Electroproduction of p-shell hypernuclei in DWIA The 13th International Conference on Hypernuclear and Strange Particle Physics Petr Bydˇ zovsk´ y Nuclear Physics Institute, ˇ Reˇ z, Czech Republic in collaboration * with D.J. Millener (BNL), F. Garibaldi and G.M. Urciuoli (Rome) Outline: Introduction Formalism of DWIA Results: elementary elektroproduction electroproduction on 9 Be, 12 C, and 16 O targets Uncertainty of predicted cross sections Summary and outlook * the results will be published in an archival paper by Hall A Hypernucleus Collaboration Petr Bydˇ zovsk´ y (NPI ˇ Reˇ z) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 1 / 23
23
Embed
Jefferson Lab - Electroproduction of hypernuclei...Sotona and Frullani, Prog. Theor. Phys. Suppl. 117 (1994) 151 Excitation Energy (MeV) 20 MeV × GeV 2 sr nb MeV exc dE e dE K W d
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Electroproduction of p-shell hypernuclei in DWIA
The 13th International Conference on Hypernuclear and Strange Particle Physics
Petr BydzovskyNuclear Physics Institute, Rez, Czech Republic
in collaboration∗ with D.J. Millener (BNL),
F. Garibaldi and G.M. Urciuoli (Rome)
Outline:IntroductionFormalism of DWIAResults: elementary elektroproduction
electroproduction on 9Be, 12C, and 16O targetsUncertainty of predicted cross sectionsSummary and outlook
∗the results will be published in an archival paper by Hall A Hypernucleus Collaboration
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 1 / 23
Introduction – Why do we study electroproduction of hypernuclei?
γ-ray and reaction spectroscopy of Λ hypernuclei→ information on the YN interaction, its spin-dependent part
in the reaction spectroscopy we can study higher energy states, Λp
DWIA calculations with a structure from standard Shell-model→ we learn on the effective (in medium) YN interaction
reaction mechanism in DWIA
electroproduction– a better energy resolution than in the π+ and K− induced productions;– a large momentum transfer to the hypernucleus: q > 250 MeV/c;– strong spin-flip, the highest-spin states in multiplets dominate;– the electro-magnetic part is well known and the one-photon exchangeis a good approximation → production by virtual photons – simplification;– if K+ detected → production on the proton → other hypernuclei.
suitable kinematics: – a very small electron scattering angle→ very small Q2 = −q2 and sufficiently big virtual photon flux;– kaon is detected along the photon direction→ very small kaon angle
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 2 / 23
Introduction – kinematics, cross sections
e + AZ −→ e′ + K+ + AΛ(Z−1)
laboratory frame:
Φ
θe
θ
p
p'
γ
q
p
pH
Scattering (Leptonic) Plane
Reaction (Hadronic) Plane
z
x
y
e
e
K
K
K
^
^
1
input kinematics: Ee,Ee′ , θe , θKe ,ΦK
→ ε, Γ, q = pe − p′e, Q2 = −q2, s = W 2, t,...
the unpolarized lab cross section in hypernucleus electroproduction
d3σ
dE′e dΩ′e dΩK= Γ
[dσT
dΩK+ ε
dσL
dΩK+ ε
dσTT
dΩK+√
2ε(1+ε)dσTL
dΩK
]Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 3 / 23
Introduction – previous calculations for E94-107 in Hall ASotona and Frullani, Prog. Theor. Phys. Suppl. 117 (1994) 151
Excitation Energy (MeV)0 10 20
MeV
⋅
GeV
2sr
nb
ex
c d
Ee
dE
KΩ
de
Ωd
σd
0
2
4
-Binding Energy (MeV)-10 -8 -6 -4 -2
Cro
ss S
ecti
on
(n
b/s
r^2/G
eV
/MeV
)
0.0
0.5
1.0
1.5
12C(e, e′K+)12Λ B M. Iodice,... M. Sotona,... et al,
Phys. Rev. Lett. 99, 052501 (2007)
16O(e, e′K+)16Λ N
F.Cusanno,... M. Sotona,... et al,
Phys. Rev. Lett. 103 (2009) 202501
Binding Energy (MeV)-20 -15 -10 -5 0 5 10 15
Me
V
⋅G
eV
2s
rn
b
ex
c d
Ee
dE
KΩ
de
Ωd
σd
0
1
2
3
4
5
9Be(e, e′K+)9ΛLi G.M. Urciuoli,... M. Sotona,... et al,
Phys. Rev. C 91 (2015) 034308
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 4 / 23
Formalism of DWIA – many-particle matrix element
Calculation of dσx/dΩK for γv + A→ K+ + H∗ in DWIA
* L. Tang et al, Phys.Rev.C 90 (2014) 034320; T.Gogami PhD Thesis, private communication
kinematics differ mainly in Eγ , Q2, and ΦK ;
in E01-011, photons are almost real, Q2 ≈ 0, → photoproduction approximationis possible, see the next talk by Toshio Motoba and JPS Conf. Proc. 17, 011003 (2017).
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 13 / 23
Comparison with E01-011 data on 12C(e, e′K+)12Λ B and calculations by Motoba-san
Experimental dataa our results with SLA Motoba-san (SLA)b
17.515 3+ 2.045 +17%F. Cusanno etal, P. R. L. 103 (2009) 202501
fit and theory with Voight functions
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 17 / 23
Angular dependence of the cross sections
4 5 6 7 8 9 10 11 12
θKe
L [deg]
0
1
2
3
4
dσ
/(dΩ e
dΩ
Kd
Ee)
[n
b/(
sr2G
eV)]
SLA 1+
SLA 2+
SLA 3+
BS3 1+
BS3 2+
BS3 3+
16O (e,e’K
+)16
ΛNE
e= 3.66, E
e’= 1.45 GeV
θe= 6
o, Φ
K= 180
o
17 MeV multiplet 1+ 2
+ 3
+
2+
1+
3+
different angular behavior for the 2+ and3+ states is from the nucleus structure
a weak dependence on the elementaryamplitude (3+) is due to the small Q2
information on the nucleus structure andthe elementary amplitude
4 6 8 10 12
θKe
L [deg]
0
0,5
1
1,5
2
2,5
dσL
/dΩ
K [µ
b/s
r]
TLTTTL
4 6 8 10 12
θKe
L [deg]
SLA BS3
Q2 = 0.058 GeV
2
EL
γ = 2.21 GeV
p(e,e’K+)Λ
4 5 6 7 8 9 10 11 12
θKe
Lab [deg]
0
100
200
dσ
/dΩ
K [n
b/s
r]
TLTTTLds
4 5 6 7 8 9 10 11 12
16O (e,e’K
+)16
ΛN
E = 17.515 MeV, JP = 3
+
BS3 model
SLA model
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 18 / 23
Uncertainty in the DWIA calculations
the model for elementary production, e.g. SLA, BS3, ...
the kaon wave function – the eikonal approximation– parameters of the kaon-nucleus optical potential– more precise kaon wave function (Klein-Gordon equation)
the nuclear structure – the full basis of p-shell states– a larger model-space calculation of the OBDME→ the strength is distributed among more states
single-particle wave functions in the radial integral– harmonic oscillator × Woods-Saxon wave functions– parameters of the W.-S. potential
approximations– effective factorization × full folding– off-shell effects in Jj (energy conservation on elementary level is violated)
uncertainty in input kinematics – angles, momenta→ averaging arround a central kinematics (with a weighting function)
Petr Bydzovsky (NPI Rez) Electroproduction of hypernuclei HYP 2018, June 24-29, 2018 19 / 23
Uncertainty from the elementary production
separated lab cross sections for 12C(e, e′K+)12ΛB in central kinematics of E01-011