Excitations and decays of 2n-halo nucleikouichi.hagino/lecture2/Tokyo...Coulomb breakup of 2n halo...
Transcript of Excitations and decays of 2n-halo nucleikouichi.hagino/lecture2/Tokyo...Coulomb breakup of 2n halo...
Excitations and decaysof 2n-halo nuclei-Coulomb breakup-2-nucleon emission
γ
breakup due to an external Coulomb field→ observe two emitted neutrons
Coulomb breakup of 2n halo nuclei
(if there is no bound excited states)
breakup due to an external Coulomb field→ observe two emitted neutrons
experimental data:T. Nakamura et al., PRL96(’06)252502 T. Aumann et al., PRC59(‘99)1252
6He
Coulomb breakup of 2n halo nuclei
Dipole excitations
Response to the dipole field:
ground stateexcited states
continuum states:
g.s. correlation? or correlation in excited states?
6He(0+) → 6He(1-) → α + n + ng.s. state excited state
6He
role of the correlation in Coulomb breakup
the ground state: with correlation excited state: with correlation (red), w/o correlation (blue)
E1 strength: enhanced due to the correlation
6He
role of the correlation in Coulomb breakup
the ground state: with correlation excited state: with correlation (red), w/o correlation (blue)
E1 strength: enhanced due to the correlation
what is the role of the ground state correlation?
Both FSI and dineutron correlations: important role in E1 strength
g.s. correlation? or correlation in excited states?
g.s. correlation + FSI
g.s. correlation only (no nn interaction in the final state)
g.s.:odd-l only(no dineutron correlation)+FSI
6He(0+) → 6He(1-) → α + n + n
g.s. correlation? or correlation in excited states?
g.s. correlation + FSI
g.s. correlation only (no nn interaction in the final state)
g.s.:odd-l only(no dineutron correlation)+FSI
6He(0+) → 6He(1-) → α + n + n
cf. cluster sum rule
no di-neutron in the ground state: reduce the E1 strength← due to a smaller Rc-2n (3.63 → 2.61 fm) +→
11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)cf. the ground state density
the energy distribution of the two emitted neutrons
11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
similar
6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
Energy distribution of emitted neutronsshape of distribution: insensitive
to the nn-interaction (except for the absolute value)strong sensitivity to VnCsimilar situation in between 11Li
and 6He
Coulomb excitations A problem: an external field is too weak
6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
Energy distribution of emitted neutronsshape of distribution: insensitive
to the nn-interaction (except for the absolute value)strong sensitivity to VnCsimilar situation in between 11Li
and 6He
Coulomb excitations A problem: an external field is too weak
other probes?
two-neutron transfer reactions two-nucleon emission
11Li 6He
K.H., H. Sagawa, T. Nakamura, S. Shimoura, PRC80(‘09)031301(R)
p3/2 resonance for 5Heat 0.91 MeV
p1/2 resonance for 10Liat 0.54 MeV
s-wave virtual state in 10Li
(scattering length:a =-30 +12
-31 fm) (cf. s-wave scattering length:a = +4.97 +/- 0.12 fm)
distribution for 11Li: consistent with preliminary expt. data (T. Nakamura et al.)
T. Nakamura et al., unpublished
can the spatial distribution of the two neutrons be determined experimentally?
C.A. Bertulani and M.S. Hussein, PRC76(‘07)051602(R)K. Hagino and H. Sagawa, PRC76(‘07)047302
if information on rc-2n and rnn is available, the opening angle could be estimated as:
core nucleus
neutronneutronGeometry of Borromean nuclei
Btot(E1)matter radius
“experimenad data” of the opening angle
Geometry of Borromean nuclei
Cluster sum rule
only the g.s. properties
Btot(E1)
matter radius
(11Li)(6He)
K.H. and H. Sagawa,PRC76(’07)047302
“experimental data” for the opening angle
Geometry of Borromean nuclei
Cluster sum rule
reflects the g.s. correlation
di-neutron correlation
Btot(E1)
matter radius
(11Li)(6He)
K.H. and H. Sagawa,PRC76 (’07) 047302
“experimental data” for opening angleGeometry of Borromean nuclei
other probes?
3-body model calculations
but, average value only no accessible to the detailed
structure
di-neutron correlation
(11Li)(6He)
NB.
if no correlation, <θ12> = 90 deg.
the deviation from this value reflects the degree of correlation
<θ12> = 65 deg. is not inconsistent with the di-neutron correlation (cf. an average of the two peaks)
“experimental data” for the opening angle
scattering length: diverges at zero binding
bound unbound
Borromean systems and Efimov physics
1/a
Coulomb breakup of 19B
K.J. Cook, T. Nakamura, Y. Kondo, K. Hagino, et al., PRL124, 212503 (2020)
a < -50 fm for n-17BA. Spyrou et al., PLB683, 129 (2010)
a = -50 fma = -100 fm
Coulomb breakup and two-nucleon emission
Dµ
Coulomb breakup
distrub a nucleus by an external field
emission of two nucleons
two-nucleon emission decay
unbound nucleus (3body resonance)← nuclear reactions
spontaneous 2N emission without the perturbation
→ cleaner information?
B. Blank and M. Ploszajczak, Rep. Prog. Phys. 71(‘08)046301
probing correlations from energy and angle distributions of two emitted protons?
Coulomb 3-body system ・Theoretical treatment: difficult・how does FSI disturb the g.s. correlation?
2-proton radioactivity
a “true” two-nucleon emission decays
(Z,N)
the drip-line
(Z-1,N)
(Z-2,N)
(Z+1,N)
(Z+2,N)
E
unbound (resonances)
a “true” two-nucleon emission decays
(Z,N)
the drip-line
(Z-1,N)
(Z-2,N)
(Z+1,N)
(Z+2,N)
E
unbound (resonances)
p emission
p emi.
two successive 1p emissions
a “true” two-nucleon emission decay
(Z,N)
the drip-line
(Z+1,N)
(Z+2,N)
E
unbound (resonances)
p emission
p emi.
two successive 1p emissions
(Z,N)
(Z+1,N)
(Z+2,N)
pairing
pairing
if Z is even
direct transition from (Z+2,N) to (Z,N)
forbidden
a “true” two-nucleon emission decayif the life-time is long enough (e.g. 10-14 sec. or more) → “radioactive” 2 proton emission decaysV.I. Goldansky, Nucl. Phys. 19 (‘60) 482
x
(an analogous phenomenon)
13654Xe82
mass excess= ‐86.43 MeV
13655Cs81
mass excess= ‐86.34 MeV
13656Ba80
mass excess= ‐88.89 MeV
∆
∆forbidden
ββ
double β decays
Kamland-ZEN
Experimental data of radiaoactive 2p decays
theoretical predictions:V.I. Goldansky, Nucl. Phys. 19 (‘60) 482Y.B. Zel’dovich, Sov. Phys. JETP 11 (‘60) 812
the first measurement: 45Fe nucleus: M. Pfutzner et al., Euro. Phys. J. A14 (‘02) 279
J. Giovinazzo et al., PRL 89 (‘02) 102501
*the first measurement of 2p-decay of 6Be: 1966.but τ = 7.15 (47) x 10-21 sec., and thus is not categorized as “radioactive” decays
Experimental data of radiaoactive 2p decays
theoretical predictions:V.I. Goldansky, Nucl. Phys. 19 (‘60) 482Y.B. Zel’dovich, Sov. Phys. JETP 11 (‘60) 812
the first measurement: 45Fe nucleus: M. Pfutzner et al., Euro. Phys. J. A14 (‘02) 279
J. Giovinazzo et al., PRL 89 (‘02) 102501
B. Blank and M. Ploszajczak, Rep. Prog. Phys. 71 (‘08) 046301
45Fe
1.14 44Mn+p1.68
(MeV)
43Cr+2p
0
a picture with CCD camera(expt. in a gas chamber)
analysis of angular distribution: consistent with a 3-body calculation with p2 ~30% and f 2 ~ 70%
K. Miernik et al., PRL 99 (‘07) 192501
subsequent measurement for 45Fe
Experimental data of radiaoactive 2p decays
Diproton-likecorrelation
2-proton decay of 45Fe
K. Miernik et al., PRL99 (‘07) 192501
experimental data
calculations (Grigorenko)
M. Pfutzner, M. Karny, L.V. Grigorenko, K. Riisager,Rev. Mod. Phys. 84 (‘12) 567
M. Pfutzner, M. Karny, L.V. Grigorenko, K. Riisager,Rev. Mod. Phys. 84 (‘12) 567
diproton correlation: unclear in many other systems (theoretical calculations: not many)
However, it has not yet been clarified why 2-peaked structure? why a larger peak at forward angles?
(there has not been such discussions)
6Be45Fe
L.V. Grigorenko et al.,PLB677 (’09) 30
experimental data
completely different distributions between 6Be and 45Fe
the reason: has not yet been understood
(not many people want to do Coulomb 3-body calculations)
Experimental data of radiaoactive 2p decays
Effect of di-proton correlation on 2p decays
similar
166C10 = 14C + n + n 17
10Ne7 = 15O + p + pdi-neutron correlation di-proton correlation
if there is di-proton correlation in unbound state, how does it influence the 2p-emission decay?
T. Oishi, K.H., and H. Sagawa, PRC90 (‘14) 034303
Di-neutron/di-proton correlation in the momentum space
Fourier transform
θr = 0: enhanced
θk = π: enhanced
r r’
*this can be understood also in terms of the uncertainty relation.
6He
6He
Two-particle density in the r space:
Two-particle density in the p space:
Di-neutron/di-proton correlation in the momentum space
r rθ12
k k
θ12
6He
6He
2-particle density in the r-space 2-particle density in the p-space
a consequence to 2-particle emission decays
is this really the case? → let us confirm it with a time-dep. approach
description of a tunneling decay with a time-dep. approach
change the potential at t = 0
description of a tunneling decay with a time-dep. approach
|ψ(t)
|2(a
rb. u
nits
)
change the potential at t = 0timeevolution
apply this method to a 3-body model
|ψ(t)
|2(a
rb. u
nits
)description of a tunneling decay with a time-dep. approach
application to 6Be → 4He + p + p decay
1.5Γ1.96(5)3/2Jπ
≈== −
E
2p
[MeV] E
- 0.1
- 0.2
0.092(6)Γ1.370Jπ
=== +
E
α
even though the width of the intermediate state (5Li) is large, the situation is close to a “true” 2p emission
6Be 5Li + p 4He + 2p
T. Oishi, K.H., and H. Sagawa, PRC90 (‘14) 034303
T. Oishi, K.H., and H. Sagawa, PRC90 (‘14) 034303
T. Oishi, K.H., H. Sagawa, PRC90 (‘14) 034303
consistent with the expectation
application to 6Be → 4He + p + p decay
L.V. Grigorenko et al.,PLB677 (’09) 30
comparison to the data→ a much longer time evolution is
needed
According to Grigorenko, theoretical calculations do not converge up to R~ 105 fm due to the long range Coulomb int. ← a numerical challenge
2 neutron emission decays
R.J. Charity, Eur. Phys. J. Plus 131 (‘16) 63
LAND (GSI)10He (‘10), 13Li (‘10), 26O (‘13) MoNA (MSU)
16Be (‘12), 26O (‘12), 13Li (‘13) SAMURAI (RIKEN)
26O (‘16), 28O (under analysis)
2-neutron emission decay of 26O
22O 23O 24O 25O 26O
24O
25O
26O
749 keV
18 keV2n decay
(neutron drip-line)
E. Lunderbert et al., PRL108 (‘12) 142503 (MSU)C. Caesar et al., PRC88 (‘13) 034313 (GSI)Y. Kondo et al., PRL116 (‘16) 102503 (RIKEN)
27F → 26O → 24O + 2n (all the expt. used this reaction)
E(26O) = 150+50-150 keV (MSU)
< 40 keV/120 keV (GSI)(68%/95% conf. level)
= 18 +/-3 +/-4 keV (RIKEN)
Edecay = 18 +/- 3 +/- 4 keV
E. Lunderberg et al., PRL108 (‘12) 142503
C. Caesar et al., PRC88 (‘13) 034313
MSU
GSI
RIKEN
Y. Kondo et al., PRL116(’16)102503
Edecay = 150 +50-150 keV
Two-neutron decay of 26O
22O 23O 24O 25O 26O
24O
25O
26O
749 keV
18 keV2n decay
(neutron drip line)
9C 10C 11C 14C 15C 16C 17C 18C 19C 20C 22C12C 13C
12N 13N 16N 17N 18N 19N 20N 21N 22N 23N14N 15N
13O 14O 15O 16O 17O 18O 19O 20O 21O 22O 23O 24O
17F 18F 19F 20F 21F 22F 23F 24F 25F 26F 27F 29F 31F
Y. Kondo et al., PRL116(’16)102503
bound unbound
almost bound!
the new data for the two-body subspace (25O)
E = + 770+20-10 keV
Γ = 172(30) keV E = + 749 (10) keVΓ = 88 (6) keV
Y. Kondo et al., PRL116(’16)102503
consistent with the n + 24O model
25F
n
nV
V
cf. expt.: 27F (201 MeV/u) + 9Be → 26O → 24O + n + n
the bound g.s. of 27F
sudden p-removal
24O
n
nV’
V’
24O
n
n
spontaneousdecay
the same config. (the initial wave packet)
FSI Green’s function
K.H. and H. Sagawa,PRC89 (‘14) 014331;PRC93 (‘16) 034330
continuum states
theoretical analysis with a 3-body model
the decay spectrum:
= G(E)
cf. the Coulomb breakup of Borromean nuclei
*D0 (the external field) is not necessary for a spontaneous decay
theoretical analysis with a 3-body model
the decay energy spectrum
without nn interaction
with nn interaction
η = 0.1 MeV
Epeak = 18 keV (input)
cf. e1d3/2(25O) = 0.749 MeV
K.H. and H. Sagawa, - PRC89 (‘14) 014331 - PRC93(‘16)034330
the initial state: the bound state of 27F with a pure (d3/2)2 config.
insensitive to how 26O is created
dP/dE: properties of 26O as a 3-body resonance rather than 27F
the decay energy spectrum K.H. and H. Sagawa, - PRC89 (‘14) 014331 - PRC93(‘16)034330
the 2+ state of 26O
the 2+ state of 26O
K.H. and H. Sagawa, PRC90(‘14)027303; PRC, 93(‘16) 034330.
(d3/2)21.498
0+0.018
2+1.282
(MeV)
Γ = 0.12 MeV
3-body model calculation:
the data: a prominent second peak at E = 1.28 +0.11
-0.08 MeV
[jj](I) = 0+,2+,4+,6+,…..
0+
2+4+6+
with residualinteraction
I=0 pair pair
a textbook example of pairing interaction!
(d3/2)21.498
0+0.018
2+1.282
(MeV)
26O
(0.418) dineutron correlation
Ecorr for the 2+ state of 26O
role of 3N interation?
comparison to other calculations
with
density with a bound state approximation:di-neutron corr. in 26O
(d3/2)2 : 66.1%(f7/2)2 : 18.3%(p3/2)2 : 10.5%(s1/2)2 : 0.59%rms radius = 3.39 +/- 0.11 fm
3-body model
1.0 A1/3 (fm)
w/o
weight:8π2r4sinθ
correlation enhancement of back-to-back emissions
K.H. and H. Sagawa, PRC89 (‘14) 014331; PRC93 (‘16) 034330
cf. Similar conclusion: L.V. Grigorenko, I.G. Mukha, and M.V. Zhukov,PRL 111 (2013) 042501
the angular correlation of the emitted neutrons
density of the resonance state (with the box b.c.)
r-space p-space
main process: initial state (d3/2)2 (s1/2)2 or (p3/2)2 , (p1/2)2
rescattering due to pairing interaction*higher l components: largely suppressed due to the centrifugal pot.
(Edecay ~ 18 keV, e1 ~ e2 ~ 9 keV)
(s1/2)2: 99.37%(p3/2)2: 0.56%(p1/2)2:0.07%
rescattering
L.V. Grigorenko et al.,PRL111 (‘13) 042501
main process: initial state (d3/2)2 (s1/2)2 or (p3/2)2 , (p1/2)2
Report: if you need a credit, solve the following problems and send me the answers by Nov. 30
1. Consider the ground state of a 1-dimensional harmonic oscillator (h.o.).
i) evaluate the expectation value of x2
ii) Suppose that an external field F = x is applied to the ground state. Calculate the probability to populate the state k of the h.o.
iii) Evaluate the total probability by summing Pk for all k.Show that the total probability coincides with the expectation value of x2 evaluated in 1-i).
2. Tell me the most interesting topic/subject which you found in my lectures (within a few sentences).