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).

hagino.kouichi.5m@kyoto-u.ac.jp

2. Tell me the most interesting topic/subject which you found in my lectures (within a few sentences).