Structure of light Λ hypernuclei by (e,e’K+) reaction
E. Hiyama (RIKEN)
Using these targets, we have these light Λ hypernucei by (e, e’K+) reaction at Jlab. Here I will focus on these Λ hypernuclei.
n n
Λ
n n
np
3H 3nΛ
nnp
6 Li
n
6 He
Λ
Λ
44He 44He
nnp
7Li
n
7He
Λ
Λ
44He 44He
targetResultant hypernucleus
n
n
np
10B
44He
n
44He
10Be
44He
n
44He
target Resultant hypernucleus
Λ
Λ
Outline
(1) Introduction
(2) n n
Λ
3nΛ
n
6 He
Λ
44He
n
7He
Λ
Λ
44He n 44He
n
44He
Λ
10BeΛ
These Λ hypernuclei can be produced by (e, e’K+) at Jlab.What is interesting and important to study theseΛ hypernuclei?
Λ
Sec.1 Introduction
In order to understand the baryon-baryon interaction, two-body scattering experiment is most useful.
YN and YY potential models so far proposed (ex. Nijmegen, Julich, Kyoto-Niigata) have large ambiguity.
1) To understand baryon-baryon interactions
Total number of Nucleon (N) -Nucleon (N) data: 4,000
・ NO YY scattering data
・ Total number of differential cross section
Hyperon (Y) -Nucleon (N) data: 40
Study of NN intereactionhas been developed.
since it is difficult to perform YN scattering experiment even at J-PARC.
Major goals of hypernuclear physics
2) To study the structure of multi-strangeness systems
nn
Once the Hamiltonian is determined, it is possible , using few-body calculation method (GaussianExpansion Method), to precisely calculatethe structure of many-body systems consisting of neutrons, protons and hyperons.As a result, we can predict new phenomena such as we have never imagined before.
2) To study the structure of multi-strangeness systems
nn
p
p
Y
Hypernucleus =
Many-body system of
neutrons, protons, hyperons
np
pY
nn
Hypernucleus
No Pauli principleBetween N and Λ
Λ
γnucleus
hypernucleus
Due to the attraction ofΛ N interaction, theresultant hypernucleus willbecome more stable againstthe neutron decay.
neutron decay threshold
Λ
N
Λ particle can reach deep inside, and attract the surrounding nucleons towards the interiorof the nucleus.
Nuclear chart with strangeness
Λ
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 Λ particle is injected into neutron-rich nuclei ?
Question: How is structure change when a Λ particle is injected into neutron-rich nuclei ?
α Λ
7HeΛ
n n n n
Λ
3nΛ
C. Rappold et al., HypHI collaboration Phys. Rev. C 88, 041001 (R) (2013)
JLAB experiment-E011,Phys. Rev. Lett. 110,12502 (2013).
α
Λ6HeΛ
n
Section 2
three-body calculation of 3nΛ
n
Λ
n E. Hiyama, S. Ohnishi,B.F. Gibson, and T. A. Rijken,The paper will be publised inPRC as a Rapid communication soon.
What is interesting to study nnΛ system? n
Λ
n
S=0
The lightest nucleus to have a bound state is deuteron.
n p
n+p threshold
J=1+
-2.22 MeV
S=-1 (Λ hypernucear sector)
n
Λ
3H (hyper-triton)
d
Λ
n+p+Λ
d+Λ
0.13 MeV J=1/2+
Exp.
Exp.
Lightest hypernucleus to have a bound statep
n
Λ
n
nnΛ breakup threshold
?They did not report thebinding energy.
Observation of nnΛ system (2013)Lightest hypernucleus to have a bound state
scattering length:-2.68fm
-23.7fm
n
Λ
n
NN interaction : to reproduce the observed binding energies of 3H and 3He
NN: AV8 potentialWe do not include 3-body force for nuclear sector.
Theoretical important issue: Do we have bound state for nnΛ system? If we have a bound state for this system, how much is binding energy?
nnΛ breakup threshold
?They did not report thebinding energy.
How about YN interaction?
Non-strangeness nucleiN Δ
N N
N
Δ
300MeV
80MeVΛ
Σ
On the other hand, the mass differencebetween Λ and Σ is much smaller, thenΛ can be converted into Σ particle easily.
Nucleon can be converted into Δ.However, since mass difference betweennucleon and Δ is large, then probabilityof Δ in nucleus is not large.
ΛN
N Λ
Σ
n
Λ
n n n
Σ+
YN interaction: Nijmegen soft core ‘97f potential (NSC97f) proposed by Nijmegen group reproduce the observed binding energies of 3H, 4H and 4He ΛΛΛ
To take into account of Λ particle to be converted intoΣ particle, we should perform below calculation usingrealistic hyperon(Y)-nucleon(N) interaction.
n p
Λ
3HΛ
d+Λ
-0.13 ±0.05 MeV
1/2+
Exp.
1/2+
-0.19 MeV
Cal.
0 MeV
-BΛ
-BΛ -BΛ
0 MeV 0 MeV3He+Λ 3H+Λ
1+
0+
-2.39
-1.24
-2.04 0+
1+
-1.00
Exp.Exp.
4HeΛ 4H
Λ
-2.28
-0.54
-2.33
-0.57
0+
1+
0+
1+
Cal. Cal.
n
p
p
Λ
4HeΛ4H
Λ
Λ
What is binding energy of nnΛ?
n
p
n
Λ
nnΛ threshold 1/2+
We have no bound state in nnΛ system.This is inconsistent with the data.
Now, we have a question.
Do we have a possibility to have a bound state in nnΛ system tuningstrength of YN potential ?
0 MeVn
Λ
n
It should be noted to maintain consistency with the binding energiesof 3H and 4H and 4He.
ΛΛ Λ
-BΛ
VT ΛN-ΣN X1.1, 1.2
n
Λ
n
VT ΛN-ΣN VT ΛN-ΣNX1.1 X1.2
When we have a bound state in nnΛ system, what are binding energies of 3H and A=4 hypernuclei?
Λ
n
Λ
n
np
Λ
n
p
Λ
n
We have no possibilityto have a bound statein nnΛ system.
Question: If we tune 1S0 state of nn interaction,Do we have a possibility to have a bound state in nnΛ?In this case, the binding energies of 3H and 3He reproducethe observed data?
n
Λ
nT=1, 1S0 stateI multiply component of 1S0 state by 1.13 and 1.35. What is the binding energies of nnΛ ?
Some authors pointed out to have dineutron bound state innn system. Ex. H. Witala and W. Gloeckle, Phys. Rev. C85, 064003 (2012).
nnunbound
-0.066MeV
0 MeV
-1.269 MeV1S0X1.13
1S0X1.35
nnΛ
1/2+
unbound unbound
-1.272 MeV
n
Λ
n
N+N+N
1/2+
-13.93 (-13.23)MeV-8.48 (-7.72)
Exp.1/2+
3H (3He)
Cal.
-7.77(-7.12) -9.75 (-9.05)
We do not find any possibility to have a bound statein nnΛ.
Cal.Cal.
n n0 MeV
Summary of nnΛ system:Motivated by the reported observation of data suggestinga bound state nnΛ, we have calculated the binding energy of this hyperucleus taking into account ΛN-ΣN explicitly.We did not find any possibility to have a bound state in thissystem. However, the experimentally they reportedevidence for a bound state. As long as we believe the data, we should consider additionalmissing elements in the present calculation. But, I have no idea.Unfortunately, they did not report binding energy.
Then, I would like to suggest experimentalists:To perform search experiment of nnΛ system to concludewhether or not the system exists as bound state experimentally.
n n
Λ
n n
np3H 3nΛ
(e,e’K+)
α
Λ
6HeΛ
n
6HeΛ
α +n
0.89 MeV P3/2
Λ
5He+nΛ -3.12 MeV
1-
0 MeV
5He
6HeΛα Λ
L=05He
Λ
0.17 MeV
α
Λ
n
6HeΛ
Question: Can we reproduce the data ?How do the 3 particle locate to each other?Is there neutron halo in 6He hypernucleus?Λ
Valence neutron is very looselycoupled to the α+Λ system.
α +n+Λ
密度 ρn(r) = ∫|Ψ(6He)|2dRdr^
r
Λ
α
Λ
n
r.m.s α-Λ 2.8 fm α-n 5.0 fm
Halo nucleus 6Heα-n 4.5 fm
Larger than 6He
Three-layer structure
7He
Λ
Λ
n n
7He
Λ
α
Λ
7HeΛ
n
Observed at JLAB, Phys. Rev. Lett. 110, 12502 (2013).
n
6Hen n 6He : One of the lightest
n-rich nuclei
7He: One of the lightest n-rich hypernucleiΛ
α
α
Λ
0+
2+
α+n+n
-1.03 MeV
0 MeV
BΛ : CAL= 5.36 MeV
1/2+
3/2+5/2+
5He+n+nΛ
α+Λ+n+n0 MeV
-6.19 MeV
-4.57
Neutronhalo states
6He7HeΛ
CAL: E. Hiyama et al., PRC 53, 2075 (1996), PRC 80, 054321 (2009)
BΛ :
EXP= 5.68±0.03±0.25
Observed at J-Lab experiment Phys. Rev. Lett.110,012502 (2013).
Exp:-0.98Λ
One of the excitedstate was observed at Jlab.
7Li(e,e’K+)7ΛHe
(FWHM = 1.3 MeV)
Fitting results
Third peak?
At present, due to poor statics,It is difficult to have the third peak.Theoretically, is it possible tohave new state?Let’s consider it.
0+
2+
α+n+n0 MeV
6He
-0.98
1.797 MeVΓ=113 ±20 keV
(2+,1-,0+)?
Γ= 12.1 ±1.1 MeV
Exp.
-0.97 MeV
1.79 MeV
2.5 MeV
Γ=
Γ=
theoryMyo et al., PRC 84, 064306 (2011).
Core nucleus
1/2+
3/2+5/2+
5He+n+nΛ
α+Λ+n+n0 MeV
-6.19 MeV
-4.57
Neutronhalo states
7HeΛ
Λ7HeΛ
n n
α
-3.12
-1.88 Γ=0.7 MeV5/2+
3/2+ -2.04, Γ=0.5 MeVNew prediction
0+
2+
α+n+n0 MeV
6He
-0.98
1.797 MeV
Γ=113 ±20 keV
(2+,1-,0+)?
Γ= 12.1 ±1.1 MeV
Exp.1/2+
3/2+5/2+
5He+n+nΛ
α+Λ+n+n0 MeV
-6.19 MeV
-4.57
Neutronhalo states
-3.12
-1.88 Γ=0.7 MeV5/2+
3/2+ -2.04, Γ=0.5 MeV
7HeΛ
2+
If we find these two excited states at Jlab,in 6He, existence of the second 2+ stateis promising. Please search the second 2+
state in 7He at Jlab. Λ
If we find these two states at Jlab, these existencecontribute to unstable nuclear physics.
Response of super-deformed states by addition of Λ particle
Section 3
10BeΛ
spherical Normal deformed (ND)
Super-deformed(SD)
We have various kinds of nuclear shape, such as spherical, normal deformed and super-deformed shapes. Especially,
it is known that super-deformed shape is related to the appearance of a large shell gap at a 2:1 axis ratio of the nuclear deformation for specific particle numbers.
What happens when a Λ particle is added to such ND and SD states?
Λ Λ
0+1
0+2
NormalDeformed (ND) states
Super-deformed (SD) states
core nucleus
2+1
2+2
Does energy gain goin parallel way for both typesof states?
Λ
Λ hypernucleus
No !
What happens when a Λ particle is added to such ND and SD states?
0+2
2+2
0+1
2+1
Energy gain by Λ-particle addition
ΔE (ND state) > ΔE (SD state)
ND state
SD state
core nucleus
Λ hypernucleus
Level crossing
ND state
One example in10BeΛ
10BeΛ
Y. Zang, E. H., and Y. Yamamoto, Nucl. Phys. A 881, 288 (2012):
E. H. and Y. Yamamoto, Prog. Theor. Phys. 128, 105, (2012).
Λ
9Be10BeΛ
α+α+n
3/2-
1/2+5/2-
Interesting phenomena such as level crossing is seen in 9Be and 10Be combination.Λ
It is well known that , in the 1/2+ state,a valence neutron is located in 1S 1/2 orbit
in the simple shell model configuration.It is a kind of SD state.
When a Λ particle is injected into each state,is there any change of energy spectra?
10BeΛ
9BeΛ
ND
SD
ND
5/2
1/2+
3/2-
α + α +n α + α +n+ Λ
-10.52 MeV
-8.14
-7.35
-1.58
+0.1
+0.6 MeV
MeV
BΛ = 8.94 M
eV
CAL
( B
Λ = 9.11 0.22 MeV)
EXP
10BeΛ
9Be
Level reversion is occurred by addition of a Λ particle.
10B(e,e’K+)10Be (Jlab E01-11)
ND
ND
SD
1-, 2-
2-, 3- 0+ , 1+
Small spin-splitting is
neglected to show.
Λ
If we observepositive states andnegative states,we find thatΛ-separationenergies are dependenton the degree ofdeformation.Please observe the positive parity states at Jlab.
n n
Λ
n n
np
3H 3nΛ
nnp
6 Li
n
6 He
Λ
Λ
44He 44He
nnp
7Li
n
7He
Λ
Λ
44He 44He
n
n
np
10B
44He
n
44He
10Be
44He
n
44He
Λ
Λ
Summary
Please confirm whether ornot we have bound state,
It is interesting to have ahuge halo structure.
Please observesecond 3/2+ and 5/2+ state.This is important for the study of neutron-rich nuclei.
Please observethe positive parity state.
In this way, the experiment at Jlab isvery important for theorists to study the structure of multi-strangeness systems.
I hope we have many data at Jlab in the future.
Thank you!