Leonid Grigorenko

Flerov Laboratory of Nuclear Reactions

Joint Institute for Nuclear Research

Dubna, Russia

Theoretical basics and modern status of radioactivity studies

Lecture 5: Nonresonant phenomena. Astrophysical applications

Halo and excitation modes

Excitation MODES idea is introduced to describe strong enhancements of various cross sections connected ONLY with initial structure and reaction mechanism. This is in sharp contrast with RESONANCE phenomena, which should be, by definition, insensitive to initial conditions and method of population.

Nucleon halo

8Li H = 1.55

6Li H = 1.62

8B H = 1.77

6He H = 1.81

11Li H = 2.27

< RN-CM(core) >

< RN-CM(halo) >

11Be H = 2.41

H =

"Haloism coefficient"

Nuclei near driplines can form kind of planetary system consisting of compact “core” and “valence” nucleons remotely orbiting it and residing mainly in classically forbidden region

G.N. Flerov, A.S. Ilyinov (1982)

Nucleon halo. Borromean nuclei

Major example: soft dipole mode Proposed by Ikeda in 1988

There is a strong low energy peak even without any final state interaction

- Photodissociation - Coulex

Yg.s.

D Yg.s.

| < Plane wave | D | Yg.s.> |2

Normal WF Weakly bound (halo) WF

Estimate of soft dipole mode in on-neutron halo system

corehalo/skin

E1

str

en

gth

fu

ncti

on

E

Giant dipole resonancePigmy resonance/

soft dipole mode

np

Soft dipole mode in two-body and three-body continuum

Well understood in two-body systems

Poorly understood in two-body systems

strong

p-wave

1

0+

p-wave

strong

core

strong

p-wave

s-wave

weak

core

E1

11Be 11Li

Soft dipole mode in 17Ne

L.V.Grigorenko, K.Langanke, N.B.Shul’gina,

M.V.Zhukov, PLB 641 (2006) 254.

Very expressed soft dipole peak has been

predicted for 17Ne

For the recent results on GSI S318 experiment

0 2 4 6 8 10 120.00

0.25

0.50

0.75

1.00

Grigorenko and Zhukov,

NPA 713 (2003) 372.

W(s2) = 50 %

W(s2) = 93 %

W(s2) = 25 %

W(s2) = 5 %

dB

E1(E

)/d

E

(e2 fm

2 M

eV

)

E (MeV)

T. Oishi, K. Hagino, and H. Sagawa PRC 84, 057301 (2011)

“Effect of proton-proton Coulomb repulsion on soft dipole excitations of light

proton-rich nuclei”

Soft dipole mode in 8He

Large uncertainty in the 2+ 8He state energy E(2+) = 2.7 - 3.6 MeV D.R. Tilley et al. NPA 745 (2004) 155

“Standard” R-matrix: energy ~3.6 MeV and Wigner limit width ~0.6 MeV

Low-energy events are not reproduced in any of the cases

E1 contribution can modify the positions of 2+ state up to about 3.9 MeV

M.S.Golovkov et al., PLB 672 (2009) 22 L.V. Grigorenko et al., Part. Nucl. Lett. 6 (2009) 118

0 5 10 150

5

10

15

20

1+ ?

2+1 ?

8He coincid.

6He coincid.

E1 strength

function

Nu

mb

er o

f ev

ents

E8He (MeV)

0+ g.s.

0

5

10

15

0

20

40

60 (c)

Nu

mb

er o

f ev

ents

polynomial "background"

Bohlen et al.

Num

ber

of

even

ts

0 2 4 6 8

(d)

6He+n+n

threshold

E* (MeV)

2+, no E1

1

2+, with E1

1 + 2+

0

50

100 (b)Meister et al.

(m

b/M

eV)

0

5

10

15Markemroth et al.

(mb/M

eV)

(a)

Corrected first 2+ states position in 8He

IsoVector Soft Dipole Mode in 6Be

Large cross section above

2+ and no resonance

DL = 1 identification –

some kind of dipole

response

No particle stable g.s. –

can not be built on

spatially extended g.s. WF

Built on the spatially

extended 6Li g.s.

A.S.Fomichev et al., PLB 708 (2012) 6.

Experimentally observed and theoretically discussed: IVSDM as a specific form of SDM

Astrophysical applications

For astrophysical application knowledge of BOTH resonant and nonresonant radiative capture cross sections can be needed depending on specific situation. While RESONANT radiative capture requires the knowledge of resonance properties only, for understanding of nonresonant capture studies of excitation modes are required

Modes of (2р) radioactive capture

A

A

A

Direct

nonresonant

capture

EW(E)

Sequential

nonresonant

capture

Direct

resonant

capture

AA

AA

AA

A

A

E

W(E)

AProton threshold

Sequential

resonant

capture

rp-process at high density and temperature.

15O, 18Ne, 38Ca : J.Gorres, M.Wiescher, and F.-K.Thielemann,

PRC 51 (1995) 392.

68Se, 72Kr, … ,96Cd : H.Schatz et al., Phys. Rep. 294 (1998) 167.

rp-process waiting

points

True 2p resonance

Proton resonance15

F

18Na

2p

p

2p

p

12O

16Ne

19Mg 21

Mg

19Na

19Ne

16F

15O

14O

16O

17Ne 18

Ne

17F

20Na

20Mg2p

13O

Halo

Reverse to soft dipole mode

Reverse to true 2р decay

Reverse to sequential 2р

decay

Resonant radiative capture Nucleosynthesis: Saha (chemical

balance) equations

Proton capture Two-Proton capture

Need to know ONLY particle and gamma

widths

Problem of resonant radiative capture is just time-reversed problem of

radioactive decay

Nonresonant radiative capture

For nonresonant radiative capture to halo nucleus we need to understand soft dipole

excitations

0.1 1 10

Görres et al.

PRC 51 (1995) 392

Grigorenko et al.

PLB 641 (2006) 254

0.02

N 2 A

v

(

cm6/s

)

T (GK)

p

p

2p

p

13O

16Ne

19Mg 21

Mg

19Na

19Ne

16F

15O

14O

16O

17Ne 18

Ne

17F

20Na

20Mg2p

2p radiative capture 15O(2p,)17Ne

competes with 15O(a,)19Ne

«waiting point» 15O T1/2 = 122 s

Resonant radiative

capture on 3/2-

Nonresonant radiative

capture on 1/2+, 3/2+

Application to nuclear astrophysics

Competition between a and 2p capture

15O(2p,)17Ne versus 15O(a,)19Ne

Densities (in g/ccm) at which the production rate of 17Ne by 2p-capture on 15O equals the production rate of 19Ne by α capture as function of temperature and α-particle mass abundance Xa = 4 Ya.

1E2

1E4

1E6

1E8

1E10

1E12

1E14

1E41E6

1E8

1E10

0.0 0.2 0.4 0.6

T

(GK

)

Xa

Upper

(a)

0.0 0.2 0.4 0.6

(c)

Gorres, et al.

Xa

0.0 0.2 0.4 0.6

(b)

Median

10.0

7.0

5.0

4.0

3.0

2.0

1.5

1.0

0.8

0.6

0.4

0.3

0.2

0.15

0.1

Xa

Democratic decay

10He. Extreme importance of reaction mechanism

The resonance is, by definition, something insensitive to population conditions. However, when resonances become sufficiently broad, their OBSERVABLE properties may become sensitive to initial state properties and reaction mechanism details. Thus, such broad resonances may obtain properties characteristioc for excitation modes. Broad ground state resonances are typical for democratic 2n decays of nuclei beyond the neutron dripline.

Origins of ideas

Two-proton radioactivity: Predicted theoretically

Democratic decay concept: Inspired by experimental data

Bochkarev et al., NPA 215 (1989) 215 (1989)

Goldansky, NPA 19 482 (1960)

Geesaman et al., PRC 15 1835 (1977)

p-p scatering

length a ~ 30 fm

Geesaman et al.:

10He populated from 11Li in a sudden removal model

Removal of a deeply bound proton from 11Li

Large center-of-mass recoil effects, population of

different Jp

Abnormal radial extents for formfactors of excited states

10He populated in transfer and in

knockout from 11Li

10He spectrum from transfer

10He spectrum from 11Li

Fourier transform of 11Li source function

(no 10He FSI)

10He spectrum from 11Li is a pileup of

different Jp

10He data calculation with FSI calculation

“no FSI”

10He spectrum from 11Li is dominated by

the initial state contribution

Recently studied true 2n emitters: 10He: Golovkov et al., PLB 672, 22 (2009),

Johansson et al., NPA 842, 15 (2010), Sidorchuk et al., PRL 108, 202502 (2012),

Z. Kohley et al., PRL 109, 232501 (2012).

13Li: Aksyutina et al., PLB 666, 430 (2008),

Z. Kohley et al., PRC 87, 011304(R) (2013).

16Be: Spyrou et al., PRL 108, 102501 (2012).

26O: Lunderberg et al., PRL 108, 142503 (2012), Caesar et al., PRC 88, 034313 (2013), Z. Kohley et al., PRL 110, 152501 (2013).

10He populated in transfer and alpha removal from 14Be

14Be has extreme halo configuration

1400 1600 1800 2000 2200 2400 26000.0

0.2

0.4

0.6

0.8

1.0 6Be

Sum 0+ (bins 1-3)

Sum 2+ (bins 4-7)

bin8 2.99 < E* < 4.50 MeV

bin9 4.50 < E* < 7.69 MeV

bin10 7.69 < E* < 11. MeV

No

rmal

ized

dis

trib

uti

on

K|| (MeV)

7Be(9Be,6Be)X

MSU, 2010

Charity et al.

6Be example from MSU