Three-body radiative capture reactions in astrophysics

Three-body radiative capture reactions in astrophysics

L.V. Grigorenko

K.-H. Langanke and M. Zhukov

FLNR, JINR, Dubna and GSI, Darmstadt

Modes of two-proton radiative captureModes of two-proton radiative capture

A

A

A

Directnonresonant capture

E

W(E)

Sequentialnonresonant capture

Directresonant capture

AA

AA

AA

A

A

E

W(E)

AProton threshold

Sequential resonant capture

rp-process at high temperature and density.

15O, 18Ne, 38Ca : J.Görres, M.Wiescher, and F.-K.Thielemann, PRC 51 (1995) 392.

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

Could be important in the regions of nuclear chart, where there are “ridges” connected with paring and intermediate system is not nuclear stable.

Analogy with true 2p emission.

p

p

2p

p

13O

16Ne

19Mg 21Mg

19Na

19Ne

16F

15O14O 16O

17Ne 18Ne

17F

20Na

20Mg2p

Conventional approachConventional approach

The capture rate do not depend on number and properties of the intermediate states. Only on the sum of widths to these states. Paradox if we consider situation without intermediate states. Typical situation: and the reaction rate depends only on gamma width. Problem: if the production rate decrease.

YA 2 1/2 NA2 2 pp, v Yp

2YA,

pp, v 2 i

p,pv i

p,i p, vi .

E k 12

2

E ER2 2/4

2J2R 12J1 12J2 1 ,

K. Nomoto, F. Thielemann, and S. Miyaji, Astron. Astrophys. 149 (1985) 239. Introduced to study nonresonant capture. We consider only resonant part

pp, v A1 A2 A3

A1A2A3

3/2 2JF 122JI 1

2mkT

3exp E3R

kT

i p,i

3R

3R 2p 3R

3R i p,i

Direct resonant two-proton captureDirect resonant two-proton capture

All the states should be taken into account in the final nucleus, not only those accessible by a sequence of binary captures

This equation reflects nothing more than current conservation complete thermal equilibrium and a detailed balance

Typical situation: and hence the reaction rate depends only on gamma width.

If the true 2p decay is the only decay branch of the state, and

the reaction rate depends only on gamma width. need to know

the reaction rate depends only on 2p width. 2p

L. Grigorenko, M. Zhukov, PRC 72 (2005) 015803. S-matrix formalism for 3→3 scattering

2p, v pp, v A1 A2 A3

A1A2A3

3/2 2JF 122JI 1

2mkT

3exp E3R

kT

2p i p,i

3R .

2p i p,i

3R 2p i p,i

2p

2p

,2 p ip i

Theory of two-proton radioactivityTheory of two-proton radioactivity

Bound orbital

Unbound orbital

No bound orbitals !

Classical case: one particle emission is always possible

Quantum mechanical case: it could be that both particles should be emitted simultaneously

2p radioactivity (“true” 2p decay) suggested in : V.I. Goldansky, NP 19 (1960) 482 Coulomb three-body problem in continuum is intractable in general case First consistent quantum mechanical treatment of 2p radioactivity :

L. V. Grigorenko, et al., PRL 85 (2000) 22. L. V. Grigorenko, et al., PRC 64 (2001) 054002. L. V. Grigorenko, M. V. Zhukov, PRC 68 (2003) 054005.

Subject : 6Be, 8Li*, 12O, 16Ne, 17Ne*, 19Mg, 30Ar, 34Ca, 45Fe, 48Ni, 54Zn, 58Ge, 62Se, 66Kr

Recent status of 2p decay studiesRecent status of 2p decay studies

f wave

p wave 3-body

di-proton

0.9 1.0 1.1 1.210-22

10-20

10-18

10-16

R-matrix

R-matrix, no p-p

rc = 6.91 fm

rc = 4.76 fm

4526Fe

(

MeV

)

E2p (MeV)

10-1

10-3

10-5 T

1/2

(s)

4.56 s f wave

p wave

3-body

di-proton

1.2 1.3 1.4 1.5 1.6 1.710-22

10-20

10-18

10-16R-matrix, no p-p

rc = 7.24 fm

rc = 4.99 fm

5430Zn

(

MeV

)

E2p (MeV)

10-1

10-3

10-5

R-matrix T1/

2 (

s)

4.56 s

2p radioactivity suggested: 1960 Discovery of 2p radioactivity: 2002 45Fe : M. Pfutzner, et al., EPJA 14 (2002) 279. 54Zn : B. Blank, et al., PRL 94 (2005) 232501. 48Ni : B. Blank, et al., PRC 72 (2005) 054315. Planned research:

45Fe correlations (MSU) 19Mg (GSI)

R-matrix, no p-p

R-matrix

di-proton

3-body

rc = 4.84 fm

p wave

1.0 1.1 1.2 1.3 1.4 1.510-22

10-20

10-18

10-16

rc = 7.02 fm

f wave48 28

Ni

(

MeV

)

E2p (MeV)

10-1

10-3

10-5

T1/

2 (

s)

4.56 s

Practical application to 2p capturePractical application to 2p capture Waiting points of r-p process: 15O, 18Ne, and 38Ca. T1/2 for β+ decay : 122 s, 1.67 s, and 0.44 s.

Possibility to bridge the waiting points by 2p capture: J. Görres, M. Wiescher, and F.-K. Thielemann, Phys. Rev. C 51 (1995) 392.

Only sequential processes taken into account. 15O(2p,)17Ne omitted: 3/2 state at 1288 keV (Q2p=344 keV)

18Ne(2p,)20Mg 38Ca(2p,)40Ti omitted: 0 state at 2100 keV (Q2p=550-740 keV)

0.1 110-35

10-25

10-15

N 2 A

v (

cm6 /s

)

T (GK)

38Ca (2p,)40Ti

50.1 110-50

10-40

10-30

10-20

10-10

N 2 A

v (

cm6 /s

)

T (GK)

15O (2p,)17Ne

0.02

Direct nonresonant two-proton captureDirect nonresonant two-proton capture

Single particle 1- states are highly excited, low-lying 1- states are complicated particle-

hole excitations. Thus low-lying 1- states have small BE1 values.

In conventional approach the dBE1(E)/dE values are considered as transitions to “wings”

of known low-lying states (having small BE1 values) or GDR. Thus they are small.

The nonresonant E1 exhaust large part of the cluster sum rule just above Coulomb barrier independently on the details of spectrum of narrow states.

For calculations in the Gamow peak region the simplified three-body model with only one FSI is applied.

L. Grigorenko, K.-H. Langanke, M. Zhukov, preliminary. Domination of the E1 process (e.g. E2 is “exosted” by resonant capture)

1

0+

core coreE1

“Soft E1” mode in proton dripline nuclei“Soft E1” mode in proton dripline nuclei

Existence of “soft E1” mode now established in neutron-rich nuclei.

Cluster sum rule exhausted within several MeV above 2p threshold.

Possibility of “soft E1” in proton-dripline nuclei.

Calculations predict a strong and narrow E1 peak in 17Ne.

The 2p capture rate is dominated by the nonresonant E1 for T < 0.050.08 GK and T > 0.41.0 GK

0.1 1 1010-50

10-40

10-30

10-20

10-10

Gorres et al. total Gorres et al. resonant

upper, median, lower rates total from Grigorenko and Zhukov nonresonnat E1 "OFSI" model

0.02

N 2 A

v (

cm6 /s

)

T (GK)

15O (2p,)17Ne

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 %

dBE

1(E

)/dE

(e2

fm2 M

eV

)

E (MeV)

ConclusionConclusion

We found that for resonant two-proton radiative capture all the states should be taken into account in the final nucleus, not only those accessible by a sequence of binary captures.

The widhts of the states - “true” two-proton emitters (those having no sequential decay path) are calculated within quantum mechanical three-body model tested on a variety of three-body decays.

For nonresonant two-proton radiative capture the contribution of E1 transition directly from continuum can be large. E.g. in 17Ne this transition dominates the 2p capture rate practically in the whole temperature range.

The importance of this class of phenomena in the heavier nuclei, which are rp-process waiting points to be understood.