3- and 4-body systems: Exotic atoms / molecules , Light hypernuclei, 3- and 4-nucleon systems, 3-quark systems, multi-cluster structure of light nuclei, 4 He-atom tetramer

Section 2 Four-body calculation of n n 7 He n He 6 He n 6

n n 7 He : One of the lightest n-rich nuclei He: One of the lightest n-rich hypernuclei 7 Observed at JLAB, Phys. Rev. Lett. 110, 12502 (2013). CAL: E. Hiyama et al., PRC53, 2075 (1996), PRC80, 054321 (2009) 6 He Prom

p 2+ 0 MeV t par 7 ticle d eca y He ++n+n 0 MeV +n+n 0+ 5

-1.03 MeV Exp:-0.98 B B :C AL 5/2+ + 3/2 -4.57 = 5. Jla 36 Ph b e E M 01 ys. xp XP= e eV 25 Re ri 02 v. me 5.6

(2 Lett nt 80 01 .1 .0 3) 10 3 . , 0. He+n+n -6.19 25 1/2+ Halo states Section 3 Four-body calculation of n t 6

H n E. H, S. Ohnishi, M. Kamimura, Y. Yamamoto, NPA 908 (2013) 29. n n H 6 t =1.90.4 MeV 1/2+ 1.70.3 MeV Phys. Rev. Lett. 108, 042051 (2012). FINUDA experiment

t+n+n+ 1 .0 =4 B P: EX t+n+n 4 .1 0.3 MeV eV n M n H+n+n t

n n 6 H:super heavy hydrogen 5 H t Before experiment, the following authors calculated the binding energies by shell model picture and G-matrix theory. (1) R. H. Dalitz and R. Kevi-Setti, Nuovo Cimento 30, 489 (1963). (2) L. Majling, Nucl. Phys. A585, 211c (1995). (3) Y. Akaishi and T. Yamazaki, Frascati Physics Series Vol. 16 (19 Akaishi et al. pointed out that one of the important subject to study th ypernucleus is to extract information about N-N coupling.N coupling. Motivating the experimental data, I calculated the binding energy of 6 H and I shall show you my result.

Before doing full 4-body calculation, it is important and necessary to reproduce the observed binding energies of all the sets of subsystems in 6H. Namely, All the potential parameters are needed to adjust in the 2- and 3-body subsystems. H 6 H 6 H 6 n n

n n t n n t Among the subsystems, it is extremely important to adjust the energy of 5H core nucleus. t Framework: To calculate the binding energy of 6H, it is very important to reproduce the binding energy of the core nucleus 5H. transfer reaction p(6He, 2He)5H A. A. Korcheninnikov, et al. Phys. Rev. Lett. =1.90.4 MeV 87 (2001) 092501. 1/2+ 1.70.3 MeV

t+n+n To reproduce the data, for example, R. De Diego et al, Nucl. Phys. A786 (2007), 71. calculated the energy and width of 5H with t+n+n three-body model using complex scaling method. The calculated binding energy for the ground state of 5H is 1.6 MeV with respect to t+n+n threshold and width has 1.5 MeV. Even if the potential parameters were tuned so as to reproduce the lowest value of the Exp. , E=1.4 MeV, =1.5 MeV, we do not obtain any bound state of 6H. Exp: 1.7 0.3 MeV =1.9 0.4 MeV + = 2.44 MeV = 0.91 MeV 1.69 MeV 1.17 MeV

0 MeV t+n+n+ 4 H+n+n =0.23 MeV t+n+n 0+ E=-0.87 MeV - 2.0 H+n+n 4 -2.07 MeV 0+ On the contrary, if we tune the potentials to have a bound state in 6 H, then what is the

energy and width of 5H? = 1.90.4 MeV 1/2 Phys. Rev. Lett. 108, 042051 (2012). + FINUDA experiment 1.70.3 MeV 5 H 5 0.3 MeV eV t

H+n+n 4 M t+n+n+ n n t+n+n+ .1 1 .0 =4 B P: EX t+n+n 6 H H:super heavy hydrogen

But, FINUDA group provided the bound state of 6H. n t n How should I understand the inconsistency between our results and the observed data? (1) We need more precise data of 5H. A. Korcheninnikov, et al. Phys. Rev. Lett. 87 (2001) 092501. =1.90.4 MeV 1/2+ 1.70.3 MeV t+n+n To get bound state of 6H, the energy should be lower than the present data. It is planned to measure the energy and width of 5H more precisely at RCNP by Prof. Tanihata this year. His proposal was approved recently . We cited this experiment. However, you have many

different decay widths. Width is strongly related to the size of wavefunction. Then, I hope that The decay width will be determined by Tanihata san in the future. [3] A.A. Korosheninnikov et al., PRL87 (2001) 092501 [8] S.I. Sidorchuk et al., NPA719 (2003) 13 [4] M.S. Golovkov et al. PRC 72 (2005) 064612 [5] G. M. Ter-Akopian et al., Eur. Phys. J A25 (2005) 315. (2) In our model, we do not include NN coupling explicitly. The coupling effect might contribute to the energy of 6 H. Non-strangeness nuclei N S=-1 80 MeV

S=-2 N N 25MeV 300MeV N Probability of not large. N in nuclei is In hypernuclear physics, the mass difference is very small in comparison with the case of S=0 field. Then, in S=-1 and S=-2 system, N-N and -N couplings might be important. A. Gal and D. J. Millener, arXiv:1305.6716v3 (To be published in PLB. They pointed out that N-N coupling.N coupling is important for 6H.

It might be important to perform the following calculation: n n H 6 t n n + 3N N =1.90.4 MeV Phys. Rev. Lett. 108, 042051 (2012).

1/2+ 1.70.3 MeV FINUDA experiment t+n+n+ 5 H .1 1 .0 =4 B P: EX t+n+n 0 MeV M eV Cal: -0.87 MeV 4 H+n+n N-NN coupling Exp: -2.3 MeV

This year, at J-PARC, they performed a search experiment of (E10 experiment) of 6H. If E10 experiment reports more accurate energy, we can get information about N-NN coupling. N t+n+n+ 4 No peak?! H+n+n 0.3 MeV FINUDA data 6 H Theoretically, we might understand by the following reason. If the state is resonant state, the reaction cross section would be much smaller than that we expect. => I should calculate reaction cross section 6Li (,K)6H with Haradas help. How should we understand 6H issue?

To investigate it, the study of nn system is suited. Section 4 three-body calculation of n n 3 n E. Hiyama, S. Ohnishi, B.F. Gibson, and T. A. Rijken, The paper will be submitted in PRC this week. nn breakup threshold ? They did not report the binding energy. n

n HypHI collaboration observed bound state of nn system. It is considered that N-N coupling.N coupling play an important role to make bound state. t n If we inject triton cluster into nn system, we have 6H. n n n t The three-body system of nn system is useful hyperucleus for discussion about

whether 6H is bound or unbound. Namely, if we have a bound state in nn system, there is possibility to have a bound state in 6H. Important issue: Do we have bound state for nn system? If we have a bound state for this system, how much is binding energy? n n n n + N coupling. NN interaction : to reproduce the observed binding energies of triton and 3He NN: AV8 potential In S=0 sector N+N+N 0 MeV - 7.72 MeV

1/2+ - 8.48 MeV -7.77 MeV Cal. 1/2+ 1/2+ 3 He 3 H n n n p Exp. p

p Exp. 1/2+ -7.12 MeV Cal. Important issue: Do we have bound state for nn system? If we have a bound state for this system, how much is binding energy? n n n n + N coupling. YN interaction: to reproduce the observed binding energies of NSC97f potential H, 4H and

3 4 He 4 N N -B 4 N 3 0 MeV -1.24

-2.39 1+ p What is binding energy for nn? -B 0+ 4 He+ -0.54 H 0 MeV 3 1+ H+

1+ -0.57 -1.00 0+ -2.04 -2.28 Exp. N 4 H He He Cal. 0+ -2.33

Cal. Exp. d+ H 3 1/2+ -0.13 0.05 MeV Exp. -0.19 MeV Cal. 1/2+ 1+ 0+ 1/2+ nn

We have no bound state in nn system. Now, we have a question. Do we have a possibility to have a bound state in nn system tuning strength of YN potential ? When we have a bound state in nn system, what are binding energies of 3H and A=4 hypernuclei? VT N-N coupling.N X1.1, 1.2 n n VT N-N coupling.NX1.1 VT N-N coupling.N When we have a bound state in nn system, what are binding energies of 3H and A=4 hypernuclei? We have no possibility to have a bound state in nn system.

And then, it would be difficult to say to have a bound state in 6H. Question: If we tune 1S0 state of nn interaction, Do we have a possibility to have a bound state in nn? In this case, the binding energies of 3H and 3He reproduce the observed data? Some authors pointed out to have dineutron bound state in nn system. Ex. H. Witala and W. Gloeckle, Phys. Rev. C85, 064003 (2012). n n T=1, 1S0 state I multiply component od 1S0 state by 1.13 and 1.15. What is the binding energies of nn n n nn unbound 0 MeV

-0.066MeV 1 S0X1.13 -0.118 MeV 1 n n unbound nn S0X1.15 unbound 1/2+ -0.043MeV N+N+N H (3He) -8.48 (-7.72) We do not find any possibility to have a bound state in nn.

3 -7.77(-7.12) -9.75 (-9.05) -10.09 (-9.38)MeV 1/2+ Exp. Cal. Cal. Cal. 1/2+ Section 5 Summary Summary 1) Motivated by observation of neutron-rich hypernuclei, He, 6H , nn, I performed four-body calculation of them. 7 In 7He, due to the glue-like role of particle, We may have halo states, the 3/2+ and 5/2+ excited state.

We wait for further analysis of the JLAB experiment. I performed a four-body calculation of 6H. But, I could not reproduce the FINUDA data of 6H . The error bar of data is large. Analysis of E10 experiment at J-PARC reported to have no peak. n n To study6H issue, I calculated nn system taking N-N coupling.N coupling explicitly. However, I could not find any bound state keeping consistency with observed data of 3 3 3 H, A=4 hypernuclei, H and He. This fact would suggest to have no bound state in 6H. To conclude whether or not 6H has a bound state,

it think that it would be better to perform search experiment at Mainz. I hope to have conclusion for this issue in the future. Thank you! In hypernuclear physics, currently, it is extremely important to get information about N-N coupling. Question: Except for 6H, what kinds of hypernuclei are suited for extracting the N-N coupling? Answer: H, 4 He 4 n n n p

p p 4 H 4 He -B -B He 4

0 MeV 3 He+ -1.24 -2.39 1 H 4 0 MeV 3 1+ + -1.00 0+ -2.04

Exp. Exp. N N H+ N 4 He H 4 0+ N

N N N N coupling. + NNN N + N NNNN coupling. E. Hiyama et al., Phys. Rev. C65, 011301 (R) (2001). H. Nemura et al., Phys. Rev. Lett. 89, 142502 (2002). A. Nogga et al., Phys. Rev. Lett. 88, 172501 (2002). PN coupling.=1.12 % PN coupling.=2.21% Another interesting role of N coupling.-particle in hypernuciei, namely effective NN 3-body force generated by the

N coupling.-particle mixing. N1 N2 N3 N1 N2 N3 N coupling. N coupling. N1 N2 N3 N1 N2 N3 N1 N2 N3 3N+ space

N1 N2 N3 Effective 3-body NN force Effective 2-body N force N1 N 2 N3 How large is the 3-body effect? N1 N2 N3 Y. Akaishi, T. Harada, S. Shinmura and Khin Swe Myint, Phys. Rev. Lett. 84, 3539 (2000). 3 He +

+ 3 He + N coupling. They already pointed out that three-body force effect is important within the framework of (3He+)+(3He+N coupling.). n n t 6 Then, I use t+n+n+ 4-body model for H and take the same t-n potential employed by N. B. Schulgina et al., Nucl. Phys. A597, 197 (1996 .

H 6 3 H-n scattering t n n n It was difficult to reproduce the experimental energy and width of 5H, then, they introduced phenomenological attractive t-n-n three-body force. t H 5 Using complex scaling method which is one of the powerful method to obtain nergy and width of resonant state, I tune the strength , S3b, tnn three-body force.

S3b=-57 MeV Energy and width of 5H using tnn three-body force Exp. E=1.7 0.3 MeV , =1.9 0.4 MeV As the strength of tnn three-body force is larger, the energy of 5H becomes low and width becomes narrower. H 6 n n I take t- potential to reproduce The binding energies of 0+ and 1+ states of 4H. In this case, N-N coupling.N coupling is renormarized into N interaction.

t H 6 I take potential to reproduce the binding energy of 3H. n n t =1.90.4 MeV =1.37 MeV 1/2+ 1.5 MeV 1.70.3 MeV I focus on 0+ state. t+n+n n 1+ n

t n 0+ n H 5 Then, what is binding energy of 6H? n 6 H t

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